Molecular infrared lasers using resonant laser pumping

Prog. Quant. Electr.. Vol.6, pp. 245 293.

0079-6727/80/1001 0245 $05.00/0

~ PergamonPressLtd., 1980. Printedin Great Britain.

MOLECULAR INFRARED LASERS USING RESONANT LASER PUMPING A. Z. GRASIUK*, V. S. LETOKHOVt and V. V. LOBKOt * Lebedev Physical Institute, U.S.S.R. Academy of Science, Leninsky Prospekt, 53, Moscow 117924, U.S.S.R. t Institute of Spectroscopy, U.S.S.R. Academy of Science, 142092 Troitzk, Moscow Region, U.S.S.R. CONTENTS 1. Introduction--Physical Background 1.1. Frequency conversion of laser radiation 1.2. Population inversion conditions 1.3. Kinetic equations

245 246 249 250

2. Pumping and Lasing in a Fundamental Band 2.1. Population inversion conditions--first lasers 2.2. NH3 laser 2.2.1. First experiments 2.2.2. Spectroscopy 2.2.3. Schemes of NH3 laser and principal characteristics (single pulse operation) 2.2.4. High pulse repetition rate operation

251 251 253 253 254 255 260

3. Excitation of Combination Band or Overtone and Lasing in a "Hot" Band 3.1. Population inversion conditions 3.2. Excitation of an overtone band 3.3. Pumping in a combination band 3.4. CF4 laser 3.4.1. Principal characteristics 3.4.2. Gain coefficient self-absorption 3.4.3. Oscillation spectrum--identification of transitions 3.4.4. High pulse repetition rate operation

261 261 263 263 264 265 268 269 276

4. Excitation of the Fundamental, Combination or Difference Band and Laser Action on a Difference band 4.1. COs and N 2 0 lasers pumped by HBr laser 4.2. COs laser pumped by COs laser 4.3. Other lasers

277 277 278 279

5. Multiphoton Pumping 5.1. Two-photon excitation of molecules 5.2. Two-photon pumped lasers

281 281 283

6. Population Inversion in Molecular Mixtures Due to a Collisional V-V Energy Transfer 6.1. Population inversion conditions 6.2. Laser schemes

284 284 286

7. Incoherent Optical Pumping

287

8. Conclusion--applications and outlooks

288

References

290

1. I N T R O D U C T I O N - - P H Y S I C A L

BACKGROUND

One of the general trends in the development of modern quantum electronics consists in the coverage of a maximally broad spectral range (from the submillimetre region to the soft X-ray) with laser sources. This problem can be solved, in principle, because there is now a lot of devices which produce laser radiation almost in any frequency range of the u.v., visible, and i.r. regions. These devices are, for instance, nonlinear optic ones (parametric oscillators, up-converters, and down-converters, Raman lasers, etc.) and conventional lasers having a broad gain profile (dye and semiconductor lasers). Such progress in quantum electronics opens the way for wide applications of tunable laser radiation in spectroscopy where most tasks do not require a high peak or average power. 245

246

A, Z. GRASIUK, V. S. LETOKHOV and V. V. LOBKO

However, many applications of tunable lasers set stronger requirements--e.g, a combination of high pulse energy and high peak power with a high pulse repetition rate (i.e. high average power). In such cases, the high peak power is necessary for nonlinear interaction of light with matter, and high average power provides the required yield of the laser process. From this point of view, the up-to-date achievements of quantum electronics in some spectral ranges still cannot meet such demands. The dye lasers have made it possible to cover the whole visible range at a rather high level of peak power ( 10 4 10 ~ W ) and average ones (0.01-100 W). Molecular lasers operating at many lines of vibrational-rotational molecular (HF, DF, CO, COE) transitions have made it possible to cover some spectral intervals of the medium-ix, range at a considerable level of both peak (106-108 W) and average (10-10 s W) power. However, the problem of the coverage of the whole medium-i.r, region, from 2 to 20 gm, e.g., is far from a solution. Such a coverage is very important in order to solve the problem of resonant interaction of laser radiation with molecules using their vibrational transitions. Such an interaction forms the basis for multiphoton i.r. laser photochemistry, laser isotope separation, laser purification methods, etc. Thus, many modern applications demand medium-i.r, lasers which combine a high pulse energy, high peak and average powers, high conversion efficiency, narrow linewidth, and a wide tuning range. 1.1. Frequency Conversion of Laser Radiation One of the "golden rules" of quantum electronics is that given a source of powerful coherent radiation at the frequency e)o, one can always (in a suitable medium) convert it to coherent radiation at lower frequencies coc ~ ego - KT/h, where Tis the temperature of the medium. In other words, by exciting a suitable medium with powerful laser radiation at too, we can always obtain amplification and hence generate coherent radiation at lower frequencies. There are two types of such laser radiation frequency conversions: resonant and off-resonant. Figure 1 shows simple schemes of quantum transitions in a medium which realize frequency conversion of radiation. At resonant conversion optical pumping we excite an upper quantum state, and for proper conditions a population inversion is created between the excited levels. The physics of such conversion dates back to the first days of quantum electronics, when N. G. Basov and A. M. Prokhorov proposed the so-called three-level pumping scheme of a molecular generator, t~ Dye lasers using coherent pumping by pulsed and c.w. lasers at fixed frequencies give an excellent example of the realization of resonant frequency conversion in modern quantum electronics (see the monograph, Ref. 2). It should, however, be noted that the first resonant frequency converters of laser radiation have been created on the basis of semiconductor lasers optically pumped with powerful laser pulses. ~3'4) Thus, at resonant pumping, there is an inversion of the population arising in the active medium.

2 top

tOp

0

0

A

t,oc

2

[3

FIG. 1. Energy-level diagrams for q u a n t u m transitions for resonant (A) and off-resonant IBI frequency conversion. The wide arrows here and below correspond mainly to converted radiation.

In the case of off-resonant pumping, there is no need to obtain the inversion. Off-resonant frequency conversion consists in achieving amplification in a medium by nonlinear optic

Molecular infrared lasers using resonant laser pumping

247

techniques. Among off-resonant frequency converters, the Raman lasers form a promising class of devices. In contrast to the resonant converters, the off-resonant ones require, as a rule, higher pumping intensities (107-109 W/cm2). Nevertheless, the availability of sufficiently powerful pulse lasers--in particular Nd-glass lasers--have made possible the use of stimulated Raman scattering (SRS) to produce high power tunable radiation (see Refs. 5 and

6). We must note that the first experiment on resonant optical excitation of molecules to an amplification level was realized quite a long time ago, tT) using a flame source for the incoherent pumping of CO2 molectiles in the wavelength region of 4.4 #m. This method, of course, is applicable only to selected molecules, and so has not gained wide use yet. The first powerful pulsed atmospheric-pressure CO2 lasers using a transverse electric discharge (TEA lasers) (8) made it possible to follow the afore-mentioned "golden rule" of quantum electronics to explore the medium-ix, range using molecular gases as the active media, and vibrational-rotational molecular transitions as active quantum transitions. The physical principles of operation and possible schemes of vibration-rotation transitions for such resonant frequency conversion of powerful CO2 lasers were discussed as early as in the report, Ref. 9. A powerful CO2 laser can generate at any one of several tens of vibrational-rotational lines at spectral intervals in the region from 9 to 11 #m. In this region there are the vibrational absorption bands of a great number of molecules. Therefore, the hope was quite well-founded of finding suitable molecules for the attainment of a population inversion by pumping with CO2 laser pulses. Figure 2 shows the energy-level diagrams for the vibrational molecular transitions which were proposed in the report, ~9)both for pumping and lasing. In the first scheme (Fig. 2a), the combination or overtone vibration-rotation transition (vl + v2 or 2vl) is excited, and a population inversion arises at the allowed vibration-rotation transition between the excited levels. In the case of absorption, such a vibrational band can be observed only due to thermal excitation of the lower vibrational state, and therefore it is called a "hot" band. In this scheme, a comparatively weak combination band is pumped and a strong one is used for lasing. In another scheme (Fig. 2b), the fundamental vibrational band is excited, and lasing takes place on the difference band which corresponds to a transition from one vibrational mode to another. Here, by contrast, pumping is realized at the strong transition and lasing takes place at the weak one. The scheme shown in Fig. 2b is somewhat reverse of the one which is shown in Fig. 2a, and they both complement each other, having opposite advantages and disadvantages.

~÷v2 :-v2

v3

m m

~,

~

C

D

FIG. 2. Energy-leveldiagrams for resonant optical pumping of V-R molecular transitions (from Ref.

15). In the scheme shown in Fig. 2c, the same vibrational band (but different vibration-rotation transitions) are used both for pumping and lasing. With an equilibrium distribution of the molecules over the rotational states, it is possible to excite the R-lines of the fundamental vibrational band and to attain laser action in the Q- and P-branches of the same vibrational band. The abundance of vibration-rotation states in a polyatomic molecule allows, of course, a greater number of potential schemes of pumping and lasing. For instance, pumping and laser action are possible on combination and difference bands (Fig. 2d) or at two-photon pumping of the vibrational-rotational states instead of overtone excitation, and

248

A.Z. GRASIUK, V. S. LETOKHOV and V. V. LOBKO

so on. All these schemes have been successfully realized in experiments, and are being considered below in more detail. It should be noted that, in the first investigations, the vibrational molecular bands in the i.r. range were considered as a potential analogue of the electronic absorption bands of dye molecules in the visible range. It was supposed that such vibrational bands could be used for a systematic coverage of the medium-i.r, region by laser sources with considerable peak and average power. The further development of these ideas provided support for the validity of such an approach. What is more, the development of powerful pulsed molecular lasers operating at other wavelengths (HF at 2.7 #m, D F at 3.6/~m, CO from 5 to 7/~m; see Ref. 10 and Fig. 3) essentially broadens the class of laser pump sources for the frequency conversion in different regions of the medium-i.r. co2 PUMPED - -

[]

DOUBLED CO2 PUMPED - -

CO

1

III

PUMPED-

II II

[

[

HB, PUMPED -H F PUMPED

--

I III I

I

[

[

I

I

STA.DARD - - I I I LASERS

11m

I

HFDFHBr CO

CO 2 1111£.

0

4

8

12

16

20

X~m FIG. 3. Lasing wavelengths of gas-discharge lasers (bottom) and optically pumped molecular lasers. To the left are lasers used for pumping of molecules. The solid horizontal strips correspond to the regions of lasing on many adjacent V R transitions (from Re[ 151.

Effective conversion may considerably increase the quality of the radiation--i.e, increase its energy density per cm 3, and reduce its divergence and spectral width. In this case, two important problems of quantum electronics can be solved at the same time: new intervals of the spectral range can be covered by powerful laser sources, and the brightness of the coherent radiation can be increased. Recently, some successful experiments on the off-resonant conversion of the CO2 laser frequency have been performed. This conversion is based on stimulated Raman scattering at the rotational transitions of hydrogen molecules. (11,12) It should be kept in mind that such an approach imposes rather strong requirements on the parameters of the CO2 laser used for pumping. This is due to the decrease in Raman gain with the wavelength. This type of Raman lasers are at their initial stage of development now. An increasing demand for powerful tunable i. r. lasers will, however, stimulate rapid progress of this promising method of powerful frequency conversion. The present review deals only with resonant frequency conversion of the radiation of powerful i.r. lasers (mainly CO2 lasers). With such conversion the optical pumping of molecular gases is performed, and as a result lasing takes place at new wavelengths. In this connection we want to mention the first review of this problem, (13) published by Chang, a coauthor of the first successful experiments on laser action both in the far -~ 3) and medium -~ 4) i.r. ranges, using pumping by pulsed and c.w. CO2 lasers. Unlike the review, (13) we do not consider here at all the far-ix, region, purely rotational molecular transitions and c.w. pumping and lasing. In this paper the primary emphasis is given to pulsed lasers in the medium-i.r, region, with high conversion efficiency and considerable power. It is known that the most important results here were obtained after the publication of the review, 1~3) including successful applications of this type of lasers for i.r. multiphoton laser photochemistry. This justifies the necessity of the present review. We should also mention a short article on the topic of our review published recently in Ref. 15.

Molecular infrared lasers using resonant laser pumping

249

The review consists of several parts. In Section 1.2, consideration is given to the principle of operation of molecular lasers on vibrational transitions and the conditions for attaining a population inversion. The role of the processes of rotational and vibrational relaxation and the general requirements for a pumping source are discussed. In Section 1.3, the kinetic equations are given which describe the processes of optical pumping of molecules and the achievement of population inversion and amplification. Sections 2-7 describe lasers utilizing different schemes. For most of the schemes, there are simple formulas in the first paragraphs which make it possible to evaluate the amplification coefficient and threshold pump fluence. CF4 and N H 3 molecular lasers are considered in detail. The CF4 laser operates in the important 16 pm region on a large number of vibration-rotation transitions. The N H 3 laser operates in the region from 11 to 13.7 pm, and has as high an efficiency as the TEA CO2 lasers. The final section considers some applications of these lasers, the first successful experiments, some unsolved problems, and it also offers some outlooks on the development of pulsed molecular lasers in the medium-i.r, range with resonant laser i.r. pumping.

1.2. Population Inversion Conditions The physical principle of lasers using optical excitation is simple enough. Under resonant optical pumping using a laser or thermal radiation, field-induced transitions take place which may result in a nonequilibrium distribution of molecules over the vibrational and rotational levels, and give rise to a population inversion and amplification at certain transitions. In studying the kinetics of the inversion under the action of resonant radiation, one has to take into account the following: apart from stimulated transitions, collisional processes of the molecular relaxation in the gas take place, resulting in strong coupling between the resonant levels and those which do not interact directly with the radiation. Such collisional processes bring back the molecules to equilibrium in the end. It is the relaxation processes that determine the basic requirements placed upon the parameters of a pump source: its intensity, fluence, pulse duration and frequency of radiation. The principal relaxation processes in a gas are rotational-translational (R-T) relaxation, vibrational-vibrational intraand intermode (V-V(V')) relaxations, and vibrational-translational (V-T/R) relaxation. R-Trelaxation results in equilibrium between the rotational and translational degrees of freedom of molecules in a characteristic time from 10 - 9 to 10-11sec-atm316) V-V relaxation leads to the establishment of a definite temperature, either for one vibrational mode in resonant exchange of vibrational quanta (V-V), or among different modes (V-V'). The times of the (V-V) and (V-V') processes are usually from 10 -8 t o 10 - 9 , and from 10 - 7 to 10-8#sec-atm respectively. "6-a8) In the process of the V- T/R relaxation, acting usually during 10- 5_ 10 - 6 sec.atm,(l 6,18) thermal equilibrium is established between all degrees of freedom of the molecule at the temperature To + AT, where To and ATare the initial temperature of gas, and its increase due to absorbed energy respectively. Spontaneous radiative transitions in the i.r. range have a very low rate Wsp(W~v 1 = Z'sp = 10 - 2 to 1 sec), and hence they have no effect on the kinetics of optical pumping. The general condition of a thermal equilibrium disturbance in a gas consists of the following fact: The probability of stimulated pump transitions, W = aI (where tr is the resonant absorption cross-section of the pump transition; I is the intensity of the pump), should exceed the deactivation rate of the vibration-rotation states excited, W~,t = zc,,~~ (where rco~is the time ofcollisional deactivation of rotation or vibration-rotation states). The occurrence of amplification in the various schemes depends on the ratio between W and Wool •

If

rl7,1_7.> W> "Cvlv,,rvl_v

(1.1)

laser action can arise both on transitions between different vibrational modes, or within one vibrational manifold respectively.

250

A. Z , GRASIUK, V. S. LETOKHOV a n d V. V. LOBKO

When the relation W > rR-lr

(1.2)

is valid, amplification and oscillation are also possible at purely rotational transitions. Under c.w. operation, it is more difficult to attain non equilibrium states, since the pumping rate is:low, in this case, and the requirements on the deactivation rate of the operating levels are more stringent. It is necessary to reduce the gas pressure usually below i torr. Such a reduction leads to a decrease in the gain. Under c.w. operation, lasing has been achieved at a great number of rotational transitions in the submillimetre range. The operation of lasers with c.w. optical pumping for the i.r. range has been studied recently in two works, tTA9) Submillimetre lasers with optical pumping are not considered in the present review, since it deals with lasers in the medium-i.r, region of the spectrum. The interested reader is referred to the conference proceedings ~2~ and the reviews, Refs 13 and 21. 1.3. K i n e t i c E q u a t i o n s To analyse the population inversion conditions and laser action in optically pumped pulsed gas lasers one can use, in a first approximation, kinetic equations for the population of the molecular vibration-rotation levels. Strictly speaking, this means that, firstly, we neglect the effects of coherent interaction. Such an approximation is quite justified, since, as a rule, multimode lasers are used as pumping sources, and the excited molecules are distributed over very many states with different projections of the angular m o m e n t u m J on the direction of light-wave polarization. Secondly, the velocity distribution of the molecules is not taken into account, because the power broadening of the molecular transitions is comparable to or higher than the value of Doppler broadening. In these approximations the populations of the vibrational-rotational levels noj,, (v" = 0,J = J")

and

hi j, (v' - 1,J = J ' )

are described by the equations: 3no~,,/Ot =- ( n l l s g j g l ~ -

no~)W~j,, ~ ÷ (Noqs., -

no~,,)/Lo , + (N~qj,,

f j n l , r / O t = (no~ -- n l a g ~ / g l j ) W c S j , ~ + ( N l q J, - - n l j , ) / ' g r o t q- ( N ~ q j , c~I/OZ = - a , ( n o ~ -

-

-

no.r,)/'cv nl.r)/r v

v v

(1.3) (1.4) (1.5)

nltjg~/gB)l

N0 + N 1 = N

(1.6)

In these equations, Wand a~ are the probability and cross-section of absorption at a resonant transition respectively; n0j,, and n 1j, are the poluation densities of the rotational sublevels of the ground and excited vibrational states; N 0, N 1 and N are the densities of molecules in the states v = 0, v = 1, and their total density; N~, N~I are the quasi-equilibrium population densities of the states v = 0, v = 1; gj and qj are the statistical weights and relative populations of the rotational state respectively, 6j,/~ and 6j,,~ are Kroneker symbols; Z is the direction of propagation pumping of the radiation; and ~,,~ = r ~ _ ~,. Equations (1.3)-(1.6) should be complemented with initial and boundary conditions, which for a rectangular pump-pulse have the form: I ( t -- O) = I o I(Z

exp [ - a , ( n oe~ - n lel s g j g'~ ) Z

]

(1.7) (1.8)

-- O) -- I o

where n~]~and n~')t~are the equilibrium initial populations of the resonant rotational levels, and t, 6,,(no~

__ n e

, llJg~/gl~) = o~,,

designates the initial absorption coefficient of the resonant pumping transitions. If ~, or the excitation length Z o are small and the change in I ( Z ) can be neglected, eqs (1.3) and (1.4) can be integrated. Such integration makes it possible to evaluate, at once, the gain (absorption)

Molecular infrared lasers using resonant laser pumping

251

for any pair of vibration-rotation states. With the Z-dependence of I ( Z ) allowed for, the solution of eqs (1.3)-(1.6) becomes cumbersome, and simplifying physical assumptions are usually needed. It should be noted that in eqs (1.3)-(1.5), allowances are made only for processes of laser molecular excitation and collisional redistribution of their energy between different energy states. Because of this, they do not describe the development and formation of a pulse of converted laser radiation. Now we consider some specific schemes for optical pumping of molecules by laser radiation to convert its frequency. 2. P U M P I N G AND LASING IN A F U N D A M E N T A L BAND

2.1. Population Inversion C o n d i t i o n s - - F i r s t Lasers

Such a scheme was first realized in Ref. 22 and analysed in Ref. 23. The results of the analysis are briefly presented below. Figure 4 illustrates an energy-level diagram for the vibration-rotation states, and indicates several transitions participating in the build-up of the population inversion. However, the possibility of attaining amplification in such a scheme is not evident. Let us consider the case when the relations times satisfy L,,, << -t-p<< z V v and

V=I PUHPING

R-BRANCH

--

LASING -- Q AND

- - P-BRANCHE S

V--O FIG. 4. Energy-level scheme for optical pumping and lasing in the fundamental band at change of rotational quantum number.

Wrro t << 1, meaning that the vibration-rotation relaxation can be neglected, and thermal equilibrium is established on the rotational sublevels in the process of pumping. If we consider the rotational gas temperature to be constant and sum the eq. (1.4) over J ' we get

~ N I / O t -- (no~ - nll~gJglj)W.

(2.1)

Taking into account eq. (2.1), and assuming that the pumping pulse has a rectangular shape, we can obtain the following expression for N 1 NI(zp) = N{1 - exp [ - ( q a + q~ga/g~)Wrp]}/{1 + g~qa(gaq~)- t}.

(2.2)

It may be seen from eq. (2.2) that saturation of Nl(z~,) will be attained if the condition ~p "~ hvp/a(qa + q=gpg~l)

(2.3)

is fulfilled; here, % is the energy fluence of the pump pulse. If we neglect the exponential term in eq. (2.2), N, and N O take the values N 1 -- N / { 1 4- g~qp(gpq~)- 1};

No __ N/{1 + gaq~(g~qp)-1}.

(2.4)

The sign of the absorption coefficient for the transition 0J" ~ 1J' depends on the sign of the parameter h- = 1 - (g.r,nl.r/g.rn~, r, ), which is proportional to the population difference. If the rotational energy of the molecule is expressed as F I J ) = B J ( J + 1), then ~¢= 1 exp [F(J") - F ( J ' ) + F(fl) - F(ct) ]. If we consider the pumping and emission in the P- and Rbranches it is easy to see that ~,-is negative for all transitions with a frequency smaller than that of the pumping frequency. This means that if pumping takes place on the R-branch, lasing is possible both on the R-branch with J' 1. If pumping takes place on the P-branch, the population inversion can be attained on the P-branch only for JPQE 6 / 4 . C

252

A . Z . GRASIUK, V. S. LETOKHOV a n d V. V. LOBKO

J" > ft. These conclusions are illustrated in Fig. 5a, b, where the calculated values of the absorption (amplification) coefficients % are given for different branches of excitation and emission, and where %, is determined from the relation % = a,,~,n~>~,,. If pumping takes place on the Rbranch, it follows from the relations (2.4), that N ~ / N o = exp(2Bfl/KT)> 1; i.e. total population inversion is attained in contrast to the case of pumping on the P-branch, when N~/No < 1, and only partial inversion takes place. -I

'

T

T

-(15 ne

~x 0

0

i

0 -'~

5

I0

15

20

25

J'

I5

20

25

J'

-I

m <

-0.5 o 0.5

0

i'

1

5

I0

FIG. 5. Normalized gain coefficients in the P-branch (a) and R-branch (b) at p u m p i n g in P ( R ( - ) branches and with B = l c m L T=300K.

) and

O f great interest is the dependence of % on the value of the rotational constant B of the molecule being excited. It is shown in Ref. 23 that with an increase in B the absolute values of the extremes o f % increase as well. In this case, the relative width of the curve x(J') decreases, and the coordinate of its m a x i m u m shifts along the J ' axis towards J ' = 0 (Fig. 6a, b). The behaviour of the dependence of % on pressure p is similar to the dependence of the product a, noj,, on pressure, if the assumptions used in the calculations are fulfilled. - 2

-I

P - Q5 =

o

~

i -ts

o.t~,,,t

/

\

\ ,,~

r

.,

0.5

z

j,-

~

-

<

o.t¢-' I,W

~

L5

/

~

0 \

i

1

<

I

'l

\

rl,m 1.5

\v/ 2,5

5

I0 Q

15

20

J'

/

O

i

'! ,.~

//

'\

2 0

/ /

,.Jo

/ X

2

tts,~

0.5

'"~ 5

I I0

15

20

J"

b FIG. 6. Normalized gain coefficients in the P-branch (a) and R-branch (b) as the function of rotational constant B at p u m p i n g in the P ( ) and R ( ) branches and T = 300 K.

Molecular infrared lasers using resonant laser pumping

253

These conditions for a population inversion in an excited band are the most optimal ones, since in this case it is possible to attain gain at a great number of molecular transitions at once. In another limiting case (Zp << Zrot, Wzp -~ 1 ), the gain may be attained at no more than two transitions. The scheme of optical pumping considered above has some important features: the frequency conversion of radiation takes place with a very high quantum efficiency (95-98 ~o), and at many frequencies at the same time. Moreover, as the fundamental band is excited, a considerable gain can be achieved even at a relatively small population inversion. The first laser of this type was reported in Ref. 22, where the molecular gas H F at a pressure of 0.01-0.5torr was pumped by H F laser radiation. The results of these experiments demonstrated the possibility of laser action at the fundamental band under optical pumping. However, neither the active medium nor the pumping source were optical from a practical point of view. An essential step was the use of a CO 2 laser as a source of p u m p radiation, because of its high efficiency, low cost, and the possibility of attaining high pulse and average powers. In this sense, the creation of the N H 3 laser described below was a qualitative step forwards. 2.2. N H 3 Laser 2.2.1. First experiments. In Ref. 24 the laser action in N H 3 was demonstrated for the first time by pumping it with a C O 2 TEA laser. The spectral characteristics of the N H 3 laser were investigated in Refs 25-27. Among these papers, the work of Ref. 27 should be noted. It shows that nitrogen as a buffer gas increases considerably the spectral range of the laser action (lasing was observed at m a n y lines). Since then, the N H 3 laser has been investigated in a lot of papers. However, in most of them ~24- 27.29 35) the laser pulse energy was in the range between fractions of mJ and tens of m J, and besides the efficiency was no higher than a few percent (Table 1). Such modest energies did not distinguish the N H 3 laser among a family of other optically pumped molecular lasers, and restricted its applications. -

TABLE 1. Lasers operating on the fundamental vibrational band optically pumped with the C O 2 laser

Pumping

Laser

Line

Frequency (cm 1)

Active medium

Frequency range (crn 1)

9R(16 9R(30 10R(14 10R(6) 10P(32 9R(30 9R(30 9R(16 9R(30 9R(30 9R(16 10R(14

1075.99 1084.64 971.93 966.25 932.96 1084.64 1084.64 1075.99 1084.64 1084.64 1075.99 971.93

NH~ NH 3 NH 3 NH 3 NH 3 NH3-N 2 NH 3 NH3-N 2 NH 3 N 2 NH3-N 2 C2H 4 C2H 4

780.5 827.7 872.6 847.4 814 723-1070 827.7 780.5 770-890 753-931 910.7 910.7

Energy (mJ) 4 0.5

Efficiency ('o) J 0.3

Refs 24 25, 26 25

-up to 60 750 up to 1400 ---

-several 20 ---

27 34 65 39, 40 33 25 25

That is why the investigations of Refs 28, 36, 38-40 and 45 were most important for practical applications. They resulted in creating an N H 3 laser of a new type. In such an N H 3 laser, the pulse energy, specific energy peak power, efficiency and tuning range were comparable with those of the CO 2 TEA lasers. There emerged two points which have been of principal importance: On the one hand, it was found that an optimal addition of nitrogen as a buffer gas allows one to increase by many times the pulse energy, power, efficiency and tuning range of the N H 3 laser; on the other hand, special optical schemes have been developed, which have included in particular radiation resistant dispersive elements. C36-4°) Such

254

A . Z . G~ASlUK, V. S. LETOKHOV and V. V. LOBKO

schemes allowed one to attain both high peak and average powers in the N H 3 laser. In the following section we shall discuss the principal properties and features of such N H 3 lasers, based on N H 3 N 2 mixture. (28'36,38-4°-45) 2.2.2. Spectroscopy. Figure 7 shows the partial vibrational rotational energy level diagram for the v 2 mode of the N H 3 molecule. Inversion doubling splits each vibration-rotation level into two: the symmetric level (s) and the antisymmetric one (a). The splitting increases with an increase of the vibrational quantum number v, and is maximal for the v2 mode. The R-branch of the v 2 absorption band has two transitions, sR(5.0) and NH 3 LASER

SPECTROSCOPY

II i!

4

LASING j830835 CM-I ~809-816 CM-I

/

1

~789

LASlNG 7 8 0 . 5 CM ~ r ~

~J-

0

6 5 2--

V

J

780CM -I

~828

PUMPING 1 0 7 6 CM"t-- ~ - ~

7

798CM -I

~771

V It

JL

CM~

PUMPING 1084,6 CM-I

I

I

FIG. 7. Energy-leveldiagramforsome V-RlevelsandtransitionsofNH3moleculeinthefundamental vz band. K sub-levelsare not indicated for simplicity. aR(6.0), whose frequencies are close to the frequencies of the 9R(30) (v = 1084.64cm ] ) and 9R(16) (v = 1076cm -1) lines of the CO 2 laser respectively. The offset of the pumping frequency 9R(30) from the absorption frequency of sR(5.0) line is 7 × 10 -3 cm 1, and for aR(6.0) such an offset from 9R(16) is 8 × 10 - 2 c m - 1. It should be noted that the multiplet sR(5, k) has a linewidth of 0.15 cm-1.~411 The 9R(30) linewidth of the CO 2 laser is usually 0.03 c m - 1. Therefore, it is possible to excite a number of K sublevels of the (0,s(5, k) (1, a(6, k)) transition. In a saturation regime, population inversion and lasing could arise at the transitions on the P-branch with different K: (l, a(6, K)) --* (0, s(7, K)) Similarly, the 9R(16) line can be used to excite the (0, a(6, K)) ~ (1, s(7, K)) transitions and attain laser action on the (1, s(7, K)) --. (0, a(8, K)) transitions. As noted above, the addition of a buffer gas at a rather high pressure (tens or hundreds oftorr) ~23'27.36 40.45) is a promising technique to increase the tuning range of the N H 3 laser. Indeed, fast rotational relaxation due to collisions between the buffer gas molecules and the operating one result in a population inversion on many vibration-rotation sublevels and hence laser action at many frequencies. Using a selective resonator we can achieve effective oscillation on every separate vibration-rotation transition. However, some special studies (18"3638-4°4s) have shown that just nitrogen is an optimal buffer for the N H 3 laser. It provides not only laser action at many frequencies) 2v 28.33) but it also sufficiently improves the energy characteristics of the N H 3 laser--i.e, increases its pulse energy and conversion efficiency. Such a favourable effect is caused by the fact that some rotational levels of the nitrogen molecule almost coincide with (or are close enough to) certain rotational levels of the ground state of the N H 3 molecule. Some of these resonant levels are the final states of laser transitions. In such a case, an efficient

Molecular infrared lasers using resonant laser pumping

255

resonant collisional interaction can take place between the N H 3 and N 2 molecules. The collisions deplete the final rotational states in the ground vibrational band of the N H 3 molecules and maintain the population inversion. One can see from the following sections that it is these resonant N H 3 levels which are responsible for the most powerful oscillations. 2.2.3. Schemes of N H 3 laser and principal characteristics (single pulse operation). Spatial homogeneity of the exciting radiation is extremely important in order to obtain high pulse energies, powers and efficiency. Besides, to achieve high energy simultaneously with good frequency tuning, it is necessary to have resonators with radiation resistance dispersive elements. Therefore, the most promising schemes o f N H 3 laser are those which comply with these requirements. In Ref. 28, longitudinal optical pumping was carried out with a nonfocussed C O 2 laser beam. This made it possible to attain the spatial homogeneity of the excitation over a rather large volume of the active medium. The scheme in Ref. 28, however, had the following defect: the CO z laser cell which was inside the N H 3 laser cavity introduced active losses and deteriorated the oscillator parameters. The scheme with separated cavities, ~36-4°'4445) which is shown in Fig. 8, has got no such disadvantage. The CO 2 TEA laser beam from the zeroth order of the grating G 1 (100ram-1, the blazing angle is 30 °) propagates almost normally to the grating G 2 (75 m m - 1 , the blazing angle is 23 °) and is directed into the N H 3 laser cell in the first order of the grating G 2. A stainless-steel tube with NaC1 Brewster angle windows was used as the N H 3 laser cell. The cell was 180 cm long and had a clear aperture of 70 mm. The selective resonator was formed by a spherical mirror M 2 with radius of curvature R = 10 m, and with the grating G 3 (100 m m - 1). The mirror M 2 and the grating G 3 w e r e connected through the zeroth order of G 2. The N H 3 laser radiation was emitted from the first order of G 2 through two beams: The first one, containing 70 'Yoof the total energy emitted as oscillator radiation, propagated from G 3 towards G2; the second beam, containing 30 ~, of the energy emitted as radiation, propagated from the mirror M 2 towards G 2. The N H 3 laser frequency can be tuned by turning the grating G 3.

ITEACO2LASERCEL t GI

G2 , FIG. 8. Optical scheme of the NH 3 laser using a selectiveresonator; G~, G2 and G 3 are diffraction gratings, MI and M2 are mirrors with their radii of curvature 20 and 10m respectively. It should be emphasized that the resonator of the N H 3 oscillator has got only radiation resistant dispersive elements (metallic gratings). This allows one to use such lasers at a high repetition rate to attain both high peak and average powers t45) (see below). As noted above, the addition of N 2 to N H 3 resulted in a substantial improvement of laser performance. Pumping with the 9R(30) line, the N H 3 laser energy increases by more than one order of magnitude (pumping with the 9R(16) line the energy increases 2 or 3 times). Studies of the influence of He and H 2 as buffer gases have shown that the oscillation energy increases about two times. Figure 9 shows how to ascertain an optimal N H 3 - N 2 mixture and its optimal pressure. It shows the dependence of the N H 3 laser pulse energy (at the frequency of 828 c m - 1 ) on the total pressure of the N H 3 - N 2 mixture for the different N H 3 N 2 mixtures. One can see that N H 3 / N 2 = 1/75 is an optimal mixture. In turn, the optimal pressure of the mixture must be chosen depending on the pumping energy fluence.

256

A . Z . GRASIUK, V. S. LETOKHOV and V. V. LOBKO

0,8

0,6 >.(.9 Z

0,4

o,2 L ¢-//

,

-

o-,25

J d

.-v~o t

GAS MIXTURE

PRESSURE, TORR

FIG. 9, Dependence of NH 3 laser output energy on the total pressure of N H 3 - N 2 mixture at varying N 2 concentrations at the pump with the 9R(30) line of CO 2 laser.

The use of high pressures of N H 3 - N 2 brings about a considerable decrease in the rotational relaxation time of the excited band in its turn; such an effect makes possible the tuning of the N H 3 laser frequency. Table 2 shows some results of investigations of such tuning. The scheme of the N H 3 laser in this experiment was the same as given in Fig. 8. Table 2 shows that the maximum pulse energy on some lines exceeds 1 J, with the efficiency being 20 ~0. It is interesting to compare the data from Table 2 with the energy-level diagram for the N H 3 and N 2 molecules, which is given in Fig. 10. Such a comparison indicates that the maximum laser energy and efficiency are attained on those lines whose final states of the radiative vibration-rotation transitions are close to the appropriate rotational energy levels of the N 2 molecule. TABLE 2. Parameters of the NH 3 laser optically pumped with 9R(30) CO 2 laser line (vv = 1084.64 cm 1). Operating mixture is N H a - N 2 = 1:75 - 1:100 with the total pressure of 60torr (at the pump fluence of 0.8 J/cm 20.8 J/cm2) ~39'4ol

Frequency (cm 1) 888.1

872.6

Transition

Pulse energy (J)

Energy efficiency (17o)

Frequency (cm - 1} 814.3 812.0 809.7 798

Transition aP(6, 3) sP(6,4) aP(6, 5) aP(7, 0)

Pulse energy (J)

Energy efficiency [ '!.)

0.85 0.6 0.55 0.7

13 9 8 11

sP(4, K) aP(3,0) aP(3, 1) aP(3, 2)

0.55

8

0.8

12

sP(5, K) aP(4, 0) aP(4, 1) aP(4, 2)

1.25

19

797.4

aP(7,2)

0.7

1.4

21

796.0

aP(7, 3)

0.7

11

1.3 1.1 1.1 0.9 1.1 1.2 1.25 1.3 1.3 1.2

20 17 17 14 17 18 19 20 20 18

794.0 791.8 789.0 780.4 779.7 778.2 776.4 774.0 770.9 760.3

aP(7, 4)

0.35 0.45 0.6 0.5 0.5 0.35 0.3 0.3 0.5 0.07

5 7 9 7 7 5 5 5 7 I

aP(7, 1) 868 853.6 852.2 851.0 847.4 834.7 834.0 832.0 828.0 816.8 816.2 815.4

aP(4, 3) sP(6, K) aP(5, 1) aP(5,2) aP(5, 3) sP(7, K) aP(6, 0) aP(6, 1) aP(6, 2)

aP(7,5) aP(7, 6) aP(8, 0) aP(8,2) aP(8, 3) aP(8, 4) aP(8, 5) aP(8, 6) aP(9, 6)

Molecular infrared lasers using resonant laser pumping

257

IB 6OO n'~~ 3 CM - I .

,6 m

5OO

Ct(7,K)

4OO"

--15

i

,3 zx)o-

.

-[~===1

A'~lc.-'

• A~2CM

-I

a , ~ , : 3 ~ -~

I00 S(3'K) { ~ ( 3 ' K ) ~

ROTATIONAL

Iz ,,

~ ~

'~--

I0

~

8

"~"

7 6

LEVELS N2

NH 3

FIG. 10. Energy-level diagram for a NH3 laser on NH3-N 2 mixture: s(d,K), a(J,K) are final states of the NH 3 laser; I' are rotational levels of the ground vibrational state o f N 2 molecule, corresponding to the angular momentum quantum numbers from 6 to 18; the arrows show the collisional deactivation of final laser states of NH 3.

Figure 11 shows some typical time histories of the N H 3 laser pulses at a frequency 828 cm- 1, for varying pressures of the N H 3 - N 2 mixture. Since the intensity at the pulse peak is much higher than that in its tail, the peak and tail will be absorbed in different ways. Indeed, the saturation intensity is I s = h v / 2 o T 1 , where hv is the quantum energy, T1 is the spin-lattice relaxation time (in our case 7"1 = r v r/R, where ~v T/R is the vibrational-translational relaxation time), a is the pump absorption cross-section, which, in turn, is given by

(2.5)

o -- g ( v ) v 2 / 8 ~ c 3 T ~ p

NH

LASER

MIX'TURE NH~: N= I:100 PULSE PASSED CO2PULSE I 0 0 TORR

Z

70

\.

TOR~

nr

O

30rORR

I~1~TORR,

t.~ fit.

PUMP I NG C O l .

TIME

500n$

FIG. 11. Temporal behaviour of lasing and pumping pulses of an NH 3 laser on N H 3 - N 2 = 1:100 mixture (the NH~ laser frequency is 828cm-t).

258

A.Z. GRASIUK, V. S. LETOKHOV and V. V. LOBKO

where g(v) is the line shape function and rsp is the spontaneous decay time. At an NH 3 pressure of > 1.5 torr, the collisionally broadened absorption line width exceeds the Doppler line width, which (for NH 3 at room temperature) is given by the formula A v o ~-

1.5 x 10-6v

[cm-l].

(2.6)

In case of collisional broadening, the line-shape function is a Lorentzian %)2 + (Av+ot)2]

g ( v ) = AV~oYrC[(v -

(2.7)

where (v - v0) is the detuning of the pumping frequency v relative to the absorption line resonance frequency Vo, and AV+o~ is the collisional half-line-width. The pressure broadening coefficients for the NH 3 lines are: (41) Ksn 3 sH3 = 28 MHz/torr is the coefficient of selfbroadening, and KNH3- N2 = 3.8 MHz/torr is the coefficient of broadening by N 2. From this it follows that for N H 3 - N 2 mixtures AVco~ ~

PNH+ + 0.14PN2.

(2.8)

Thus, it follows from eqs (2.5)-(2.8), that at high pressures (when Avco t >> A v o , v - % ) the saturation intensity I x is I+ ~ P~, since z v_ r/R ~ P~- ~. In other words, at a constant pumping intensity it is possible to vary I s, and hence to vary the lasing conditions by varying the pressure Pz of the mixture. In Ref. 39 the following empirical formula has been obtained for I s I, -- (0.025 x P~ + 1.2)

(MW/cm 2)

(2.9)

where Pz is the pressure in torr. The measurements of I, and the linear absorption coefficient of the pump c~, for the sR(5.0) line resulted in a , = l . 5 × 10-~6cm z and z.NH3 - NH3 = 450 #sec-torr/39) The investigations of the oscillation dynamics (Fig. 11) shows V - T/R that the typical CO 2 laser-pulse time history (a short spike and a long tail) is not the optimal one for attaining of high N H 3 laser conversion efficiency. Indeed, on the one hand, the pumping pulse spike being reasonably intensive is too short to provide a steady state oscillation. As a result, only a low efficiency transient oscillation arises and most of the pump peak energy passes through the active medium without conversion (Fig. 11). On the other hand, the pump pulse tail, being long enough to provide steady-state oscillation, has a relatively low intensity and does not lead to saturation throughout the whole length of the active medium. In other words, the optimum pump pulse shape should be rectangular or almost rectangular. Figure 12 shows the dependence of the average number of quanta absorbed by one NH 3 molecule for oscillation on the pressure of the mixture of N H 3 N 2. One can see that each N H 3 molecule participates several times in the following cycle: pumping ~ rotational relaxation --. induced emission -+ (rotational relaxation + collisional deactivation)

ARSORPT I ON

J

Z

6

~

uJ

I z

z

t.~ w

0 .1.

1:50

/

0.5

~" fL;SING I~08~m~ 0

l

I

|

I

I

20

40

60

80

I00

GAS

MIXTURE

PRESSUREp

m

0

TORR

FIG. 12. Pressure dependence of the average number of quanta absorbed ( • • • ) and emitted (O O O) by one NH 3 molecule in N H 3 - N 2 mixture under lasing conditions. The dashed line shows the pressure dependence of absorption cross-section.

Molecular infrared lasers using resonant laser pumping

259

pumping. The average number of absorbed quanta is greater than the number of emitted ones \ n ) L (quantum yield 40 %). Such a relation between (n)A and (n)/. indicates that there are non-radiative transitions which decrease the efficiency of the N H 3 laser. The specific energy is an important parameter for lasers. An increase in the specific energy is connected with an increase of the density of spatially homogeneous pumping. A certain advantage in this sense is obtained using light-guides. A light-guide 1.2 x 2 cm was used in the first experiment with an N H 3 laser, 124>and later in several w o r k s ] 29" 30.32.33) In Ref. 34 a rectangular light-guide was used with a cross-section of 8 x 6 mm and a length of 1 m. It enabled the authors to attain a pulse energy up to 60 mJ with an efficiency of several percent and specific energy up to 1 J/1. Yet the use of spherical focussing lenses deteriorates the spatial homogeneity of pumping. However, a combination of a special raster focussing system and a rectangular light-guide results in a spatially homogeneous pump throughout a length up to 1 m. Such a system, which was used previously in Raman lasers, ~42'43) has proved very efficient for optically pumped molecular lasers as well. The principle of operation of the focussing raster is the following: The raster consists of a number of square prisms. The combination of prisms splits the pumping beam in' 9 many beams. Each of these beams has a square cross-section, and passes through the same place in the focal plane of the raster. This results in a square light spot which has a homogeneous intensity distribution. The form and size of the spot together with its intensity distribution throughout the spot do not, under certain conditions, depend on the spatial characteristics of the pump beam. If we combine this spot with the input of the light-guide, the beams, reflected from its walls, create a homogeneously illuminated column of active medium throughout the length of the lightguide. Such a scheme, as applied to N H 3 lasers, is shown in Fig. 13. The pumping radiation RASTER ~ I

^. MPI"

~

I IH I[

NHI~'--LASER \\

I

I I //

II

~p=lO84.6¢mL NH~ LASER WITH RASTER-LIGHTGUIDE PUMPING FIG. 13. Optical scheme of a light-guide N H 3 laser with a raster-type pumping system.

was focussed into a 70 cm long light-guide with a short-focus raster-type system (F = 25 cm), the focal cross-section of the spot being 7 x 7ram. The BaF z raster consisted of two intersecting systems of wedges forming a system of rectangular prisms. The copper lightguide has a square cross-section of 7 x 7 mm. The resonator of the N H 3 laser consisted of a totally reflecting copper mirror 15 mm in diameter, and a flat ZnSe plate. The principal parameters of the N H 3 laser are given in Table 3, which shows that the specific energy can be as high as 12J/1. Some decrease in efficiency TABLE 3. Principal parameters of raster-light-guide optically pumped NH 3 laser ~138-4°1

O p t i m u m gas mixture

NH 3 N z

Total pressure (torr)

1:200 1:150

230 280

Light-guide

NH 3 laser output parameters

Length (cm)

Crosssection (cm 2)

Pulse energy (J)

Energy efficiency

('J/o)

Specific energy output (J/l)

70 70

1x 1 0.5 x 0.5

0.35 0.2

10 6

5 12

* Pumping was performed by the 9R(30) CO 2 laser line (v~, = 1084.64cm ~) with the p u m p energy of 3.5J.

260

A.Z.

GRASIUK, V.

LETOKHOVa n d

S.

V. V.

LOBKO

could be caused by large diffraction losses because of the small cross-section of the lightguide. 2.2.4. High pulse repetition rate operation. The pulse repetition rate and the average power are very important parameters of a laser, together with its pulse energy, peak power, and efficiency. Indeed, in many applications only the combination of both high peak and average powers determines the ultimate efficiency of a technological process. For instance, the N H 3 laser has already been used successfully for laser isotope separation of 12C and 13C, with isotopically selective dissociation of the CC14 molecules. 144) That is why an increase in average power on account of a high pulse repetition rate operation ( H P R R O ) of the N H 3 laser is of particular interest for laser isotope separation and laser chemistry. The work of Ref. 45 describes the N H 3 laser operating under H P R R with the pulse repetition rate up to 100 Hz. Oscillation was obtained as N H 3 was pumped in a non-selective resonator* by a H P R R CO 2 laser. The N H 3 - N 2 mixture was pumped with the 9R(30) CO 2 laser line. Because of the non-selective resonator there were six lines in the N H 3 laser spectrum: the four most intense of them had the frequencies 833, 828, 800 and 780cm ~. The energy in these lines constituted 30, 60, 7 and 2 7/o of the total energy respectively. It should be kept in mind that all results presented below concerning energy and average power represent the total oscillation energy on the lines mentioned previously. It must also be born in mind that the mixture of N H a - N 2 used in Ref. 46 was not optimal: NH3/N 2 = 1/50. Due to this fact, the efficiency (about 16 '70) was somewhat lower than that in the above-described single pulse regime. In Ref. 45 the dependence of energy and average power on pulse repetition rate was studied. Figure 14 shows the dependence of laser pulse energy on the pulse repetition rate at the 9R(30) line of a CO 2 laser. One can see that as the pulse repetition rate increases, the pulse energy drops. Such a drop can be explained by heating of the active medium. On the one hand, such heating causes a reduction of particle density along the cavity axis: on the other hand, the heating increases the thermal population of the lower (final) laser levels. Both effects decrease the laser pulse energy. However, even though the pulse energy decreases, the average power of the N H 3 laser increases as the pulse repetition rate increases up to 100 Hz (Fig. 14). The maximum average power reached 20 W and was limited only by the average power of the p u m p source. Figure 14 shows that as the pulse repetition rate increases above

20

PUMPING NH 3

Nz

1084.6 I

CM - I

,50

500

•

i~..~/, ~

400

(z"

/,," -~e...O~

>

300

o =

"'

ua

O ,a

5

200

Z ua

w w

'"

-+ I O 0

I

£

I

5

I0

i

REPETITION

FIG. 14. Dependence of the

£

l

i

£

~

50 RATE,

-J

~ll

I00 PPS

laser pulse energy (0 • • ) and average power (© © ©) on pumping CO2 laser pulse repetition rate. NH 3

* The schemewas similarto that givenin Fig. 8: however,instead of the diffraction grating 6:3 there was a copper spherical mirror with its radius of curvature R ~ 20 m.

Molecular infrared lasers using resonant laser pumping

261

100 Hz the average power can be also increased, the efficiency being rather high. It should be kept in mind that in this case it is possible to increase essentially the efficiency (and hence the average power) by circulating the N H 3 - N 2 mixture in the N H 3 laser cell. It is of importance that the average power of the NH~ laser is comparable to the power of CO 2 lasers with conventional pulse repetition rates. The use of a selective cavity (Fig. 8) makes it possible to attain a high repetition rate for each line over the range from 890 to 770 c m - ~, as was attained in single pulse operation. High peak and average powers, as well as the possibility of tuning the N H 3 laser frequency over the range between 890 and 730 c m - ~, allow the use of the N H 3 laser for quite a number of practical applications. 3. E X C I T A T I O N O F C O M B I N A T I O N BAND OR O V E R T O N E A N D L A S I N G IN A " H O T " BAND

3.1. Population Inversion Conditions Such a scheme of optical pumping was considered in general in Ref. 46. In this scheme (Fig. 2a) an overtone or a combination level is under excitation. In both cases the absorption crosssections are usually smaller by two or three orders of magnitude than that of the fundamental band. However, lasing takes place in a strong band, which is allowed in the harmonic approximation. If the lower laser level has energy E >> kT, its equilibrium thermal population is very small. Therefore, even the excitation of a small fraction of molecules to a higher level gives rise to a laser effect. To determine the populations of the higher laser levels n2s, we may use eqs (1.3), (1.4) and ( 1.6), neglecting the influence of vibrational-vibrational relaxation-i.e. assuming that Zp 4< z v_ v, as well as the dependence I(Z). In this case it is possible to solve the system of equations in a general form. (46) Now we consider some more specific cases. Let the relation Zp << zrot be valid. Then the pumping radiation disturbs the equilibrium distribution of molecules over the rotational states 0J" and 2J'. During a pumping pulse a "'peak" is formed in the distribution n2j, when J ' = fl, and a "hole" in the state "0~". Obviously, in this case gain is possible only for the transitions 2fl ~ 1J during r e. The gain is given by the expression: 1401 7e = 7a0-210"o21 ~1 - exp [-eegpqs(1 + g ~ g ~ l ) e x p ( - E / K T ) ( d t ~ ) g s q ~ ) - l ] / ( 1

+ g,g~l)

- qjgpexp(-E/KT)/q~gt~ }

(3.1)

where ~Ii1,) -- hvegpq s e x p ( - E/KT)/aozg~q ~

(3.2)

is the threshold pump fluence which makes the absorption equal to zero on the transitions in the lasing band, and ~, is the initial absorption coefficient at the resonant transition 0a ~ 2ft. From eq. (3.1) it follows that if the ratio eP/ea,' (~) is fixed, the dependence of~g on pressure P coincides with the corresponding dependence of ~(P), since o-2 ~(P)/ao2(P ) = const. This means that before the pressure P~ is reached, when the Doppler width of the absorption line is comparable to the collisional one, an increase in ~, is observed. When P > Pt, a02 at the centre of the absorption line is decreased as P - ~, therefore ct,(~g) remains constant. When P a p p r o a c h e s P2, at which the collisional broadening of the absorption line is comparable to the spacing between the lines, the decrease ofo'02 slows down, and with a further increase in P it terminates completely. This leads to an increase in ~a and %. When the pulse energy ep is fixed and P~ < P < Pz, ag decreases, since in this pressure range el~~increases as a02~, and with P > P2, ~g begins to rise. Let us consider another case when the excitation pulse duration satisfies the relation r,o, ~
-

gs'qJ exp ( -- E / K T ) / q , q s }.

(3.3)

In this expression e~,~~ is the threshold pump fluence for the second case: 3(tl, -- hvpgJ'qs e x p ( - E/KT)/ao2q~qj,g ~.

(3.4)

262

A.Z. GRASIUK,V. S. LETOKHOVand V. V. Loar(o

It follows from a comparison ofeq. (3.2) with (3.4) that el2) is q , 1 times higher than ect~~. The pressure dependence of~g in this case behaves like in the first case. The comparison between eqs (3.1) and (3.3) shows that with ep >> ~~11 and ep >> °~tz) for the first and second cases th th ' respectively, the gains ~g are practically equal. In Ref. 46, consideration is given to the case when Lo, ~< zp ~< Z v - v , but, nevertheless, W L o ' >> 1--i.e. the pumping rate is much higher than the rate of rotational relaxation. Here, ~g depends on Zp/Lo,, and attains its maximum for the transition 2fl ~ 1J. A quasiequilibrium molecular distribution over the rotational sub-levels can be achieved only with ZP > LoJq. If the p u m p pulse parameters do not satisfy the conditions of excitation above, eqs (1.3)-(1.6) should be solved exactly. The gains in this case will have intermediate values relative to the limiting cases considered. In Ref. 47, the analysis of the OCS laser operation was given for the case of a weak quasistationary excitation when the following relations are fulfilled: dNo/dt(dNz/dt)z

v .< N O

(3.5)

dno~/dt -- dn2~/dt = 0

(3.6)

qo~(q21~) -< 1.

(3.7)

Such a situation is realized for a rather wide range of operating pressures in m a n y gases when weak bands are pumped. Under the assumptions made, the population of the higher resonant rotation level is described by the expression: ~4748~ 0

n2~ = Noq21J [2 + (WLo,)

-I

P]

-1

(3.8)

It follows from eq. (3.8) that n2a is inversely proportional to pressure, and that n2a is saturated at P :2; W L o,,° where Z,o ,° is the rotational relaxation time at 1 torr pressure. The Boltzmann population of the lower laser levels increases linearly when the gas pressure increases over any range of its variations. Therefore, there should be an optimal operating gas pressure P,,p,, as well as a maximum P ..... at which lasing is still possible. For Pop, and P,,~xthe following relations may be written: ~49) Pop, -- W ( Z ° o t ) 3 o o K ( T / 3 0 0 ) l / z { 2 1 / 2 [ e x p ( E , J Pmax

0 - W(Zrot)3ooK(T/300)

1,2 ' f~exp

- E o ~ ) / K T ] x'2 - 2}

[(E~., - E o ~ ) / K T ] - 2}-

(torr) (torr).

(3.9) (3.10)

Deriving these formulae we took into account only the transitions nza ~ nlj , and those from the rotational sub-levels n2j, populated in the process of rotational relaxation were neglected. As will be demonstrated in the analysis of the C F 4 laser operation, just these conditions are valid for the occurrence of a laser spectrum in a non-selective cavity. This is due to a high gain coefficient in the schemes of optical pumping considered above. The results obtained are still valid at pumping overtones and combination bands of a higher order. The possibility of excitation of the fourth and fifth overtones has been experimentally demonstrated in Ref. 50. These overtones of the C H 3 C N molecule were excited by a c.w. dye laser. The evaluated cross-sections of transitions for these overtones were 1.8 x 10 2 4 ClTI 2 and 2.4 x 10 2s cm 2 respectively. The scheme for laser frequency conversion considered has certain advantages, which are as follows. First, gases can be pumped at high pressures and long paths since the absorption coefficients on both overtones and combination vibrational transition are relatively small. This is the principal advantage of the pumping scheme, because at a high gas pressure it is possible to attain continuous tuning of the converted radiation frequency, due to the fact that molecular transitions are collisionally broadened/-sl" 129) Moreover short light pulses can be obtained by mode-locking/~2) Besides, at high pressure it is much easier to choose suitable molecules for rather a limited number of pumping frequencies of powerful and efficient i.r. lasers. At last, the lower laser level is populated only slightly, and so population inversion and lasing can be obtained without saturating the resonant transition by the p u m p radiation. This specific feature of the scheme reduces considerably the requirements on the power of the laser pumping source.

Molecular infrared lasers using resonant laser pumping

263

This scheme is being utilized at present in lasers operating o n O C S , (53) C F 4, NOCI, C54) CF3I, (31) N 2 0 , ~55) and other molecules. 3.2. Excitation o f an Overtone Band In Ref. 56 the radiation of a tunable Nd-laser excited the transition v = 0 ~ v = 2 of the HC1 molecule, and luminescence was observed on the transitions in the band v = 2 ~ v = 1. The first laser with one-photon pumping of an overtone was realized in the OCS molecule.(53.57) In Ref. 53 the pumping source was a CO 2 laser operating at the 9P(22) line. Its pulse power was 3 MW, with a pulse width of 250 nsec. The semi-confocal resonator of the OCS laser was formed by gold mirrors with holes 3 m m in diameter for the input p u m p radiation and output laser one. The optimal OCS pressure was 0.8 torr for the p u m p intensity used in the experiments. The energy-level scheme for the OCS molecule and the transitions consistent with pumping and lasing are given in Fig. 15. It can be seen from Ref. 53, that lasing took place in the P- and Q-branches of the 02°0-0110 band at frequencies of 524, 741, 526 and 787 cm ~ respectively. The analysis of laser action kinetics under experimental conditions t53) has shown that the pumping of the transition (v = 0, J = 5) ~ (v = 2, J = 4) populates the higher level to a value of 2 x 1015 cm 3. At r o o m temperature, the population of the lower 0110 level is 5 x 1015 c m - 3, and the population densities of the final laser states, J = 4 and J = 5 being respectively 4 x 1013 and 5 x 1013 c m - 3. Thus, population inversion is easily attainable in the absence of rotational relaxation, but is impossible (under the conditions of this experiment) when such a relaxation exists. The authors of Ref. 53 note that by pumping an OCS laser with a more optimal geometry, it would be possible to obtain a population inversion in the entire 02°0-01 '0 band. In such a case, lasing would be possible in the presence of rotational relaxation. This will allow (in principle at least) frequency tuning with a spacing of 0.4cm-1.

_f~__/J = 4 .IL m

PUMPI N

9 P22 C02) v-v

V=2 --LA S ING

Q4

~ ;"-R-T V=I

d=5 t

V=0 FIG. 15. Energy-leveldiagram for pumping and lasing transitions in an OCS laser. The laser peak output power obtained in Refs 53 and 57 was 1 kW, with an efficiency of 0.03 %. Such a low efficiency is explained by a short vibrational relaxation time (1.3 x 10 - 6 sec-torr for the v2 mode), which is comparable to the evolution time of the lasing. 3.3. Pumping in a Combination Band Laser action on such a scheme (Fig. 2a) was first observed in C F 4 and NOC1 molecules. (54) To excite the combination (v 2 + v3) band of NOC1, the radiation of a C O z laser was used at the 10P(34) line. Lasing took place within the (v z + v3) ~ v3 band at two lines, at frequencies 588.5 and 698.5 cm - 1. The optimal lasing conditions occur for a pressure of 1.3 torr and a gas temperature of 200 K. The energy conversion efficiency (calculated using the absorbed p u m p energy) reached 10 %.

264

A.Z. GRASIUK,V. S. LETOKHOVand V. V. LoBI
In a later experiment ~311using N OCI, 10 lasing lines were observed in the frequency range 589-608 cm-~. The low operating pressure in the NOC1 laser probably resulted lrom the rapid collisional deactivation of the higher active vibrational level. In the same work, C31Joptical pumping of the CFaI molecule was realized using the 9P(30), 9P(34) and 9P(36) lines of a CO 2 laser. Laser action was observed at 733.6, 736.8 and 738.4 c m - 1. The bands corresponding to excitation and lasing in CF3I are the same as those in NOC1. As the fundamental v~ band is excited there is no lasing, although the v~ ~ v3 and v t ~ v5 bands are allowed by the symmetry selection rules. This may be explained by the excitation of high vibrational levels of the polyatomic molecules in an intense i.r. field (see Section 5). In Ref. 58 there was information about the optical pumping of the 15NH a molecule by the radiation of the P2-1(6) line of H F laser. The most intense oscillations were observed at wavelengths 14.3, 14.8, 15.7 and 16.0#m, and much weaker lasing was seen at 15.2 and 17.8 #m. It has been found that the lines at 14.3 and 14.8 #m correspond to transitions from higher levels which are populated directly by the pumping radiation. The 15.7 and 16.0 #m lines are cascade transitions from levels excited by lasing at 14.8#m. In this work, one observed a considerable effect of the laser transitions between purely rotational levels on the generation intensity in the medium-i.r, region. No operating vibration-rotation levels of SNH 3 were identified. The most probable scheme of this laser is as follows. The radiation of the H F laser excites the va + 2v 2 combination vibration mode; lasing at the first step appears in the (v4 + 2v2) ~ (v 2 + v4) band, and at the second step in the (v2 + v4) ~ v a band. In Ref. 59, laser action was achieved with the C z D 2 molecule pumped with CO 2 laser radiation in the 9.6 #m region. There were 15 laser lines observed in the wavelength range 17.4 20.4 #m, with the pumping and lasing energies 2 J and 2 mJ respectively. The laser lines 499.7 and 562.6 c m - ~, observed with pumping by the R(12) line of a CO2 laser up to pressures of 65 torr, are most intense. The corresponding gain reaches 0.025 c m - ~. The results of a preliminary identification of the transitions excitated suggests that the C z D 2 molecules are pumped in the 0 ~ (v4 + vs) band, as well as in the v5 ~ (2v 5 + v4) and v4 - , (2va + v5) bands. The v4, (v4 + vs) and 2V4 vibrational states, in this case, are the lower laser levels. A more reliable spectroscopic interpretation of the results is complicated, due to considerable degeneration of the excited vibrational states, which may consist of several sub-levels due to the anharmonic splitting. Laser action in ~5 N 2 0 , 1'~N15NO, 1~N ~4NO ' H C O O H and ~3CS2 molecules was achieved in Ref. 55 using an H F laser as a p u m p source. For different isotopic molecules of N20, where pumping and lasing occur in the 0 --* (vl + v3) and (v I + v3) ~ v~ band respectively, lasing is observed in the 4.6~tm region. The laser action on H C O O H and 13CS2 molecules corresponds to 5.7 and 6.9#m respectively. The most probable schemes of these lasers correspond to the following transitions: 0 --* (v3 + vg(2v3)) ~ v3 ( H C O O H ) and 0 - , (v~ + 2v3(2v 2 + 2 v 3 ) ) ~ (vl + v3(2v 2 + v3)) (13C82).

3.4. CF4 L a s e r In 1977, Tiee and Wittig ~54~created a CF 4 laser operating in the 16 #m region using optical pumping by a pulsed CO 2 laser. At once, it received the attention of many investigators. The interest in this laser is explained by the following factors. The 16#m region is of practical importance from the standpoint of laser separation of uranium isotopes t6°) through molecular photodissociation by intense i.r. radiation. 161) The CF 4 laser is a relatively powerful source of laser radiation. Its pulse energy is sufficient to realize different schemes for photodissociation of polyatomic molecules. The C O 2 laser used to excite CF a is one of the most efficient sources ofi.r, radiation. Therefore, the total C F a laser efficiency may be rather high. And lastly, in the CF 4 laser the frequency can be tuned with a small discrete interval. This is necessary for isotopically selective excitation of heavy molecules with a small isotopic frequency shift--e.g, about several tenths of cm-1. The possibility of such tuning is determined by the rich energy-level structure of a spherically symmetric molecule. 162~

Molecular infrared lasers using resonant laser pumping

265

The appficability and potential use of the CF 4 laser for isotope separation of heavy elements were confirmed by experiments on U F 6 photodissociation. (63"64) 3.4.1. Principal characteristics. The CF 4 laser operates on the scheme considered in Section 3.3. The CF 4 molecules are excited by the TEA CO 2 laser radiation in a comparatively weak 0 ~ v2 + v4 band and gain arises in the (v2 + v4) --* v2 band, which is allowed in a harmonic approximation and therefore is strong. In the first work, (54) the CF 4 laser action was obtained only by pumping the R(12) line of a CO 2 laser in the 00°1-02°0 band*. In this experiment, a 350 cm long gas cell filled with CF 4 was cooled down to 155 K, since the lowest v2 laser level is spaced only 435cm-~ from the ground state, and is considerably populated at room temperature. The lasing frequency of the CF 4 laser in such conditions was 615 c m - 1, the output pulse energy was 4 x 10- 3 j, with the absorbed energy in the gas being 0.15 J. This corresponded to an energy conversion efficiency of 3 % (relative to absorbed energy) and quantum yield of about 5 ~o. In Ref. 54 and other works describing the CF 4 laser, different optical schemes were used to separate the radiations of pumping (9.6 #m) and lasing (16 #m). Two of them are shown in Fig. 16a, b. In these schemes, a prism is used as a dispersive element (Fig. 16a), and a plate of Ge (Fig. 16b) set so that it transmits and reflects the 9.6 and 16#m radiations respectively with different polarizations. CF 4 C E L L

CO z INPUT o

TEA

%~,

LOW PRESSURE C02MODULE G A I N ( E L L 5:3

,

. ~

,

•

~

CF4 CELL

"

~,.'-~',.

"

UkUU;

I~

L

Go

)W,.. _ ~ ] Li F b

16M. m

FIG. 16. Optical pumping schemesofCF4 laser (from Refs 67 and 72). The arrows and points show the light polarization plane. Later on, in Ref. 31, the same authors obtained in the CF 4 laser 12 frequencies throughout a range 612-653 c m - ~ by pumping with the 9P(4)-P(12) and 9R(10).-9R(22) CO 2 laser lines. They observed (L-- 280 cm) that the threshold of the CF 4 laser was from 0.15 to 0.25 J/cm 2 depending on pumping frequency. The laser turned out to operate in the pressure range 0.1-10 torr on the P- and R-branches of the (v2 + v4) ~ v2 band. However, for the Q-branch the maxifnum operating pressure was no higher than 2 torr. The authors explain this result by the influence of self-absorption of the CF 4 laser radiation in the v4 band. The value of absorption is a maximum for the lasing Q-branch. It is noted that the optimal working pressure Pop, depends on pumping frequency and energy. The value of Pop, in this case increases as the pumping energy increases, and the energy of CF 4 laser, in turn, grows as the gas cell temperature drops. Considerable fluctuations of CF 4 laser energy from pulse to pulse were observed at a fixed pumping energy. They were caused by the narrowness of the absorption lines and an instability of the CO 2 laser radiation spectrum. With the amplification length 560 cm and a temperature of 155 K, all the radiation lines were superradiating. Very similar results were obtained also in Refs 37 and 66. In Ref. 37 a pumping scheme was used without any element having a low optical damage threshold (see Section 2, Fig. 8), and * In this Section.in connectionwith the CF4 laser, all the lines of the excitingC O 2 laser correspond to the 9.6 #m region.

266

A.Z. GRASlUK, V. S. LETOKHOV and V. V. LOBKO

the CF4-1aser pulse energy was 30 mJ. In the work Ref. 66, lasing of CF 4 was observed also with pumping at the R(6) and R(8) lines of a CO 2 laser, and at a C F 4 pressure of about 30 torr. A temperature-controlled germanium etalon was used as a coupling mirror in the CO 2 laser cavity to attain laser action on CO 2 laser lines and stabilize the CF 4 laser energy. The etalon stabilized the CO 2 laser frequency and allowed better coincidence with the absorption lines of CF 4. The ultimate pulse energy reached 20 mJ. The spectrum of the CF 4 laser turned out to be independent of CF 4 pressure in the ragne 0.1 30 tort. In more detail, and with maximum resolution, the emission spectrum of the C F 4 laser was investigated by Jones et al. (67) They produced over 80 laser lines on the isotopic molecules 12CF4, 13CF4 and 14CF4. The authors 1~'7~also observed the importance of stabilizing and tuning the CO 2 laser frequency to increase the conversion efficiency and the frequency range of the CF 4 laser. For this purpose, the radiation o f a c.w. CO 2 laser (P = 27 torr), 168~its cavity length mechanically stabilized and the frequency tuned, was injected into the cavity of the exciting CO 2 laser. Such a TEA CO 2 laser with a narrow spectral width of the radiation line and with the frequency tuned near the centres of the amplification lines by about _+60 MHz, allowed stable and single-frequency operation of the CF 4 laser. In the work Ref. 69, a laser on the isotopic molecule 12C~ 80 2 was also used to p u m p 12CF,~ and 13CF 4 lasers. This enabled seven lasing lines to be produced in addition for the 12CF 4 molecule. There were eight laser lines observed on the 13CF 4 molecule, two of them under pumping by a 12C~802 laser. The maximum pulse energy o f a CF 4 laser has been obtained so far in Refs 70 and 71, and equals 0.1 J when pumping is performed on the R(12) line o f C O 2 laser. The authors of Ref. 70 used a CO 2 laser with a pulse energy of 10 J, and the total length of the cell filled with C F 4 was 600cm. Under such conditions the quantum yield calculated from absorbed CO 2 laser energy was about 5 %. Such a rather powerful laser system is characterized by the following features: firstly, the absence of absorption saturation in CF 4 because the CF 4 laser conversion efficiency does not decrease as the p u m p energy increases; secondly, a decrease of CF 4 laser energy fluctuation from pulse to pulse; and thirdly, a decrease of laser energy sensitivity to temperature variations as compared with smaller laser setups. In Ref. 70 the conclusion is drawn that it is possible to scale the CF 4 laser pulse energy up to 1 J. tn Ref. 71 the same energy (0.1 J) was obtained using a CF 4 gas cell 200 cm length and a CO 2 laser with pulse energy 8 J as the p u m p source. The spectral width of the TEA CO 2 laser output was narrowed and stabilized by injecting c.w. CO 2 laser radiation36s) This technique increased the conversion efficiency seven times. The quantum conversion efficiency achieved in Ref. 71 was about 103o. In Ref. 72 the quantum conversion efficiency of a CO 2 laser pumping radiation into the CF 4 laser output was about 15 ?o- The energies of pumping and absorption being respectively 0.4 and 0.15 J, the output energy obtained at the frequency of 615 cm 1 was 12 mJ. To achieve such a high conversion efficiency, a TEA CO 2 laser with a narrow and stable radiation line ~73~ was used in Ref. 72 (Fig. 16b). Besides, a telescopic system was used to couple the p u m p beam of the CO 2 laser into the CF 4 laser cavity. The temporal behaviour of the CF 4 laser was also measured with a resolution of about 2 nsec. The build-up time o f C F 4 laser oscillation equals 50 nsec, which made it possible to evaluate its gain coefficient. Its value of 0.03 cm ~ was in good agreement with the results of direct measurements of 7~74~ (see also below). The intensity modulation of the CF 4 laser pulse observed in Ref. 72 is connected with beats of its axial modes, the spectral width of the output being from 40 to 80 M H L Some characteristics of the C F 4 laser which are essential in choosing the optimal conditions for its operation are studied in Refs 49 and 77. The dependence of the time histories and CF 4 laser pulse energy on CF 4 pressure were measured in Ref. 77 at a p u m p fluence of 2 J/cm 2. By analogy to Ref. 49, the optimal pressure of CF 4, P,,p, is about 3.5 torr (Fig. 17), and the lasing pulse duration decreases as P increases. Such results can be explained by a balance between the pumping rate and the rotational relaxation of the upper laser level. In Ref. 47 consideration is also given to more rapid increase of the lower laser levels population as compared with the upper one when the pressure increases (see eqs t3.8) and (3.9)). Figure 18 shows the temperature dependences of the maximum operating pressure ~ ....

Molecular infrared lasers using resonant laser pumping /,~vP

267

curve

>,

.

0

5

.

.

.

_ ,

I0 15 C,os plessure iTorrJ

20

25

FIG. 17. Dependence of the CF 4 laser output energy on pressure at different temperatures (pumping at 9R(12) line of a CO 2 laser) (from Ref. 49).

svp limit

A

2C

15 C~ t-

"6 O. o

IG

E

5

.

;.30

1.2

.

.

.

i

.

150

.

.

.

I

,

,

,

,

A

200 250 . . . . Gas ~emperature ( K )

,

3(}0 '

'

,

I

350

0

0.~

c

06

"5 0.4 C:)

0.2 0 100

0 I 150

I

200

250

300

350

Gas temperature (K)

FIG. 18. Dependence ofmaximum operating pressure (a) and output energy (b) ofa CF4 laser on gas temperature (from Ref. 49).

268

A.Z. GRASIUK, V. S. LETOKHOV and V. V. LOSKO

and the C F 4 laser output energy obtained in Ref. 49 with the p u m p fluence of about 4 J/cm{ As the temperature is reduced from 300 to 100 K, the pulse energy increases by one and a half orders of magnitude, and P ......increases by 4.2 times, equalling 23 torr at 110 K. It is worthy of attention that CF 4 laser operation was observed up to 320 K, as distinct from all other experiments. The maximum output pulse energy of up to 30 mJ has been obtained in Ref. 37, with the p u m p energy and fluence being respectively 2 J and 28 J/cm 2, and the cell being filled with CF 4 at optimal pressure, and 180cm long. The authors believe that a relatively low conversion efficiency of the CF 4 laser (according to their estimations, such an efficiency was about 4 '~'~owith respect to absorbed energy) is caused particularly by the process of rotational relaxation and the action of the competing transition in the (v z + v4)-, v4 band. Such transitions are also allowed in a harmonic approximation, and so must be strong enough. At present there is no available information on the possibility of CF 4 laser operation in the (1'2 -t- Y4) ~ Y4 b a n d .

3.4,2. Gain coefficient -se(]-absorption. One of the most important characteristics of any laser is the gain coefficient and its dependence on different experimental conditions. Appropriate measurements have been carried out in Ref. 74, where some information has been obtained about the value of the gain coefficient ~, its dependence on the pressures of both CF 4 and He and CO buffer gases, and on the value of the CF~ laser radiation selfabsorption and its initial vibrational level. The measurements were taken in an oscillator amplifier scheme. The active medium of the oscillator and the amplifier was excited using the pulses of two different TEA CO 2 lasers. Their frequencies were stabilized by a discharge in the cells filled with a mixture of CO 2 and N 2 - H e at a low pressure of about 10torr. ~73) The dependence of ~ on the pressures of CF~ and He are illustrated in Fig. 19a, b (the dependences for He and CO are the same). In the case of pure CF 4, when the pressure P ~ 1 torr, the p u m p intensity was 1.3 MW/cm 2, and the active medium was 200cm long, super-luminescence was observed on the operating transitions in the 16/~m region. Therefore the dependence ~ (Pc~4) with Pc,4 ~ 1 tort may be disturbed due to a decrease in inversion population taking place in the case. The non-linearity of the ~(Pcvs) function could also be caused by the gain saturation, self-absorption and collisional deactivation of the active sub-levels. It follows from Fig. 19a that the gain of the CF~ laser in the case of pumping by the R(12) line of a CO z laser may be as great as 0.03 cm 1 at the pressure of 5 torr. The addition of the CO and He buffer gases (Fig. 19b) to CF 4 leads to a decrease in ~, which can be explained by deactivation of the upper laser levels. In the work discussed above, Cv4)it has been shown that the gain of the CF 4 laser increases up t o C F 4 pressures of ~ 5 torr. The existence of an optimal pressure from 3 to 4 torr for the CF 4 laser energy "~149~4) can be explained by the fact that the p u m p in these works was carried out by the use of a CO z laser with a broad spectral output of about 0.03 cm ~ width, Indeed, the experiments of Refs 31, 49 and 54 show and this is confirmed by calculations in a simplified model (see eq. (3.9t) that P,,p, increases with an increase in the excitation fluence and hence the rate of pumping transitions W = ol. In the case of a CO 2 laser operating under single-mode conditions and at the centre of the R(12) line, which coincides well with the peak of the CF 4 absorption, only one transition becomes excited with a small offset (about 30 MHz~W)). So, at similar pumping energies, this corresponds to much larger values of a and 1 (and therefore W = ol) than in the case of a broad spectrum of pumping, when only a small fraction of the pumping radiation excites the CF 4 transition. Therefore, for a CO 2 laser with a narrow output spectrum the optimal pressure o f C F 4 may be much higher than 4 tort. The measurements of the self-absorption coefficients for the C F 4 laser lines ~741have shown that their values differ essentially in the P(R)- and Q-branches. For the/:'(615.1 cm 1)_ and Q(630.8 c m - ~)-branches at T -- 130 K they equal 0.12 cm - 1/amagat and 1.58 cm -- ~/amagat. The analysis of the temperature dependence of self-absorption shown that in the P- and Qbranches it is caused by the transitions in the v2 --, (v 2 + v4) hot band (CF~ lasing takes place in the same (v2 + v j ~ vz band). The interpretation of the results about self-absorption in

Molecular infrared lasers using resonant laser pumping I

I

I

269

!

3.5 3.C ~ 25 ~ 2C Z

fs

A

OE

oJ

I

I

[

~

I

2

3

4

--

--

PCF4 (torr)

I

3"5~,~11

i

I

I

I

•

2,5' 20

r CF4

_z 15

"

B

0,5 0 0

I 5

I -'-"-'-T ~ 15 ZO

I 10

25

P~ (tort) FIG. 19. Dependence of the gain o f C F 4 laser on C F 4 gas pressure (a) and pressure of He (b) (from Ref. 74).

the R-branch (643.1 and 645cm-~) has turned out to be ambiguous. The complicated character of the self-absorption can probably be explained by the total influence of absorption from both the ground state in the v4 band and the excited state v2 in the v2 (v z + v4) band. The absorption o f C F 4 laser radiation in the va band is possibly only due to an accidental coincidence with the tetrahedral structure lines, but it derives from the ground state where, when cooled to 130 K, almost all molecules (98 ~o) can be found. In the v2 (v2 + v4) band, the coincidence with the frequencies of the CF4 laser emission can be achieved automatically, but in the v2 state at T = 130 K there is only about 1.5 ~o of the molecules. It is obvious that in the first case, the dependence of absorption on the CF 4 pressure may be complex, e.g., due to collisional broadening of the absorption lines. This is responsible for the results in Ref. 74 for two lines of the R-branch. 3.4.3. Oscillation spectrum--identification of transitions. In the foregoing experiments, the differences between the CF 4 laser frequencies was, on the average, less than several c m - ~, and its value was determined mainly by the discreteness of the pumping TEA CO 2 laser frequencies. Because of the speculations above, the discreteness of the frequencies in the 16/~m region should be about 0.1 c m - 1. The ultimate discreteness of the CF4 laser frequency tuning must be determined by the energy state structure of its operating levels. The first attempts to study this structure were made in Refs 75-77. In Ref. 75 the absorption spectra of 12CF4 in the 0 ~ (v2 + v4) band were obtained near the R(10), R(12) and R(18) lines in the

270

A.Z. GRASIUK, V. S. LETOKHOV and V. V. LOBKO

range of _+0.066 cm-1, using a laser diode spectroscopy technique. The maximum linear absorption coefficient • was measured at the peak near the R(12) line of the CO 2 laser. At 100K its value was 9 × 1 0 - 4 c m ~/torr. Near the R(10) and R(18) lines ( + 4 0 MHz) for the same temperature the value of ~- was no higher than 1 - 2 x 10 4 cm 1/torr. In Refs 76 and 77 the corresponding spectra of 12CF 4 were measured in the interval _+0.125 cm 1 near the P(6) and R(6) R(16) lines using a tunable high-pressure CO 2 laser with the intensity being about 3 × 103 W/cm 2. It follows from Refs 75 77 that for the R(12) line of the CO 2 laser there occurs the best coincidence with the intense peaks of the ~2CF4 absorption, which explains the maximum output energy of the CF~ laser during pumping at this line. The analysis of the 12CF 4 absorption spectra in Refs 77 79 has shown that these spectra have a more complex structure than that usually observed for triply-degenerate vibrations of 12C 1:4.

4 0 ~R +lR ol:> l "2R!R / '~

"ZP,°R

%

650

Op'oR " ~"~{1

/I/ / / {/ji/

(J

°R-'-

"\

E hl m

4p,oQ ire

630

, ~ ~ * I R ~

A

Z hi >
hl (/)
610

•Io,Op -1QOp +ZROP I

I

I

1050

I

I

1070

1090

EXCITATION WAVENUMBER, CM-J

-2P R

l

-1O ,OR

ooo 1~(:F4

/f

. . . ,,r. Lr4

650 (.9

{ D

~j

-4p,

I-*

630

i'-2°o +' R

610

B

P

/

,

1040

', 1060

ExCiTATION

I +ZROpI 1080

wAVENUMBER,

CM-I

FIG. 20. Dependencesof the 12CF4laser frequencies (a) and ~3CF4, t4CF4laser frequencies (b) on pumping frequencies (from Rel~ 31, 66, 67, 80 and Ref. 67 respectively).

Molecular infrared lasers using resonant laser pumping

271

spherically-symmetric molecules. In these works, the formation mechanism for the output spectrum and the tuning characteristics of the CF 4 laser were investigated. The interest in the first problem was initiated for the following reasons. On the one hand, experiments show that the output spectrum remains constant over a wide pressure range (1-30 torrt66))--i.e, the contribution of rotational relaxation becomes inessential. On the other hand, as will be shown below, the data on pumping and lasing frequencies of the CF 4 laser cannot be interpreted in terms of ordinary transitions in the P-, Q- and R-branches, since in this case it should be assumed that the angular moments J of the pumped molecules and the lasing ones differ greatly. However, this assumption is inconsistent with the inessential role of the rotational relaxation. The knowledge of the tuning characteristics is necessary to obtain a desired frequency in the 16ktm region. Figure 20a, b shows the experimental data on the output spectra of all isotopic CF 4 lasers observed by the authors of Refs 31, 66, 67 and 80. From these Figures it follows that the lasing frequencies o f C F 4 lasers are arranged mainly along several straight lines, the slopes of which, K, equal + 1, - 2.1, + 3.8 and 0. It is obvious that ordinary transitions in the P-, Q- and Rbranches may be responsible only for the straight lines for which K equals + 1 and 0. Frequencies with K = + 1 correspond in the first case to lasing in the same branch as the pumping, and in the second case to lasing in the Q-branch. The straight lines with K being + 3.8 and - 2 . 1 , as well as some scattered experimental points, have not been explained. To explain the mechanism of formation of the output spectrum and estimate the real tuning characteristics of the C F 4 laser we shall consider the structure of its energy levels. The state under excitation v2 + v4 consists of two triply-degenerate vibrational sublevels F~ and F 2. This result follows from the direct product of the symmetry types of the v2 and v4 vibrations: E x F 2 = E l + Fa.t62) Transitions from the ground state are allowed by symmetry only to the rotational levels of the F 2 state, which are split into three sub-levels due to the Coriolis interaction, t62) Coriolis sub-levels are characterized by the rotational quantum number R taking the following values: J - l, (J - l) + 1. . . . . J + l, where J, l are the total and vibrational angular moments of the molecule (l = v, (v - 2) .... 1(0)). The transitions satisfying the selection rule AR = 0 are most intensive in linear absorption spectra of the fundamental bands of the triply-degenerate vibrations of spherical molecules. J _= R for the ground and v2 states. The rule AR = 0 is not rigorous, and its violation is often observed for overtonest81~ and combination vibrations. 182~Since the optical pumping of the CF 4 molecule is performed at high ( ~ 106 W / c m 2) intensities of laser radiation, account must be taken of the transitions both with AR = 0 and AR :~ 0. Figure 21 illustrates the energy level scheme of the CF~ laser, with a tetrahedral splitting of the Coriolis sub-levels allowed for. There is no ENERGY LEVELS DI~QRAMOF CF4 LASE# R I

.._oR PUMPtNG 9]~m -II

J=R

FIG. 21. Energy-level scheme for CF 4 laser. To the left of the rotational levels of the v4 and (v 2 + v4) vibrational lines are Coriolis sub-levels, The tetrahedral structure is shown by circles. The wide solid and dashed vertical arrows denote pumping of the {v2 + v4) band and self-absorption in the v4 (nu) band. The inclined solid and dashed arrows in the lasing band correspond to coupled and uncoupled transitions. The curved arrows denote the process of rotational relaxations.

272

A.Z. GRASIUK, V. S. LETOKHOV and V. V. LOBKO

Coriolis splitting in the ground and v2 states, and consequently the transition frequencies in the pumping and lasing bands of the CF 4 laser are described by the same expression v -- vo + 2BJ [(1 - ()AJ + CARl - cU2 + Av* + Aft

(3.11)

where v0 and B stand for the centre of band and rotational constant of molecule; AJ, AR are changes of total and rotational angular momenta; ~ is the Coriolis interaction constant; a is the effective value of molecular rotational constant variation at vibrational excitation; and Av* and Aft describe the shift of centres of the branches and their tensor (tetrahedral) structure. By the use of expression (3.11) it is possible to deduce the following formula for the K parameter Av,,s _ ff 2B[(1 - ()AJ + CAR] - 2~J + Aft*},.,

K--aVex c

({2B [(] z ~

+ ~

2~+~c

(3.12)

where Aft* allows for the contribution of the tetrahedral rotational structure. In the general case there are nine branches in both the pumping and lasing bands of the CF 4 laser. This corresponds to 81 values of the K parameter, 28 of them differing essentially. With allowances made in the radiation only for those transitions which are possible without rotational relaxation, the number of values for K is decreased by a factor of three, and there are only 10 combinations with different values of K. If we neglect the last two members in the numerator and denominator in expression (3.12), K will be determined only by the value of the Coriolis constant (. Analysis shows that almost all experimental results for the 12CF4, I3CF4 and t 4 f F 4 lasers can be explained with the values of I(f being respectively 0.363, 0.348 and 0.333, and no allowance made for rotational relaxation (Fig. 20a, b, solid lines). So, in the CF 4 laser, emission transitions take place only from those sub-levels which are populated directly by the pumping radiation. A small scatter in the experimental points with respect to the estimated direct lines is due to the influence of the members 2~J and Aft* in expression (3.12). In Ref. 77 the positive sign has been chosen for ( on the basis of the assumption that transitions with AR = 0 are most intense in the linear absorption spectrum (v2 + v4 band). The analysis of the high-resolution diode spectra of ~2CF4 in the (v2 + v j band (s3) shows that the most intense transitions are those with AR ¢ 0 (see below), the sign o f ( being opposite in this case. Tables 4-6 present the results of the identification of the pumping and lasing transitions of all isotopic CF 4 lasers. On the basis of estimations made for some parameters of 2CF4 the tuning characteristics of the 12CF 4 laser can be calculated with an account oftetrahedral splitting of the rotational levels of the (v2 + re) state. In the general case, their structure is rather complex (Fig. 22). This is due to the fact that the slope of the tuning characteristics is determined as a whole by the

T

:s 0

150 K

,1.UJ

630

:: '"" " '"-,

+1 Q '//~"/................

+IQ

W

620

0 p ,,," /"

a::

.;

0p

I,,lJ

0p

<

+2 R

._J I /

1040

I

1050 EXCITATION

' I

-.

1060

, ''" i

[070

WAVENUMBER,

I

1080 CM -t

FIG. 22. Simplified theoretical tuning characteristics of 12CF4 laser for the pumping and lasing branch pairs +2R, op: +2R, +IQ; op, op; 0p, - IQ; T = 150K. Dotted parts of the absorption bands correspond to non-overlapped tetrahedral structure.

273

Molecular infrared lasers using resonant laser pumping TABLE 4. Identification of pumping and lasing transitions for 12CF 4 laser*

CO 2 laser

Line

Frequency (cm - ~)

P(14)

1052.2

P(10)

1055.63

P(8) P(6) P(4)

1057.30 1058.95 1060.57

R(6)

1069.01

R(8) R(10)

1070.46 1071.88

R(12) R(14) R(16) R(18)

1073,28 1074.65 1075,99 1077.30

R(20) R(22) R(24)

1078.59 1079.85 1081.09

~2CF4 laser Frequency (cm- ~) 617.0 630.8 620.0 652.2 648.2 645.0 609.6 630.8; 642.4; 631.8 640.9 614.7 618.2 636.7 615.1; 612.2; 640.9 630.8; 641.9 643.1 630.8; 645.5

631.3 643.0

615.7 613.7 631.5

631.4

Pumping transition

Lasing transition

2p(58) - t P(37) - 2p(44) 2P(44) - 2P(38) - 2p(31) + I Q(42) - ~P(15) -2p(24) °R(4) - ~Q(17) - ~Q(28) + 2R(21 ) + 2R(21 ) + 2R(27) ÷2R(33) ÷ 2R(38) + ~R(27) + 2R(43) + 2R(49) + t R(34) ÷ 2R(59)

2p(58) °Q(36) - 2P(44) °R(42) °R(36) °R(29) °P(43) °Q(14) °R(22) - ~Q(5) °R(16) °P(29) °P(23) ÷ 2R(21) °P(29) cIP(35) ÷ 2R(38) °Q{28) ÷ 2R(43) ÷ 2R(49) ~Q(35) ÷ 2R(59)

* In accordance with Ref. 83 pumping and lasing transitions for the case of K = + 1 were chosen with IARJ = 2 (Tables 4-6).

TABLE 5. Identification of pumping and lasing transitions for 13CF4 laser

CO 2

laser

Line

Frequency (cm - ~)

P(18) P(14) P(12)

1048.66 1052.2 1053.92

P(8) P(6) P(4)

1057.30 1058.95 1060.57

R(2) R(4) R(6)

1066.04 1067.54 1069.01

R(8)

1070.46

R(10) R(12)

1071.88 1073.28

R(14)

1074.65

R(18)

1077.30

13CF4 laser Frequency (crn- t ) 513.7 617.1 618.7 629.5 643.3; 640.3 613.4 625.0 633.9 640.4; 646.6; 648.4 616.0 652.9; 612.9 611.1 615.0 606.8 629.5 629.5

644.0

641.3 647.8

654.2

Pumping transition

Lasing transition

- 2p(63) 2P(49) 2P(42) - 1P(27) - 2p(29) - 2p(22) + 1Q(29) - 2p(16) - IQ(11) ~Q(22) ~Q(33) -~Q(33) + 2R(23) IQ(44) + 2R(29) + 2R(34) IQ(65) + 2R(40) + 1R(26) + t R(32)

2p(63) - 2p(49) - 2p(42) °Q(26) °R(27) OR(20) op(30) - 2p(16) °R(10) °R(21) °R(32) °R(32) °P(25) °R(43) °P(31) °P(36) °P(66) °P(42) °Q(27) °Q(33)

274

A. Z. GRASIUK, V. S. LETOKHOV and V. V. LOBKO TABLE 6. Identification of pumping and lasing transitions for 14CF4 laser

14CF4laser

CO 2 laser Line

Frequency (cm- ~)

Frequency (cm - ~)

Pumping transition

Lasing transition

P(20) P(18) P(16)

1046.85 1048.66 1050.44

2P(61 ) ~P(36) - 2p(47) 2p(47)

P(14)

1052.2

P(12) P(10)

1053.92 1055.63

P(8)

1057.30

P(6) R(2) R(4)

1058.95 1066.04 1067.54

611.8 627.3 615.2 649.8 616.8 627.3 643.7 627.5 640.5; 641.2 621.7 627.1 612.2 643.4 616.6 647.0 613.6 627.3; 627.5 633.4:633.5 608.2 636.5 627.2; 627.8 639.2 627.9 624.0 643.5 627.4 644.9

- 2P(61 ) °Q(35) - 2p(47) °R(45) - 2p(40) °Q(26) °R(32) °Q(17) °R(25) 2P(20) °Q(12) °P(29) °R(27)

R(6)

1069.01

R(10)

1071.88

R(14)

1074.65

R(18)

1077.3

R(20) R(22)

1078.59 1079.85

- 2P(40)

~P(27) 2P(34) ~P(18) 2P(27) zP(20) JP(13) + ' Q(28) ~Q(28) +2R( 19 ) - ~Q(39) +2R(24) + ~R(16) +2R(25) ÷2R(36) + 2R(36) + ~R(31) + 2R(46) + ~R(38) + 2R(57) +2R(63) + IR(44) + 2R(67)

°P(21 )

"R(38) °P(26) °Q(17) +2R(25) °P(38) + 2R(36) °Q(32) "2R(46) °Q(39) + 2R(57) +2R(63) °R(45) + 2R(67)

Coriolis splitting constant of the upper laser level. Within the limits ofa tetrahedral structure, this slope is similar for all pairs of branches, and equals + 1. Therefore, with K 4: + 1, the tuning characteristics are "two-dimensional" which leads to an ambiguity of the CF 4 laser spectrum at an overlapped tetrahedral structure in the absorption spectrum. The tetrahedral structure of the v2 state was not taken into account in the calculations, since there was no information on the parameters characterizing its value. Besides, there is every reason to believe that the tetrahedral structure in the v2 state is much smaller than for the (v 2 + v4) state. This transpires from the analysis of emission spectra of all isotopic CF 4 lasers which shows that the experimental points for the absorption and emission with K = + 1 agree well with the straight line. It is just this result that may be expected at a small value of the tetrahedral splitting of the rotational levels of the v 2 state.* The validity of ideas about the role of the tetrahedral splitting is confirmed by experiments. From Ref. 67 it follows that at K ~ + 1 there are CF 4 laser lines with spectral widths of up to 2 cm-1 as the pumping is done by the fixed frequency pulse of a TEA CO2 laser, with its spectral width being about 0.01-0.02 cm-- 1. For pairs of branches with K = + 1, the spectra of the CO 2 and CF# laser output are almost equal. The same results can be obtained directly from the calculated tuning characteristics of the CF 4 laser (Fig. 22). This Figure shows that quasi-continuous (with a frequency spacing corresponding to the tetrahedral structure) tuning of the CF 4 laser frequency is possible when the tetrahedral structure Avtetr overlaps in the laser emission band. This condition may be written as 2 B [(1 - ( ) A J + ( A R ] - 2ctJ -- Avtetr.

* The last data I112) confirm this assumption.

(3.13)

Molecular infrared lasers using resonant laser pumping

275

The possibility of tuning the CF 4 laser frequency with a small discreteness has been studied in experiments. (77"s*) In Ref. 77 t2CF, laser oscillation was obtained at several different rotational tetrahedral components near (+0.125 cm - t ) the R(10) and R(12) lines using a continuously tunable high-pressure CO 2 laser. No high-resolution control has been carried out over the frequency variation in the 16 FLmregion. Yet, according to the mechanism of the output spectrum formation of the CF 4 laser with a non-selective cavity (see above), its frequency is determined only by the pumped energy state of the (v2 + v4) band. Therefore, optical pumping of different tetrahedral components automatically implies a CF 4 laser frequency variation in the 16#m region. The 12CF4 laser frequency tuning in Ref. 84 was obtained by changing the pumping frequency of the TEA C O / l a s e r t66) near the R(12) line and derived from a variation of the CO 2 absorption in the 16/~m region. In this work it has also been concluded that the spectral width of the CF 4 laser radiation line is comparatively narrow and much smaller than that of the pumping radiation. This results from the discrete structure of the CF 4 laser radiation spectrum which consists of some narrow (about 2 × 10- 3 cm 1, the pressure of CF 4 being several torr and the temperature about 120 K) lit ,~s, the spectral interval between them is much larger and has a value of ~ 0.02 c m - ~ (Fig. 24). Because of the different pumping conditions, the CF 4 laser oscillation must develop at a few molecular transitions pumped by the CO z laser. The conclusions about the high intensity of the transitions with AR # 0 in the excitation band of the C F , laser and the mechanism of its operation drawn in Refs 77 79 on the basis of analysis of the CF 4 laser absorption and lasing spectra got a confirmation and a full explanation later in Ref. 83. This work is concerned with high-resolution spectroscopy of the 1 2 C F 4 molecule in the (v2 + v4) excitation band of the l Z C F 4 laser. The absorption spectrum of 1 2 C F 4 was measured by the method of diode laser spectroscopy with a resolution of about 10 - 4 c m - 1 in the following intervals: 1063.3-1064.3 cm-1, 1064.8 1065.4cm-1, 1066.9-1068 c m - ~ and 1068.6-1069.5 c m - ~. This allowed a detailed analysis of its structure. The results obtained consist in the following. The value of the anharmonic splitting A of the vibrational levels with the F 1 and F 2 symmetries of the (v2 + v4) state is rather small i

~

t

,

i

,

i

~

I

i

i

I

i

r

I

t

~

r

WAVENUMBER, CM-I I IO52

L

I

I

I

I

I

1 0 5 8 / 1 0 6

,

I I064.

I B

.9

p

i 106,5.0

,

~

i .i

~ 2

i

,

I

i

.3

4

WAVE

NUMBER,

CM

-)

FIG. 23. Absorption spectrum of 12CF 4 in the (1/2 -~- V4) band with the resolution of 0.04 c m - 1 (upper) and diode spectrum in the range 1064.8-1065.4 c m - ~ (lower) (from Ref. 83). Upper: pressure 100 torr, T = 300 K. the absorption cell length is 10 cm. lower: pressure 5 torr, T = 152 K, the absorption cell length is 170 cm.

276

A.Z. GRASIUK,V. S. LETOKHOVand V. V. LOBKO

(A = 0.5757 c m - ~) and turns out to be smaller than the value of the splitting of the rotational sub-levels I2B(4J I even when J > 4. As a result, the selection rules for transitions allowed in i.r. absorption become more complex: in the absorption spectrum, instead of three branches with AJ = 0, _+ 1 and AR = 0, there are nine branches observed with AJ = 0, +_ 1 and AR = 0, _+ 1, + 2. In this case, transitions with AR --~ 0 turn out to be the most intense. The absorption spectrum of 12CF4 in the range 1050-1080cm -~ produced by a Fourier spectrometer with resolution of 0.04 cm-~, as well as the diode absorption spectrum in the region 1064.8-1065.4 c m - 1, are illustrated in Fig. 23. As shown in Ref. 83, the main part of the absorption lines correspond to transitions with A R ~ 0 and agrees well with the results of calculations. Table 7 gives the basic spectroscopic constants of ~2CF4 in the (v 2 + v j band. Also the molecular transitions near the R(12), R(10) and R(4) lines of the ~2CO 2 laser and the R(14) line of the ~2C~SO2 laser are identified here. Near the R(12) there are absorption lines corresponding to the tetrahedral structure of the +2R(28) and +2R(29) transitions (see Table 4). TABLE7. Spectroscopic constants of the (v2 + vJ band for ~2CF~ molecule4~3j

Constant

Value (cm- ~)

m

(band centre) A B0 B ~* g = -(3/7)1'2Z ** h = -2(3/7)1~2F4, Z2 Z4.` F2 F4,

1066, 4098(4) 0.5757 (17) 0.191688 (20) 0.191442 (20) -0.36047 (16} -2.32 (8) × 10 5 3.7 (6) × 10- 7 9.96 (21) × 10 5 -1.7l (4) × 10 4 3.8 (5) × 10 ~' 1.42 (17} × 10 ~

* The ~4 constant is dimensionless. ** The Z4,, F,,,, Z2, Z~.s, F 2 and F4~constants correspond to the Hecht formalism.~'2~

3.4.4. High pulse repetition rate operation. The possibility of creating a C F 4 laser with a high pulse repetition rate operation ( H P R R O ) , and hence a high average power, has been studied in Refs 85 and 86. The H P R R O C O 2 laser with its pulse energy of up to 5 J and a repetition rate up to 200 H z was used as a p u m p i n g source in these works. ~sv) The average power of such a laser is 1 kW, and so the optical p u m p i n g scheme consisted only of elements with high optical d a m a g e threshold and was similar to that from Refs 39 and 40. The gas cell, filled with CF~, 180 cm long and with the internal diameter of 6.7 cm, and made of stainless steel, was cooled by nitrogen v a p o u r to a temperature of from 90 to 150 K, according to the pulse repetition rate. Figure 24 shows the dependence of the C F 4 laser o u t p u t energy on the pulse rate for pure C F 4, and with helium added, the p u m p i n g energy being of 4 J (0.8 J/cm2). The addition of helium reduces the pulse energy, but the thermal conditions in this case become better. This allows a considerable increase in average power on account of an increasing pulse rate (Fig. 24b). The m a x i m u m power, about 1 8 0 m W , has been obtained for the mixture CF4/He = (2 torr)/(1 torr), with the repetition rate being about 55 Hz. ~sS~ In Ref. 86 an H P R R O C O 2 laser was used, its radiation frequency was stabilized by the injection technique, ~vl~ and the average power of the C F 4 laser was m u c h higher. In pure C F 4, at a pressure of 4torr, the optimal pulse rate was a b o u t 8 0 H z and the rate of longitudinal gas flow of 22 m/sec; the average power of the C F 4 laser was 2.5 W. The peak power of the CF~ laser pulses in this case remained constant up to 50 Hz frequency. Higher

Molecular infrared lasers using resonant laser pumping

277

E 8 ),-

6 W

zh i

4

I"

=)

2

I-

I

o

0

E

160

,~'

120

=,,i

3=

I

I

I

0

o

eO

,.,

40

O.

I

O

=:

U,I

O

I

20

I

40

I

60

REPETITION

I

80

RATE,

I

I00 PPS

b FIG. 24. Dependences of the output pulse energy (a) and average power (b) o f C F 4 laser on repetition rate of pumping pulses with energy of 4 J: 1 - 2 torr of CF4; 2 - 2 torr of CF 4 + 0.5 torr of He: 3 - 2torr o f C F 4 + 1 torr of He.

average powers of the laser can apparently be attained with an increase in the active gas flow rate and addition of helium. 4. E X C I T A T I O N O F T H E F U N D A M E N T A L , C O M B I N A T I O N DIFFERENCE BAND AND LASER ACTION ON A DIFFERENCE BAND

OR

Such a family of optically pumped lasers is based on the energy-level diagrams which are shown in Fig. 2b, d. So to determine the gain and threshold p u m p fluence formulae (3.1) (3.4) should be used. The highest gain can be attained by pumping the fundamental band. The lowest gain is obtained by pumping the difference band. In the second case, the low gain is determined by a weak absorption of the pumping, and a relatively low (thermal) population of the initial vibrational level to be excited. 4.1. C O 2 and

N20

Lasers Pumped by H Br Laser

Such lasers (~4) all have identical energy-level diagrams (Fig. 25). The pumping radiation results in transitions in the fundamental 00°0-00°1 band, and laser action takes place at the vibration-rotation transitions of the 00 ° 1-1 °00 difference band. In Ref. 14a, CO 2 was taken as the active medium and an HBr laser operated as a p u m p source (Fig. 25). Its P2 [(6) line ()o -- 4.23/~m) almost coincides with the RE20) line of the 00°0-00°1 band in C O 2. Laser action was obtained at the 00°1-10°0 difference band with a power conversion efficiency of 41 ~o. In the first experiments (~4a) the cell was 12 cm long and the CO2 pressure was 1 atm. In Ref. 14c the gas pressure was increased up to 33 atm. and the CO 2 laser resonator length decreased down to 1 mm. In Ref. 14 oscillation was obtained for N 2 0 molecules as well. Due to overlapping of the rotational lines in C O 2 at high pressures, it is possible to use some extra (more intensive) lines of the HBr laser for pumping. At high pressures it is impossible to reach a saturation regime of the pumping at 4.3pm, because of continuous and strongly overlapping hot bands which correspond to the v3 ~ 2v 3, 2v 3 -~ 3v 3 transitions, etc. Therefore, it is expected that the penetration depth of the pumping radiation will be 0.1 m m at the absorption band maximum, up to very high fluxes of the pumping. The emission band at high pressures also becomes continuous. When the pressure is higher than 17 atm., maximum generation can be observed at the transitions of the P line (near 10.3 #m).

278

A. Z. GRASIUK,V. S. LETOKHOVand V. V. LOBKO 0111

00ol

10.8 ~m

N20 LASER

m

OUTPUT

Jo2°o 4.4~#m

Her LA.q£R INPUT

01tO

ooOo GROUND STATE FIG. 25. Vibrational energy-level schemes for CO 2 and N20 lasers with their fundamental 001 band being pumped by an HBr laser (from Ref. 14b).

The N 2 0 laser, (1~b)pumped by a HBr laser at wavelength 4.5 #m, operates in a similar way. But this line contains only a small fraction of the HBr laser energy. So a mixture of C O 2 - N 2 0 is more optimal for high-pressure (to 42 atm. "4m) NeD lasers. In this case, the pumping radiation excites the CO 2 molecules and then energy is transferred to the N 2 0 molecules V V exchange of the excitation (see Section 6). The fact that it is possible to use the fundamental band for optical pumping at high pressures of the operating gas is an obvious advantage of the CO 2 and NeD lasers. However, their frequency range does not differ from that of their corresponding electric-discharge lasers based on the same active media. Other lasers of this type have proved more promising in covering new spectral ranges. 4.2. CO: Laser Pumped by COa Laser In such a laser the pumping radiation results in transitions in the 02°0 00°1 difference band. Laser action also occurs in the 00°1 10°0 difference band (Fig. 26). Such a laser was described for the first time in Ref. 88. Its idea is based on specific features of the structure of two difference vibrational bands with a common upper level (Fig. 2). The energies of the vibrational levels 10°0 and 02°0 are close. Therefore, the time during which a thermal equilibrium is reached between them will be of the order of the rotational relaxation time Tr,,, which in pure CO a equals 1.5 × 10-lo sec_atm.(Sg) The processes of collisional vibrational

oo°J

[I0°0'0#0],

oOoo #o],,

FAST / "~, RELAXATION Ixi%

L

r,= fo-9S~C'ATM"X

0 l'O

00°0

GROUND

FIG. 26. Vibrational energy-level diagram for C O

2

'

STATE

laser at 10.6/tm pumped by a 9.6/~m CO~ laser.

Molecular infrared lasers using resonant laser pumping

279

exchange between the 00°0, 0110 and 10°0 levels also have a rather short relaxation time 21 = 1 0 - 9 sec-atm.tg°) The vibrational relaxation of the 00°1 level is much slower--z 2 = 3.8 × 10-6 sec_atm.~91~ Thus, at pulsed resonant saturating optical pumping in the 02°0-00°1 band and the pulse duration satisfying the requirement ~v >> zl, the populations of the 02°0 and 00°1 levels become equal, while rapid relaxation processes maintain thermal equilibrium populations between the 02°0 and 10°0 levels. Such a thermal equilibrium demands that N 1 0 , o -- N 0 2 o e x p ( - A E / k T ) , where AE is the energy difference between the 02°0 and 10°0 levels, and N 1oo and N02o o a r e their populations. Thus, for saturation in the 02°0-00°1 band, there is a population inversion between the 00°1 and 10°0 levels. Therefore it is possible to obtain a gain g in the 00°1-10°0 band approaching g = b: [ e x p ( A E / k T ) - 1 ], where ~" is the absorption coefficient of the 10°0-0°01 band without optical pumping. The p u m p source in Ref. 88 was a TEA CO 2 laser with pulse energy up to 10J. The laser was tuned to the maximum output in the P-branch of the 00°1-02°0 band by a diffraction grating. The pumping radiation was reflected from a mirror with focal length 60 cm, and was then directed into the cell with CO2. The p u m p beam caustic waist was 2.5 cm 2, and the maximum of the radiation fluence was 2.5 J/cm 2. The glass cell with C O 2 w a s placed in a high-Q resonator, and the pumping radiation, with wavelength of about 9.6 #m, was oriented at a certain angle to the resonator axis. The resonator was formed by two copper gold-coated mirrors: a flat mirror, 10mm in diameter, and a concave one with its radius of curvature being 2 m. The threshold p u m p fluence was 0.5 J / c m 2. The optically pumped oscillator had an output of up to 110 mJ and energy efficiency of 14 ~o (the efficiency was determined as the oscillator output energy divided by the p u m p energy which excited the volume of the active medium confined by the resonator caustic). In such a case, the resonator of the oscillator had the following construction: one mirror was totally reflecting, and the other one has a hole of 3 m m in diameter and a radius of curvature of 2 m. The m a x i m u m of laser pulse energy E~ can be evaluated as follows, as the transition 02°0-00°1 is saturated by pumping. Since the saturation regime leads to Noo 1 = No2~o, we have E l -- hvtNo2~ o [1 - exp ( - A E / k T ) ] Vfl

(4.1)

where AE = 103 cm 1, V is the volume of resonator caustic, hv I is the energy of the laser radiation quantum, and/3 is the coefficient related to losses in the resonator and output mirror transmission. When the resonator geometry is similar to that used in Ref. 88 with V = 50 cm 3, No2o o = N Oe x p ( - E 1 / k T ) (where N O is the density of C O 2 molecules, E I = 1285 cm-1), then at P = 100 torr, T = 440 K, we obtain E z = 0.021 J. Nevertheless, at such parameters of the CO 2 gas and resonator, one found 0.11 J for the experimental value of the output energy of the pulse emitted from the resonator through a mirror, with the transmission coefficient being 10 ~/o. From the energy losses in the resonator we conclude that each molecule passes the 02°0-00°1-10°0-02°0 cycle from 40 to 50 times. 4.3. Other Lasers The operation of the OCS laser ~92~ is similar to the scheme used in Ref. 14. The second harmonic of the 9P(30) line of the CO 2 laser is used to p u m p the R(24) line in the 00°0-00°1 band of OCS. Laser action takes place in the 00°1-10°0 band in the region of 8.3 #m and can be observed at pressures of up to 55 torr. The m a x i m u m conversion coefficient of the pumping energy may be as great as 4 ~o, which at the output energy at 8.3 #m equals 0.25 mJ. The OCS laser can also be pumped by the second harmonic frequencies of the 9P(26)-9P(28) and 9P(32)-9P(34) lines of the C O 2 laser. In Ref. 93, optical pumping of different isotopic CO 2 molecules was carried out by H F laser radiation. Oscillation was observed on t 2C~ 602, 12CI 8O2, 12C~ 6O~ 80 and 13C~ 6018 0 in the 4.3 and 10.6pm regions, and on ~2C1SO2 and 12Cl60180 at 17#m as well. Figure 27 shows a simplified energy-level diagram of 12C~aO 2. The P(6) line of the H F laser excites the R(8) transition of CO 2 in the 00°0 ~ [10°1, 02°1 ]n band. The oscillation is

280

A.Z. GRASIUK, V. S. LETOKHOV and V. V. LoBKo 14

6

[10Oo]ll

~

10 6

[01~0]~

::~

io

7.~ 6 OOOO FIG. 27. Energy-leveldiagram and lasing transitions for ~2C~O2 molecule pumped by HF laser (from Ref. 93). observed directly on the transitions from the excited rotational sub-level at the R(8) (17.46 pm)line in the [10°1, 02°11, ~ 0111 band and R(8)(4.346 # m ) a n d P(10) (4.370 p m ) o f the [10°l,02°l]n ~ [10°0,02°0]n hot band. At not very low pressures of CO2, additional laser transitions appear from other rotational sub-levels in the region of 4.3 #m. The 4.3 #m laser band observed is intense, and so the lower laser vibrational level [10°0,02:'0]. is pupulated quickly. Such an effect leads to inversion between [10°0, 02°0~ll and the 01 '0 levels. The corresponding laser lines lie in the 17 #m region. There are both the cascade transitions and those from rotational levels which are populated in the process of rotational relaxation. Similar results are observed for the 12Cl60180 molecule. The lasing in the 10.6#m region observed for all isotopic molecules corresponds to standard transitions in the 00°1 --, [10°0, 02°0]j band. The upper laser level 00°1 is populated due to fast collisional vibrational-vibrational energy transfer CO2(02°1) + CO2(00°0) ~ CO2(00°1) + CO2(02°0).

(4.2)

Ref. 95 reports combined excitation of the CO 2 laser operating in the region of 4.3 #m. In contrast to Ref. 14a, the v3 vibration of CO 2 as well as the 00°2 state are excited in a gas discharge. Then the molecules from this state are transferred to the [10'q, 02-'1 ], level by radiation of an auxiliary TEA CO 2 laser operating on the I sequence band. ~96~At a comparatively low pressure of the mixture C O 2 - N 2 He ( ~ 30 torr) and a low content of CO 2 ( ~ 1 '~o), the collisional de-excitation rate of the state [10°1, 02"~1]~ is smaller than the radiative transition rate from the 00°2 state. As a result, a gain and laser action take place in the

Molecular infrared lasers using resonant laser pumping

281

E10°1, 02°1 JEll--E10°0, 02°0]L~ bands. This scheme allows, in principle, laser action both in the 14 and 16 #m regions, due to transitions in the [10°1, 02°1 ]LH--01'I bands respectively. For a pump intensity of the CO 2 laser of 50 kW/cm 2, lasing with an intensity of 1 kW/cm 2 has been obtained in the 4.3 #m region. There is a paper tl°7~ which is concerned with optical pumping by CO laser radiation. Despite its high pulse energy, the CO laser is unsuitable for converson of its frequency because of the long pulse duration (usually several tens of #sec) and the cascade mechanism of lasing. Such factors complicate an effective excitation of the single vibrational-rotational transitions in molecules. Nevertheless, in Ref. 107, lasing was attained o n C O F 2 (10#m) and O~3CS (8.6 ~om) by exciting the 0200 and 001 vibrational states. Oscillation was observed on the 0200-0100 and 00°1-10°0 difference bands respectively. 5. M U L T I P H O T O N

PUMPING

5.1. Two-Photon Excitation of Molecules Multiphoton resonant* electron-vibrational processes in molecules, molecular and ionic crystals are under discussion in the reviews, Refs 97 and 98. The development of powerful i.r. lasers has opened up a basic possibility of exciting multiphoton transitions between vibration-rotation molecular levels. Multiphoton transitions are of great interest from the standpoint of selective excitation and spectroscopic investigation of vibrational molecular levels for which single-photon transitions are forbidden. At present there are several experiments on two-photon spectroscopy 1'~9I°°1 and optical pumping C1°~1°2~ of vibration rotation molecular transitions. The general theory of multiphoton processes was developed long ago. {~°3} Specific calculations for two-photon absorption transitions between vibration rotation levels of diatomic molecules are presented in Ref. 104. The two-photon absorption coefficient /£[2] c a n be expressed as t~°5~

/£~21 __ WIz2~NqjZF

(5.1)

where N is the density of molecules, qs is the fraction of molecules at the rotational level J, F is the i.r. radiation intensity, and the probability of two-photon transition wJ 21 at a harmonic perturbation by a single-frequency, 09, radiation may be written as: 1~°3) W22]

(2rc)3~2Fztm2112/c2h2A09.

(5.2)

In eq. (5.2), A~o is the spectral width of the two-photon transition, and the general expression for the composite matrix element ( M 21 ) can be taken from Ref. 105. The estimate o f M 21 is a calculation of infinite sums over the intermediate states. Reference 104 considers the case of molecules with a large constant dipole moment, when one may neglect the contribution of electronic and vibration-rotation transitions forbidden in the dipole approximation. Since there are rigorous selection rules for rotational and vibration-rotation transitions, M 21 is the sum of only a few terms. Figure 28 shows the schemes of two-photon absorption between initial (i) and final ( f ) states for the cases when there is no intermediate (int) level (a), and when there is such a level (b) which is coupled to the ground state by a single-photon transition. Similar schemes illustrating intermediate and final transitions can take place in other branches as well. The most interesting particular case of two-photon absorption is resonant excitation of the V = 2 level, since in this case the laser frequency ~o ~ 09ol and the W [2] probability resonantly increases proportional to (6~0)- 2, where 609 is the offset relative to the intermediate state. For typical molecular parameters, the increase of W E21equals q > 10s(ri09)- 2, where 609 is given in cm- ~. The expression for W t2~ in the case of excitation of the O-branch in the presence of an intermediate level has the form W[21 02

. . _

Tt.(/~t01 )4 F 2 [1 - (4J - 1) (4J 2 - 1)- 1]/30h4Ao3(6cg)2

* Nonresonant multiphoton processes are not considered.

(5.3)

282

A.Z. GRASIUK, V. S. LETOKHOV and V. V. LOBKO

V

't

IX I

r

I

J

i

f

Ilr

1

1

J-I

~ I

I

I I

I

int

i

i

I 4

j

8~

]

1,,

;

J+l

i I

11

i i

IL

'

j

J-I o

o

b

l~'lG. 28. Energy-level diagram for the two-photon absorption transitions between initial (i) and final 1) levels via intermediate levels of r = 0 and 1 in the absence (a) and presence (b) of a quasi-resonant intermediate (int) sub-level for the R- and P-branches respectively.

where Yo~ and Am are the dipole moment of single-photon transition and the spectral width of the two-photon transition 0 --* 2 respectively. The value of~c12l for the HC1 molecule in the O-branch estimated from eq. (6.3), with J = 5 , F = 107W/cm 2, 6 a ) = 1 0 c m -1 and P = i torr, is equal to 8 x 10- 5 c m - 1. The presence of an intermediate level leads to a considerable increase (5-6 orders of magnitude) of the coefficient of two-photon absorption. It is this factor that explains why to date lasing at two-photon optical pumping has been obtained only in schemes with a close intermediate level, and observed in 14NH3 ~1°1) and 12CH3F/102) It should be noted that one of the peculiarities of schemes with multiphoton optical pumping is that it is possible to convert the exciting radiation frequency, not only to the region of lower, but also higher frequencies--i.e. 0) 1 ~ 2cov. The second peculiarity lies in the necessity of a rather careful and accurate choosing of the molecules for multiphoton optical pumping according to the scheme in Fig. 29b. This is caused by the fact that most polyatomic (with 4-5 or more atoms) molecules at intensities of about 106 W/cm 2 can be excited to high vibrational states near the dissociation limit/6~ In some cases, molecules are not only irreversibly destroyed, but also their optical pumping proves to be inefficient. This is probably due to the facts that: (1) the molecules are excited not to one but to many vibrational levels up to the dissociation limit; (2) excitation takes place simultaneously from many rotational levels; I106) and (3) the molecules are in intermediate vibrational states for a short time ( ~ 0.1-1 nsec), u 071 These factors complicate accumulation of molecules at a certain energy level and reduce the number of transitions where lasing could arise. Actually, there is a similar problem in optical pumping of molecules using singlephoton excitation mainly in fundamental bands. It is possible to eliminate the excitation of many vibrational-rotational states by: (1) choosing molecules with a smaller number of atoms (usually no more than four) and high values of anharmonicity and the rotational constant: and (2) exciting weak overtones and

J /(5.4)

294MHz

2

I

1 2+

P18, 10.4 ~m

16,~m

~ ~ 35cm

15.4) ~- 5250 MHz

1-

1+

l P34, 10.4/am I

0"8cm- 1

(5,4)

~

(J,K)

t

00+

FIG. 29. Energy-level diagram for NH 3 laser using two-photon i.r. pumping (from Ref. 101 ).

Molecular infrared lasers using resonant laser pumping

283

c o m b i n a t i o n vibrations. These requirements can be satisfied by efficient lasers using optical p u m p i n g on H F , CO2, CF4, N O C I , N H 3 and other molecules. And, on the contrary, lasing on the polyatomic molecules C z H 4 and SF6t26"108) is not efficient. 5.2. Two-Photon Pumped Lasers In the cases when the p u m p i n g p h o t o n energy is not enough for direct excitation of the second vibrational level, such excitation can be performed in a t w o - p h o t o n (stepwise) way. Typical examples for this are the N H 3,~1°1" l o9.1 lO) C H 3F, ~102) and S F 6 ~1° 8) lasers excited by a C O 2 laser. The SF 6 laser described in Ref. 108 was historically the first. Its design was similar to that of the O CS laser. ~53) But, in contrast to Ref. 53, two lines of the C O 2 laser--10P(14) and 10P(12)--were used to p u m p the v 3 m o d e of the S F 6 molecule. Lasing occurred probably in the 2v 3 ~ (v 2 + 2 v j band, and the S F 6 laser operated at the fixed frequency v 1 -- 628.74 _+ 0.02 cm 1. The optimal pressure of S F 6 w a s 55mtorr. An increase in pressure caused the rotational relaxation time to be reduced and the lasing to disappear. The authors of Ref. 108 believed that with an increased p u m p i n g intensity, the S F 6 laser would be able to operate at higher pressures and in the presence of rotational relaxation which would provide frequency tuning. Further experiments, however, have probably not confirmed these suggestions. The N H 3 laser using t w o - p h o t o n p u m p i n g of the second vibrational level V = 2 of the v2 m o d e seems to be a more promising device of this kind.U o 1.109. x1o) To excite the V = 2 level, two synchronized C O 2 lasers at the 10P(34) and 10P(18) lines were used. It may be seen from Fig. 29 that the frequencies of these lasers do not provide exact resonance. The saturation of a t w o - p h o t o n transition at an N H 3 pressure of P = 1 torr corresponds to the p r o d u c t of p u m p i n g intensities Iv1 × l o 2 -- 1013 ( W / c m 2 ) 2 . In Refs 101 and 109, the beams of b o t h C O 2 lasers operating in the TEM0o mode were made spatially coincident by a Ge beam splitter. The p u m p i n g radiation reached the m a x i m u m p r o d u c t of intensities 2 × 1013 (W/cm2)2 at the waist of the caustic. The laser was coupled out t h r o u g h a hole 1 m m in diameter in the resonator mirror. The observed laser wavelengths and frequencies are given in Table 8. In Ref. 109, the authors modified the scheme of Ref. 102. A ZnSe plate was used as an output mirror, the resonator was 125 cm long, the active medium volume under p u m p i n g was 125 cm 3, and the energies of the p u m p i n g beams became 0.1 and 0.5 J respectively. As a result, the output energy at Z = 15.88ym (v = 629.7cm 1) and £ = 15.95ym (v -- 626.96cm -1) reached 1 m J, and the conversion efficiency calculated from the absorbed energy was 10 ~o. In Ref. 110, where a similar technique was used to p u m p N H 3 molecules by two C O 2 lasers, lasing was observed at some more lines (Table 8b). Using a scheme similar to that described in Ref. 101, the authors u 02) obtained lasing on the C H 3 F molecule. The C O 2 lasers in this case operated on the 9P(14) (vvl = 1052.19 cm - 1) and 9P(30) (Vp2 = 1037.4 c m - 1) lines, and excited the (0, 1, 1 ) ~ (2,3,2) vibrational-rotational transition of the v 3 mode of CH3F. Lasing was obtained on one ( 2 , 3 , 1 ) ~ (1,4,1) transition, which corresponds to the TABLE8. Wavelengths and frequencies of the NH a laser using two-photon pumping of the second vibrational level of the v2 mode: (a) Refs 101, 109: (b) Ref. ll0 (a} Transition

Wavelength (gm) Frequency (cm-~ ) (b} Transition

Wavelength (#m) Frequency (cm- l )

JPQE

6/4

- E

(2-, 5, 4) (2 ,5,4) (2-, 5, 4) (2 +,5,4) (2 +, 5, 4) (2 +, 5, 4) (2 +, 4, 4) (2 +, 4, 4) (2 +,5,4) (1 +,6,4) (2 +,4,4) (1-,6,4) (1-,4,4) (1-,5,4) (1-,5,4) (1-,4,4) 35.50 281.69

12.11 26.10 19.55 825.76 383.14 511.51

13.72 15.88 18.93 15.95 728.86 629.72 528.26 626.96

(1 +, 4, 3) (2 +, 6, 3) (2 +, 5, 3) (2 +, 5, 3) (2 +, 4, 3) (0 ,5,3) (1-,5,3) (1 ,4,3) (1-,5,3) (1 ,5,3) 12.00 833.33

13.23 13.66 15.78 755.86 732.06 633.71

15.86 630.52

284

A . Z . GRASIUK, V. S. LETOKHOV and V. V. LOBKO

wavelength 2 = 9.75 #m (v = 1025.65 c m - 1). The authors of Ref. 102 note the possibility of gain at the intermode transitions in the 2v 3 ~ v5 (2 = 16#m) and 2% ~ % ()~ = 11/~m) difference bands.

6. POPULATION INVERSION IN MOLECULAR MIXTURES DUE TO COLLISIONAL V VENERGY TRANSFER The idea of a laser using excitation energy transfer was first proposed and discussed in Ref. 111 for the example of a C O 2 laser. It was proposed to excite the operating mixture of C O 2 - N 2 - H e with the addition of vapour of an alkali metal by the resonant radiation of a flash-lamp filled with the vapour of a similar metal.

6.1. Population Inversion Conditions In the general case, the principle of operation of such lasers consists in the following. Suppose that the conditions of resonant optical pumping of molecules or atoms of a certain kind a mixed with molecules of another kind b are fulfilled (Fig. 30). If the energy of vibrational or electronic-vibrational (electronic) motion of molecules (atoms) of the kind a is close to the vibrational energy of molecules of the kind b, this may result in a fast selective collisional excitation of the vibrational states of the molecules which do not interact directly with the radiation. The rate of such excitation for the b molecules may exceed the rate of their relaxation, and this gives rise to gain and lasing at the transitions of the b molecules. The closeness of the energy values of the working molecules (or an atom and a molecule) may be either accidental, or these may be molecules of different isotopic composition whose isotope shift value is usually small. V-V

ooo, >

TRANSFER

\ ~

°1

,o.o

10~0

0~20

00o0 a

•

00o0

in

b

FIG. 30. Simplified energy-level scheme for V V transfer laser operation in case of CO 2 isotopic molecules mixture.

Molecules in the ground electronic state are often the object of resonant excitation in this scheme of optical pumping, t~*a) but there are experiments where the vibrational energy of the excited electronic state ~113j or the energy of the purely electronic motion in the atoms Ij 14t are used. The creation of a tunable gas i.r. laser has stimulated the theoretical discussion of gain in binary and triple mixtures of isotopic CO 2 molecules when one of them is under resonant pumping. The use of a mixture of isotopic molecules as the working gas allows a considerable reduction of the pressure necessary for continuous tuning. It is possible, due to the isotope frequency shift of the molecular vibrations, that the adjacent vibrational rotational lines mutually overlap at rather low pressures, about 1 atm. Let us consider the resonant optical pumping of the 02°0 00~1 band of the 12C1602 molecules in a mixture with other CO 2 isotopic species which do not interact directly with the

Molecular infrared lasers using resonant laser pumping

285

pumping (Fig. 30). The kinetic equations considered below are true for any mixtures of a and b active molecules. If the pumping pulse duration r e satisfies the condition (6.1)

Zro, << r e << z v _ v,

the balance equations for the CO 2 molecules may be written as (115) ON~)o l/C)t

b ~ = (No2~,o -- N o~o , l ) W q + Noo,,1Noo~oKba -- N o~o o l N obo o o K a b

~ N b o ~ l / 3 t = N oao q N o obo K , b

-- N obo ~ I N o. o o K b ,

(6.2)

(6.3)

with the initial conditions b 1 (t = 0) = Noo~ a 1 (t = 0) = 0. Noo.~

(6.4)

I n these equations, N~ and N~ are the population densities of the ith vibrational level for the 1:2C160 2 molecules (a) and the CO x molecules of another isotopic species (b). K,b and Kbaa r e the rate constants of resonant energy transfer between the a and b molecules. The first term in the right hand part ofeq. (2.7) describes the resonant interaction of the 12C~602 molecules (kind a) with the pumping; the second and third terms describe the mutual resonant transfer of energy between the a and b molecules in the 00°1 state. Equations (6.2)-(6.4) must be solved together with equations like (1.5), (1.7) and (1.8). The system of equations considered allows an analytical solution only under the assumption that the radiative excitation rate of the a molecules is much smaller than the rate of quasi-resonant energy transfer between a and b molecules. Within the assumptions made, when the pressure of isotopic CO z molecules equals 1 atm. and the temperature is 400 K, a gain of ~ 2 x 10- 3 c m - 1 may be achieved both under pulsed and c.w. operation. Under pulsed operation, the pumping fluence required is 10 J/cm 2, and under c.w. operation this gain may be obtained with a pumping flux density of about 106 W/cm 2, which can be realized in optical waveguides. Such intensity values are quite attainable by the use of conventional up-to-date lasers. The use of a mixture of isotopic CO 2 molecules as an active medium allows continuous frequency tuning in the range 8.9 12.5~m at a pressure of about latin. This range is completely covered by collision-broadened adjacent vibration-rotation lines at atmospheric pressure in a mixture of three isotopic CO 2 molecules. Figures 31 and 32 show the calculated spectra in the region of 8.9-12.5 #m for four isotopic molecules, and the gain profiles in the region of overlapping of vibrational-rotational bands for different mixtures of isotopic molecules. It should be noted that eqs (6.2) and (6.3) permit that the average number of quanta stored in the v3 vibration of CO 2 is much smaller than unity. In this pumping scheme, this is implied by the low population of the initial 02°0 state. In exciting CO 2 molecules in the 00°0-00°1 band by a strong absorption of pumping radiation, it is necessary to take into account a much greater number of vibrational states, e.g., within a temperature model, t~6) In Ref. 117 E~ CM "-I

i 12C 1602 13CI602 14Cl602

12Cil!02

:soo

tO00 ~

1 3

800

8#0

880

2 Z

920

?

960

3 ~ 3

1000

4 Z

1

I0,0

WAVENUMBER

~080

C M- I

FIG. 31. Spectra of CO 2 laser on different isotopic molecules in the region 800-1120cm-t 112.5-8.9 #m).

286

A. Z, GRASIUK, V. S. LETOKHOV and V. V. LOBKO t

L :fLLL

IE

a

0

b

X Z

t,J

(.9 9Jr

esl

9JJ

WAVENUMBER, C M - I c

g~

e~z

gJj

WAVENUMBER, CM-I el

FIG. 32. Vibrational-rotational gain bands for isotopic mixtures: (a) pure t zC~ 602; (b) mixture ~2ca6cz-lzC~SO2= 1:1.45: (c) mixture 12C1°O2 ~3C1602=4:1.5: (d) mixture t2C1°O2 13C1602-~2C~802 = 2:1:1. (P=l.latm., T=400K, L=100cm, E p = l O J / c m 2, r e = 2 × 10-7sec.)

appropriate calculations were carried out for the mixture C 0 2 - N 2 0 , where the CO 2 molecules were excited in the 4.3/~m region. In Ref. 118, consideration was given to C O z and C O 2 - N 2 0 optically pumped molecular lasers operating on the lines of the 0 0 n --, [10°(n - 1), 02°(n - 1) ]~Ji (n = 1, 2, 3) sequen'ce bands. Simultaneous lasing at the lines of the sequence bands in a CO 2 laser with optical pumping of the v3 vibration was theoretically studied in Ref. 119. 6.2. Laser Schemes The laser with its inversion due to collisional transfer of vibrational excitation was first reported in Ref. 14d. In this work, generation was produced on N 2 0 molecules mainly in the R-branch of the 00°1 ~ [10°0, 02°0][ band in the pressure range of up to 42 atm. The 00'~1 vibrational state of the N 2 0 molecules was populated due to V-V transfer from the CO 2 molecules whose similar state was excited by a TEA HBr laser. The rate of quasi-resonant energy exchange between the CO 2 and NzO molecules is more than two orders of magnitude higher that the relaxation rate of their 00°1 states. This leads to a relatively large gain of the N 2 0 laser, which enabled the authors of Refs 120 and 121 to obtain continuous frequency tuning in the range of about 5 c m - 1 with the resolution o f 0 . 0 1 4 c m - 1 with the use of a very short resonator (1.8 mm). The frequency was tuned by changing the pressure in the laser which caused the optical length of the resonator and the spectrum of its modes to change. The optical pumping scheme of CO a molecules in Refs. 94 and 122 was more complex. It combined collisional and radiative excitation. The pulsed HBr laser excites the mixture of HBr and CO z molecules. As a result of collisions, the vibrational excitation from the HBr molecules is transferred to the 00°1 vibration of CO 2. Then the C O 2 molecules are quickly transferred to the [10°0, 02°011.[[ states by CO 2 laser radiation at a rate exceeding the rate of its collisional deactivation. Gain and lasing arise in the [10°0, 02°0]L,-0111 bands (at 14 and 16 #m respectively). The laser pulse energy of about 1 mJ was achieved in the 16~tm region. 194j There is a whole group of I/ V transfer lasers (operating on different molecules) using resonant optical pumping of the C O molecule by the second-harmonic of a CO 2 laser (92) and subsequent V-Venergy transfer to lasing molecules. The CO molecule is ideal for the storage of vibrational energy and its subsequent transfer to some other molecules. This is caused by a very slow vibrational-translational relaxation rate, of 1.9 × 10-3sec-~/torr. The availability o f just one vibration ensures high selectivity of the vibrational excitation transfer. In Ref. 92, the P(14) transition of CO was excited. It coincided to a good accuracy (0.003 c m - i) with the double frequency of the 9P(24) line of the CO z laser. The frequency was doubled in a proustite (CdGeAs2) crystal. The second harmonic conversion efficiency was up to 8 %. Figure 33 shows a simplified energy-level diagram for CO and for molecules excited in the process of vibrational energy transfer. For all active molecules, gain and lasing arise in the

Molecular infrared lasers using resonant laser pumping

287

difference band in the range 8-11.5 #m. The maximum conversion efficiency takes place for the C O - C O 2 mixture, and reaches 7.3 ~o. It should be noted that the upper active level of the CzH 2 laser corresponds to the 0100°0 ° vibrational mode being inactive in i.r. absorption. This feature points to a relative universality of the optical pumping method under consideration. The authors of Ref. 92 formulate general requirements for the structure of vibrational and rotational molecular levels, which enable more efficient optical pumping and frequency conversion.

?

v•1

200C

'S Doubled CO2

n~ W Z u,J

Pump 10OO

2x

-

O0

0

1 001

0001

""

8.3),m

Loser !0.6_/~m

I

i000

Loser

o? O0

,o..(. II~0

1

¢ Loser 8F m

P (241 9.6-~m Bond

I0°0

CO

OCS

Loser 1

CO2

NzO

101

C2H2

10°0

CS2

1000

1

tose¢ 7 9 5/~m

_.~0100 OOOI

S,H 4

FIG. 33. Simplifiedenergy-leveldiagram for molecules pumped by nearly resonant V-V energy transfer from CO moleculesexcited by frequency-doubledCO2 laser (from Ref. 123). Later in Ref. 123, the same authors obtained laser action on six lines of Sill 4 in the region 7.9-7.99 #m, using a similar C O - S i l l 4 vibrational energy transfer technique. Lasing was observed at pressures of up to 35 torr, the energy conversion efficiency being 0.6 ~o. This is the first case when laser action has been produced on a non-linear molecule by V - V transfer. 7. INCOHERENT OPTICAL PUMPING Optical pumping of molecules and gain on molecular transitions was first carried out using incoherent sources. C7) Some points of optical pumping with incoherent sources were discussed in Refs 124 and 125. In Ref. 124 it was proposed to use the radiation of the molecules themselves at a high temperature or in a gas discharge as a source of their pumping. The radiating ability of vibration-rotation molecular bands at 1000 K amounts to 10 ~o of the total black-body radiation. At such incoherent pumping, the selectivity of the populations of certain vibrational states (and respectively a gain) can be achieved owing to the fact that the lower laser levels often are inactive in i.r. absorption (e.g. the 10°0 level of CO2, NzO and many other molecules). At present there are experimental works known concerning optical pumping with incoherent radiation sources, t7'126) In Ref. 7 the •3 vibration of CO 2 was pumped by the radiation of hot combustion products of CO burned in oxygen. In Ref. 126 a molybdenum foil heated by a pulsed discharge was used as a pump source. In Refs 7 and 126, c.w. radiation of about 1 mW and pulse energy of 40 mJ respectively were obtained, the pulse duration was 20 msec. Although the results of optical pumping of molecular gases by black body radiation at a high temperature are rather optimistic, (~25) its experimental realization and the

288

A. Z, GRASIUK, V. S. LETOKHOV and V. V. LOBKO

achieving of the expected characteristics encounter considerable difficulties, technical ones for the most part. The general disadvantage of such laser is a low conversion efficiency of black-body radiation energy into coherent laser radiation. Such a low efficiency is connected with a number of factors. The principal ones are in the following: Firstly, thermal pumping sources have a much broader emission band than the absorption band of the active molecules; Secondly, in the process of incoherent pumping, the vibrational states which do not participate in the creation of a population inversion are also excited. Such a process leads to an undesirable increase in the active gas temperature; Lastly, the conversion efficiency of the thermal pumping energy into i.r. pumping radiation is rather low (see above). All these factors are probably responsible for the fact that lasers using incoherent pumping have so far not gained wide-spread use, and are not being of importance in laser physics.

8. C O N C L U S I O N - - A P P L I C A T I O N S

AND OUTLOOKS

The optically pumped molecular i.r. lasers considered in the present review are efficient and rather simple resonant frequency converters of powerful i.r. lasers radiation. Their further development is brought about by the demands of laser radiation applications. Among them we should note first of all, selective action of laser radiation on matter, and particularly selective i.r. multiphoton photochemistry which arose several years ago. 1~2~1This new trend in selective action of laser light on atoms and molecules has been discussed in hundreds of works, which are summarized in the review, Ref. 128, and the monograph, Ref. 129. The basis for multiphoton i.r. photochemistry is a strong excitation of the vibrations in a polyatomic molecule by resonant action of an i.r. radiation pulse whose frequency is tuned to the vibrational absorption band. If the i.r. laser pulse has. a sufficiently high fluence (0.01-100 J/cm 2 for different molecules), the polyatomic molecule is able to absorb several tens ofi.r, photons due to multiphoton and (or) multi-step processes, their total energy being about equal to the dissociation energy of the molecule. If the laser pulse is shorter than the average time of collisions between molecules (about 100 nsec at a pressure of about 1 torr), strong excitation and dissociation through intense i.r. radiation can obviously be carried out on particular molecules in a gas mixture, without involving the rest of the molecules, which do not strongly interact with the i.r. radiation. This process has been studied in some detail, and is being used in experiments on laser isotope separation, laser purification of materials and chemical synthesis, t~2s. ~29) mainly by CO 2 lasers working in the range 9 11 #m. This, of course, essentially limits the potentialities of i.r. multiphoton photochemistry. It is very important to overcome this limitation on excitation frequency, and have the possibility of exciting any suitable vibrational band of any molecule. For this purpose we should like to have i.r. lasers in the region 2 20 #m (5000-500 cm- ~), with their energy and pulse duration as discussed above. The process ofmultiphoton excitation and dissociation can be facilitated substantially by acting on a molecule with two-frequency, or even multi-frequency, radiation. ~13°J Such a technique enables us to act simultaneously both on the lower and the upper vibrational molecular transitions, having different absorption frequencies because of anharmonicity. This specific feature of excitation of the upper vibrational states is illustrated in Fig. 34, which shows in a simplified manner the evolution of the i.r. absorption spectrum of a polyatomic molecule near some fundamental 0-1 absorption band as the rate of vibrational excitation rises. In the typical case, there is a broadening and a "red" shift taking place at positive anharmonicity, and wings in the absorption arising as vibrational excitation increases (see Ref. 128). It is clear that i.r. radiation being in good resonance with the lower vibrational transitions may be far from resonance for transitions between highly excited states. Of course, to some extent such an offset of the exciting frequency from the absorption line is compensated for by absorption band broadening and by weak absorption in the vibrational quasi-continuum (the wings in Fig. 35). However, optimal for i.r. photodissociation is the case of at least two-frequency irradiation, ~I3°~ when i.r. radiation at the v~ frequency

Molecular infrared lasers using resonant laser pumping

W ~

289

absorption

Ed,ss

.

~

m

~

0-I

0 :°

~-mode

the

rest

of modes

FIG. 34. Evolution ofi.r, absorption in fundamental band for different values of vibrational energy W deposited in polyatomic molecule.

resonantly excites lower transition, and i.r. radiation at the I)2 frequency excites transitions in the strong absorption region of the vibrational quasi-continuum. F r o m this point of view, of great interest for multiphoton i.r. photochemistry are molecular resonant frequency converters of powerful i.r. lasers which make it possible to "reproduce" the frequencies of one laser in order to cover new spectral regions. The first experiments on application of the optically pumped medium-i.r, molecular lasers have been already performed with success. And what is more, the development of 16 #m lasers (e.g. CF4 lasers optically pumped with a CO 2 laser) was stimulated by the needs of multiphoton i.r. photochemistry for the U F 6 molecule. The same concerns the development of the NH3 laser. Let us consider some experiments on the application of the resonantly laser pumped molecular lasers in i.r. multiphoton photochemistry. The N H 3 laser was successfully used for isotopically selective dissociation of CC14 molecules with different carbon and chlorine isotopes. (44) One of the N H 3 laser frequencies (780.5 c m - 1) is close to that of the v3 mode ofCC14 (775 cm 1). With a laser pulse fluence of about 2 J/cm 2 there was irreversible dissociation of CC14 with an enrichment factor of about 4 - 6 for the 23C isotope, and about 1.15 for 37C1. The dissociation yield of CCI~ under the action of an N H 3 laser pulse was 2-3 orders higher than that for a C O / l a s e r pulse, the frequency of which coincided with the combination band (v I + v2 + v4).(t31) Thus, if the N H 3 laser efficiency is even over 1%, it is advantageous to convert the radiation of the CO 2 laser on N H 3, and then act on the CC14 molecule. Isotopically selective dissociation ofCC14 was also performed by the simultaneous action of N H 3 and CO 2 laser pulses. In that case, there were two possible dissociation processes: (1) the CO a laser excited the weak combination vibration (v l + v2 + v4), and the N H 3 laser dissociated the excited molecules; or (2) the N H 3 laser excited the fundamental v 3 vibration and the CO 2 laser dissociated the excited molecules. Both processes are far from being optimaP 132233) when the N H 3 laser isotopically-selectively excites the strong v3 vibration and the longer-wave laser dissociates the excited molecules in the region of maximum absorption in the vibrational quasi-continuum. Experiments similar to these were produced in Ref. 134 on SeF 6 molecules, where the N H 3 laser at a frequency of 780.5 cm-~ with the pulse energy of 50 mJ excited the v3 band. Isotopically selective dissociation o f 74-82SEF6 molecules was achieved under strong overlapping of vibrational absorption bands. In recent work, ~135) the dissociation yields of CC14 were compared for two cases when the fundamental v3 vibration was excited by an N H 3 laser radiation pulse at a frequency 771 c m - 1, or the combination vibration (v I + v2 + v4) was excited by a C O 2 laser pulse at a frequency 980 c m - 1. Since, at the same absorbed energy, the dissociation yields were different, a conclusion was drawn about "mode selectivity" in multiphoton dissociation ofCC14 molecules by i.r. radiation. Similar results were obtained in Ref. 136, where experiments were produced with SF5NF z molecules excited by a CO 2 laser. The CF 4 laser was successfully used for multiphoton excitation and dissociation of UF 6 molecules363.64.137.138) The fact that the U F 6 molecule was not efficiently photodissociated before the creation of this laser points to its practical value. In Re['. 64, the authors investigated the dissociation of U F 6 using the radiation of a CF 4 laser (615 c m - 2) to excite

290

A.Z. GRASIUK, V. S. LETOKHOVand V. V. LOBKO

the P - b r a n c h in the 0 1 band of the v3 vibration mode. It was found that the threshold dissociation fluence (1 J/cm 2) for U F o was lower than that for SF~,. The use of two-frequency i.r.i.r, excitation ~°31371 resulted in a substantial increase (10-100 times) of the UF~, dissociation yield. The C O 2 laser with its radiation dissociating the molecules excited by the C F 4 laser was used as a second-step source. As the C O 2 laser frequency changed from 900 to l l l 0 c m 1, an increase in dissociation yield was observed. This suggests that there is a structure in the vibrational quasi-continuum, one of its maxima near the frequency of 1157 cm 1, which corresponds to the (v 2 + l;3) vibration. In two-frequency dissociation of UF~, in the volume under irradiation there is visible luminescence, which disappears in singlefrequency excitation. Results in m a n y respects similar to these have been obtained in Ref. 138, using i.r.u.v, excitation. In this work, the source of u.v. radiation was an N 2 laser. However, it should be noted that in the works considered there has been no isotopic selectivity observed in UF~, dissociation. Optically p u m p e d lasers have extensive applications, not only in experiments on selective excitation and dissociation of molecules, but also in laser high-resolution spectroscopy. One of the most successful works in this respect is Ref. 121, where a tunable high-pressure C O 2 - N 2 0 laser was used to measure high-resolution spectra (see Section 6). The absorption spectra of N H 3 and C2H 4 were measured with a resolution of a b o u t 0.012cm 1. For the N H 3 molecule, in this case new spectroscopic information was obtained. It is of great interest for molecular spectroscopy to measure with high resolution the output frequencies of optically p u m p e d lasers. This is due to the fact that the accuracy of appropriate spectral measurements may be much higher than in the case of conventional absorption spectroscopy. And finally, the investigation in the spectra of optically p u m p e d lasers is often the only way of studying the energy level structure of molecules in highly excited vibrational states. The needs for laser molecular spectroscopy, multiphoton i.r. photochemistry, and particularly its applications, will, no doubt, stimulate further progress in the development of i.r. molecular frequency converters, until the whole medium-i.r, region is covered. Widening the laser frequency range m a y be considered a most important problem. The use of a highpressure continuously tuned C O 2 lasers for optical p u m p i n g of molecules especially holds much promise here, lTm because this facilitates the matching of the p u m p frequency with the absorption frequency of a suitable v i b r a t i o n - r o t a t i o n molecular transition. The first successful experiments in this direction have been already performed. ~771 The next step is to achieve the required pulse energy, peak and average powers. These problems can be solved using such well-known methods of q u a n t u m electronics as an increase in volume, and fast transverse flowing of the active molecular medium. In the future, we hope to have not only laboratory systems, but also commercial molecular frequency converters, of the C O 2 laser at least.

REFERENCES 1. N. G. BASOVand A. M. PROKHOROV,ZhETF (Russian) [JETP] 28, 249 (1955). 2. F. P. SHAFER(editor) Dye Lasers. Springer Series Topics in Applied Physics, Vol. 1, Springer-Verlag, Berlin, Heidelberg, New York (1973). 3. N. G. BAsov, A. Z. GRASIUKand V. A. KATULIN,Dokl. Akad. Nauk SSSR (Russian), 161, 1306 (1965). 4. N. G. BASOV,A. Z. GRASIUK,V. F. EFIMKOV,I. G. ZUBAREV,V. A. KATULINand Yu. M. POPOV,J. Phys. Soc. Japan 21 (suppl.), 277 (1966). 5. A. Z. GRASIUK,Sot;. J. quant. Electr. 4, 269 (1974). 6. A. Z. GRASIUKand I. G. ZUBAREV,Appl. Phys. 18, 235 (1979). 7. 1. WIEDER,Phys. Lett. 24A, 759 (1967). 8. A. J. BEAULIEU,Appl. phys. Lett. 16, 504 (1970). 9. V.S. LETOKHOV,Molecular lasers with pumping by infrared laser radiation, Report presented at Illrd Con£ on Chemical and Molecular Lasers, 1 3 May, St. Louis, Missouri, U.S.A. (1972). 10. R. L. PRESSLEY(editor) Handbook oJ'Lasers with Selected Data on Optical Technology. Chemical Rubber Co, Cleveland (1971). 11. R. L. BYERand W. R. TRUNTA,J. Opt. Soc. Amer. 68, 1622 (1978). 12. P. RABINOWITZ,A. STEIN,R. BRICKMANand A. KALDOR,Appl. phys. Lett. 35, 739 (1979). 13. T.Y. CHANG,in Nonlinear Infrared Generation, edited by Y.-R. SHEN,Springer Series Topics in Applied Physics, Vol. 16, Spri~ager-Verlag, Berlin, Heidelberg, New York (1977).

Molecular infrared lasers using resonant laser pumping

291

14. T.Y. CHANG,O. R. WOOD II, Appl. phys. Lett. 21, 19 (1972); ibid. 22, 93 (1973); ibid. 23, 370 (1973); ibid. 24, 182 (1974). 15. C. R. JONES, Laser Focus, p. 69 (1978). 16. J. D. LAMBERT, Vibrational and Rotational Relaxation in Gases, Clarendon Press, Oxford, U.K. (1977). 17. C. B. MOORE, Advances Chem. Phys. 23, 41 (1973). 18. A. B. CALLEARand J. D. LAMBERTin Comprehensive Chemical Kinetics, edited by C. H. BAMFORDand C. F. H. TIPPER, Vol. 3, Elsevier Publishing Company, Amsterdam, London, New York. 19. N.V. KARLOV,YU I B. KONEV,YU. N. PETROV,A. M. PROKHOROVand O. M. STELMAH,Pifma ZhETF (Russian) [JETP Lett.] 8, 22 (1968). 20. Infrared Physics 16, 171-207, Proc. Int. Conf. Infrared Physics, Zurich, 11-15 August (1975). 21. M. ROSENBLUTH,R. J. TEMKIN and K. J. BUTTON, Appl. Opt. 15, 2635 (1976). 22. N. SKRIBANOWITZ,I. P. HE~MAN and M. S. FELD, Appl. phys. Lett. 21,466 (1972). 23. A. L. GOLGER and V. S. LETOKHOV"Kvantovaya Electronica (Russian) [Soy. Quant. Electr.] 1 (13), 30 (1973). 24. T. Y,, CHANG and J. P. MCGEE, AppL phys. Lett. 28, 526 (1976). 25. E. J. DAN1EL1WlCZ,E. G. MALK and P. D. COLEMAN, Appl. phys. Lett. 29, 557 (1976). 26. T. Y. CHANG and J. D. McGEE, Appl. phys. Lett. 29, 725 (1976). 27. S. M. FRY, Opt. Comm. 19, 320 (1976). 28. B. I. VASILEV,A. Z. GRASIUK and A. P. DYADKIN, Kvantovaya Electronica (Russian) [Soy. Quant. Electr. ] 4, 1085 (1977). 29. R. G. HARRISON, F. A. AL-WATBAN, Opt. Comm. 20, 225 ~1977). 30. B. WALKER, G. W. CHANTRY and D. G. Moss, Opt. Corn, un. 23, 8 (1977). 31. J. J. TIEE, C. WITTIG,J. appl. Phys. 49, 61 (1978). 32. T. YOSHIDA, N. YAMBOYASHI,Opt. Commun. 26, 410 (1978). 33. N. YAMBOYASHI,T. YOSHIDA, K. MIYAZAKI and K. FUJISAWA, Opt. Commun. 30, 245 (1979). 34. MOCHIZUKI,M. YAMANAKA,M. MORIKAWA,C. YAMANAKA,J. Opt. Soc. Amer. 68, 672 (1978). 35. E. D. SHAW and C. K. N. PATEL, Opt. Commun. 27, 419 (1978). 36. B.I. VASm'EV,A. P. DYADKIN,N. P. FURZIKOVand A. B. YASTREBKOV,Pis'ma ZhTF (Russian) [JETP Lett. ] 5, 439 (1979). 37. B. I. VASIL'EV,A. Z. GRASlUK, A. P. DYADKIN and N. P. FURZIKOV, Kratk. Soob. Fiz. FIAN (Russian) 38, 34 (1978). 38. B. 1. VAS1L'EV,A. Z. GRASIUK,S. V. EFIMOVSKII,V. G. SMIRNOVand A. B. YASTREBKOV,Kvantovaya Electronica (Russian) [Soy. Quant. Electr.] 6, 648 (1979). 39. B.I. VASIL'EV,A. Z. GRASIUK,A. P. DYADKIN,m. N. SUKHANOVand A. B. YASTREBKOV,Kvantovaya Electronica [Soy. Quant. Electr.] 7, 116 (1980). 40. A. Z. GRASIUK, Appl. Phys. 21, 173 (1980). 41. C. H. TOWNES and A. L. SHAWLOW,Microwave Spectroscopy, McGraw-Hill Publishing Co. Ltd, New York, London, Toronto (1955). 42. A. Z. GRASIUK, I. G. ZUBAREV,A. V. KOTOV, S. I. MIGHAILOVand V. G. SMIRNOV, Kvantovaya Electronica (Russian) [Soy. Quant. Electr.] 3, 1062 (1976). 43. A. Z. GRASIUK and I. G. ZUBAREV, Appl. Phys. 17, 211 (1978). 44. R. V. AM~ARTSAUraIAN,Z. A. GRASlUK, A. P. DYADKIN, N. P. FURZmOV, V. S. LETOKHOVand B. I. VASIL'EV, Appl. Phys. 15, 27 (1978). 45. V. Yu. BARANOV,A. Z. GRAS1UK, A. P. DYAD'K1N et aL, AppL Phys. 17, 317 (1978). 46. A. L. GOLGER and V. S. LETOKHOV,Kvantovaya Electronica (Russian) [Soy. Quant. Electr. ] 5(17), 106 (1973). 47. E. ARMAND1LLOand J. M. GREEN, J. Phys. D: Appl. Phys. 11, 421 (1978). 48. V. S. LETOKHOV and A. A. MAKAROV,ZhETF (Russian) [JETP] 63, 2064 (1972). 49. J. M. GREEN, J. Phys. D: AppL Phys. 12, 489 (1979). 50. K. V. REDDY, R. G. BRAY and M. J. BERRY, Advances in Laser Chemistry, edited by A. H. ZEWAIL, Springer Series in Chemical Physics, Vol. 3, p. 48, Springer-Verlag, Berlin, Heidelberg, New York (1978). 51. V. N. BAGRATASHVIH,I. N. KNYAZEV and V. S. LETOKHOV, Opt. Commun. 4, 154 (1971). 52. O. R. WOOD, R. L. ABRANS and T. J. BRIDGES, Appl. phys. Lett. 17, 376 (1970). 53. H. R. SCHLOSSBERGand H. R. FETTERMAN,Appl. phys. Lett. 26, 316 (1975). 54. J. J. TIEE and C. WITTIG, AppL phys. Lett. 30, 420 (1977). 55. A. H. BUSHNELL,C. R. JONES, M. I. BUCHWALDand M. GUNDERSEN,IEEE J. Quant. Electr. QE-15, 208 (1979). 56. R. V. AMBARTSUMIAN,V. M. APATIN and V. S. LETOKnOV, Pis'ma ZhETF (Russian) [JETP Lett.] 15, 336 (1972). 57. Yu. R. KOLOM[ISKY,V. S. LETOKHOV and O. A. TUMANOV, Kvantovaya Electronica (Russian) [Soy. Quant. Electr.] 3, 1771 (1971). 58. C. R. JONES, M. I. BUCHWALD, M. GUNDERSEN and A. H. BUSHNELL, Opt. Commun. 24, 27 (1978). 59. H. N. RUTT and J. M. GREEN, Opt. Commun. 26, 422 (1978). 60. B. J. JENSEN,J. G, MARINUZZI, C. P. ROmNSON and S. D. POCKWOOD, Laser Focus 12, 51 (1976). 61. V. S. LETOKHOV, Usp. Fiz. Nauk (Russian) 125, 57 (1978). 62. K. HECHT, J. mol. Spectr. 5, 355 (1960). 63. J. J. TIEE and C. WITTIG, Opt. Commun. 27, 377 (1978). 64. P. RABINOWlTZ, A. STEIN and A. KALDOR, Opt. Commun. 27, 381 (1978). 65. J. J. TIEE, T. A. FISCHER and C. WITTIG, Rev. sci. Instr. 50(8), 958 (1979). 66. S. S. ALIraPIEV,G. S. BARONOV,N. V. KARLOV,A. I. KARCHEVSKn,V. L. MARTSlNKIAN,SH. SH. NABIEVand E. M. KHOKHLOV,Pis'ma Zh. TF (Russian) [JTP Lett.] 4, 167 (1978). 67. C. R. JONES, J. M. TELLE and M. I. BUCHWALD, Paper presented at Xth Int. Quantum Electronics Conf., Atlanta, May June, Paper K-7 (1978). 68. J. R. IZATT,C. J. BUDH1RAJAand P. MATHIEU, IEEE J. Quant. Electr. QE-13, 396 (1977). 69. V. G. AVERIN,S. S. ALIMPIEV,G. S. BARONOV,N. V. KARLOV,A. I. KARCHEVSKI'V. L. MARTSINKIAN,SH. Sn. NABW.V, B. G. SARTAKOVand E. M. KHOKHLOV, Pis'ma ZhTF (Russian) [JTP Lett.] 4, 1309 (1978).

292

A.Z. GRASIUK, V. S. LETOKHOV and V. V. LOBKO

70. J. J. TILE and C. WITTIG,J. Opt. Soc. Amer. 68, 672 (1978). 71. V. Yu. BARANOV,D. A. KAZAKOV,V. S. MEZHEVGV,A. N. NAPARTOVICH,M. Yu. ORLOVand V. D. PtSMENNY, Kvantovaya Electronica (Russian) [Sots. Quant. Eleetr.] (in press). 72. A. STEIN, P. RABINOWITZ and A. KALDOR, Opt. Lett. 3, 97 (1978). 73. A. G1RARG, Opt. Commun. 11, 346 (1974). 74. R. C. ECKHARDT, R. HINSLEY, M. PILTCH and S. ROCKWOOD, Opt. Lett. 4, 112 (1979). 75. L.J. Rsdziemski, JR., R. F. BEGLEY,H. FLICKER, N. G. NERESONand M. J. REISEELD,Opt. Lett. 3, 241 (1978). 76. YU. A. GOROKHOV,S. V. EFIMOVSKY,I. N. KNYAZEVand V. V. LOBKO, Pis'ma ZhTF (Russian) [JTP Lett. ] 4, 1481 (1978). 77. I. N. KNYAZEV,V. S. LETOKHOV and V. V. LOBKO, Opt. Commun. 29, 73 (1979). 78. V. V. LOBKO, Kvantovaya Electronica (Russian) [Soy. Quant. Electr.] 6, 841 (1979). 79. Yu. A. GOROKHOV,S. V. EFIMOVSKY,I. N. KNYAZEVand V. V. LOBKO,Kvantovaya Electronica (Russian) [Sotr. Quant. Electr.] 6, 2382 0979). 80. B.I. VASIL'EV,A. P. DYADKIN,N. P. FURZIKOVand A. B. YASTREBKOV,Pis'ma ZhTF (Russian) [JTP Lett.] 5, 439 (1979). 81. K. Fox, J. tool. Specif. 9, 381 (1962). 82. J. C. HILtCO, J. Physique 31,289 (1970). 83. C. W. PATI"ERSON,R. S. McDOWELL, N. G. NERESON,R. F. BEGLEY,H. W. GALBRAITHand B. J. KROHN, J. tool. Specif. 80, 71 (1980). 84. S. S. ALIMPIEV,G. S. BARONOV,N. V. KARLOV,A. I. KARCHEVSKY,V. L. MARTSINKIAN,SH. SH. NABIEV.B. G. SARTAKOV and E. M. KHOKHLOV, Kvantovaya Electronica (Russian) [Soy, Quant. Electr.] 6, 553 (1979). 85. V. YU. BARANOV,B. 1. VAS1L'EV,E. P. VELIKHOV,Yu. A. GOROKHOV,A. Z. GRASIUK,A. P. DYADKIN,S. A. KAZAKOV,V. S. LETOKHOV,W. D. PISMINNYand A. I. SrARODYBXSEV,Kvantovaya Electronica (Russian) ISot,. Quant. Electr.] 5, 940 (1978). 86. V. Yu. BARANOV,G. S. BARANOV,E. M. VOINOV,S. A. KAZAKOV,A. 1. KARCHEVSKY,V. S. MEZHEVOV,V. D. PISMENNY and A. I. STARODYBTSEV,Pis'ma ZhTF (Russian) [JTP Lett. ] (in pres). 87. V. YU. BARANOV,E. P. VEL1KHOV,S. A. KAZAKOV,D. D. MALJUTA,V. S. MEZHEVDV, W. G. NIZJEV, S. V. PIGULSKY,V. D. PISMENNYand A. I. SrARODYBTSEV,Kvantovaya Electronica (Russian) ISoc. Quant. Electr. ~6, 811 (1979). 88. V. I. BALYKIN,A. L. GOLGER,YU I R. KOLOMIISKY,V. S. LETOKHOVand O. A. TUMANOV,Kvantovaya Electronica (Russian) [Soy. Quant. Electr. 1 l, 2386 (1974). 89. R. L. ABRAMSand P. K. CHEO, Appl. phys. Lett. 14, 47 (1969). 90. C. K. RHODES, M. T. KELLY and A. JAVAN, J. chem. Phys. 48, 5730 (1968). 91. A. S. BIRJUKOV,V. K. KONJUKHOV,A. CH. LUKOVMKOVand P. I. SERIKOV,ZhETF (Russian) IJETP 166, 1248 (1974). 92. H. KILDAL and T. F. DEUTSCH, Appl. phys. Lett. 27, 500 (1975). 93. M. I. BUCHWALD,C. R. JONES, H. R. FETTERMAN and H. R. SCHLOSSBERG,Appl. phys. Lett. 29, 300 (1976). 94. R. M. OSGOOD, Appl. phys. Lett. 32, 564 (1978). 95. T. A. ZNOTINS, J. REID, B. K. GARSIDE and E. A. BALLIK, Opt. Lett. 4, 253 (1979). 96. B. J. FELDMAN, R. A. FISHER, C. R. POLLACK, S. W. S1MONSand R. G. TERKOVICH, Opt. Lett. 2, 16 (1978). 97. A. M. BONCH-BRUEVlCHand V. A. KHODOVOI, Usp. Fiz. Nauk (Russian) 85, 1 (1965). 98. V. I. BREDIKHIN, M. D. GALANIN and V. N. GENKIN, Usp. Fiz. Nauk (Russian) ll0, 3 0973). 99. W. K. BISHEL, P. J. KELLY, C. K. PHODES, Phys. Rev. A13, 1817 (1976). 100. W. K. BISCHEL, P. J. KELLY and C. K. PHODES,Phys. Rev. AI3, 1829 (1976). 101. R. R. JACOBS, D. PROSNITZ, W. K. BISCHEL and C. K. RHODES, Appl. phys. Lett. 29, 710 (1976). 102. D. PROSNITZ, R. R. JACOBS, W. K. BISCHEL and C. K. RHODES, Appl. phys. Lett. 32, 221 (1978). 103. L. D. LANDAU and E. M. LIESHITZ, Kvantovaya Mechanica, Moscow (1963). 104. A. L. GOLGER and V. S. LETOKHOV, Kvantovaya Electronica (Russian) [Sot,. Quant. Electr.] l, 870 (1974). 105. F. V. BUNKIN, ZhETF (Russian) IJETP] 50, 1685 (1966). 106. A.S. AKHMANOV,V. YU. BARANOV,V. D. PISMENNY,V. N. BAGRATASHVIL1,YU. R. KOLOMIISKY,V. S. LETOKHOY and E. A. RYABOV, Opt. Commun, 23, 357 (1977). 107. L. Y. NELSON, S. J. HOVERSON,J. F. NEWTON and S. R. BYRON, M N S W Report 77-1064-4, January (1978). 108. W. E. BARCH, H. R. FETTERMAN and H. R. SCHLOSSBERG,Opt. Commun. 15, 358 (1975). 109. H. PUMMER, W. K. BISCHEL and C. K. RHODES, J. appl. Phys. 49, 976 (1978). 110. A. N. BOBROVSKY,A. A. VEDENOV,A. V. KODZHEVNICOVand A. N. SOBOLENKO Pis'ma ZhETF (Russian) [JETP Lett.] 29, 589 (1979). 111. A.V. ELETSKY,L. Yu. EFREMENKOVAand B. M. SMmNOV,Dokl. Akad. Nauk SSSR (Russian) 194, 298 (1970). 112. R.S. McDOWELL, C. W. PATTERSON,C. R. JONES, M. I. BUCHWALDand J. M. TELLE, Opt. Lett. 4, 274 (1979). 113. M. C. LIN, 1EEL J. Quant. Electr. QE-10, 516 (1974). 114. A. B. PE~ERSEN and C. WITTIG, AppL phys. Lett. 27, 305 (1975). 115. A. L. GOLGER and V. S. LETOKHOV, Kvantovaya Electronica (Russian) [Soy. Quant. Electr.] 2, 1508 (1975). 116. B. F. GORDIETS, N. N. SOBOLEV,V. V. SOKOWKOVand L. A. SHELEPIN,IEEE J. quant. Electr. QE-4, 796 (1968). 117. B. I. SrEPANOV,S. A. TRUSHIN and V. V. CHURAKOV,K vantovaya Electronica (Russian) [Soy. Quant. Electr. ] 3, 1320 (1976). 118. I. M. BERTEL, B. F. KUNTSEVICH, V. O. PETUKHOV, S. A. TRUSHIN and V. V. CHURAKOV,Zh.~Prikl. Spektr. (Russian) 28, 804 (1978). 119. V. O. PETUKHOV,S. A. TRUSHtN and V. V. CHURAKOV,Pis'ma ZhTF (Russian) [JTP LetE] 4, 1461 (1978). 120. T. Y. CHANG, J. D. MCGEE and O. R. WOOD, Opt. Commun. 18, 57 (1976). 121. T. V. CHANG and O. R. WOOD, IEEE J. quant. Electr. QE-13, 907 (1977). 122. T. J. MANUCCIA,J. A. S~REGACK,N. W. HARRIS and B. L. WEXLER, AppL phys. Lett. 29, 360 (1976). 123. T. F. DEUXSCHand H. KILDAL, Opt. Commun. 18, 124 (1976). 124. P. A. BOHAN and G. I. TALANKINA, Optica i Spectroscopia (Russian) 25, 536 (1968). 125. P. A. BOHAN, Optica i Spectroscopia (Russian) 26, 773 (1969).

Molecular infrared lasers using resonant laser pumping

293

126. P. A. BOHAN, Optica i Spectroscopia (Russian) 32, 826 (1972). 127. R.V. AMBARTSUMIAN,V. S. LETOKHOV,E. A. RYABOVand N. V. CHEKALIN,Pis'ma ZhETF (Russian) [JETP Lett.] 20, 597 (1974). 128. R. V. AMI3ARSUMIANand V. S. LETOrd4OV,in Chemical and Biochemical Applications of Lasers, edited by C. B. MOORE, Physics of Quantum Electronics, Vol. 3, p. 161, Academic Press, New York (1977). 129. V.N. BAGRATASHVILI,V. S. LETOKHOV,A. A. MAKAROVand E. A. RYABOV,Multiphoton Processes in Molecules at IR Laser Excitation, Ed. Sov. Inst. Scient. Techn. Inform., Moscow (1980). 130. R. V. AMBARTSUMIAN,YU. A. GOROKHOV,V. S. LETOKHOV,G. N. MAKAROV,A. A. PURETZKYand N. P. FURZlKOV, Opt. Commun. 18, 517 (1976). 131. R.V. AMBARTSUMIAN,YU. A. GOROKHOV,V. S. LETOKHOV,G. N. MAKAROVand A. A. PURETZKY,Phys. Lett. 56A, 183 (1976). 132. R. V. AMBARTSUMIAN,YU. A. GOROKHOV,G. N. MAKAROVand A. A. PURETZKY, Kvantovaya Electronica (Russian) [Soy. Quant. Electr.] 4, 1590 (1977). 133. V. M. AKULIN,S. S. ALIMPIEV,N. V. KARLOV,A. M. PROKHOROV,B. G. SARTAKOVand E. M. KHOKHLOV,Pis'ma ZhETF (Russian) [JETP Lett.] 25, 428 (1977). 134. J. J. TIEE and C. WITTIG, Appl. phys. Lett. 32, 236 (1978). 135. B. I. VASIL'EV,N. A. VISHNYKOV,V. Z. GALOCHKIN,A. Z. GRASIUK,A. P. DUADKIN,A. K. ZHIGALKIN,V. A. KOVALEVSKY,V. N. KOSINOV,A. N. ORAEVSKY,A. N. SUKHANOVand N. F. STARODUBTSEV,Pis'ma ZhETF (Russian) [JETP Lett.] 30, 29 (1979). 136. J. L. LYMAN,W. A. DANEN, A. L. NILLSON and A. NOVAK,J. chem. Phys. 71, 1206 (1979). 137. S. S. ALIMPIEV,A. P. BABICHEV,G. S. BARONOV,N. V. KARLOV,A. I. KARCHEVSKY,S. YU. KULIKOV,V. L. MARTSINKIAN,SH. SH. NABIEV,S. M. NIKIFOROV,A. M. PROKHOROV,B. G. SAR~fAKOV,E. P. SKVORTSOVAand E. M. KHOKHLOV,Kvantovaya Electronica (Russian) [Soy. Quant. Electr.] 6, 2155 (1979). 138. R. V. AMBARTSUM1AN,V. M. APATIN, N. G. BASOV,A. Z. GRASIUK,A. P. DUADKIN and N. P. FURZIKOV, Kvantovaya Electronica (Russian) [Soy. Quant. Electr.] 6, 2612 (1979).