Stimulated emission and relaxation processes in molecular crystals

STIMULATED EMISSION AND RELAXATION PROCESSES IN MOLECULAR CRYSTALS

V.V. EREMENKO and L.A. OGURTSOVA Institute for Low Temperature Physics and Engineering, Academy of Sciences of the Ukrainian SSR, 47 Lenin Avenue, Kharkov 310164, USSR

I

NORTH-HOLLAND

-

AMSTERDAM

~HYSICSREPORTS (Review Section of Physics Letters) 166, No. 6 (1988) 353—396. North-Holland, Amsterdam

STIMULATED EMISSION AND RELAXATION PROCESSES IN MOLECULAR CRYSTALS V.V. EREMENKO and L.A. OGURTSOVA Institute for Low Temperature Physics and Engineering, Academy of Sciences of the Ukrainian SSR, 47 Lenin Avenue, Khartov 310164, USSR Received January 1988

Contents: Introduction 1. Lasers using complex organic molecules 2. Absorption of emitted light by excited molecules 2.1. Reabsorption preventing light generation 2.2. Peculiarities in the emission of organic molecules with triplet—triplet reabsorption 2.3. On the relaxation of upper triplet states in complex organic molecules 3. Temperature dependence of stimulated emission in molecular crystals 3.1. Light generation by doped molecular crystals at 300 and 77K 3.2. Stimulated emission of doped molecular crystals at 4.2 K 3.3. Stimulated emission and light generation by the cxciton system

355 355 358 360 362 364 365 366 369

3.4. Stimulated emission and stimulated Raman scattering in some molecular crystals 4. Effect of relaxation of vibrational levels on stimulated emission 4.1. Hot luminescence and relaxation processes in crystals 4.2. Hole burning and excited state relaxation 4.3. Lifetimes of vibrational levels of the ground state of dopant molecules determined by stimulated emission 5. Optical transitions stimulated by nonequilibrium phonons 5.1. Generation of nonequilibrium phonons and propagation in anthracene crystals 5.2. Effect of nonequilibrium phonons on the emission from doped molecular crystals 6. Conclusion References

375 378 378 379 380 385 385 386 391 392

374

Abstract: In the present paper experimental results on the emission of organic molecular crystals with strong optical pumping are analysed. Incoherent processes are studied, namely stimulated emission, vibrational state saturation, nonequilibrium phonon generation, optical transitions stimulated by nonequilibrium phonons, etc. Experimental data on light generation by doped molecular crystals at 300 and 77 K are presented. A comparison is made between the parameters of light generation in crystals on the one hand, and liquid and polymer solutions on the other hand. Reabsorption of the emission by the excited molecules preventing light generation is considered. Spectral and kinetic studies of stimulated emission of crystals in the temperature range 1.6—40 K are presented. The advantages of doped molecular crystals below 20 K over liquid and polymer solutions as Q-switched frequency transformers are emphasized. Much attention is paid to stimulated emission of molecular crystals at low temperatures to study vibrational and phonon relaxation. Relaxation times of vibrational levels of the ground state of the impurity molecule are obtained for a number of doped molecular crystals. Data on the

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V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

355

relaxation of vibrational levels obtained by stimulated emission, hot luminescence and hole burning are analysed. Vibrational relaxation times in the ground and excited states of an impurity molecule are compared. The role of host crystal phonons in the evolution of the emission is studied. Generation and propagation of nonequilibrium phonons are discussed. Phonon lifetimes are estimated by kinetic and spectral studies.

Introduction In laser spectroscopy it is sometimes efficient to study the energy spectrum of generated light and relaxation processes in an active element. Recently low temperature incoherent laser spectroscopy of molecular crystals revealed a number of phenomena such as nonlinear luminescence quenching, thermal effects and nonequilibrium phonon propagation, excitation energy transfer to the excited singlet levels and stimulated Raman scattering, etc. A number of these phenomena are discussed in the review article “Fluorescence of molecular crystals at high levels of optical pumping” [1]. The present paper is concerned with the processes appearing with high power laser pumping of impurity molecules in a solid crystal matrix that is a single crystal grown under equilibrium conditions. At first it was assumed that, while exciting crystals at 4.2 K which have narrow bands or lines of electron—vibrational spectra, only low threshold stimulated emission would be observed. However, first experiments with optical pumping of crystals revealed a number of phenomena that require more fundamental studies of all possible processes. Laser pumping can result in coherent or incoherent states of the excited molecules. In the present paper excitations are considered that do not lead to coherence in a molecular system, though the degree ofinversion can be very high. In any case, it can result in stimulated emission. The following incoherent processes can occur in molecular crystals at low temperatures with high laser pumping: 1. Heating of the sample. 2. Spontaneous luminescence or phosphorescence. 3. Nonlinear luminescence quenching. 4. Three- and four-level spectroscopic model stimulated emission. 5. Nonequilibrium phonon generation. 6. Energy transfer to excited levels. 7. Saturation of vibrational states. 8. Optical transitions stimulated by nonequilibrium phonons. 9. Raman and stimulated Raman scattering. 10. Light absorption of excited and population inverted systems by singlet—singlet (S1—S~)and triplet—triplet (T—T~)transitions. In fact, we studied all these processes, and we observed some of them for the first time. Others were described elsewhere. A simple list of processes occurring with optical pumping shows that light generation itself is an efficient method of studying both the crystal energy spectrum and relaxation. Therefore, this paper is concerned with the above phenomena, except section 1, where a brief description ofcomplex molecule lasers is given. 1. Lasers using complex organic molecules

In the first solid (ruby and Nd:glass) and gas lasers, and in lasers where rare-earth ions are used as active impurities, the laser action occurs on transitions with rather narrow luminescence bands. In all

356

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

these systems a three- or four-level energy scheme is used to achieve population inversion. It is impossible to create the required conditions for light generation in a system of particles with only two narrow levels by optical pumping [21. Organic molecules, whose energy levels are given in fig. 1, embedded in different media (liquid and solid) have rather wide absorption and emission bands (—.2000 cm’) at room temperature. This is one of the reasons why they were not considered as possible lasing media. However, before the invention of the first lasers, in 1960, it was shown [31that with intense optical excitation appreciable light amplification is possible in organic molecules at a number of frequencies. A similar idea was stated regarding colour centers in KC1 crystals [4]. Later some authors discussed possible organic molecules for use as active laser media [5—7].Besides, their light generation properties were calculated by considering the vibrational structure of the electronic levels [8,9]. Theoretically, organic molecules used as active laser media were reported in 1966—67 [2, 10, 111. Actual experimental conditions for generation of light in solutions of organic molecules were defined, and the generation mechanism in these systems was considered. The mechanism of light generation in organic molecules is described by a scheme of two broadened levels. Possible amplification was estimated in the framework of two broadened electronic—vibrational levels [10, 111. The lower level, S, belongs to the ground electronic state (level 1), the upper one, S1, to the quasi-equilibrium state (level 2) (fig. 1). The amplification factor k at a frequency ~ for this system has the form [111 k21(~)=K21(V)l,\~ / n2

—

n1 B2~(v)) B12(i.’)\ ~

(1)

‘

where I(21(P) = (hvlc)nB21(v) = nu21 is the limiting gain factor for n2 = n. Here n2 and n1 are the numbers of molecules occupying the higher, S1, and lower, S, electronic levels, n = n1 + n2 B21(i’) and B12(v) are the Einstein coefficients for stimulated emission and absorption, respectively, averaged over the entire vibrational levels. For complicated molecules B12(~)and B21(zi) are not equal and related by

L\si

Ve?

/J

T

Fig. 1. Simplified scheme of energy levels of an organic molecule and possible transitions.

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

357

the general relation [10]

_____

=

exp[—h(v~1 v)/KT].

(2)

—

This relation takes into account the equilibrium distribution of particles over the vibrational sublevels of the ground and excited electronic states. Taking into account eq. (2) the gain factor of the medium takes the form (assuming C1 = C2, since the statistical weights are the same for singlets): k21(v)

=

K21(v)(

—

~

exp[—h(v~1

—

v)IKT]).

(3)

According to eq. (3) amplification at the frequency ,i can be larger than zero even for n2 to occur the following inequality should be satisfied: n21n1 >exp[—h(v~1

—

v)/KT].

-~

n1. For this

(4)

For v

~ these conditions are related to the population inversion of the levels 2 (Si) and 1 (S). For V < Vet amplification occurs even if n2 < n1. The larger ~‘e1 v is (i.e., the larger the Stokes shift is), the smaller n2!n1 is, and the easier it is to achieve amplification. Consequently, appreciable amplification is observed in compounds having both large 1(21 and i~ Such parameters are realized in molecules with large values of the probability of spontaneous optical transitions. The two-level scheme approximately defines the properties of light amplification and generation in organic molecules. Light generation can be prevented by triplet and excited singlet levels (fig. 1) due to reabsorption by these states [2, 12, 13]. The accumulation of particles in a metastable level appears to be the main channel of losses impeding the generation of laser light. An analysis of the luminescence dependence of the light generation threshold taking into account the accumulation of particles on the triplet level indicated [10] that organic molecules with a high luminescence quantum yield, low probability of triplet state population, wide luminescence and absorption bands with a considerable shift relative to each other and small radiative lifetimes of the excited states are the most favourable for light generation on allowed transitions. The light generation mechanism can be described to a good approximation by a four energy level scheme [9], especially when the vibrational structure of the absorption and luminescence spectra of organic molecules (Spolsky system, molecular crystals at low temperatures) is allowed and the system is —

—

excited by laser radiation. The light generation conditions are mainly met for the luminescence line that is the most intense in the spectrum [2]. Light generation by organic molecules was first observed in liquid solutions [14—17].Then it was obtained in polymer matrices [17—20],in Spolsky systems [21], in gelatine films [22],in molecular crystals at room [23] and low [24,25] temperatures, in vapours [26] and in liquid crystals [27]. At present light generation is achieved in a wide variety of organic molecule solutions with pumping of active media by coherent and incoherent light sources. The spectral range that can be generated runs from 280 to 1250 nm [28—33].The transformation efficiency of pump energy into generated light is about 70% for the best dyes (rhodamine 6G) excited by Q-switched solid state lasers [34]. Experimentally the shortest pulses were about 30 fs [35].

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

358

Table 1 Optimal emission of organic molecule lasers Frequency (nm) tuning 1. 590—615 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

490—509

335—345 380—430, BBO 562—584, DFL 583—620, DFL 548—590, DFL

Active medium

Linewidth (nm)

rhodamine 6G 12 rhodamine 6G 7-diethylamino0.007 4-methylcoumarin coumarin-102 0.01 rhodamine 6G rhodamine 6G 2.7 x 10 rhodamine 6G rhodamine 6G p-terphenyl 0.00012 ethanol—toluene 1: 1 0.55 rhodamine 6G 0.001 0.04 0.15 0.4 rhodamine 6G (1.01 rhodamine C 0.01 0.25

(cm 360 0.3

1)

Pulse duration

Power

Energy

7Ofs 7Ofs 140 Ps

30MW 10GW 7 mi/pulse

250mJ

0.4 2.Sps 0.003 6ns 8 x 10~~ 5 ns 10 p.s 0.8 10 p.s 0.1 7 ns 3 2 Ps 0.03 1 p.s 1.2 IOns 4.5 4Sps 12 15 ps 0.3 IOns 0.3 iOns 7.5 Sps

Efficiency

(%)

Pumping

Ref.

[38] 0.7

20MW

SOmJ

11 MW 0.25 MW

55 mJ 2.5 J 4 mJ

N~-laser

[39] [40]

lamp YAG:Nd

[431

lamp lamp XeCl-laser YAG:Nd

several MW 9 10

[41]

[44] [47] [46] [45] [42] [48] [49] [49] [49] [49]

One of the most important generation characteristics of organic molecules is the possibility of frequency tuning. As a rule, the tuning region of a compound is large and coincides with the luminescence bandwidth. The generation frequency is extremely sensitive to changes of the parameters of the laser system. Therefore, the number of tuning techniques is quite large. Selective cavities make it possible to achieve smoothly tuned frequencies with narrow emission lines. The advantages of selective cavities are described elsewhere [28,36, 37]. Table 1 gives some optimal emission parameters of organic molecule lasers [38—49].As can be seen, organic solution lasers are powerful sources of coherent emission. Their minimum pulse duration achieved is about 30 fs [35]. In fact, very narrow emission lines are achieved for the entire pulse duration. Lasers with Nd activated yttrium aluminium garnet (Nd3~:YAG) are considered to be the most favourable for frequency tuning [50, 511. To date distributed feedback laser (DFL) systems are of great practical importance. These lasers are simple, convenient and have a narrow linewidth with high energies without any additional dispersion elements (table 1). However, it should be noted that the possibility of tuning is both the main advantage and the weak point of these active media. As the generation frequency is sensitive to changes of all the laser parameters, its stabilization is the actual problem [52, 531. From the viewpoint of emission frequency stabilization, doped molecular crystals can be more convenient. At present further application of organic lasers as sources of powerful monochromatic emission, tunable in the UV, visible and near infrared regions, is generally considered for the solution of spectroscopic, photochemical, biological and medical problems.

2. Absorption of emitted light by excited molecules Light absorption by excited molecules, i.e. transitions to higher singlet (5) and triplet (T) levels, is possible with high excitation when the equilibrium particle concentration in the S 1 and T levels is large.

V.V. Eremenko and L.A. Ogurt.sova, Stimulated emission and relaxation processes in molecular crystals

359

This should be taken into account while studying spectra and stimulated emission. Wide electron— vibrational bands in visible and UV spectra correspond to the above transitions. Before the invention of lasers, light absorption by long-lived excited molecular levels was studied by pulse photometry or flash-photolysis [54,55]. A low temperature flash-photometer permitting the study of both triplet—triplet absorption spectra and excited triplet level relaxation is described in ref. [56].The development of laser technology resulted in flash-photometers of nanosecond [571 and picosecond [58] resolution, which made it possible to study singlet—singlet absorption spectra and relaxation. Now much

experimental data are available on T—T~and 5—5,, absorption spectra of complex molecules [59—74]. Table 2 Data on triplet—triplet absorption T—T, absorption maximum

Compound

Temperature, state

Solvent

(nm)

(cm~’)

naphthalene

liquid

paraffin

415.0 391.5 372.0 416.7 416.7

24100 25550 26880

solid, 77K

EPA

solid, 77K

isopentane, n-butane, 3:3

293 K 4.2 K

77K naphthalene-d,

293 K

1-chloronaphthalene phenanthrene

phenanthrene-d

1,

PMMA durene

HMB PMMA

77K

HMB

77K

durene

293 K

PMMA

130K

HMB

293 K

PMMA

130K 4.2 K

HMB biphenyl

.

Extinction coefficient

Oscillator strength

Ref.

0.06

[59]

0.05

[60] [61]

10000

10000 24000 480±50 25465 215±41) 26950 24 000 25465 14000 26960 24 066 ±25 25414±25 23957 ±25 25357±25 26 146±50 26736±50 23950 ±50 25300±50 24128 ±25 25 501±25 26880 ±50 24045 ±25 25450 ±25 26 148 ±50 26941 ±50 28278±100 24077±25 25435 ±25 23556 ±25 25002 ±50 20460 ±20 21 951±50 23495 ±100 20165±50 21 528 ±50 20050 ±20 22030 ±50 23 561±100 20 189±50 21515 ±50

Relative intensity

[63] [63] 0.05 10 4.5 10 4.6 0.2 1.0 10 5

[63] [63]

[63] [63]

[63] [63]

[63]

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

360

Table 3 Data on singlet—singlet absorption S 1—S~absorption maximum Compound

Solvent

(nm)

anthracene 1,4.biphenylbutadiene 1,6-biphenylhexatriene 1 .8-biphenyloctatetraene 1.12-benzoperylene

PMMA methanol cyclohexane methanol PMMA

424 445 430 465

I ,2-benzocoronene

PMMA

3.4-dibenzoanthracene

PMMA

(cm’)

Extinction coefficient

Oscillator strength 1.3—1.7 1.3—1.7 1.3—1.7 0.16 0.08 0.13 0.21 t).1 0.1 0,13 0.13

[68] [71]

18200, 19300 21500,22700 23600 15500, 17000 19500 20600 23500 24700

50000 4—iO5 i0 io~—i~~ i04—i05 13200 7000 19000 15700 13500 13000 11800 12000 5800 16600

0.15 0.26

[69]

3700

(1.03

14500, 16500 19000 20000 22500, 23500

Ref.

[69]

[69]

Tables 2 and 3 give the positions of the T—T~and S—S,, absorption maxima and extinction coefficients (oscillator strengths) for a number of organic molecules in various solvents. The values of the absorption coefficients for these transitions are of great importance since for high concentrations of ~ and T states strong absorption by S 1—S,, and T—T,, transitions can occur and distort the spectroscopic parameters. 2.1. Reabsorption preventing light generation The problem of reabsorption of the emitted light by excited molecules, thus preventing light generation, appeared before the stimulated emission of organic molecules was obtained. This is connected with the fact that in the first attempts to generate light from organic molecules T—S transitions of complex molecules were used [75—79].Reabsorption as a factor preventing light generation was first observed in ref. [12]. When the conditions for amplification and light generation in organic molecule solutions by triplet—singlet (T—S) transitions are considered, the triplet is the upper energy level of the laser transition. Accumulation of particles in this level is a necessary condition to gain amplification. Accumulation of molecules in the triplet state depends on the absorption efficiency of the pump energy by the S—S1 channel, the probability W of S1—T transition and the triplet state lifetime (TT). For molecules with a high probability of conversion to the metastable state and long-lived triplet states it is not difficult to sufficiently decrease the ground state population in order to achieve inversion in the T—S channel. In 1958 the decrease of the ground state population S was found to be about 50% for a series of molecules [80]. The main characteristics which define the efficiency of pumping for population of the triplet level T are the absorption spectrum in the S—Si channel and the quantum yield of conversion into the metastable state T, yWI(A~+W).

(5)

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

361

The pumping efficiency of the T level is defined by the pumping rate yBu, where B is the Einstein coefficient and u the spectral pumping density in the ~ channel. The expression for the pumping rate yBu required to obtain a gain factor in the 1—S channel which is equal to the loss coefficient k105, for the frequency at the maximum of the gain band KTs(v) (V = Vmax), is of the form [81]

~ç

—h svIftKT

yBu = le 1

where

=

(6)

TT(k10551b) +r1

is the spectral half-width KST( ~),

t~p

f3

—

~

—

b

i/max),

2qI8iw~,~

=

nv

5,

(7)

n is the concentration ofparticles, v is the velocity of light in the mediumtfor anda spectral q the emission width ~quantum V ~S[81] yield in the T—S channel. According to eq. (6), the optimal lifetime r~’ —h ~‘/KT =

____________

Vi + eh ~v/i9KT

(8)

loss

For this lifetime the light generation threshold is as low as possible. Thus, in the framework of the three-level scheme compounds with an emission spectrum as narrow as possible and a lifetime defined in eq. (8) have the slowest threshold pump rates. Calculations for V = 800 cm ‘[81] show that generation of light in T—S transitions can be realized for substances with TT

5.

=

The estimated critical excess of the inverse density N/V for a number ofmolecules in PMMA at 77 K (namely: a-bromonaphtalene, ~V = 6580 cm1, TT = 2 x 102 s; benzophenone, i~V= 3900 cm1, rT =

6 x iO~s; coronene, i~V = 800 cm1, TT = 9 s) indicated [82]that the required excess for light generation is greater than the concentration attainable per unit volume since N/V is about 1020 cm3 for a-bromonaphthalene, 3 x 10~cm ~ for benzophenone and 1022 cm3 for coronene. Consequently, the main difficulties in realizing light generation by means of T—S emission of organic molecules results from the small probability of the radiative T—S transition due to inhibition in the system and broad emission bandwidths [81].As far back as 1961 it was suggested that these difficulties due to broad bandwidths could be avoided by the Spoisky method [83]. Indeed, using Spolsky systems or doped molecular crystals at 4.2 K one can obtain emission linewidths up to 1 cm1, which will decrease the required inverse density by more than three orders of magnitude. However, the excitation of triplet levels of organic molecules by light of high intensity results in the appearance of reabsorption of their own emission by T—T,, transitions [12],which prevents generation by the 1—S transitions. It should be noted that for organic molecules overlap of the 1—S emission bands and T—T,, absorption bands is the rule rather than the exception. Besides, the concentration of particles ~T in the triplet state for the T—T,, absorption factor and for the emission gain factor in the T—S channel is the same [12,84]. Taking into account nonlinear absorption due to excitation of the system, the conditions for light generation are of the form kamp +

k

105, + gloss

=

0

,

where kioss

=

(hv/c)n5 B~~(~)+ (hV/c)nTBTT(i.’)

(9)

362

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

are variable losses resulting from nonlinear absorption. In the case of triplet—triplet reabsorption, eq. (9) can be satisfied only when the Einstein coefficient for 1—1,, absorption is less than that for stimulated emission by T—S transitions. From this viewpoint triplet—triplet reabsorption should impede light generation due to allowed T—T~absorption transitions and forbidden 1—S emission transitions. Up to now amplification or light generation by triplet—singlet transitions in frozen liquid and polymer solutions of organic molecules has not been observed experimentally. The small gain factor of the 1—S transition and reabsorption of the T—S emission by T—T,, transitions should be considered as the principal reasons preventing light generation in these systems. Doped molecular crystals are more promising to obtain stimulated emission by the 1—S transitions. The low temperature phosphorescence spectra of a number of complex molecules in crystalline matrices consist of extremely narrow lines (about 1 cm’). The narrowing of the 1—1,, absorption band [62,85] in a crystalline tnatrix is, in fact, absent at low temperatures. Therefore, selecting host and dopant at 4.2 K, a system can be found without reabsorption by the T—T,, transitions. Narrow emission lines and radiative lifetimes of the T state as short as possible permit obtaining high gain factors to observe stimulated emission. An acenaphthenequinone doped 1 ,4-dibromonaphthalene crystal seems to satisfy the above requirements [86]. Under sufficiently high Q-switched excitation by UV and green harmonics of a Nd:glass laser, amplification on the 17223 cm’ vibronic transition has been observed [86]. The analysis of available data [87] makes it possible to draw the conclusion that the T—T,, absorption spectrum does not overlap with the impurity phosphorescence lines. To obtain light generation using allowed transitions, eq. (9) can be satisfied even if T—T,, reabsorption occurs [88, 89]. Thus, from the viewpoint of reabsorption the allowed transitions in

organic molecules appear more favourable for light generation. However, in this case reabsorption by both Si—S,, and T—T,, transitions should be taken into account even with excitation of organic molecules by 0-switched pulses [17—19].Time dependent populations of the excited singlet S1 and lower triplet T levels were calculated for such real excitation pulses [88, 89]. Besides, the time interval during which losses due to T—T,, reabsorption for a given ratio 0T/0s can be compensated was also defined (u is the absorption factor per molecule). Moreover, it was shown that if only reabsorption by S~—5, transitions is taken into account, it is necessary for light generation that ~ At present reabsorption in the S1—S,, and T—T,, channels with lamp and 0-switched pulse pumping is taken into account in a large number of works [90—105]in order to optimize the generation parameters of organic molecules. It has been shown that a low generation threshold and maximum laser efficiency are realized only for molecular systems where minimization of reabsorption of emitted light and light generation by singlet and triplet excited molecules is possible. 2.2. Peculiarities in the emission of organic molecules with triplet—triplet reabsorption Emission studies with reabsorption by T—T,, transitions at low temperatures are of great interest since they make it possible to obtain information about the excited states of complex molecules and the ways of excitation energy relaxation. Experimental studies of peculiarities in the emission of a number of molecules in polymethyl methacrylate (PMMA) at 77 K under conditions of intrinsic 1—1,, reabsorption began in 1963 [106].It was shown that if the emission spectrum overlaps partially or totally with the T—T~absorption spectrum, it is distorted to a different degree depending on the method of excitation or observation [12, 106, 107]. The emission intensity decreases in the strongest T—T1 absorption (fig. 2). Analysis of the effect of triplet—triplet reabsorption on the T—S emission kinetics has shown

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

400

.500

ô00

363

~,iz,n

Fig. 2. Emission and T—T absorption spectra ofdiketone in PMMA under pulsed excitation. 1: T—T absorption; 2: emission with front excitation; 3: emission of a long sample (32mm); 4: emission of a long sample (55 mm) excited by a flash of 4000 J.

Fig. 3. Decay curves of diketone in PMMA emission (A = 510 nm), under flash excitation of (1) 450 J, (2) 4000 J.

[12,82, 108] that under conditions of intrinsic reabsorption of the 1—S emission by T—T~transitions the decay law was exponential and the emission lifetime did not change for small sample sizes. The 1—S emission intensity in the output of the sample is [108] t)], (10) = N 0hvA [1 exp(—1k0 e~ —

where 1 is the sample length, N

0 is the number of particles in the I level per unit volume, k0 is the initial absorption factor of 1—1,, transitions at frequency i.’, and A the radiative probability of I level decay. The function (10) has an inflection point for kol=eAr,

(ii)

i.e., an increase of the sample length and of the T—T,, absorption factor (hence, of the pumping power) shifts the inflection point towards longer times. Figure 3 shows the experimental evidence for this conclusion [108]. For k0 0 the function (10) transforms into an exponential. Therefore, if reabsorption does not occur in the entire emission band the decay law is different for different spectral regions depending on k0. The T—T,, absorption factor can be determined from kinetic curves distorted by reabsorption [109]. Similar changes of the phosphorescence kinetics for 1—1,, reabsorption were also observed for triphenylene, biphenylene oxide and carbazole [109—113]. Consequently, for intrinsic triplet—triplet reabsorption there is no appreciable physical change of the relaxation time. The decay curve is deformed at different decay stages due to a decrease of the total energy in the output of the sample. In the case of impurity triplet—triplet reabsorption the emission intensity of the sample is [112,113] —~

NA h 0

eA2~_~~)t

2k0

[1_exp(_lkoeA2r)],

(12)

364

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

N0½~

~5.

/ V\ / ~

/

x

/7 V

t~’2

£75

ê

0

V

2

5

~ z~’s

Fig. 4. Emission intensity as a function of time for different y.

where A1 is the decay probability of the I level of the luminescence centre, A2 the decay probability of the metastable level of the absorbing centres. Figure 4 shows ~ as a function of time for different values of y = A1 IA2 calculated with eq. (12). Three types of decay curves can be obtained depending on the ratio A11A2, namely: y = 1 (A1 = A2): intrinsic triplet—triplet reabsorption; y <1 (A1 < A2): owing to the prompt decay of reabsorbing impurities the system becomes transparent before the luminescence centres begin to emit; y > 1 (A1 > A2), but close to unity: deviation from an exponential is observed on different portions of the decay curve; but the larger y is, the smaller the deviations from an exponential are, even for finite decay stages. Impurity T—T1 reabsorption by excited PMMA states seems to have been observed in studies of the luminescence of europium chelates [114—116]. 2.3. On the relaxation of upper triplet states in complex organic molecules In view of the possibility of population of the higher triplet levels under reabsorption, the question arises as to what occurs in molecules after they are excited into the T~levels. The transition of the excited I,, molecules to the quasi-equilibrium T state can occur via two routes, namely either a radiationless or a radiative one. In the former case the relaxation process can take place with the participation of the excited singlet ~state. Data on triplet—triplet emission from naphthalene vapours [117] and triphenylene in n-hexane at low temperature [118] proved to be erroneous [110,119]. The possibility of a 0-switched laser based on triplet—triplet transitions was reported in ref. [120].Indirectly this indicates that the total time of triplet—triplet relaxation is not too small (T ~ 10b0 s). This is evidence that in organic molecules the triplet levels form a separate system. If this system is excited relaxation should occur to the lowest triplet state. A closed system of triplet levels is confirmed by some data [110] and experiments performed with molecules with different probabilities of conversion to the metastable state [121]. Activated cylindrical polymer blocks cooled down to 77 K were excited by flash lamps. Simultaneously their ends were irradiated by the second harmonic of a Nd:glass laser, which coincides with the T—T~absorption. The

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

365

Fig. 5. Decay curves of molecular emission in PMMA with high (a, Michler ketone) and low (b, chrysene) probabilities of conversion to the metastable state.

emission kinetics was recorded. The experimental results for all molecules studied (chrysene, coronene, Michler ketone and diketone) appeared the same. Any decrease of the population of the lower triplet state due to irradiation by a short harmonic pulse was not observed (fig. 5). The moment of excitation is easily seen in the decay curve. The appearance of a characteristic spike is due to a temporal violation of equilibrium of the I level. When the pulse is removed the population recovers, in fact, to the same level and the decay continues with the same decay constant. Estimates indicated that if there were other relaxation mechanisms of higher triplet excitations (say, via the excited singlet S1 level) in addition to the return to the lower triplet state, then for molecules with a low transition probability to a metastable state they would be easily observed in the decay curve from the decrease of the intensity after irradiation with 0-switched green light. This gives evidence that the singlet level system does not take part in relaxation processes if the transition to the metastable state is uniform for all molecules, i.e., the triplet level system is closed. 3. Temperature dependence of stimulated emission in molecular crystals Despite the rapidly developing effort devoted to the search of new active laser media, up to now a wide class of organic molecular crystals have not been studied as to their light generation properties. It is known that the possibility of stimulated emission in molecular crystals was discussed before light generation in complex molecular solutions was obtained. Apparently, these objects did not attract attention because of difficulties in the preparation of single crystals of high optical quality. Moreover, molecular crystals possess low mechanical qualities especially under high thermal cycling. However, molecular crystals have special characteristics as active laser media. Analysis of stimulated emission in these objects makes it possible to solve some problems in solid state physics and to study relaxation processes. In a doped molecular crystal a number of molecules forming the crystal lattice is replaced by other organic molecules. If the concentration of impurity molecules is not high then resonance interaction of

366

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

the molecules is negligible. As to their optical characteristics, they can be described by the oriented gas model, taking into account the interaction between impurity centres and the crystal lattice. At temperatures above 100 K the absorption and luminescence spectra of doped crystals usually present wide bands, sometimes with a vibrational structure. The spectra are similar to those of solid polymer and liquid solutions. The absorption and luminescence spectra of impurity molecules can be polarized due to their particular orientation in a lattice. Cooling down to 20 K usually leads to an appreciable

change of the electron—vibrational spectrum of a doped crystal. As a rule, the spectrum acquires a line structure, which makes it possible to obtain much information on the electronic and vibrational transition energies and lattice vibration energies. In general the optical spectrum of a doped crystal consists of narrow zero-phonon lines (ZPL) (pure electronic and vibronic transitions) and wide phonon

sidebands (PSB). Zero-phonon lines correspond to a radiative transition in an impurity centre without any change of the vibrational state of the matrix. Phonon sidebands are due to radiative transitions with formation and annihilation of phonons. The ratio of the ZPL integrated intensity to the total ZPL and PSB intensity (Debye—Waller factor) is determined by the electron—phonon interaction and the sample temperature. In pure molecular crystals population inversion of the lowest exciton band with respect to the vibrational bands of the electronic ground state is easily obtained. In doped molecular crystals there are two possibilities of population inversion (of the upper laser level): direct absorption of the exciting light by an impurity or excitation of the impurity due to exciton energy transfer from the host matrix. To generate light from doped molecular crystals it is important to select a host—impurity system. In addition to the conventional requirements to an impurity, namely high luminescence quantum yield, large absorption factor, the absence of reabsorption in the excited state and photochemical stability, it is necessary that an impurity is well embedded in the host matrix. The latter mainly defines the spectroscopic characteristics of a doped crystal at low temperatures (the narrow emission line spectrum), as well as the possibility of obtaining high impurity concentrations and a high optical quality

of crystals. While selecting a host—impurity system one should take into account the chemical structure and sizes of the components in order to obtain the most efficient laser frequency transformers. One of the problems in obtaining such frequency transformers is growing single crystals of high optical quality of substances which have high excitation energies and are transparent in the light generation region, permit fine surface working and withstand low temperatures under intense optical pumping. 3.1. Light generation by doped molecular crystals at 300 and

77 K

Light generation at room temperature was first realized in an anthracene doped fluorene crystal [23].

Anthracene is easily embedded into the fluorene lattice, which makes it possible to get single crystals of good optical quality. The crystal was excited in the impurity absorption band by a nitrogen laser (A = 337.1 nm, t~t= 4 ns, W = 1 kW). Single-crystal plates of 0.2—2 mm thick were cut along the cleavage plane (the ab-plane). The generated emission with A = 408 nm propagated normally to the

cleavage planes, which served as a natural cavity. The emission was strongly polarized along the crystal b-axis (with the larger refractive index, n1). The generated line coincided with the most intense diffuse maximum in the luminescence spectrum. Its fine structure was dependent on the active crystal length L explained by the mode structure: z~A A A n12L~

(13)

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

367

Similar results were obtained in 2,3-dimethylnaphthalene, dibenzofurane, sym-octahydroanthracene crystals doped with anthracene and in p-terphenyl crystals doped with naphthacene [122,123] (table 4). All the crystals, except for p-terphenyl with naphthacene, were grown by the Bridgman technique. Plates of 0.1—2 mm thick cut along the cleavage plane were used for these studies. Naphthacene doped p-terphenyl crystals were vacuum sublimated. The best results were obtained for anthracene in 2,3-dimethylnaphthalene. The maximum power achieved was about 100W (—40 MW/cm3), the pulse duration was about 3 ns, the efficiency 1—10%. The divergence ofthe generated emission depended on the diameter of the focussed excited spot. In the best case the generated spot was 5 mm in diameter separated from the crystal by 300 mm. When the crystal was in optical contact with a sapphire plate the generation threshold dropped abruptly. This made it possible to generate about a thousand pulses till a crater appeared in the crystal. Crystal cooling resulted in a decrease of thermal damage. Laser frequency tuning was achieved when the crystal studied was in optical contact with a plane-parallel quartz plate. The air gap between the crystal and the plate formed an additional Fabry—Perot interferometer [23]. Furthermore, partial cleavage of the crystal studied, forming a wedge-shaped air gap, did not considerably distort the cavity and made it possible to achieve frequency tuning and mode selection while moving the crystal normally to the exciting beam (by changing the active diameter of the air gap [122]). Analysis of crystals of the type of diarylethylene doped naphthalene and biphenyl indicated that at room temperature their luminescence spectra consisted of broad bands. Single-crystal plates cut from Bridgman grown crystals were excited to the impurity absorption band by the third harmonic of a Nd:glass laser (A = 353.3 nm, At = 20 ns, W= 2MW). This resulted in a sudden increase of the most intense band, which simultaneously became narrower [25]. Figure 6 shows such a change of the emission spectrum of a naphthalene crystal doped with $3~3-dinaphthy1ethylene(1313-DNE). The intensity of the band corresponding to the vibronic transition to the 1600 cm’ vibrational level increased nonlinearly. If the excitation energy density is about 0.06i/cm2, the emission spectrum presents a single line of 1 nm in width. An estimate of the gain factor k=

N*B 2

(14)

2

8i,-cz’ A~r 0n

(where N* is the concentration of excited molecules, n the crystal refractive index, v the frequency of maximum luminescence, A ~‘ the half-width of the luminescence band, and r0 the excited state lifetime) showed that if the excited spot is 4 mm in diameter (d) the amplification kd along the excited layer can Table 4 Light generation in doped molecular crystals at 300 K Impurity

Host

A (nm)

~A (nm)

Ref.

anthracene anthracene anthracene anthracene naphthacene ~~-dinaphthyIethylene ~-naphthyl-p-biphenylethylene

fluorene dibenzofuran ) 2,3-dimethylnaphthalene ~ octahydroanthracene J p-terphenyl naphthalene naphthalene

408

1

[23]

408—410

1

530 394 394

1 1 1

[122] [123] [127] [127]

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

368

~

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Fig. 6. Emission spectra of naphthalene doped with 1313-DNE (T 300K). (1) Excitation by a PRK-4 lamp; (2)—(4) excitation by UV light with an energy density of 0.006, 0.02 and 0.06 i/cm2, respectively.

I 350

400

450 A, iztn

Fig. 7. Change of the emission spectrum of a 313-DNE doped 3, naphthalene crystal with an impurity concentration of 7 x 10°cm versus crystal size (T=’ 300K). (1) Emission spectrum of a crystalline plate with PRK-4 excitation; (2) emission spectrum of a crystalline plate with 0-switched UV excitation of 0.04 i/cm2 (3), (4) emission spectra of crystal powders with UV excitation of the same energy, with crystallite sizes of 0.5 and 0.05 mm, respectively; (5) emission spectrum of a powder moistened by an immersion liquid with crystallite sizes of 0.05 mm, with 0-switched excitation.

change from 3.2 to 32 with a change of impurity concentration from 7 x 1018 to 7 x iO’9 cm3. The emission intensity 9 = l’~can change from 24 X iO’5. This amplification is sufficient for the appearance of light generation. For all the studied crystals based on naphthalene and biphenyl [124,125] the stimulated emission spectra taken from the ends and from the surfaces of the crystal plates were similar. This is evidence of

repeated reflection of the light inside the crystal due to the large refractive index. This assumption is confirmed by experiments studying the dependence of the stimulated emission spectrum on the crystal size [124].Figure 7 gives the emission spectra of a naphthalene crystal doped with 1313-DNE with stationary excitation (1) and with Q-switched UV excitation of 0.04 J/cm2 (2). (3) and (4) are the emission spectra of crystal powders with harmonic UV excitation of the same energy, the crystallite sizes being 0.5 mm and 0.05 mm, respectively. Decrease of the crystal sizes makes the emission spectrum similar to that taken with stationary excitation. The gain factor for one pass is estimated to be kd 0.05, i.e., in fact there is no amplification. However, the fact that the emission spectra of such crystals still differ from the luminescence spectra is evidence that the light repeatedly passes through the —

crystal and is amplified. Reflection decreases if the powder is moistened by an immersion liquid. Polarization studies of the stimulated emission indicated that the emission is depolarized [124].This again is evidence that the emitted light repeatedly passes through the crystal. A decrease of the crystal temperature results in some narrowing of the luminescence spectrum. For a 1313-DNE doped naphthalene crystal the luminescence bandwidth A V decreases by a factor of about 5 as the temperature is lowered from 300 to 77 K. The narrowing of the emission band leads to an increase

of the gain factor. Therefore, under intense excitation the same changes in the emission spectra are observed for lower excitation energies at the transition from room to liquid nitrogen temperature [124]. The other characteristics of the stimulated emission at liquid nitrogen temperature are the same as

those at room temperature.

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

0

2

4~em

Fig. 8. Spatial distribution of the intensity of the light generated by naphthalene doped with ~f3-DNE (1) and 3-NBE (2); l is the diameter of the spot.

369

90° Fig. 9. Direction diagram of the light generated by naphthalerte doped with 313-DNE (1) and ~3-NBE(2).

The first observation of stimulated emission from a naphthacene doped anthracene crystal excited by the second harmonic of a ruby laser (A = 347 nm) was reported in ref. [126].Stimulated emission was confirmed by a change ofthe emission spectrum with higher pumping, an increase of the intensity of the green band in the luminescence spectrum and narrowing of the band, as well as by a decrease of the emission lifetime. To generate light in a cavity [127]naphthalene crystals doped with 1313-DNE and ~3-naphthyl-pbiphenylethylene (~3-NBE)grown by the Bridgman technique were cut. The working surfaces of these crystals were first ground and then polished. Active elements of 10 x 5 x 5 mm3 were prepared in this way. An optical cavity was formed by dielectric reflectors with reflection coefficients R 1 = 0.5 and R2 = 0.8 for A 400 nm, which were in optical contact with the ends of the active element by means of silicone glue. The mirrors were aligned with an accuracy of about 2’. The excitation was transverse; the third harmonic of an Nd:glass laser was focussed onto a crystal by a cylindrical lense. The spot was 10 mm long and about 1 mm wide. The emission spectra, direction diagram and polarization were investigated. The emission spectrum was photographed by a STE-i spectrograph separated from the cavity by about 50 cm. The radiation was not focussed onto the slit of the spectrograph. Simultaneously the emission field was photographed at different distances from the cavity. The emission spectrum consisted of a single line of about 1 nm width. The radiation was polarized. Figure 8 presents photomicrographs of the spatial distribution of the emission intensity of naphthalene crystals doped with 1313-DNE and 13-NBE at 10 cm distance from the cavity for pumping energies above the threshold. The divergence of the emission was 15°for the naphthalene crystal doped with 13t3-DNE and 70 for that doped with ~-NBE(fig. 9). The large angular divergence seems to be due to insufficient optical quality of the crystals. 2 were achieved when the polarization vector generation thresholds of about 0.01 i/cm of Minimum the excitinglight emission was directed along the cavity axis and simultaneously parallel to the normal to the surface of the active element where the ordinary and extraordinary beams are. -~

3.2. Stimulated emission of doped molecular crystals at 4.2 K

Doped molecular crystals have no advantages as compared with liquid and polymer solutions when they are used as Q-switched frequency transformers or active laser elements at room and nitrogen temperatures. On the contrary, insufficient optical quality of the crystals and poor mechanical

370

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

characteristics make them incompetitive for use in quantum electronics. At low temperatures (say, 20 K) a number of advantages of doped molecular crystals appear, since under these conditions their absorption and luminescence spectra consist of quite narrow bands (about 1—10 cm~). And this considerably improves the spectral and energy characteristics of these active elements. Stimulated emission was recorded in a number of doped molecular crystals when they were excited in the absorption band of the impurity [25, 125, 127—131] and in that of the matrix [132—134].In the latter case the impurity is excited due to energy transfer from the matrix. When crystals were excited in the impurity absorption band by the third harmonic of a Nd:gass laser (A=353.3nm, At=2Ons) or a Nd3~:YAGlaser (A=354.7nm, At=8ns), stimulated emission was observed in naphthalene, biphenyl, dibenzyl, p-terphenyl and fluorene crystals (table 5). Aromatic hydrocarbons, diarylethylene and diaryldivinylbenzene derivatives as well as some heterocyclic compounds were used as dopants. In the case of crystals based on naphthalene and biphenyl plane-parallel plates cut along the cleavage planes were used for the experiments. Crystals based on dibenzyl and p-terphenyl were sawn. The luminescence spectra of most of the crystals studied are characterized by narrow lines on some continuous background [135], which is defined by the electron—phonon coupling. The narrow bands of spontaneous emission and the high luminescence quantum yield, the short excited state lifetimes (about i0~s) characteristic of the crystals studied, as well as the possibility to obtain high impurity concentrations make it possible to achieve large gain factors with relatively low pumping levels [129,130]. The gain factor (four-level scheme) for a number of crystals is estimated to be 10 n x i03 cm~[130],i.e. two orders of magnitude larger than that at room temperature. Since the gain factor is large, stimulated emission in crystals results from positive feedback due to reflection from the crystal surfaces and scattering inside the crystal, i.e. without a cavity. The emission parameters of such a generator (generation threshold, line half-width, emission divergence) are defined by the quality and perfection of the crystal. The generation threshold is sufficiently low (table 5) and the spectral density of the generated emission is high due to narrow lines. Experimentally, the generation linewidth is observed to change within 0.5—10 cm1. Simultaneous recording of the emission kinetics and the spectra with excitation of the crystal by the third harmonic of a Nd3~:YAG laser [136] made it possible to trace the evolution of the radiation as a function of pumping with an anthracene doped biphenyl crystal as an example. Light generation in this crystal evolves at 24631 cm’, which corresponds to the most intense vibronic line in the luminescence spectrum. The variation of the emission intensity ~ with the pumping power consists of two parts due to luminescence and to light generation (fig. 10). A sharp decrease of the emission lifetime is observed for excitation power densities W corresponding to the inflection point of the curve. Beginning from these values of W the emission kinetics reproduces the Q-switched excitation (fig. 11). This excitation power density is the light generation threshold. The values of the generation threshold, Uthr~ given in table 5 confirm the correct selection of host—impurity systems. On the basis of simple geometrical considerations it was shown [137] that convenient matrices for diarylethylenes and diaryldivinylbenzenes are naphthalene and biphenyl. Two naphthalene molecules in the lattice can be replaced by a diarylethylene molecule, and three naphthalene molecules can be replaced by one of diaryldivinylbenzene. The acceptable solubility of these dopants in naphthalene does not result in appreciable strains of the crystal lattice around an —

impurity and does not deteriorate optical properties of naphthalene. Naphthalene is not suitable as a matrix due to its friability. It cracks under powerful excitation at low temperatures. Its high volability requires continuous protection of the surfaces.

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

/02

~

~

k(J/em2s

Fig. 10. Emission intensity as a function of excitation power density of anthracene doped biphenyl.

371

—t Fig. 11. Emission kinetics of an anthracene doped biphenyl crystal: 2 s, and (a) excitation pulse; (b) emission kinetics for W= 5 x iO’ J/cm (c) for W=104J/cm2s.

The correspondence of molecular forms and sizes suggested that biphenyl could be advisable as a matrix for anthracene and biphenyl derivatives of ethylene (table 5). Biphenyl is relatively stable to low

temperatures and intense optical pumping. It is easily worked. P-terphenyl appeared to be a relatively stable and good matrix. The crystallographic properties of p-terphenyl are similar to those of normal paraffins. The phenyl rings in a terphenyl molecule are sufficiently mobile and can turn with respect to a single bond by a certain angle. This lability of p-terphenyl makes it possible to arrange molecules of different configurations in the lattice. However, these peculiarities are favourable for the appearance of molecules of various configurations around an impurity, which results in the formation of a large number of multiplets. This multiplet structure appears in the luminescence and light generation spectra. On the basis of the above experimental data polyphenyls present crystals of good optical quality. They endure high excitation densities, allow fine surface working and are stable under intense optical pumping at low temperatures. The main advantage of active elements based on doped crystals is their frequency stability. The light generation frequency does not depend on the pumping power, nor on the impurity concentration. For the majority of crystals smooth tuning over a small frequency range is possible without an appreciable change of the light generation parameters by varying the sample temperature. Figure 12 shows an example of such tuning. The temperature dependence of the position of the generated line is defined by that of the luminescence. As was mentioned above, the transformation coefficient of excitation to the light generation energy is high for doped crystals. For example, the transformation coefficient of the radiation energy of the third harmonic of a Nd:glass laser to the generated radiation energy at 25206 cm’ in a naphthalene crystal doped with 1018 cm ~ 1313-DNE is 25%. This large transformation coefficient makes it possible to obtain lasers ofhigh radiation volume density. For the above crystal the radiation density is 30MW/cm3 [1291. When a doped crystal is irradiated in the host absorption band, an impurity is excited by energy

372

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

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)~ 25205 252i27

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transfer from a matrix. Under these conditions naphthacene and perylene doped anthracene [132,133] was studied with excitation by a nitrogen laser (A = 337.1 nm), as well as naphthacene in anthracene and stilbene crystals, perylene in pyrene crystals and 1313-DNE in biphenylene oxide crystals excited by a frequency tripled Q-switched Nd:glass laser (A = 353.3 nm) [134]. Naphthacene doped anthracene crystals [132, 133] were sublimated hexagonal plates of about 1 ~imthick with a well-developed ab-plane (--~0.25cm2), where the pumping light was focussed. In the most perfect crystals stimulated emission passes through the plate end and is characterized by a threshold. The degree of polarization is 10—20 for pumping above the threshold. Crystalline plates of about 1 mm thick from Bridgman grown crystals were used to study doped stilbene, pyrene and biphenylene oxide [134]. Since their absorption factor is high (about i04 cm’) in the pumping region, the excitation was effective in a thin layer. Therefore, light generation in these crystals was absent; only amplification was observed. Amplification of the most intense host band was observed for small impurity concentrations [133,134]. For intermediate concentrations (of about 1017 cm3) host and impurity bands were amplified, and for high concentrations (above 5 X 1017 cm’) amplification of the impurity emission lines was observed. It should be noted that application of such systems to laser technology is improbable, since strong absorption leads to nonuniform excitation and to thermal inhomogeneities due to heating of the crystal by absorption of the excitation light. Thus, doped molecular crystals at 4.2 K excited in the impurity absorption band are effective frequency transformers of pulsed emission with a narrow stable frequency. 3.3. Stimulated emission and light generation by the exciton system Population inversion of the lowest exciton band with respect to the vibrational bands of the ground state is easily realized in pure molecular crystals at low temperatures. In that case the threshold power is defined by the intensity of the vibronic band in the entire spontaneous luminescence spectrum [6]. An anthracene crystal is a suitable object of study with intense exciton luminescence with a well-developed electron—vibrational structure. The first experiments that indicated the appearance of stimulated emission in anthracene crystals were carried out with excitation by flash lamps [138]. Changes of the emission intensity and spectral composition of thin anthracene crystals (about 0.5—20 p~m)at 4.2 K for different levels of excitation by a nitrogen gas laser (A = 337.1 nm, At = 12 ns) indicated that both the peak and the integrated intensities of the 23 692 cm~vibronic band increased nonlinearly and that it became much narrower. This band corresponds to an electronic transition with participation of the

totally symmetric 1403 cm~vibration. Simultaneously one could observe saturation of separate bands

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

375

of the luminescence spectrum due to nonlinear luminescence quenching for high exciton concentration

[141,142] and broadening of the bands as a result of crystal heating [139,140]. The dependence of the amplified luminescence line intensity and half-width upon the excitation power is determined by the crystal quality, its perfection, thickness, the diameter of the exciting spot, the way of observation and the temperature [143,144]. Such a behaviour of the emission of anthracene spectrum is related to the stimulated emission that evolves. An estimate of the gain factor K (K = 1000—2500 [138,139], K = 50 [140])showed that appreciable amplification across the excited layer was not possible because of its small thickness (about 0.3 ~m; the absorption factor at the excitation wavelength is 3 x i0~cm’). The amplification can become as high as about i04 along the excited layer when the spot size is 0.1 mm [120].In such a case one can observe both amplification and generation if feedback occurs due to the weak scattering. The assumption of emission amplification along the excited layer is confirmed by polarization studies [145].The degree of polarization of the initial 25 051 cm’ line does not change with increasing excitation energy. The polarization ratio for the amplified line decreases from 6.8 to 1.8 and in some cases to 1, i.e., total depolarization of the emission occurs. When the crystal temperature decreases from 4.2 to 1.5 K, the amplification effect appears for much lower excitation intensities (approximately a factor of 3) [145].This is connected with the line narrowing in the luminescence spectrum and, hence, with an increase of the gain factor. In the most perfect sublimated crystal plates the amplification of the 23 692 cm~band in surface emission was considerably smaller than that in end emission (by a factor of 10—20). The band half-width of the end emission is somewhat smaller than that of the surface emission [144].Consequently, stimulated emission emerges mainly from the crystal ends. The emission anisotropy decreases in imperfect crystals. Thick crystals with the smallest number of defects have an especially large anisotropy. In the most perfect crystals amplification of the 23 692 cm~band is observed up to 170 K, when A v is nearly doubled. The results are accounted for by light generation in the framework of the theory of ideal modes of a dielectric thin plate [144]where the total internal reflection is formed on the crystal faces due to the high refractive index (n 1.5—2). The angular divergence of a cavity in the form of a thin crystal plate is large. Analysis of the most perfect anthracene crystals studied [144]shows that light generation in the 23692 cm~luminescence band maximum begins at a conventional threshold pump intensity ~ 1 /S A v (S is the excited area; A v the luminescence bandwidth). For pump intensities ~ > I~all the crystal radiation is emitted in the amplified band: amplification appears along the largest linear crystal dimension. Light generation takes place between parallel end faces with total internal reflection and repeated passes through the active region. The emission output in other directions is due to defects, and increases with their number. Measurements of the intensity distribution over the crystal face indicated that the emission consisted of a few channels of about 0.1—0.5 mm. The surface density of the generated power reaches approximately 100MW/cm2 in such a channel. ~

3.4. Stimulated emission and stimulated Raman scattering in some molecular crystals Strong excitation of molecular crystals makes it possible to tune the Q-switched emission due to stimulated Raman scattering. While studying the stimulated emission of anthracene crystals, the light generation was observed to evolve in the the most perfect optical parts of the crystal, namely channels. In this case some workers succeeded in obtaining a generated power of about 0.4 kW from both crystal

376

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

ends by adjusting the pumping according to the dimensions and directions of the most favourable crystal areas [146,147]. This corresponds to a generated power density in the channel of about 2 x 108 W/cm2. Stimulated Raman scattering was observed in anthracene crystals under such conditions [146,147]. The source of excitation was the crystal’s own light generation at 23692 cmt. Stimulated Raman scattering was observed at 22292 cm’ (the second electron—vibrational transition with the totally symmetric 2 X 1403 cm’ intramolecular vibration) and at 20886 cm~(with the 3 X 1403 cm’ vibration). In other words, stimulated Raman scattering was observed in anthracene crystals on the totally symmetric 1403 cm’ vibration and its 2 x 1403 cm’ harmonic. The fact that these lines originated from stimulated Raman scattering was confirmed by the separation between the spectral lines and the excitation line, the threshold for the appearance of the line, the scattering bandwidth, the same as that for anthracene, and the nonlinear increase of these lines with increased pumping. The gain factor of the scattered Stokes wave is 2—3 cm~for the above generated light intensity [147]. The observed nonlinear increase of the band intensity of stimulated Raman scattering results from the multipass amplification and feedback due to reflections from the crystal ends. When an anthracene crystal of 5—30 ~imthick was excited by a tunable dye laser near the bottom of the excitation band a sharp increase of the Raman scattering line intensity with the intramolecular 1403 cm1 vibration was observed. Moreover, a drastic decrease of its intensity was found in the vicinity of the resonance [148,149]. The nonlinear dependence, anomalously high intensity, as well as the nonlinear increase of the scattered intensity with increasing sample thickness gave evidence of the stimulated character of the scattering. Up to nine Stokes components were observed on the 395, 1167 and 1403 cm’ intramolecular vibrations for a pumping level of approximately 3MW/cm2 [150]. In anthracene crystals two different ways of amplification of the emitted light can be bound in the active volume during Raman scattering: on the modes of total internal reflection with feedback due to reflection from the perfect end faces, or in a specific cavity whose length coincides with its thickness. In this case feedback appears due to the reflection from the developed parallel surfaces. In the former case, in fact, all stimulated Raman scattered light passes through the crystal ends, in the latter it goes along the normal to the surface [150]. Preresonant stimulated Raman scattering was also observed in naphthalene, p-terphenyl and stilbene crystals [151], which were excited by the third harmonic of a Nd3~:YAG laser (A = 354.7 nm, pulse duration iOns and linewidth 0.2 cm1) at 1.6 K. Plates of 1—2mm thickness cut from a Bridgman grown single crystal were the objects of study. The stimulated character of the scattering is confirmed by the threshold for the appearance of lines in the emission spectrum, their nonlinear dependence on the pumping energy and the linewidth being the same as that of the excitation. In all the cases scattering with totally symmetric vibrations is observed. Figure 13 gives the line positions of the stimulated Raman scattering (in brackets the vibration where the scattering occurs). The band positions of the 0—0 transition of the crystals studied are indicated as well as that of the excitation line. As can be seen in the figure, the 26 800 cm1 line is separated from the excitation line by 1380 cm’. As the pumping energy increases, a second line appears at 25410 cm’, separated from the excitation line by 2 x 1380 cm’. The 1380 cm1 vibration is totally symmetric and is the most intense in the Raman scattering spectrum of naphthalene [152]. A change of the pumping power by 15% results in an increase of the intensity of the first Stokes component by more than an order of magnitude. The naphthalene absorption band ends at 318 nm (31 477 cm1 0—0) [153]. Strong stimulated Raman scattering in naphthalene with the participation of the 1380 cm1 mode with —

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

I

.5.—

377

Os

)‘exc 28184~~ ‘~—

~ t?~hE/~cn’°e,7e

‘s.-.

I C

I,

,o- te~henv~°

I ~ ~::

5

V~4~i.~k ~

~

JZ’i~e,7e ~ Fig. 13. Positions of the excitation line and of the 0—0 transition and Raman scattering of the crystals studied. Vibrations participating in the scattering are given in brackets.

irradiation of the crystal by the Q-switched emission of a ruby laser [154]made it possible to double the stimulated Raman scattering frequency using a KDP crystal. In the case of p-terphenyl, whose 0—0 band is at 30 147 cm~[155],two Stokes components can be observed on the 1590 cm’ intramolecular vibration. The direction diagram ofp-terphenyl scattering for transmission indicates that in the most perfect crystals the maximum scattered intensity of the first Stokes component is observed in the direction of propagation of the pumping beam. Its degree of polarization is 0.56. The transformation coefficient of the pumping power to that of the first Stokes component of stimulated Raman scattering is about 10% for the above crystal. For stilbene the absorption and fluorescence spectra at low temperatures overlap [156—158], which is connected with the presence of dopants and defects in the crystal. The 0—0 transition is at 29 600 cm’ [158].Stilbene is excited in the absorption of its defects. This excitation does not coincide with the absorption lines. Under these conditions the first Stokes components of stimulated Raman scattering and their second harmonics at 996 and 1660Raman cm’ inscattering the Raman were intramolecular observed for a vibration pumping 2 [159]. Stimulated on spectrum the 1600 cm1 level of about 4 MW/cm was observed in a stilbene crystal at 77 K [160].Threshold conditions with the 1660 cmt vibration were achieved with excitation by ultrashort pulses of the third harmonic of a Nd:glass ‘aser at 4.2 K [161]. It should be noted that for the crystals studied the lowest threshold of stimulated Raman scattering was observed for stilbene, which seems to be connected with the fact that the excitation line lies closest to the 0—0 transition (about 1400 cm~).In p-terphenyl (v 0_0 ~‘exc= 2000 cm~)the threshold is a factor 1.5—2 higher. And in naphthalene (v00 = 3300 cm~)it is about a factor 10 higher than in p-terphenyl. We failed to perform an experiment with stimulated Raman scattering in biphenyl, where 1. theTemperature absorption band is separated from the excitation line by about 5000 cm effects on stimulated Raman scattering have not been studied in detail [151].However, it should be noted that the intensity ofthe stimulated Raman scattering line in p-terphenyl decreases by —

—

378

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

several times when the temperature changes from 1.8 to 4.2 K. At room temperature and with pump intensities as high as possible, stimulated Raman scattering was not obtained in the crystals studied. In

p-terphenyl amplification of the first Stokes component of Raman scattering was observed on the 1590 cm~vibration. In all the crystals studied [151] amplification is observed in the active volume during Raman scattering due to feedback by light reflection from the crystal faces and inhomogeneities inside the crystal. The more perfect the optical quality is, the more the directional diagram is extended in the

direction of the pumping beam. 4. Effect of relaxation of vibrational levels on stimulated emission Recently much attention has been paid to relaxation processes in complex organic molecules and crystals. It is known that the spectral and luminescence characteristics of complex molecules and, hence, the stimulated emission parameters depend on the vibrational relaxation of molecules in the ground and excited electronic states. Radiationless relaxation processes in the excited electronic states of large molecular systems are of great importance, in controlling the conversion of an absorbed quantum to an emitted one. Appreciable progress in vibrational relaxation studies was achieved with the advent of lasers. At present different methods of quantitative study of molecular vibrational relaxation are being developed, namely, direct measurements of vibrational relaxation lifetimes using ultrashort pulses and picosecond resolution [162—173], hot luminescence [174—190], hole burning [171—178], Raman scattering spectroscopy [168, 199—201], intracavity relaxation spectroscopy [202— 205], coherent effects [206—210], stimulated emission, etc. Many data are available on the relaxation times of vibrational levels of the excited states in solutions and crystals. However, such data on the relaxation of the ground states are not sufficient. Vibrational relaxation in molecular crystals is studied mainly in three ways, namely, by hot luminescence, hole burning and coherent effects. 4.1. Hot luminescence and relaxation processes in crystals Hot luminescence (HL) is the luminescence from vibrational levels of the excited electronic state that is emitted until thermal equilibrium of a luminescence centre with the environment is established. In the case of a mixed molecule thermal equilibrium is established with the crystal vibrations. HL allows us to estimate intramolecular vibration lifetimes and to define their decay channels. Since HL is emitted from nonrelaxed vibrational levels at 4.2 K when thermal population of vibrational levels is practically impossible, vibrational level lifetimes can be indicated by the HL kinetics or, in the case of stationary excitation, by the HL line intensity relative to normal luminescence. Under steady-state irradiation of a sample luminescence is excited by narrow spectral lines with a width comparable to zero-phonon linewidths. These lines are resonant with the absorption lines of a luminescence centre. The HL line intensity depends on the excitation frequency as follows. When the excitation frequency becomes insufficient to populate the initial level of a given series of hot luminescence lines the series disappears from the HL spectrum.

The lifetime of a vibrational level ~ for independent vibrations is of the form [175] -

(i(a)~(i(~

T(~)_To~i(0))ki(00))

~_0)\1 ,

(15)

V.V.

Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

379

where is the lifetime of the electronic state, i(~—+ a)/i(0—a a) the intensity ratio of a hot line (~ —a a) and a normal luminescent line (0—a a). The last term is determined by the absorption spectrum. In this way lifetimes of vibrational levels have been obtained in the first excited singlet state of anthracene and t), 1.3—3.2ps perylene molecules in various matrices at 4.2K [179,1181]: 4—6ps (1500cm (1400cm1), 2.7ps (1160cm~)and i8ps (400cm’) for anthracene, and 10—lips (1580cm1), S—2Ops (1380cm1), l3—Z3ps (1300cm1) and 35—55ps (360cm1) for perylene. Besides, the relaxation channels of the vibrational energy in the S~state have been obtained. The decay time of the 1426 cm~1vibrational state of naphthacene in p-terphenyl was determined to be 2(±)ps [182]. Direct observation of the time dependence of the emission intensity of the vibromc line using a picosecond spectrochronograph made it possible to determine relaxation times of vibrational levels of perylene in n-heptane at 4.2 K: 15.7 ±2.5 Ps (900 cm~), 21 ± 1.7 ps (710 cm’), 26 ±2.2 ps (540 cm’), and 25 ±0.5 ps (360cmt) [183].Analysis of HL kinetics of naphthacene in solid argon and methylcyclohexane at 10 K indicated that a vibrational state could be nonrelaxed for about 40 Ps [184]. On the basis of the above considerations and studies ofgaseous organic molecules [185,186] it can be concluded that a complex organic molecule has quite a lot ofinternal degrees of freedom, which totally determine the relaxation characteristics of the initial vibrational state. However, in a rarefied gas, for example, energy redistribution can be delayed by gaps in the quasi-continuum of vibrational states. When these gaps are occupied by phonons of the matrix in which the impurity molecule is embedded, the internal thermostat begins to act. Therefore, vibrational level lifetimes and relative weights of relaxation paths through different vibrations are weakly dependent on the matrix (phonon subsystem). The relaxation kinetics is mainly determined by internal interactions. If a molecule is a component of the crystal unit cell (as in the case of a pure molecular crystal) HL decays faster than in a doped system [187—190]. It was shown with an anthracene crystal as an example [189]that spreading of the vibronic excitation over the energy scale is continuous. The spreading time depends on the interaction between excitons and the intramolecular vibration. The anthracene vibronic lifetime was estimated to be r <0.1 ps [190]from the relative HL line intensity corresponding to the intramolecular vibration at 395 cm~,and from the decay time of anthracene luminescence (Cr 0 = 2 ns). Vibrational relaxation times in the ground state are much longer. Thus, vibrational relaxation in the ground state of a naphthalene by active Raman scattering picosecond spectroscopy gives 4Ops (511crystal cm1),studied 5ps (701 cm~),78ps (766cm1), Sps (863cm’) and 92ps 74ps (493cm’), l (1385 cmt) [168]. T

0

4.2. Hole burning and excited state relaxation

The hole burning effect in the absorption curves of solutions or doped crystals at 4.2 K with monochromatic radiation was found in 1974 [191,192]. It results from the selective removal of those centres that constitute the inhomogeneously broadened contour of the absorption band and have transition energies in resonance with the excitation frequency. Of great interest is the possibility of using hole burning to study vibrational relaxation in the excited and ground electronic states. At sufficiently low temperature the excited state lifetime T 1 is determined from the half-width 1’ obtained

by hole burning, viz. [193], T1

=

(2’nfl’.

380

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

The first attempt to define relaxation times of the vibrational levels of the S1 state was made for 1 vibrational sublevel proved to dimethyl-s-tetrazine durene of at 2a K [194]. The lifetime of the 523 cmof the S~state were obtained by be about 5.5 ps. Theinlifetimes large number of vibronic sublevels the hole burning technique: for tetrabutylphthalocyanine in nonane it is 1.9 Ps (515 cm 1) [195]; for different sublevels of the S 1 state of porphin in n-octane 0.9—3.6 Ps [196] and 7.5 ps (1050 cm’),1)and and 3O—4Ops (710 and 1160cm’) [196]; for tetrabenzoporphin in a glassy matrix 3.Sps (1108 cm~ 3.2ps (1302 cm1) [197].

Vibrational relaxation in the ground state can be studied by hole burning in the infrared absorption bands. For example, by irradiation of 1 ,2-difluoranthene in the infrared band at 2.4—24 K, a lifetime of 5 ns for the 1048 cm~vibration was obtained by extrapolating the hole width to zero temperature [198]. Thus, at present many data are available concerning the relaxation times of vibrational levels of the excited S

1 state of impurity molecules in crystals [167, 177—185, 194, 206—210]. The lifetimes of the S~ state of impurity molecules in crystals are about 10 12 s. In fact, literature data on the vibrational relaxation of doped crystals in the ground S state are not available, except for a single work on hole burning in the infrared absorption spectra [198]. The lifetimes of the vibrational levels of the ground states of some organic molecules in solutions are 10_h1_10_12 s [163,166, 199], and the lifetimes of totally symmetric intramolecular vibrations are 10~lo_10_ ~ s [204]. For polymethine dyes in solutions the lifetimes of the vibrational levels of the dopant molecule are estimated to be 10 ~s at 4.2 K [211]. 4.3. Lifetimes of vibrational levels of the ground state of dopant molecules determined by stimulated emission

Stimulated emission of doped molecular crystals studied at 4.2 K makes it possible to determine the lifetimes of vibrational levels in the ground state [133,212—216]. It is well known that the luminescence of a doped crystal has a duration of 10 8_ ~o s~.Sometimes the development of stimulated emission in such systems permits increasing the emission rate by two orders of magnitude when used in a 0-switched cavity [217].Under these conditions, in molecular crystals at low temperatures, relaxation processes of final vibrational levels can affect the amplification character and the energy characteristics of the laser output. This is the case when thermodynamic equilibrium fails to be established during stimulated emission on the ground state vibronic levels. If the relaxation rate of the corresponding finite vibrational level for the most intense transition is less than that for one of the neighbouring levels, then the relative intensity of stimulated emission for the most intense transition can decrease due to population of other vibrational levels. In that case the vibronic energy will be more effectively transferred to the lattice in channel 2, where the stimulated emission process evolves [212]. A similar situation was observed in a Nd:glass laser when the final state (the electronic level) was strongly populated in the regime of giant pulses. The relaxation time of this level is quite long (10~8s), which leads to a decrease of the laser output energy by 30% [218—220]. 11/2

As a rule, stimulated emission in doped molecular crystals develops on the most intense vibronic transition [130].In some crystals generation of several frequencies is observed: first, the most intense vibronic line in the luminescence spectrum is amplified. An increase of the excitation energy results in saturation of the stimulated emission intensity at this frequency, and a second, less intense line in the luminescence spectrum begins its lasing action and shows a nonlinear increase [212—215]. The emission spectra of P~-NDVBand 1313-DNDVB and the dependence of the stimulated emission intensity and the kinetics of naphthacene in dibenzyl on the excitation are examples of the generation of several frequencies (fig. 14) [136].The stimulated emission spectrum of naphthacene in dibenzyl

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

381

1 ~

~

Fig. 14. Luminescence spectra of molecular crystals of naphthalene doped with (a) P~-NDVBand (b) ~43.DNDVBat 4.2 K. Generated lines are indicated by an arrow.

consists of two lines: first, the most intense line of the luminescence spectrum (at 25258 cm1) is amplified, and as the excitation energy increases the second line (at 19 182 cm~)appears in the emission spectrum. Figures 15 and 16 show the evolution of the stimulated emission in this crystal. When the 25258 cm’ line reaches the threshold of light generation, an inflection point is observed in the dependence (curve I) of the emission on pumping (fig. 15). The duration of the emission pulse decreases down to that of the excitation pulse (fig. 16). Further increase of the excitation energy results in the appearance of lasing action at 19 182 cm~,which is seen by a sharp rise of the intensity in curve II and a decrease in curve I. Besides, the duration of the emission pulse at 19 182 cm’ is shortened from that of a luminescence pulse to that of an excitation pulse (fig. 16). In this case the shape and position of the stimulated emission pulse at 19 182 cm1 and at 25 259 cm1 are the same as those of the excitation pulse. We failed to detect the transition from one channel of light generation to the other (the delay in light generation in channel II with respect to channel I and the excitation pulse). This is evidence of a rapid decrease ofthe population inversion in channel I, which, in its turn, is related to the decay rate of the quasi-equilibrium level in light generation and the small time resolution of the detection system (ELUFT) as compared with T 55~.According to the above studies 2 x i0~s (the ELUFT resolution limit) [136]. The assumption of violation of thermodynamical equilibrium [124,128] in the ground state vibrational levels during the stimulated emission of impurity centres in a molecular crystal has been analysed in ref. [212]. Tgen

382

V. V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

512s

.

I ‘4

4

/0’

/0

/0

_

W,J/cm~’s

—~

Fig. 15. Emission intensity of a naphthacene doped dibeuzyl crystal versus excitation power density for the 25258 cm1 (I) and 19182 cm1 (II) lines,

t

Fig. 16. Emission kinetics of a naphthalene doped dibenzyl crystal. (I) The 25291cm’ line; (II) the 19182cm’ line. (a) Excitation pulse. For I, (b) W~=5 X i0~i/cm2 s, (c) W= i05 i/cm2 s. For II, (b) W— 1O~i/cm2 s, (c) W~=106 J/cm2 s.

In order to describe the stimulated emission process in doped molecular crystals, let us consider the energy model of an active centre shown in fig. 17 (the crystal is excited in the impurity absorption band). Let optical transitions occur from the same level to different vibrational sublevels of the ground state. Let us suppose that the relaxation time r 1 of the vibrational level for the most intense transition is comparable with the optical transition time (T1 r0) and that r~~ r0. Then, according to ref. [212],the balance equation for the generation of several frequencies is of the form -~

4Z,P11~

—

PumP.~

where

~pump

,

is the pumping power,

‘~thr

16

( )

V1-(~/Y1)(~-~~)’

the threshold for generation of the most intense line in the

—

3—

______

Fig. 17. Simplified energy level scheme of an impurity molecule.

V.V. Eremenko and L.A. Ogunsova, Stimulated emission and relaxation processes in molecular crystals

383

luminescence spectrum, z the area under the ith curve (E z. = 1), Y1 and Y1 the intensities of the most intense line and the ith line, respectively, ~ and e, quantities proportional to the populations of the upper ~ level, N, and the ith vibrational sublevel, N~,of the ground electronic state (populations are dimensionless). The population equation for the ith vibrational level, taking into account its relaxation time, is [212] 17

\/1(~~)(Y1/Y1).

~tTo

For the case when the luminescence spectrum of the crystal consists of two emission lines with different intensities (Y1> Y2) corresponding to the transitions to vibrational levels with relaxation times Cr2 4 r0, i~ r0, the light generation intensities were computed for various values of Y2/ Y1 and different ratios r11r0. Figure 18 shows that for low pumping energies the line corresponding to the most intense band in the luminescence spectrum begins lasing action. Intensity redistribution between the light generation lines occurs the faster (for low pumping intensity), the higher r1 is, and the less their intensities in the luminescence spectrum differ. The experimental data are in good agreement with the calculations. They were obtained for various crystals. Figure 19 presents an example of such a behaviour of the stimulated emission spectrum for naphthalene crystals doped with 1313-DNDVB and P~-NDVB.The experimental curves as well as the luminescence spectra make it possible to estimate the relaxation times of the ground state vibrational levels. Considering eq. (16) for the case of two generating lines with frequencies v1 and v2, we obtain the ratio Cr1/T0 for the excitation energy at which the light generation intensities of these lines are equal, Ppump(Ii = p2). Under these conditions the expression for r1/r0 is as follows [130]: 2+(~~1)cy2 (18) Cr1 Cr

0

~

cy

~pump’~thr

2

0

5

tV

/5J

Fig. 18. Calculated changes of the intensity of light generation lines as a function of pumping intensityf fory= Y 2/Y1 =0.3 (la, 2a), r,Ir,= 0.5 (1) and 6 (2).

0

t~’2 1?4

~f/ein

0

QI

Q3

Q2

Q* aj/cflz2

Fig. 19. Light generation intensity of naphthalene lines with (a) P~-NDVB as dopant: (1) 24091cm’’, (2) 22652cm’; (b) DNDVB as dopant (1) 23694cm’, (2) 22256cm~.

~.

384

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

where P c=

(1+y) yi thr~”i) ~

~

,

b=yc,

~=(—b+Vb2+4c)I2,

y is the intensity ratio of the lines at the frequencies v~and v~in the luminescence spectrum. Table 6 gives the relaxation times of the ground state vibrational levels of the impurity in a number of doped crystals. It is seen that the relaxation rates of the ground state vibrational levels can have different values. The relaxation times are determined by both the impurity molecule and the matrix in which it is embedded. Comparison of the relaxation times in the ground state determined by stimulated emission with those

in the first excited electronic state of perylene [179,181] and naphthacene [182,210] shows that in the ground state relaxation of the vibrational level is slower by an order of magnitude. As mentioned above, the vibrational level lifetimes in the ground state of a pure naphthalene crystal are about 10 10 s [168].That is three orders of magnitude longer than the anthracene vibronic lifetime at 395 cm in the excited state [183]. The lifetime of the 1048 cm’1 vibrational level obtained by hole burning in the infrared absorption spectrum is also long (5 ns) [198].Analysing the results it can be assumed that the interaction between the vibrations of the impurity centre in the excited state of the crystal is stronger than in the ground state, which influences the relaxation times. This assumption is confirmed by the broad absorption spectra of doped crystals in the excited state at low temperatures [62,85], while the usual absorption and luminescence spectra are line spectra. Long lifetimes of the ground state vibrational levels in doped molecular crystals allow us to expect 1

the possibility of radiative transitions in the infrared spectrum, and hence, the possibility of light generation [130]. But the estimate [221] A 21

=

~

(19)

,

taking into account the frequency w in the infrared and visible regions, indicates thespectrum. radiative 3 lower than in the that visible probability the A21 quantum for infrared is at least a factor i0 Therefore, yieldtransitions of these processes is vanishing. Table 6 Lifetimes of ground state vibrational levels of an impurity molecule in a crystal Matrix

(cm~)

Vibration (cm’)

r

Impurity

(s)

Ref.

naphthacene

dibenzyl

20258 19 182

317 1388

9 x i0~~

[2161

3-naphthyl-p-biphenylylethylene

naphthalene

25207 23585

1629 2x1629

~3~3-dinaphthyldivinylbenzene

naphthalene

23694 22256

phenyl4l-naphthyldivinylbenzene

naphthalene

perylene

anthracene

Vg~fl

10

[216]

146 1584

2 x 10~hl

[216]

24 091 22652

149 1587

5 x i0~°

[2161

21822 28849

357 1380

3

[133]

x 10_b

10~”

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

385

5. Optical transitions stimulated by nonequilibrium phonons Generation and propagation of nonequilibrium phonons through a system and their effect on the emission characteristics are important and should be taken into account with intense pulsed excitation of molecular crystals cooled down to helium temperatures. The luminescence of molecular crystals is

always accompanied by the formation of additional phonons (heat release). It is connected with fast relaxation to a quasi-equilibrium level prior to the emission. Moreover, the vibrational level system of the ground state is occupied by nonequilibrium phonons due to radiative electronic transitions. It is of great importance for crystals with strong electron—phonon interaction.

Since elementary excitations play an important role in relaxation of highly excited systems, the effect of nonequilibrium phonons on the spectral and kinetic characteristics is being studied both theoretically

and experimentally [222—232]. 5.1. Generation of nonequilibrium phonons and propagation in anthracene crystals In addition to the conventional ways of forming nonequilibrium phonons in anthracene crystals (fast

relaxation of electronic excitation to the lowest exciton band, exciton relaxation and luminescent electronic transitions), there appear some additional channels of heat release with increasing exciting light intensity. They are connected with the interaction between excitons and are nonlinearly dependent on their concentration [141,142]. Under these conditions the crystal emission yield decreases to 0.1, i.e., in fact the entire energy incident on a crystal is transformed into phonons [233]. In an anthracene crystal the exciting light is absorbed by a relatively thin surface layer (~0.5p~m).

That leads to the formation of nonequilibrium excitons in the absorption layer with lifetimes of about 0.5 ns [233].In this period most ofthe absorbed energy is converted from electronic to phonon energy. In such a case, high-frequency optical phonons are formed first (intramolecular vibrations); then high-frequency phonons are converted into low-frequency ones, and finally, acoustic phonons appear. Before the appearance of acoustic phonons the entire relaxation process is localized in the absorption layer since the propagation rates of excitons and optical phonons are small. Besides, this relaxation process is fast; the characteristic relaxation time of vibrons is 10 12~ ~o s. Acoustic phonons can leave

this layer for real time intervals since the velocity of light in an anthracene crystal is 2 x [233,234]. The absorbing layer can be regarded as a source of acoustic phonons.

106

cm/s

When one of the surfaces of a thin anthracene crystal plate was excited by a nitrogen laser, the nonequilibrium luminescence spectrum was detected. This luminescence was excited by an amplified

probe pulse of a second laser delayed with respect to the pumping pulse and directed to the front or back crystal surface. The width zI v of the 23 692 cm zero-phonon vibronic line (0—0 1402 cm’) and the intensity ratio R of the 25 036 and 25 051 cm~lines were measured in the multiplet of the phonon sideband of the 0—0 transition [235].zI v oscillates in time both at the front and at the back surface. The -

—

mean values of z~ v where oscillations occur depend on pumping intensity and temperature. These oscillations of the nonequilibrium characteristics are connected with successive reflections of phonons

from the plate surfaces [236].The perturbation propagation rate estimated from the oscillation period and the time required for a phonon to reach the back surface (the dependence of R on the delay time) are 1—3 X i05 cm/s, which is close to the sound velocity. Nonequilibrium can propagate ballistically or hydrodynamically [236,237]. The semiquantitative theory of nonequilibrium phonon propagation in an anthracene crystal neglecting the crystal anisotropy [238] is based on the fact that phonon relaxation occurs simultaneously with phonon propagation and the phonon spectrum continuously is shifted

386

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

towards lower frequencies. In this case phonon propagation continuously changes. New unidentified regimes of propagation appear. 5.2. Effect of nonequilibrium phonon on the emission from doped molecular crystals One of the peculiar features of stimulated emission in doped molecular crystals with strong electron—phonon interaction at 4.2 K is the appearance of a band in the light generation spectrum under the high laser excitation that corresponds to the spectral region of the phonon sideband. The intensity ratio of ZPL and PSB changes with excitation energy. This is explained by the effect of nonequilibrium phonons on the evolution of stimulated emission in the impurity centres [239, 240]. As an example, consider the effect of nonequilibrium phonons on the light generation processes in two doped crystals where the integrated intensity of the PSB in the ZPL + PSB band of the luminescence spectrum is more than 50%, i.e., a ~0.3 (1313-DNE and P13-NDVB in naphthalene, denoted as crystals I and II, respectively [241]). The dependence of the ZPL light generation intensity on the pumping energy for the crystals studied is complicated. The ZPL light generation intensity reaches its maximum value for a certain pumping energy density. After this a fairly sharp decrease is observed (fig. 20a,c; curve 1). The dependence of the PSB light generation intensity (25 160 cm~’and 25613 cm’~)for crystals I and II, respectively, on the pumping energy is nonlinear (fig. 20a,c; curve 2). The total intensity of the light generation band (equal to the sum of the ZPL (1) and PSB (2) integrated intensities) is proportional to the optical pumping energy (fig. 20b,d; curve 3). This demonstrates that the emission energy is transformed from one channel to another without losses, in the present case from the ZPL to the PSB. Such a redistribution of the light generation intensity over the ZPL and the PSB is not due to crystal heating during the excitation pulse [239]. Figures 21 and 22 give the results of temperature studies for a

~OO~

o ~ ~ ~J/cm’,~.,O ~ ~?E ~J/em’

2O

o

~ O

~2 ~çJ/cin

5

10

~f

4’2

~J/c~n2

/5/ j.~I O/2345BJ

Fig. 20. Peak, f, and integrated, S, intensities of the stimulated emission of the ZPL (1) and the PSB (2) and the total intensity of the ZPL and the PSB (3), as a function of excitation energy, for naphthalene doped with I3~3-DNE(a. b) and P~3-NDVB(c, d); (e. f) calculated dependences of Son the pumping power f.

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

a

:

~

/0 2030 ~A’

0 sV 2030 4i9 7~4

Fig. 21. Emission frequency of the ZPL (a) and the PSB (b) as a function of temperature.

387

/0

20 30

~O ~7~’

Fig. 22. Stimulated emission intensity of the ZPL (1) and the PSB (2) as a function of temperature.

1313-DNE doped naphthalene crystal. The stimulated emission lines are shifted towards the UV with increasing crystal temperature (fig. 21). Both the ZPL and the PSB intensities decrease with increasing temperature (fig. 22). But that of the ZPL decreases faster, since as the temperature rises the ZPL intensity in the luminescence spectrum decreases with respect to that of the PSB [242]. If the above effects (fig. 20) were due to crystal heating as a result of Stokes losses, one would expect that the emission frequency changes with changing pumping power. At the same time, at 4.2 K both the ZPL and the PSB frequencies in the stimulated emission spectrum of the entire crystals studied are independent of the pumping energy. The separation of the ZPL and the PSB in the stimulated emission spectra remains. Moreover, if the diameter of the exciting spot on a crystal decreases from 5 mm (fig. 23a) to 1 mm (fig. 23b), the stimulated emission intensity at the PSB frequency decreases strongly compared to the ZPL intensity with the same pumping power density. These experiments show that the nonlinear increase of the stimulated emission at the PSB frequency is due to the ZPL + PSB band intensity rather than to crystal heating with intense excitation.

The complicated character of the changes of the ZPL and PSB light generation intensities with increasing pumping power cannot be accounted for by the influence of the relaxation times of final

vibrational levels of the ground state of the impurity molecule [213,216], since the ZPL light generation intensity is observed to decrease and not to be saturated. In this case the above mentioned effect seems to be reasonably explained by nonequilibrium phonons participating in light generation on the vibronic

0

b~/

4’E Q3

~<

0

‘V

4’2

~73 aj/emZs

IC 0

‘V

‘.~

J/Ct77~S

Fig. 23. Stimulated emission of the ZPL (1) and the PSB (2) of a naphthalene crystal doped with ~-DNE, versus pumping energy density. (a) Excitation spot diameter 5 mm, (b) 3 mm, (c) 1 mm.

388

V.V. Eremenko and L.A. Ogurtsova. Stimulated emission and relaxation processes in molecular crystals

transition of the impurity centre. It can be expected that in light generation at the ZPL frequency the formation of phonons influencing the kinetics of the vibronic transition is stimulated by the electron— phonon interaction. This effect should depend on the strength of the electron—phonon interaction (a) and on the light generation mechanism and the relaxation of nonequilibrium phonons. The PSB light generation lines are separated from the ZPL by 43 ±3 cm which corresponds to the PSB maximum in the luminescence spectra. Their position is independent of both the impurity concentration in the crystal and the excitation energy. A comparison with neutron scattering studies at 4.2 K [243] and with the calculated phonon density of states p(u) [244] shows that the positions of the PSB light generation lines coincide with the maximum of the phonon density of states in naphthalene. Furthermore, phonons at 43 ±3 cmt are known to correspond to the lower boundary of an optical branch of the naphthalene phonon spectrum. Now let us consider the emission kinetics of doped crystals taking into consideration all possible relaxation processes in the system including the phonon effect. Let the crystal be excited by light with frequency ~pumpto vibrational level 5 (fig. 24). From this level fast nonradiative relaxation occurs to quasi-equilibrium level 4. Stimulated emission from level 4 can evolve via two channels, namely on the 4—2 transition (ZPL) with i.~ and on the 4—3 transition (PSB) with i.~. Vibrational levels 2—3 are separated from the main level by more than 1500 cm~, therefore, at 4.2 K these levels are not populated. Population inversion of the pair of levels 4—3 and 4—2 is defined by the population of level 4. Changes in time of the population of level 4, N, the emission density in the ZPL, g 0(P), and in the PSB channel, g1(P), and the nonequilibrium phonon density can be written as [245] ~‘,

=

W— A;)

£9g11(P)

B

—

g0(P) +

=

g0(P)

—

Az~hi.’1~N + B

c

0g(P)

=

—~

‘~

+

Z() -~

+

P)N

—

B

(1

+

P)g1,

(20)

(21)

g~(P)h1.~)N,

1)

g(P) =

Az1(1

z +Az1ht1(1+P)N+B~hii1(1+P)g1N,

Az1(1

+

P)N+ B

(22)

(1 + P)g1N,

(23)

where W is the bumping density, Az0 and Az1 are the probabilities of spontaneous transitions in channels 4—3 and 4—2, respectively, z0 and z1 are the relative integrated luminescence intensities of the ZPL and PSB (z0 + z1 = 1), B is the Einstein coefficient of stimulated transitions in these channels; p~,

~

~

__

Fig. 24. (a) Simplified energy level scheme of an impurity molecule and (b) the contour of ZPL

+

PSB luminescence band.

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals i.’~,I~,and

389

are the frequencies and half-widths of the ZPL and PSB, respectively, T~is the phonon lifetime, P the number of occupied phonon states, g1 the emission density in the phonon sideband ~‘1

channel independent of nonequilibrium phonons. We confine ourselves to the case when a phonon with a certain wave vector k 0 takes part in the light generation. Optical phonons with I k~>0 are negligible since their fission into acoustic phonons is much faster. By solving the set of equations (20)—(23) for the steady-state case (since the pulse duration is about 10-8 s, and the relaxation time of the excited states is less than i0~s) and taking into account

(24)

g0(P) + g1(P) = Whvt~, we obtain the expression for the stimulated emission intensity of the ZPL (g0) and the PSB 2yz P~~~Z0 P1~~~ 1 (1-y~)[(1-y~)/Az1T~-1], —

—

0

25

~

—

~

(~),

P1~,~Z1~ +

l—y~ ~

y~

(1—y~)IAz1r~—1)’

26

( )

where t~is the photon lifetime in the cavity, ~ is a quantity proportional to the quasi-equilibrium level population, ~thr is the threshold pumping power for the ZPL, y = Y1 I Y2 the intensity ratio of the PSB

and the ZPL in the luminescence spectrum. Analysis of these equations shows that the stimulated emission intensities of the ZPL and the PSB are defined by the pumping energy and the crystal parameters, namely the electron—phonon interaction (a), the excited state lifetime ~r0 = 1/A and the phonon lifetime r~.For 4 4 1, i~is linearly dependent on pumping. The ZPL stimulated emission intensity can decrease with increasing pumping energy for certain values of y, r0, and ‘ri,. The larger y and the longer T~are (i.e., if ‘r~ r0), the lower ~ is for low pumping. Figure 20 gives the calculated curves (eqs. 25, 26) of the changes of the stimulated emission intensities of the ZPL (1) and the PSB (2) as functions of the pumping power f = WIPthr for crystals having the following parameters: y = 0.8; T~IT0 0.2; a = 0.5 (fig. 20e) and a = 0.25 (fig. 20f). It can be seen that with low pumping the ZPL stimulated emission intensity decreases for crystals having a much

stronger electron—phonon interaction. The calculated curves agree with the experimental ones. Using experimental curves (fig. 19) and having performed calculations for a given crystal one can

estimate nonequilibrium phonon lifetimes if z0, z1, A and y are known. Thus, for naphthalene doped with ~343-DNE and P13-NDVB we obtain for the nonequilibrium phonon lifetimes at 43 ± 3cm’ 10_it) s at 4.2 K, which is in agreement with the estimates of some other authors [246,247]. The assumption of phonon stimulated optical transitions can be confirmed by direct detection of

nonequilibrium phonons. Experiments that give indirect evidence for this hypothesis have been carried out [248—250].Thus, a nonresonant frequency field (a green 0-switched Nd:glass laser) applied to an

UV excited naphthalene crystal doped with 1313-DNE results in a slight redistribution of the light generation intensity over the ZPL and the PSB in favour of the PSB (fig. 25). Under these conditions both the ZPL and the PSB positions are not changed. Experimentally it was shown that in the crystal studied luminescence quenching by a green Q-switched pulse does not take place [248]. Such a

behaviour of the light generation spectrum can be assigned to slight crystal heating. Indeed, as the intensity of the green 0-switched pulse increases two-phonon excitation of a naphthalene matrix to

higher singlet levels can occur. The subsequent fast radiationless relaxation can result in the formation of a large number of additional phonons and, hence, to crystal heating.

V.V. Eremenko and L.A. Ogurtsova. Stimulated emission and relaxation processes in molecular crystals

390

2<

x~. /~_

10°

10

~7’

~

~

°N

~05

v

~05

C

0/

C

02

03

~J

Fig. 25. Light generation intensity of the ZPL (1) and the PSB (2) of I3~3-DNEin naphthalene versus the energy.

5

C

C

/0

/5

Fig. 26. Light of the second harmonic of a Nd:glass laser. Generation intensity of the ZPL (1) and the PSB (2) of 3~3-DNEin naphthalene as a function of temperature.

To check this assumption temperature studies of the crystal light generation spectrum were made with steady UV excitation and in the absence of nonresonant excitation (fig. 26). As can be seen, the intensity ratio of ZPL and PSB light generation is not changed when the temperature changes from 6 to 10 K. Further temperature increase results in a relative decrease of ZPL light generation and an increase of the PSB which is much faster than with nonresonant excitation (fig. 25). A slow increase of PSB light generation with additional crystal irradiation by a green Q-switched pulse can be accounted for by Raman scattering of the nonresonant excitation on nonequilibrium phonons formed due to light generation. This leads to a decrease of the nonequilibrium phonon concentration and, hence, to a decrease of the PSB intensity. It should be noted that, when the temperature dependence of the light generation intensity was studied, up to 18 K no spectral changes in the ZPL and PSB positions were observed, which is in agreement with the studies of the temperature dependences of the light generation frequencies of the ZPL and the PSB [240] and that of the ZPL frequency in the luminescence spectrum [251]. Sufficiently long lifetimes of nonequilibrium phonons are indicated in another experiment [249]. A crystal with strong electron—phonon interaction was excited by ultrashort light pulses of the third harmonic of a Nd:glass laser, the durtion of a single pulse being about lO~s. The time intervals between ultrashort pulses fluctuated from 4 to 12 ns with the same energy in the pulse train. As can be seen in fig. 27, shortening of the time interval in the ultrashort pulse train results in an increase of the stimulated emission intensity of the PSB, which is evidence of the accumulation of nonequilibrium phonons and their influence on light generation. The above considerations confirm the assumption of the generation of nonequilibrium phonons and their participation in light generation. The existence of nonequilibrium high-frequency acoustic phonons (49 cmt) in an anthracene crystal at 1.6 K was detected by stimulated resonant Raman scattering [252] under intense optical excitation by a N 2, ~t = 4 ns, repetition rate 25 Hz). 2 laser 50kW/cm emission spectra depends not only on the It should be noted that increase of the PSB (W= in stimulated electron—phonon interaction in the system, but also on the impurity concentration. This was observed in crystals with a sufficiently strong electron—phonon interaction at impurity concentrations above 1017 cm3. The electron—phonon interaction should be considerable so that phonons are formed due to optical transitions. At the same time it should not be too strong so that the phonon lifetimes are long. In that case the phonons can be accumulated in the crystal. The concentration dependence of the

V.V. Eremenko and L.A. Ogurtsova, Stimulated emission and relaxation processes in molecular crystals

391

P38 ~PL

.~PL

P.58 -~

/

2

—A Fig. 27. Light generation spectra of naphthalene doped with 1313-DNE excited by ultrashort pulses. The time interval between the ultrashort pulses is l2ns (1) and 4ns (2).

increase of the phonon sideband makes it comparable with avalanche processes. Under certain conditions phonon avalanche can be assumed to be observed in these systems.

6. Conclusion In this report we tried to consider practically all incoherent processes in molecular crystals with strong optical excitation. Special attention was paid to doped molecular crystals and low temperatures.

Items concerning the embedded impurities and the selection of the matrix—impurity systems have been analysed. They mainly determine the spectroscopic characteristics of a doped crystal at low temperatures. As to reabsorption by the excited transitions, the possibility of light generation by allowed singlet—singlet and forbidden triplet—singlet transitions in complex organic molecules has been estimated. The peculiarities of the emission of organic molecules in triplet—triplet reabsorption and the

relaxation mechanisms of the excitation energy have been considered. Experimental results of spectral and kinetic studies of stimulated emission were presented. The advantages of doped molecular crystals below 20 K over liquid and polymer solutions of organic molecules as frequency transformers of 0-switched laser emission were discussed. It was shown that stimulated emission of molecular crystals is effective in studying relaxation processes. Saturation of ground state vibrational levels detected in stimulated emission made it possible to determine their lifetimes for a number of doped molecular crystals. The observed optical transitions stimulated by nonequilibrium phonons in crystals with strong electron—phonon interaction allowed us to estimate relaxation times of matrix phonons.

In conclusion it should be noted that stimulated emission of molecular crystals seems to be rather promising to study the effect of low temperature properties of the host matrix on the impurity emission [253].This method of “impurity probe” makes it possible to study doped crystals with low temperature

phase transitions and to reveal the influence of the impurity on their temperature and character.

392

V.V. Eremenko and L.A. Ogurtsova. Stimulated emission and relaxation processes in molecular crstals

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