Coherent multiphoton excitation of SF6 by picosecond laser pulses

CHEMICAL

Volume 111, number 1,2

COHERENT MULTIP~OTON

PHYSICS LETTERS

26 October

1983

EXCITATION OF SF6 BY PICOSECOND LASER PULSES

P. MUKNERJEE and H.S. KWOK Department of Eiecrricnl amd Comprrter Engheeril?g. State Universit;~ of New >rprx-at Buffaio, 4232 Ridge Lea Road. Amherst. New York 14260, USA Received 15 May 1981

Intensity-dependent multiphoton cscitstion was obscrvcd in SF6 molecules which have been cscited into tlxe quasicontinuum by a separate laser pulse. TJIC strong intensity dependence indicates coherent rather than incoherent excitation of UIC molecules. This is possible due to a favorable competition of Rabi precession with intramolecular energy transfer. A f310ck equation model calculation is also presented.

ing [5]. One of the predictions of the rate equation desscription is that MPE will be laser energy fluence dependent only [6] _It had been quite faithfully obeyed in many MPD experiments [7]. However, the success of the rate equation approach 1.0 model MPD experiments [8] is mostly because dissociation does not depend sensitively on the MPE process. hleasurements of the dissociation yield, product energy distributions can only study the MPE process and the QC indirectly_ More sensitive experimental methods are needed to examine the properties of the QC without any interference from dissociation_ MPE with picosecond pulses is one of the possibilities. We have previously published a picosecond laser study of SF, showing deviation from the rate equation picture indicating the oxxet of coherent interaction in the QC f9]_ However, the molecules were at room temperature and some questions may-be raised as to whether the intensity-dependent MPE observed in ref. [9] was a remnant of the initial discrete levels. In this letter, we report an experiment where the SF6 molecules are preheated to the QC before the MPE is carried out. Very strong intensity-dependent effects were observed. This indicates a definite breakdown of the master equation description of the QC. In this letter we shall also present some initial modeling effort in trying to explain the experimental observations by 3 Bloch equation calculation

1_ introduction The study of the highly excited vibrational states of a poIyatomic molecule is an important topic in chemical dynamics. The muhitude of interacting vibrational levels, often referred to as the quasicontinuum (QC), determines the chemical reactivity of molecules in the ground electronic states. It has been the subject of many theoretical and experimental studies [ 11. Questions such as the nature of energy transfer between different vibrational modes [2], the lineshape and strength of individual levels, a proper method of grouping the vibrational levels to form good subsets of the QC and the local-mode versus normal-mode description [3] are yet to be answered_ The behavior of the QC is especially important to the understand~g of collisionless infrared multiphoton excitation (MPE) and dissociation (MPD) of polyatomic molecules. With the addition of a new variable, the laser field, the behavior of the QC becomes even more complex. The traditional description of laser interaction with the QC is that since the dephasing time of coherence ( T+Jtime) is very rapid, Fermi’s golden rule is valid. Hence the rate or master equation approach can be used to model the laser-molecule interaction [4]. Although coherent interaction experiments have been carried out with poiyatomic molecules such as SF,, they are confined to the lower vibrational levels where there $ Little or no collisionless intramolecular damp0 009-26 14/84/S 03.00 0 Elsevier Science Publishers (North-Poland Physics Publishing Division)

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26 October 1984

CHEMICAL PHYSICS LElTERS

2. Experimental The experimental apparatus used in this experiment is similar to that of ref. 193. The major differ-

ence is that two separate laser systems are employed, with adjustable timing and delay between’them. One system is the optical free induction decay (OFID) picosecond laser 191. This laser is capable of delivering 2 hlW OF peak power in a variable duration pulse from 30 to 300~s. A careful characterization of this system has been performed recently [IO]. The other laser beam is a normal TEA CO, laser with no ~o~l~itud~~l mode control. This laser delivers 0.5 3 in a 100 ns pulse, and is used to preheat the SF6 moIecules. The two laser beams crossed at a alOo angle inside a 1 mm gas cell equipped with NaCl wlndows. The 100 ns TEA pulse is sent through the gas cell 1 w ahead of the picosecond laser pulse. The area of the preheating pulse is 4 mm in diameter while the picosecond pulse is only O-15 mm in diameter. Therefore there is no problem of spatial overlap between the two pulses. The pressure in the gas cell used was 30 or 40 Torr depending on the OFID pulse duration. The pressure is low enough so thar no collison can occur within the OFlD picosecond laser pulse duration to ensure true collisionless MPE. However the pressure is also high enough such that there is a reasonable absorption by the gas cell. The transmission of the OFID pulse is always kept berween 50 and 8OrO. This will ensure that the laser beam is approx~ately uniform inside the gas ceil and the transmission measurement is of sufficient accuracy. A 1 w time delay is aUowed between the heating pulse and the OFID pulse so that complete V-V (1.2 ~.lsTorr) and V-R (150 ns Torr) relaxation has occured before the probing OFID pulse is incident on the vibrationally hot molecules. However no V-T relaxation (120 w Torr) is allowed to deactivate the hot molecules. The time delay is also important in enabIing a clean detection of the OFID pulse in the presence of a strong TEA background. Experimentally a pseudo-tile-resolved detection scheme is used. Both the heating puIse and the OFID pulse can be displayed on the oscilloscope simultaneously, As usual the average number of CO2 photons absorbed by the SF6 molecule is calculated using the energy conservation relationship

(I?) = (1 - T) ~/~~~?~,

0)

where IV and L are the number density and thickness of the gas cell, T is-the transtiission and 2 is the energy fluence of the laser. As explained in ref_[9], the measured transmission T&f is a convoluted average across the changing intensity profile of the beam. A Gaussian deconvolution procedure is performed to obtain the true transmission T=Thf(l

+dlnT~~/dln~).

(3-1

Exper~enta~y, Thi was measured for each laser fluence. Then Twas derived using (2), and (n) can be calculated from (1).

3. Resdts

and discussion

By measuring the tran~ission of the heating pulse, which was allowed to lase at the P(20) line at 10.59 q, the preheating of the SF6 molecules by the multimode TEA pulse could be calculated. It corresponded to {n> = 13 and 17 for pressures of 30 and 40 Torr in the cell, respectively. To ensure that no dissociation products accumulated in the cell, the sample chamber was evacuated after each data point of laser fluence. Fig. 1 shows the absorption spectrum obtained with a weak 70 ps OFiD pulse tuned across the P branch of the 10.4 ~.rmtransition line of the CO2 laser. The absorption spectrum shows a relatively smooth profile peak at 932 cm-l. This red-shifting of the absorption maximum is a well-known signature of heated molecules. The amount of red-shift, the spectral width and the absorption maxima agree very well with published shock tube data of thermally heated SF6 [ 111. The equivalent temperature of the preheated molecules is approximately 900 K Fig. 2 shows the energy deposited by OFID pulses tuned to the P(28) line at three different pulse durations: 38,95, and 115 ps. Onecan obs&ve a marked difference in energy deposition between the different puIse durations. Experimentally, more than 80 photons were deposited by the OFID pulse in some cases.. At such high levels, the data might be contaminated by dissociation of SF6 and MPE of SF,, one of the dissociation products. However, because of the short pulse durations employed in the measurements, no

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Fig. 1. Excited-state absorption spectrum of preheated SF+ The arrow indicates the pump laser frequency. A weak picosecond probe laser is used to measure the coltisionlcss nbsorption cross section.

4.

Bloch equation

An attempt was made to explain the experimental observations using a set of Bloch equations of the form [4]

0

38 95ps

*

115ps

The diagonal elements

FIS

dpifdt

0.1

I

1

f

4

= i/fi[n,K]ji

term _

(3)

pi are given by

- @i - p,‘D’)/T, ,

(4)

where pi(‘3’ is the equ~ibriunl value of pi and T, is the population relaxation time. This form of the relaxation differs from that of ref. [4]. We believe the present form is more appropriate since it reduces properly for the case of a two-level system. The off-diagonal coherent matrix elements are given by dovldt

0.00

calculation

dpldr = ilfi [P, X] -- relaxation

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1983

significant dissociation is expected except at very high levels of excitation. For example, the RRJCM dissociation lifetime at an excess excitation.of 20 photons above the dissociation threshold is 100 ps [g] _ Hence the data depicted by fig. 2 is expected to be IMPD contamination free for W 5 60. The general trend of higher hlPE for shorter pulses at the the same fiuence is believed to be a valid observation. Fig. 2 can be compared with the results obtained in ref. [9] at P(20) where the molecules were not preheated_ One finds an even bigger spread between the different pulse durations in the present case. The slope of the curves obtained are almost of unity slope indicating no saturation whatsoever. All the effects of anharmonic shift of the resonance, decreasing absorption lmestrengths are not true for these picosecond pulses. From the present result, it can be concluded that in the QC, the absorption cross section remains constant or may even increase as the molecule is excited vibrationa~y-

950

FREQUENCY

26 October

PHYSlCS LEl-IXRS

11,111

I

I

0.01 LASER

1

I11111

f

0.1 FLUENCE

I

0

I

ttt

1

(J/cm21

Fig;. 2. Enero,v deposited by the various duration laser pukes as function of fluence.

= ifa fP.W

if - P~/Tz

3

(5)

where T2 is the dephasing time. We assume a set of equidistant energy levels resonant with the laser frequency. hioreover, to simplify the calculations, we assume that T, and T2 are equal and that they are independent of the level of excitation. This is a reasonable assumption according to the restricted intramolecu!ar ener,7 transfer~model of Stone and Goodman [X2]_ As seen from the result of

Volume 111, number 1,2

CHEMICAL PHYSICS LETTERS

f2i-l,iPi_i-l

- ~2 i,i+l Pi,j+l -

(Pj

-

Pi”‘YT2

1984

Tz are shorter than the laser pulse duration fP, pi reaches tin equ~ibrium vahre rapidly after the laser pulse is turned oh. Therefore ni is approximately proporfional to the pulse duration while pj is independent of tp_ Hence vi represents fluence dependent MPE while pi represents intensity-dependent MPE. However, even though the qualitative feature of fig. 2 can be explained, a consistent set of values of T2, and !+ that can explain’totally the experimental observations, cannot be obtained yet. From our preliminary numerical solution, it seems that sZj should increase considerably as the molecule is excited.

tlteir single- or two-quantum exchange calculation, the density of interacting vibrational levels saturates rapidly with the vibrational energy. Hence Tz, which depends on the number of interacting levels, is constant. Furthermore, if only dipole transitions~are allowed, theu only adjacent levels of the ladder are coupled. it can then be shown that at exact’resonance when the laser frequency is the same as the ladder spacing, the off-diagonal elements of the density matrix are purely imaginary. Letting @ = i/3j1e-iwr, after applying the usual rotating-wave approximation, then dPjidf=

26 October

a (6)

d&+l,ildt

= Qi,i+,/2(pi

- Pi+l)

- &t-l,JT~

z

(7)

where ~~j is the Rabi frequency given by ~$?~ii- An alternative approach is to assume the ladder to have anharmonically shifted spacings. Then firL,,,zzi-l will be given by (tz + 1)1/z ,uoEoffi where p0 is the fundamental transition moment [S] _ In (6) and (7), we have let the transition strength G$ be a~arjlloni~-rifted instead. Both ladders are permissible because of the vast density of states in the QC. Eqs. (6) and (7) are not a complete description of the laser molecule interaction because they impIy that pi decays to pf” in a time T2 after the laser pulse is turned off. Physically we expect the molecule to Sky excited until deactivating collisions occur. Moreover, the “damping” term in (6) and (7) is not due to external agents, but rather is more properly described by “internal collisions”. This internal damping must conserve energy within the molecule. We model this by assuming a parallel set of “‘heat bath” energy levels {nj] which has the same energies as {pi)_ The n i gain their population by the decay of pi, d vi/d c = (pi - pi’o’)/T, . It can be seen that pi + TQremains constant when the laser pulse is turned off. Eqs, (6). (7) and (8) form a complete set of equations describing the laser-molecule interaction. The ladder {pif can be regarded as coherent excitation and {ni) an incoherent heating of the molecule. Efforts are under way at present to solve (B), (7) and (8) and try to fit the experimental data. A general trend of the numerical results is that if the Rabi precession period !2T1 and the damping time

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(8)

5. Conclusions In summary, we have observed intensity-dependent MPE in the molecule SF6 already placed in the QC. This is a further confirmation of the breakdown of the energy fhrence scaling law for MPE within the quasicontinuum. It is believed that a coherent state is established by the intense picosecond laser pulse. This was possibIe because of the favorable competition of pi-’ with T,. We have also presented a BIoch equation modeling of the system which distinguishes between coherent and incoherent excitations. We believe this model is an improvement over the previous “modified rate equations” and may lead to a better explanation of coherent phenomena for tlte highly vibrationally excited molecuies. Further work is needed though to improve the Bloch equation calculations.

Acknowledgement This research was supported by the Department Energy, Contract No. DEAC-1 O-ER-10780.

of

References reactions (-Academic Press, New York, 1973). [2j H-S. Kwok and E. Yablonovitch, Phys. Rev. Letters 41 (1977) 745 [31 H-B. Levene and D.S. Perry, J. Chem. Phys. 81 (1984) 1772. 141 D.S. King, in: Dynamics of the excited state, cd. K.P. LawIcy (Wiley, NW York, 1982).

[ 11 W. Frost, Tircor>rof u~oIec~1~

Volume II 1, number

1,2

CHEMICAL PHYSICS LETTERS

151 CD. Cant&J, A-A. Malcarov and 1Y.H. Louise& in: Photoselective spectrosocpy, eds. J.A. Jortner, R.D. Levine and S.A. Rice (Wiley, New York, 1981). [ 6 J E. Yablonovitch and N. Bloembergen, Phys. Today 31(1978) 32. 171 P. Kolodner, C. Winterfield and E. Yablonovitch, Opt. Commun. 20 (1977) 119. [8j P-A. Schulz, AS. Sudbo, E.R. Grant, Y-R. Shen and Y-T_ Lee, J. Chem. Phys. 72 (1980) 4985.

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191 H-S. Kwok, E. Ysblonovitch and N. Bloemhergen, Phys. Rev. A23 (1981) 3094. [ 101 P. Mukhejce and H-S. Kwok, Appl. Phys. Letters 44 (1984) 180. 11 l] A.V. Nowak and J-L. Lyman, J. Quant. Spew-y. Radiat. Transfer 15 (1975) 9lX [ 121 B. Thiele, hi-F_ Goodman and J. Stone. Opt. Eng_ 19 (1980) JO_

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