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Laser intensity effects in the IR multiple-photon absorption of OsO4
Volume 80, number 1
CHEMICAL PHYSICS LETTJZRS
LASER INTENSITY EFFECTS M.N.R. ASHFOLD,
IN THE IR MULTIPLE-PHOTON
15 May 1981
ABSORPTION
OF oS04
C-G. ATKINS and G. HANCOCK
Physical CRemistry Laboratory,
Oxford University,
Oxford OXI 3QZ, UK
Received 31 March 1981
The visl%leluminescence resulting from multiple-photon absorption of CO, laser radzation in 0504 depends upon the laser intensity as well as fluenco. The use of single-mode laser pulses, shaped by electro-optic crystal switching, has enabled this intensity dependence to be determined quantitatively.
1. Introduction Several recent experimental studies of CO, laserinduced multiple-photon absorption (MPA) and dissociation (MPD) processes have shown that the yields of excited molecules or of dissociation fragments can depend upon the laser i&ens@ (w cm-*) as well as
the laser fCrte?zce(J cmm2) [l] _ Examples include studies of the formation of NH3 and CF2 radicals in the collisionless MPD of CH,NH, [2] and CFzHCl [3], the production of visible lurnkescence following infrared MPA in CrO, Cl, [4], and the product yields following MPD of CF$ [5], CF,COCF, [4], and HDCO [6] _ Intensity-dependent MPA cross sections have been observed in SF, [7], although MPD yields for this molecule, which require for their measurement considerably higher fluences than those used in the MPA experiments, have been shown to be essentially intensity independent [S] . For molecules excited above their dissociation thresholds, the competition between the rates of unimolecular decomposition and further photon absorption has been shown to result in intensity-dependent fragment
internal
energy
distributions
[9,10]
and
relative product yields [ 1 l] in MPD processes. A major problem in almost all of these investigations has been in the quantitative estimation of the intensities involved. A normal TEA CO2 laser pulse consists of a high intensity gain switched spike followed by a lower intensity tail, and is generally multimode, its temporal profile consisting of a series of intense spikes, each lasting =l ns and separated by the cavity round trip time, and caused by beating of several axial modes 0 009-2614/81/0000-OOOO/%
within the laser cavity. Intensities of such pulses are impossible to quantify, and the majority of intensity effects have been demonstrated qualitatively, for example by observations of dissociation fragments at different times durig the pulse [2,3,9] or by comparison of the effect of a multimode pulse with that caused by a single-mode, temporalIy smooth pulse of ‘tie same fluence (and hence lower peak intensity) [3,10]. We report measurements involving the use of IR laser pulses of particularly well defined temporal shape, having fast (10 ns) rise and fall times, and delivering an essentially constant output power during the @ariable) pulse length, i.e. the IR analoge of an electronic pulse generator. Specification of the absolute laser intensity across the output beam (which is spatially a well defined gaussian) thus becomes possible, and independent, quantitative measurements of fluence and intensity effects can thus be carried out_ As a fust application of this pulse shaping facility the visible emission resulting from MPA of CO2 laser radi&on in 0~04 has been investigated, and found to be intensity dependent.
02.50 0 North-Holland
2. Experimental The laser pulses were formed by slicing a constant power section from the output of a single-mode CO, laser kcillaior by-n@ns of a GaAs elec?o-optic crysk&--and subsequently am@ifying this. Fe CO2 oscillator (constructed by Oxfoid Lasers) consisted of a TEA section forced to @e on a single aiial mode by the inclusion of a low pressure low power pulsed secPublishing Company
1
Volume 80, number 1
CHEMICAL
PHYSICS LETTERS
15 May 1981
tion inside the cavity_ The output was on the P(20) line at 10.59 pm, and was restricted to the TEMoo mode by means of apertures inside the cavity. The temporal shape of the oscillator pulse could be varied to some extent by changing the gas compositions within each section, and, within the time scales of the “tailored” pulses used, 100 ns-1 ps, an essentially flat topped portion could be found either near the laser peak, or within the lower intensity tail. IXe linearly polansed oscillator output passed through a 50 mm long GaAs electro-optic crystal, across which a fast rising and falling high voltage pulse could be applied to rotate the plane of polarisation of the beam. Fig. la shows one of the oscillator pulses used after it had passed through the crystal with no voltage applied, and fig. lb shows the pulse measured through a polariser set to pass the or&inaZ oscillator output polarisation and with a 500 ns high voltage pulse applied across the crystal. The modulation is not quite loo%, as the highest voltage that could be used in the present experiments, 14 kV, is less than the calculated half wave voltage for the crystal (18 kv). The component of polarisation opposite to that of the origmal beam was selected with a polariser, and passed through a CO, amplifier (Lumonics K-l 03). giving a gain in a single pass of a factor of 10. Fig. lc shows the temporal shape of the resultant pulse, which, as can be seen, is close to the ideal of constant output power. Pulse durations of 100,200,500 and 1000 ns were used in the present experiments, with output energies of 60,40,85 and 90 mJ respectively_ The spatial profies of the pulses were all found to be gaussian with the same effective beam diameter. The IR pulses were loosely focused with a 40 cm lens into low pressures of Os04 (between 1 and 23 mTorr in the present experiments), and visible luminescence resulting from MPA was observed with a photomultiplier which viewed excited molecules in a 4
Fig. 1. Time dependence of the single-mode CO2 laser pulses, showing the effect of electro-optic switching_ In (a) the linearly polarised oscillator pulse is detected after passing through the GaAs crystal with no voltage applied across it. In (b), a 500 ns HV pulse is applied at a predetermined time during the oscillator output, and the component of the IR radiation polarised in the same direction as the original beam is detected. In (c) the component of opposite polarisation (i.e. which has been rotated by =90” for the duration of the HV pulse) is detected after amplification. Horizontal fuIl scale is 2 ,.is in each case.
Volume
80, number
1
CHEhIICAL
PHYSICS
15 May 1981
LElTERS
region in which the IR beam profile was constant. The effective diameter of the beam within this region was taken as the width of the gaussian profile at the l/e points, 3.4 mm. A fraction 1 - l/e of the total beam energy was thus contained within a circle of diameter 3.4 mm centred on the laser axis, and the average fluence $ was taken to be the total pulse energy divided by the area of this circular aperture_ Time-resolved luminescence signals were digitised and averaged for a preset number of laser shots. For each IR pulse length, fluence and intensity were simultaneously varied by attenuation of the laser beam with calibrated polyethylene sheets.
3 _ Results and discussion The time dependence of the luminescence signals from 0~0~ was very similar to that previously observed at low pressures [ 121, and consisted of an initial rise in signal to a maximum value reached at the end of the laser pulse, and followed by a much slower exponential decay. The signal maxima were found to increase linearly with 0~04 pressure in the range studied, and no evidence of collisional behaviour causing deviations from a single exponential signal decay, as has been seen at considerably higher pressures [12,13] was apparent. The signal maxima were taken as measures of the concentration of excited 0~0~ molecules, and were determined for a range of average fluences @ for each of the laser pulses used. Fig. 2 shows the observed signals for the LOOand 500 ns pulses taken at an 0~0~ pressure of 9 mTorr, clearly demonstrating that at a given fluence a decrease in the pulse length results in an increase in concentration of the excited species produced. Results for the 200 ns and 1 PS pulses confirmed this effect: furthermore single-mode 500 ns pulses were found to produce lower concentrations of excited species than multimode pulses of the same fluence and pulse length (formed by operating the CO2 oscillator with a very low gain mixture in the low-pressure section). The results strongly suggest that the laser itztelzsify is responsible for the observed effect_ At a given value of the average fluence Q the measurements of luminescence signals at four different pulse lengths T show a monotonic increase with the average laser intensity, the latter parameter being quantitatively equal to @/r_ However, this does not yield
I 02
I
I
04 06 08 IO Average fluence &J cm-’
Fig. 2. Luminescence signal from 0~04 (9 mTorr) measured as a function of average COrr laser fluence Q (calculated as explamed in the text), for two pulse lengths, 100 ns (circles) and 500 ns (squares)_
the nue intensity dependence at a given 9, as in this experiment the signal is observed as an average over the whole of the gaussian spatial beam profile viewed by the photomultiplier. Fortunately the true intensity dependence can be deconvoluted from these measurements due to this gaussian form of the laser profile [ 141; when carried out this yields for example a signal dependence as 10e7 for values of Q near 0.4 J cmm2. The true fluence dependence (which will be less steep than the composite fluence and intensity plots illustrated in fig_ 2) could not be obtained in a similar way, as the present measurements do not cover a wide enough range of fluence at constant laser intensity. Visible luminescence resulting from MPA in 0~04 has beenassigned to emission from tnpIet states formed by intersystem crossing from high vibrational levels of the ground singlet state [ 12,15]_ Linear pressure dependences of the luminescence signal within the loti-pressure region studied strongly suggest that the process is not influenced by collisions [ 161 (and hence the observed effect is not caused for example by an increase in the number of molecules collisionally de-excited in the longer pulse length lower intensity measurements). Two possibilities need to be considered for a collisionless intensity-dependent effect. The first is that the rates of transitions between levels within the ground 3
Volume
80, number
1
CHEhlICAL
PHYSICS
singlet state caused by ip;eractions with the laser field show dependences which are not simply linear in intensity (and hence the total yield of excited species formed, given by the integral over time of these rates, is not independent of intensity). Processes of this kind, qualitatively described as an intensity-dependent bottleneck in the absorption process [ 1] , have recently been theoretically justified [ 171 and are thought to explain previous observations of MPD yields being intensity dependent [2,3]. The second possibility is that the observed effect may be due to processes taking place well above the threshold for intersystem crossing_ At energies above the zero point of the triplet state, intersystem crossing rates will compete with further photon absorption and, as the latter process depends upon the iaser intensity, a higher intensity pulse will access a higher range of internal ener_q states within the singlet, and hence the triplet, manifolds than a pulse of lower intensity. If the luminescence quantum yields or radiative lifetimes of these states are markedly dependent upon excitation energy, then an intensity-dependent effect would result; this process is analogous to the intensity-dependent internal energy distributions observed in the fragments of MPD processes [9,10] _ No change in the luminescence spectrum or in its decay behaviour was observed with changes in laser intensity, effects which might result from intensity-dependent processes taking place above the energy barrier to intersystem crossing. The latter process cannot be ruled out, however, with the present experiments: accurate lifetime measurements under truly collision free conditions, for example. in a molecular beam would be needed to investigate this further. A full report of the present investigations, together with a detailed description of the pulsed laser system, is in preparation.
4. Conclusions Infrared MPD in 0~0, leading to visible luminescence is a process which depends upon the laser intensity as well as the laser fluence. Quantitative variation of laser energy and power in order to investigate these effects has been possible for the frost time with the use of well defined IR pulse shapes produced by electrooptic switching of single-mode CO, laser output.
4
LEmRS
15 May 1981
Acknowledgement
We are grateful to the S.R.C. for an equipment grant, and to Oxford Lasers for their considerable advice and assistance.
References [ I] M N-R. Ashfold and G. Hancock,
in: Gas Kmetics and Energy Transfer, Vol. 4. Specialist Periodical Report (Chem. Sot., London), to be published. [2] G. Hancock, R.J. Hennessy and T. Vdhs, in: Laser induced processes in molecules, Vol. 6, eds. K-L. Kompa and S.D. Smith (Springer, Berlin, 1978) p_ 190; XI N-R. Ashfold, G. Hancock and G-W_ Ketley, Faraday Discussions Chem. Sot. 67 (1979) 204. [ 3 ] D.S. King and J C. Stephenson, Chem. Phys. Letters 66 (1979) 33. [4] R. Naaman and R.N. Zare, Faraday Discussions Chem. Sot. 67 (1979) 242. [S] M. Rossi, J.R. Barker and D.M. Golden, Chem. Phys. Letters 65 (1979) 523. [6] G. Koren and UP. Oppenheim, Opt. Commun. 26 (1978) 449. [7] H.S. Kwok, Ph.D. Thesis, Harvard University, Cambridge, hfassachusetts (1978). [8] P. Kolodner, C. Winterfield and E. Yablonovich, Opt_ Commun. LO (1977) 119; M.C. Gower and K-W. Bdlman, Appl Phys. Letters 30 (1977) 514; J L. Lyman, SD. Rockwood and S.hI. freund, J. Chem. Phys. 67 (1979) 4545. [9] h1.N.R. Ashfold. G. Hancock and M.L. Hardaker, J. Photochem. 14 (1980) 85; CM. hfliler and R.N. Zare, Chem. Phys. Letters 71 (1980) 376. [lo] A.M. Renlund, H. Reisler and C. Wittig, Chem_ Phys. Letters 78 (1981) 40. [ 1 l] D-M. Brenner, Chem_ Phys- Letters 57 (1978) 357. [ 121 A-A. Makarov, G-N_ Makarov, A-A. Puretzkii and V-V. Tyakht, Appl. Phys. 23 (1980) 391. [ 131 R-V. Ambartzumian, Y.A. Gorokhov, G-N. hfakarov, A.A. Puretzkii and N.P. Funlkov, Chem. Phys. Letters 45 (1977) 231. [ 141 J-G. Black, P. Kolodner, K-J_ Schulz, E. Yablonovich and N. Bloembergen, Phys. Rev. A19 (1979) 704. [15] R.V. Anibartzumian, G-N. Makarov and A-A. Puretzkii, Soviet Phys. JETP Letters 28 (1978) 647. [ 161 H. Reisler and C. Wittig, Advan. Chem. Phys., to be published. 1171 hf. Quack, J. Chem. Phys. 69 (1978) 1292; Chem. Phys. Letters 65 (1979) 140; M. Quack, P. Humbert and H. van den Bergh, J. Chem. Phys. 73 (1980) 247.
CHEMICAL PHYSICS LETTJZRS
LASER INTENSITY EFFECTS M.N.R. ASHFOLD,
IN THE IR MULTIPLE-PHOTON
15 May 1981
ABSORPTION
OF oS04
C-G. ATKINS and G. HANCOCK
Physical CRemistry Laboratory,
Oxford University,
Oxford OXI 3QZ, UK
Received 31 March 1981
The visl%leluminescence resulting from multiple-photon absorption of CO, laser radzation in 0504 depends upon the laser intensity as well as fluenco. The use of single-mode laser pulses, shaped by electro-optic crystal switching, has enabled this intensity dependence to be determined quantitatively.
1. Introduction Several recent experimental studies of CO, laserinduced multiple-photon absorption (MPA) and dissociation (MPD) processes have shown that the yields of excited molecules or of dissociation fragments can depend upon the laser i&ens@ (w cm-*) as well as
the laser fCrte?zce(J cmm2) [l] _ Examples include studies of the formation of NH3 and CF2 radicals in the collisionless MPD of CH,NH, [2] and CFzHCl [3], the production of visible lurnkescence following infrared MPA in CrO, Cl, [4], and the product yields following MPD of CF$ [5], CF,COCF, [4], and HDCO [6] _ Intensity-dependent MPA cross sections have been observed in SF, [7], although MPD yields for this molecule, which require for their measurement considerably higher fluences than those used in the MPA experiments, have been shown to be essentially intensity independent [S] . For molecules excited above their dissociation thresholds, the competition between the rates of unimolecular decomposition and further photon absorption has been shown to result in intensity-dependent fragment
internal
energy
distributions
[9,10]
and
relative product yields [ 1 l] in MPD processes. A major problem in almost all of these investigations has been in the quantitative estimation of the intensities involved. A normal TEA CO2 laser pulse consists of a high intensity gain switched spike followed by a lower intensity tail, and is generally multimode, its temporal profile consisting of a series of intense spikes, each lasting =l ns and separated by the cavity round trip time, and caused by beating of several axial modes 0 009-2614/81/0000-OOOO/%
within the laser cavity. Intensities of such pulses are impossible to quantify, and the majority of intensity effects have been demonstrated qualitatively, for example by observations of dissociation fragments at different times durig the pulse [2,3,9] or by comparison of the effect of a multimode pulse with that caused by a single-mode, temporalIy smooth pulse of ‘tie same fluence (and hence lower peak intensity) [3,10]. We report measurements involving the use of IR laser pulses of particularly well defined temporal shape, having fast (10 ns) rise and fall times, and delivering an essentially constant output power during the @ariable) pulse length, i.e. the IR analoge of an electronic pulse generator. Specification of the absolute laser intensity across the output beam (which is spatially a well defined gaussian) thus becomes possible, and independent, quantitative measurements of fluence and intensity effects can thus be carried out_ As a fust application of this pulse shaping facility the visible emission resulting from MPA of CO2 laser radi&on in 0~04 has been investigated, and found to be intensity dependent.
02.50 0 North-Holland
2. Experimental The laser pulses were formed by slicing a constant power section from the output of a single-mode CO, laser kcillaior by-n@ns of a GaAs elec?o-optic crysk&--and subsequently am@ifying this. Fe CO2 oscillator (constructed by Oxfoid Lasers) consisted of a TEA section forced to @e on a single aiial mode by the inclusion of a low pressure low power pulsed secPublishing Company
1
Volume 80, number 1
CHEMICAL
PHYSICS LETTERS
15 May 1981
tion inside the cavity_ The output was on the P(20) line at 10.59 pm, and was restricted to the TEMoo mode by means of apertures inside the cavity. The temporal shape of the oscillator pulse could be varied to some extent by changing the gas compositions within each section, and, within the time scales of the “tailored” pulses used, 100 ns-1 ps, an essentially flat topped portion could be found either near the laser peak, or within the lower intensity tail. IXe linearly polansed oscillator output passed through a 50 mm long GaAs electro-optic crystal, across which a fast rising and falling high voltage pulse could be applied to rotate the plane of polarisation of the beam. Fig. la shows one of the oscillator pulses used after it had passed through the crystal with no voltage applied, and fig. lb shows the pulse measured through a polariser set to pass the or&inaZ oscillator output polarisation and with a 500 ns high voltage pulse applied across the crystal. The modulation is not quite loo%, as the highest voltage that could be used in the present experiments, 14 kV, is less than the calculated half wave voltage for the crystal (18 kv). The component of polarisation opposite to that of the origmal beam was selected with a polariser, and passed through a CO, amplifier (Lumonics K-l 03). giving a gain in a single pass of a factor of 10. Fig. lc shows the temporal shape of the resultant pulse, which, as can be seen, is close to the ideal of constant output power. Pulse durations of 100,200,500 and 1000 ns were used in the present experiments, with output energies of 60,40,85 and 90 mJ respectively_ The spatial profies of the pulses were all found to be gaussian with the same effective beam diameter. The IR pulses were loosely focused with a 40 cm lens into low pressures of Os04 (between 1 and 23 mTorr in the present experiments), and visible luminescence resulting from MPA was observed with a photomultiplier which viewed excited molecules in a 4
Fig. 1. Time dependence of the single-mode CO2 laser pulses, showing the effect of electro-optic switching_ In (a) the linearly polarised oscillator pulse is detected after passing through the GaAs crystal with no voltage applied across it. In (b), a 500 ns HV pulse is applied at a predetermined time during the oscillator output, and the component of the IR radiation polarised in the same direction as the original beam is detected. In (c) the component of opposite polarisation (i.e. which has been rotated by =90” for the duration of the HV pulse) is detected after amplification. Horizontal fuIl scale is 2 ,.is in each case.
Volume
80, number
1
CHEhIICAL
PHYSICS
15 May 1981
LElTERS
region in which the IR beam profile was constant. The effective diameter of the beam within this region was taken as the width of the gaussian profile at the l/e points, 3.4 mm. A fraction 1 - l/e of the total beam energy was thus contained within a circle of diameter 3.4 mm centred on the laser axis, and the average fluence $ was taken to be the total pulse energy divided by the area of this circular aperture_ Time-resolved luminescence signals were digitised and averaged for a preset number of laser shots. For each IR pulse length, fluence and intensity were simultaneously varied by attenuation of the laser beam with calibrated polyethylene sheets.
3 _ Results and discussion The time dependence of the luminescence signals from 0~0~ was very similar to that previously observed at low pressures [ 121, and consisted of an initial rise in signal to a maximum value reached at the end of the laser pulse, and followed by a much slower exponential decay. The signal maxima were found to increase linearly with 0~04 pressure in the range studied, and no evidence of collisional behaviour causing deviations from a single exponential signal decay, as has been seen at considerably higher pressures [12,13] was apparent. The signal maxima were taken as measures of the concentration of excited 0~0~ molecules, and were determined for a range of average fluences @ for each of the laser pulses used. Fig. 2 shows the observed signals for the LOOand 500 ns pulses taken at an 0~0~ pressure of 9 mTorr, clearly demonstrating that at a given fluence a decrease in the pulse length results in an increase in concentration of the excited species produced. Results for the 200 ns and 1 PS pulses confirmed this effect: furthermore single-mode 500 ns pulses were found to produce lower concentrations of excited species than multimode pulses of the same fluence and pulse length (formed by operating the CO2 oscillator with a very low gain mixture in the low-pressure section). The results strongly suggest that the laser itztelzsify is responsible for the observed effect_ At a given value of the average fluence Q the measurements of luminescence signals at four different pulse lengths T show a monotonic increase with the average laser intensity, the latter parameter being quantitatively equal to @/r_ However, this does not yield
I 02
I
I
04 06 08 IO Average fluence &J cm-’
Fig. 2. Luminescence signal from 0~04 (9 mTorr) measured as a function of average COrr laser fluence Q (calculated as explamed in the text), for two pulse lengths, 100 ns (circles) and 500 ns (squares)_
the nue intensity dependence at a given 9, as in this experiment the signal is observed as an average over the whole of the gaussian spatial beam profile viewed by the photomultiplier. Fortunately the true intensity dependence can be deconvoluted from these measurements due to this gaussian form of the laser profile [ 141; when carried out this yields for example a signal dependence as 10e7 for values of Q near 0.4 J cmm2. The true fluence dependence (which will be less steep than the composite fluence and intensity plots illustrated in fig_ 2) could not be obtained in a similar way, as the present measurements do not cover a wide enough range of fluence at constant laser intensity. Visible luminescence resulting from MPA in 0~04 has beenassigned to emission from tnpIet states formed by intersystem crossing from high vibrational levels of the ground singlet state [ 12,15]_ Linear pressure dependences of the luminescence signal within the loti-pressure region studied strongly suggest that the process is not influenced by collisions [ 161 (and hence the observed effect is not caused for example by an increase in the number of molecules collisionally de-excited in the longer pulse length lower intensity measurements). Two possibilities need to be considered for a collisionless intensity-dependent effect. The first is that the rates of transitions between levels within the ground 3
Volume
80, number
1
CHEhlICAL
PHYSICS
singlet state caused by ip;eractions with the laser field show dependences which are not simply linear in intensity (and hence the total yield of excited species formed, given by the integral over time of these rates, is not independent of intensity). Processes of this kind, qualitatively described as an intensity-dependent bottleneck in the absorption process [ 1] , have recently been theoretically justified [ 171 and are thought to explain previous observations of MPD yields being intensity dependent [2,3]. The second possibility is that the observed effect may be due to processes taking place well above the threshold for intersystem crossing_ At energies above the zero point of the triplet state, intersystem crossing rates will compete with further photon absorption and, as the latter process depends upon the iaser intensity, a higher intensity pulse will access a higher range of internal ener_q states within the singlet, and hence the triplet, manifolds than a pulse of lower intensity. If the luminescence quantum yields or radiative lifetimes of these states are markedly dependent upon excitation energy, then an intensity-dependent effect would result; this process is analogous to the intensity-dependent internal energy distributions observed in the fragments of MPD processes [9,10] _ No change in the luminescence spectrum or in its decay behaviour was observed with changes in laser intensity, effects which might result from intensity-dependent processes taking place above the energy barrier to intersystem crossing. The latter process cannot be ruled out, however, with the present experiments: accurate lifetime measurements under truly collision free conditions, for example. in a molecular beam would be needed to investigate this further. A full report of the present investigations, together with a detailed description of the pulsed laser system, is in preparation.
4. Conclusions Infrared MPD in 0~0, leading to visible luminescence is a process which depends upon the laser intensity as well as the laser fluence. Quantitative variation of laser energy and power in order to investigate these effects has been possible for the frost time with the use of well defined IR pulse shapes produced by electrooptic switching of single-mode CO, laser output.
4
LEmRS
15 May 1981
Acknowledgement
We are grateful to the S.R.C. for an equipment grant, and to Oxford Lasers for their considerable advice and assistance.
References [ I] M N-R. Ashfold and G. Hancock,
in: Gas Kmetics and Energy Transfer, Vol. 4. Specialist Periodical Report (Chem. Sot., London), to be published. [2] G. Hancock, R.J. Hennessy and T. Vdhs, in: Laser induced processes in molecules, Vol. 6, eds. K-L. Kompa and S.D. Smith (Springer, Berlin, 1978) p_ 190; XI N-R. Ashfold, G. Hancock and G-W_ Ketley, Faraday Discussions Chem. Sot. 67 (1979) 204. [ 3 ] D.S. King and J C. Stephenson, Chem. Phys. Letters 66 (1979) 33. [4] R. Naaman and R.N. Zare, Faraday Discussions Chem. Sot. 67 (1979) 242. [S] M. Rossi, J.R. Barker and D.M. Golden, Chem. Phys. Letters 65 (1979) 523. [6] G. Koren and UP. Oppenheim, Opt. Commun. 26 (1978) 449. [7] H.S. Kwok, Ph.D. Thesis, Harvard University, Cambridge, hfassachusetts (1978). [8] P. Kolodner, C. Winterfield and E. Yablonovich, Opt_ Commun. LO (1977) 119; M.C. Gower and K-W. Bdlman, Appl Phys. Letters 30 (1977) 514; J L. Lyman, SD. Rockwood and S.hI. freund, J. Chem. Phys. 67 (1979) 4545. [9] h1.N.R. Ashfold. G. Hancock and M.L. Hardaker, J. Photochem. 14 (1980) 85; CM. hfliler and R.N. Zare, Chem. Phys. Letters 71 (1980) 376. [lo] A.M. Renlund, H. Reisler and C. Wittig, Chem_ Phys. Letters 78 (1981) 40. [ 1 l] D-M. Brenner, Chem_ Phys- Letters 57 (1978) 357. [ 121 A-A. Makarov, G-N_ Makarov, A-A. Puretzkii and V-V. Tyakht, Appl. Phys. 23 (1980) 391. [ 131 R-V. Ambartzumian, Y.A. Gorokhov, G-N. hfakarov, A.A. Puretzkii and N.P. Funlkov, Chem. Phys. Letters 45 (1977) 231. [ 141 J-G. Black, P. Kolodner, K-J_ Schulz, E. Yablonovich and N. Bloembergen, Phys. Rev. A19 (1979) 704. [15] R.V. Anibartzumian, G-N. Makarov and A-A. Puretzkii, Soviet Phys. JETP Letters 28 (1978) 647. [ 161 H. Reisler and C. Wittig, Advan. Chem. Phys., to be published. 1171 hf. Quack, J. Chem. Phys. 69 (1978) 1292; Chem. Phys. Letters 65 (1979) 140; M. Quack, P. Humbert and H. van den Bergh, J. Chem. Phys. 73 (1980) 247.