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Observation of broadband forward hyper-Raman emission with high intensity focused laser beams
15 October
1997
OPTICS COMMUNICATIONS ELSEVIER
Optics Communications
142 (1997) 253-256
Observation of broadband forward hyper-Raman emission with high intensity focused laser beams Lu Deng as’,W.R. Garrett a, M.G. Payne a~1,D.Z. Lee b ” Chemical Physics Section. Oak Ridge Natronal Laborato?. Oak Ridge, TN 37831. USA h Department qf Physics, The UniwrsiQ qf British Columbia. Vancouver, B.C.. Cunada V5K IT3 Received 25 March 1997: revised 3 1 May 1997: accepted 9 June 1997
Abstract We show that the well known multiphoton destructive interference, which leads to hyper-Raman gain suppression in the weak pumping regime, no longer occurs under strong pumping conditions. In contrast to the weak pumping case. where no forward hyper-Raman can be observed and strong backward hyper-Raman occurs, forward hyper-Raman emission is found to be much stronger under strong pumping conditions. The emission spectrum acquires new characteristics due to the ac Stark effect introduced by the strong laser field. The frequency spectrum of the forward hyper-Raman is no longer determined by the laser bandwidth, instead a continuum of forward hyper-Raman emission is observed with the width being determined by the peak power density. We will present here a comparison between strong and weak pumping regimes. 0 1997 Elsevier Science B.V.
It is well known that certain resonant and near resonant multiphoton processes in gaseous media can be greatly modified by optical interference phenomena under well understood circumstances [l-8]. The effects, that can suppress or otherwise modify several types of laser driven transitions. involve the production and influence of internally generated wave-mixing fields. It has been shown that both even-photon and odd-photon induced transitions can become strongly influenced by such nonlinear interference effects. Resonant two-photon pumping can become strongly modified through an interference involving the phase matched parametric four-wave mixing that couples back to the ground state [l-3,5] and two-photon coupling due to the laser. On the other hand. in the case of odd-photon coupling of optically allowed transitions, interferences and their exotic consequences can be produced by the internally generated wave mixing fields that are poorly phase matched or strongly absorbed in resonant media. The effects in this category include strong suppression of odd-
’ Permanent address: Physics Department, University. Statesboro. Georgia 30460-803 I,
Georgia
Southern
0030.4018/97/$17.00 8 1997 Elsevier Science B.V. All rights reserved. PI1 SOO30-30 18(97)003 16-7
photon resonant excitations under unidirectional pumping, complex shifting of excitation profiles under multi-color cross beam pumping and the suppression of the ac Stark shifting [3-51. The strong suppression of the gain for forward-directed stimulated hyper-Raman scattering (SHRS) [h-9] and the large pressure dependent frequency shifts for SHRS profiles [ IO,1 I] are some of the most intriguing manifestations of this interference effect. It mctst be pointed out, however, that all these fascinating observations were made in the NXYZ~~ pumping regime. The theory, which has been able to predict all these manifestations of the destructive interference, is based on the conditions that the ground state is not depleted and the transitions involved are far from being saturated. Thus. the condition for establishing the quantum destructive interference thereafter derived [8], i.e. K~,,:/~‘B 1 (?~,,,/r is the absorption coefficient, : is the distance of propagation, and r is the laser bandwidth), is applicable only to the weak pumping regime. (For a review of the theory, see Ref. [ 1I]). This theory should IUZMYbe stretched to the region where either ground state depletion or saturation of the transition involved is likely to happen. Indeed, the gain for backward hyper-Raman should be kept small compared with the
254
L. Deng et al. / Optics Communications
absorption coefficient for the associated four-wave mixing field. For the two-photon excitation of the sodium 4D state, the required laser intensity must be I 10’ W/cm’ in order to avoid the saturation of the two-photon transition [7,8]. In the one-photon pumping of the sodium 4p state this is just about lo3 W/cm*. Recently, Liu et al. [13,14] have repeated experiments on the interference effects with sodium 4D which were previously reported in Refs. [7,8], and have also repeated similar measurements using lithium 3s and 4s states. Their effort was to re-examine the validity of the condition for establishing interference. Their first finding is that ~a~z/r> 1 is not the correct condition for establishing the destructive quantum interference, and the correct one should be (f32fl;)/(f,3A2) z+ 1 as given by Malakyan [9]. In the latter case, fij is the oscillator strength of the transition involved, a2 is the two-photon Rabi frequency, and A is the detuning to the upper state of the two-photon resonance. Contrary to several previous studies [4,6-81, they have concluded that the interference is dependent upon the laser intensities. We would like to point out, however, that the laser intensity used in their experiment [ 131 was above the saturation intensity for the 4D two-photon transition, rendering the comparison of the relation obtained by Garrett et al. [8], as well as the one obtained by Malakyan [9], baseless. The second finding of Liu’s experiments is the reappearance of weak forward directed hyper-Raman emission, which was totally suppressed by destructive interference in previous studies [6-81. This is not surprising given the fact that the system was hard driven in their experiments. As a matter of fact, it has been known even in the late 70s that strong pumping would certainly spoil the very delicate phase relation required for establishing quantum interference. In the transition region between weak and strong pumping regimes the situation is far more complex, and no theory is yet capable of satisfactorily explaining the rich, dynamic and complicated emission spectra. It is interesting to note that for the power densities used in these studies the forward directed hyper-Raman emission observed by Liu and coworkers is still very weak compared with the backward hyper-Raman field and the emission spectrum is still comparable in spectral content to that determined by the laser bandwidth (see Figs. 3(a). 3(b) in Ref. [13]). Essentially, they were working in such a transition region (5.6 X 10’ W/cm’), and the data had to be processed mathematically in order to show the difference. This is because at power density of 5.6 X 10’ W/cm* the two-photon Rabi frequency is just slightly larger than the bandwidth of the laser used and the system is not being driven adiabatically, hence it should not be a lot broader than the low intensity case. A much convincing demonstration of the forward hyper-Raman generation requires a Rabi frequency that is much larger than the laser bandwidth so that the system is driven adiabatically. This condition can be easily achieved using 4p one-photon pumping.
142 (1997) 253-256
In this Letter we report on a combined study on both weak and strong pumping of sodium 4p level. We show that: (i) under strong pumping condition the forward hyper-Raman reappears and the interference was defeated; (ii) unlike the backward hyper-Raman, the forward component exhibits gain over a broad continuum determined by the size of the ac Stark effect introduced by the strong laser field. One can show that with a multimode laser this gain is possible only in the forward direction. Indeed, the large ac Stark shifts greatly decrease the hyper-Raman in the backward direction. We have developed a theoretical treatment which includes these effects resulting from strong one-photon pumping of the present system. It will not be presented because of the space limitation [ 151.Studies on the strong pumping of the sodium 4D state [15] have also yielded similar results in which both forward hyper-Raman and UV four-wave mixing field exhibit much wider emission profiles. The emission profiles presented here result from the near resonance one-photon pumping of the 4P,,, or 4P,,2 state in sodium. There are two downward branches that give rise to the stimulated emissions that are of interest here. To reach the 4p levels of sodium we first frequencydoubled the output of a Lumonics HyperDye 300 pulsed dye laser (bandwidth 2 0.1 cm- ‘1 pumped by a SpectraPhysics DCR-2A Q-switched Nd:YAG laser (pulse length 7 ns). The 330.0 nm UV laser was then delivered to a conventional sodium heat pipe oven. Ar was used as buffer gas with pressure set typically at 4 Torr so that at the lower metal vapor pressures the heat pipe was not operated in the heat-pipe mode. Both forward and backward emissions involving different emission branches were analyzed using a Jarrel-Ashe 0.5 m spectrometer with suitable gratings and detectors. For the 4p -+ 3d -+ 3p --f 3s branch (4-3-3-3 branch) presented here we used a RCA Cl1314 photomultiplier to detect the emission at about 819 nm (3d -+ 3~). The experiments were carried out in two energy regions. First, a weak laser beam was used for the excitation in order to avoid saturation of the one-photon transition. The laser was unfocused with a beam diameter of about 3 mm and energy typically ranging from a few micro-Joules to a few hundred micro-Joules, depending upon the detuning selected in a given scan. Both forward and backward hyper-Raman emission in the 819 nm region were analyzed. We then increased the pump intensity to several milli-Joules to strongly saturate the one-photon transition. Both forward and backward hyper-Raman emission were recorded again and compared with the emission spectra obtained in the unsaturated regime. Special care was taken to ensure that the detection geometry for the forward and backward emissions produced identical detection efficiencies. In both directions two spatial filters (2 mm in diameter) in each arm ensured that only axial emission was injected into the spectrometer for analysis. When the laser was tuned near one-photon resonance with one of the 4p sub-levels in sodium, a difference
255
L. Deng et al. / Optics Communications 142 (IY97J 253-256 frequency field o,, is generated during the time interval in which all three fields (in a given path) are present simultaneously. However, the generated wave-mixing field (3p + 3s) is also strongly reabsorbed. With suitable excitation energy (to ensure the weak pumping) and concentrations, the gain for the ,forward component of third step of the stimulated emission processes will be strongly suppressed [IO]. Such interference involves two pathways leading to the terminal 3p level. The first pathway involves the absorption of one laser photon and the stimulated emissions of one Raman photon and one hyper-Raman photon, terminating on the 3P,,z or 3P,,, state. The second pathway is created by absorption of the internally generated four-wave mixing photon at the difference frequency w,. The two transition probability amplitudes to the 3p level have the same magnitudes but are 180” out of phase, resulting in cancellation of the 3P ,,z,3,z excitation. Fig. 1 shows the energy level diagram. In Fig. 2 we show a typical scan of the stimulated hyper-Raman profile associated with the 4-3-3-3 branch, where the UV pump laser was tuned 5 cm- ’ below the 4P,,, level. In this figure, the upper trace is for backward emission while the lower trace shows the profile for forward emission. When the pump laser was detuned close to the 4P,,, state on the low energy side, we have observed two sharp peaks in the backward emission spectrum. These two peaks are located at about 818.3 nm and 819.5 nm respectively, corresponding to the two emission pathways in the 4-3-3-3 branch, i.e. 4Pj,? + 3D5,?+ 3P,,, (X19.5 nml and 4P,,, + 3D .7/z -j 3P,,, (818.3 nm). The ratio of the two peak heights. however, is strongly dependent upon both laser intensity and the laser detuning from the 4P,,, level because of competition between emissions associated with the two 4p fine structure levels. Although the photon
4P3l2
4p1/2
6 <_t--____. 1
OSRS +-
j
%HRS
WL
Fig.
1. Energy
schemes.
level diagram
3d5f2,3t2
11 o,,,
3p3,2
7-r
3Pu2
showing
relevant
laser coupling
0.12 ,
z 0.10 *g f
T=315”
o.oot 4
818.5
B
’ 819.0
’
’
’ ’ 820.0
’
819.5 Wavelength
j
’
820.5
(nm)
Fig. 2. Scan of the SHRS profiles in the weak pumping regime for the 4P,,, + 3D,,: + 3P,,, branch at T = 315”. Laser was tuned to 5 cm-’ above the 4P,,, level. Upper trace: the forward emission profile; lower trace: the backward emission profile. Notice that the forward component is totally suppressed.
energy is closer to the 4P,,? than to the 4P,,, level, the contribution from the 4P,,, level can be significant due to the fact that the latter transition has twice the oscillator strength of the 4P,,, level. Indeed, when tuned to the low energy side of the 4P,,2 level, we have observed a region where the two peaks have comparable heights. As the laser was tuned further away from the 4P,,, state toward lower energy, the contribution from the 4PX,2 level diminishes quickly, and finally only the 4P,,? + 3D,,, + 3P,,z (818.3 nm) transition can be seen in the backward emission profile. On the other hand, if the laser is detuned to the high energy stde of the 4P,,? level. the transition 4PJ,, ---) 3D,,, + 3P,,2 (819.5 nm) dominates, and we expect to see only one peak located at 819.5 nm (see Fig. 2). In any case, however, no forward emission can be detected. We could reproduce similar spectra even when the laser intensity was varied by a factor of 5 to 8 (for instance, from 10 pJ to 80 FJ for the data shown here), as long as we keep the system from being close to the saturation regime for the given detuning. In another words, as long as the condition for weak pumping is observed, we observed no intensity dependence of the interference effects, just as reported before [6-81. These results are in agreement with the theory on destructive quantum interference encountered in the low pumping regime. When the intensity of the laser was increased significantly so that strong saturation of the one-photon excitation was established, quite different hyper-Raman emission characteristics have been observed. In this situation, the ground state is significantly depleted and large ac Stark shifts (or Autler-Townes splittings) have been introduced into both the ground state and the upper state of the one-photon resonance. A crude way to see why this strong pumping could destroy the quantum interference is to observe the atomic wave function under such strong exci-
256
L. Deng et al. / Optics Communications
142 f 1997) 253-256
ration were encountered. The observed forward hyper-Raman emission is much stronger and much broader in comparison with the backward hyper-Raman emission. We conclude that quantum interference cannot be effectively established in such strong pumping situation.
Acknowledgements
t.,..,.,,.,,...,....~ 808.5
819
819.5
Wavelength
820
820.5
(urn)
Fig. 3. Same as Fig. 2. except that laser energy was 3 m.l (same beam diameter as in Fig. 2). The intensity was several orders of magnitude above the saturation intensity for the detuning selected, and the transition was strongly saturated. Upper trace: the forward emission profile: lower trace: the backward emission profile. Notice that the forward component is much stronger and broader.
This research was partly sponsored by National Science Foundation Grant PHY-9540854 and by US Department of Energy Office of Health and Environmental Research under contract DE-AC05840R21400 with Lockheed Martin Energy System, Inc. The summer support to L. Deng from Oak Ridge Associated Universities (ORAU)/Oak Ridge Institute of Science and Engineering (ORISE) is gratefully acknowledged and experiments were carried out at the Oak Ridge National Laboratory.
References [5]. One finds that the ac Stark shift will appear in the phase factor of the atomic wavefunction just like the bandwidth of the laser. Also, a large population can appear in the upper state, even when the laser is detuned considerably from resonance. Such large and pulsing ac Stark shifts and the production of an excited state population will unavoidably change the very sensitive phase relations required for establishing the quantum interference. Once the suppression mechanism is defeated we would expect a gain for the forward hyper-Raman emission. Due to the large broad ac Stark shifts induced by strong pumping, the spectrum of the forward directed hyper-Raman emission should be much broader than that of the backward emission. In Fig. 3 we show a scan of the stimulated hyper-Raman profile associated with the 4-3-3-3 branch (4P,,, + 3D5,, + 3P3,>, 819.5 nm), where the UV pump laser was tuned 5 cm-’ above the 4P,,, level. The upper trace is for forward emission while the lower trace shows the profile for backward emission. The energy used for these measurements was typically several milli-Joules (usually 2 to 3 orders of magnitude higher than the saturation intensity at given detuning). Comparing with Fig. 2 we see the reappearance of the forward hyper-Raman emission which is much stronger and much broader than its backward directed counter-part, as expected. We have also observed the similar competition between 4P,,, and 4P,,, levels found in the weak pumping regime when the laser was detuned to the low energy side of the 4P,,, level. Such a competitive behavior exhibited characteristics that are similar to those observed in the weak pumping regime. In conclusion we have observed forward directed hyper-Raman emission in the strong excitation regime where both ground state depletion and one-photon transition satutation
111 E.A. Manykin, A.M. Afanas’ev.
Sov. Phys. JETP 21 (1967) 619; 25 (1967) 828. Dl J.C. Miller, R.N. Compton, M.G. Payne, W.R. Garrett, Phys. Rev. Lett. 75 (1980) 114; M.G. Payne, W.R. Garrett, H.C. Baker, Chem. Phys. Lett. 75 (1980) 468; M.G. Payne, W.R. Garrett, Phys. Rev. A 26 (1982) 356; M.G. Payne, W.R. Garrett, W.R. Ferrell, Phys. Rev. A 26 (1986) 1143. 131 D.J. Jackson, J.J. Wynne, Phys. Rev. Lett. 49 (1983) 543; D.J. Jackson, J.J. Wynne, P.H. Kes, Phys. Rev. A 28 (1983) 781. 141 W.R. Garrett, S.D. Henderson, M.G. Payne, Phys. Rev. A 34 (1986); Phys. Rev. A 35 (1987) 5032. 151M.G. Payne, J.Y. Zhang, W.R. Garrett, Phys. Rev. A 48 (1993) 2334: L. Deng, J.Y. Zhang, M.G. Payne. W.R. Garrett, Phys. Rev. Lett. 73 (1994) 2035. [d M.A. Moore, W.R. Garrett, M.G. Payne. Optics Comm. 68 (1988) 310. 171 R.K. Wunderlich, W.R. Garrett, R.C. Hart, M.A. Moore, M.G. Payne. Phys. Rev. A 41 (1990) 6345. [81 W.R. Garrett, M.A. Moore, R.C. Hart, M.G. Payne, R.K. Wunderlich. Phys. Rev. A 45 (1992) 6687. 191 Y.P. Malakyan, Optics Comm. 69 (1988) 315. There are numerous errors in this paper. For instance. the equations of motion and the inclusion of the ac Stark shift; Y.P. Malakyan, J. Phys. B 23 (1990) 131. 1101W.R. Garrett, R.C. Hart. J.C. Miller, M.G. Payne, J.E. Wray, Optics Comm. 86 (1991) 205. 1111W.R. Garrett, V.W. Bamett, M.A. Moore, M.G. Payne, Optics Lett. 19 (1994) 581. 1121M.G. Payne, L. Deng, W.R. Garrett. a review article to be submitted to Rev. Mod. Phys. 1131M.H. Lu. Y.M. Liu, J. Phys. B 27 (1994) 5089. 1141M.H. Lu. Y.M. Liu, Appl. Phys. B. 57 (1993) 167. 1151M.G. Payne, L. Deng, W.R. Garrett, Forward Continuum stimulated Raman emission with an intense pump laser tuned near a resonance, Phys. Rev. A, submitted.
1997
OPTICS COMMUNICATIONS ELSEVIER
Optics Communications
142 (1997) 253-256
Observation of broadband forward hyper-Raman emission with high intensity focused laser beams Lu Deng as’,W.R. Garrett a, M.G. Payne a~1,D.Z. Lee b ” Chemical Physics Section. Oak Ridge Natronal Laborato?. Oak Ridge, TN 37831. USA h Department qf Physics, The UniwrsiQ qf British Columbia. Vancouver, B.C.. Cunada V5K IT3 Received 25 March 1997: revised 3 1 May 1997: accepted 9 June 1997
Abstract We show that the well known multiphoton destructive interference, which leads to hyper-Raman gain suppression in the weak pumping regime, no longer occurs under strong pumping conditions. In contrast to the weak pumping case. where no forward hyper-Raman can be observed and strong backward hyper-Raman occurs, forward hyper-Raman emission is found to be much stronger under strong pumping conditions. The emission spectrum acquires new characteristics due to the ac Stark effect introduced by the strong laser field. The frequency spectrum of the forward hyper-Raman is no longer determined by the laser bandwidth, instead a continuum of forward hyper-Raman emission is observed with the width being determined by the peak power density. We will present here a comparison between strong and weak pumping regimes. 0 1997 Elsevier Science B.V.
It is well known that certain resonant and near resonant multiphoton processes in gaseous media can be greatly modified by optical interference phenomena under well understood circumstances [l-8]. The effects, that can suppress or otherwise modify several types of laser driven transitions. involve the production and influence of internally generated wave-mixing fields. It has been shown that both even-photon and odd-photon induced transitions can become strongly influenced by such nonlinear interference effects. Resonant two-photon pumping can become strongly modified through an interference involving the phase matched parametric four-wave mixing that couples back to the ground state [l-3,5] and two-photon coupling due to the laser. On the other hand. in the case of odd-photon coupling of optically allowed transitions, interferences and their exotic consequences can be produced by the internally generated wave mixing fields that are poorly phase matched or strongly absorbed in resonant media. The effects in this category include strong suppression of odd-
’ Permanent address: Physics Department, University. Statesboro. Georgia 30460-803 I,
Georgia
Southern
0030.4018/97/$17.00 8 1997 Elsevier Science B.V. All rights reserved. PI1 SOO30-30 18(97)003 16-7
photon resonant excitations under unidirectional pumping, complex shifting of excitation profiles under multi-color cross beam pumping and the suppression of the ac Stark shifting [3-51. The strong suppression of the gain for forward-directed stimulated hyper-Raman scattering (SHRS) [h-9] and the large pressure dependent frequency shifts for SHRS profiles [ IO,1 I] are some of the most intriguing manifestations of this interference effect. It mctst be pointed out, however, that all these fascinating observations were made in the NXYZ~~ pumping regime. The theory, which has been able to predict all these manifestations of the destructive interference, is based on the conditions that the ground state is not depleted and the transitions involved are far from being saturated. Thus. the condition for establishing the quantum destructive interference thereafter derived [8], i.e. K~,,:/~‘B 1 (?~,,,/r is the absorption coefficient, : is the distance of propagation, and r is the laser bandwidth), is applicable only to the weak pumping regime. (For a review of the theory, see Ref. [ 1I]). This theory should IUZMYbe stretched to the region where either ground state depletion or saturation of the transition involved is likely to happen. Indeed, the gain for backward hyper-Raman should be kept small compared with the
254
L. Deng et al. / Optics Communications
absorption coefficient for the associated four-wave mixing field. For the two-photon excitation of the sodium 4D state, the required laser intensity must be I 10’ W/cm’ in order to avoid the saturation of the two-photon transition [7,8]. In the one-photon pumping of the sodium 4p state this is just about lo3 W/cm*. Recently, Liu et al. [13,14] have repeated experiments on the interference effects with sodium 4D which were previously reported in Refs. [7,8], and have also repeated similar measurements using lithium 3s and 4s states. Their effort was to re-examine the validity of the condition for establishing interference. Their first finding is that ~a~z/r> 1 is not the correct condition for establishing the destructive quantum interference, and the correct one should be (f32fl;)/(f,3A2) z+ 1 as given by Malakyan [9]. In the latter case, fij is the oscillator strength of the transition involved, a2 is the two-photon Rabi frequency, and A is the detuning to the upper state of the two-photon resonance. Contrary to several previous studies [4,6-81, they have concluded that the interference is dependent upon the laser intensities. We would like to point out, however, that the laser intensity used in their experiment [ 131 was above the saturation intensity for the 4D two-photon transition, rendering the comparison of the relation obtained by Garrett et al. [8], as well as the one obtained by Malakyan [9], baseless. The second finding of Liu’s experiments is the reappearance of weak forward directed hyper-Raman emission, which was totally suppressed by destructive interference in previous studies [6-81. This is not surprising given the fact that the system was hard driven in their experiments. As a matter of fact, it has been known even in the late 70s that strong pumping would certainly spoil the very delicate phase relation required for establishing quantum interference. In the transition region between weak and strong pumping regimes the situation is far more complex, and no theory is yet capable of satisfactorily explaining the rich, dynamic and complicated emission spectra. It is interesting to note that for the power densities used in these studies the forward directed hyper-Raman emission observed by Liu and coworkers is still very weak compared with the backward hyper-Raman field and the emission spectrum is still comparable in spectral content to that determined by the laser bandwidth (see Figs. 3(a). 3(b) in Ref. [13]). Essentially, they were working in such a transition region (5.6 X 10’ W/cm’), and the data had to be processed mathematically in order to show the difference. This is because at power density of 5.6 X 10’ W/cm* the two-photon Rabi frequency is just slightly larger than the bandwidth of the laser used and the system is not being driven adiabatically, hence it should not be a lot broader than the low intensity case. A much convincing demonstration of the forward hyper-Raman generation requires a Rabi frequency that is much larger than the laser bandwidth so that the system is driven adiabatically. This condition can be easily achieved using 4p one-photon pumping.
142 (1997) 253-256
In this Letter we report on a combined study on both weak and strong pumping of sodium 4p level. We show that: (i) under strong pumping condition the forward hyper-Raman reappears and the interference was defeated; (ii) unlike the backward hyper-Raman, the forward component exhibits gain over a broad continuum determined by the size of the ac Stark effect introduced by the strong laser field. One can show that with a multimode laser this gain is possible only in the forward direction. Indeed, the large ac Stark shifts greatly decrease the hyper-Raman in the backward direction. We have developed a theoretical treatment which includes these effects resulting from strong one-photon pumping of the present system. It will not be presented because of the space limitation [ 151.Studies on the strong pumping of the sodium 4D state [15] have also yielded similar results in which both forward hyper-Raman and UV four-wave mixing field exhibit much wider emission profiles. The emission profiles presented here result from the near resonance one-photon pumping of the 4P,,, or 4P,,2 state in sodium. There are two downward branches that give rise to the stimulated emissions that are of interest here. To reach the 4p levels of sodium we first frequencydoubled the output of a Lumonics HyperDye 300 pulsed dye laser (bandwidth 2 0.1 cm- ‘1 pumped by a SpectraPhysics DCR-2A Q-switched Nd:YAG laser (pulse length 7 ns). The 330.0 nm UV laser was then delivered to a conventional sodium heat pipe oven. Ar was used as buffer gas with pressure set typically at 4 Torr so that at the lower metal vapor pressures the heat pipe was not operated in the heat-pipe mode. Both forward and backward emissions involving different emission branches were analyzed using a Jarrel-Ashe 0.5 m spectrometer with suitable gratings and detectors. For the 4p -+ 3d -+ 3p --f 3s branch (4-3-3-3 branch) presented here we used a RCA Cl1314 photomultiplier to detect the emission at about 819 nm (3d -+ 3~). The experiments were carried out in two energy regions. First, a weak laser beam was used for the excitation in order to avoid saturation of the one-photon transition. The laser was unfocused with a beam diameter of about 3 mm and energy typically ranging from a few micro-Joules to a few hundred micro-Joules, depending upon the detuning selected in a given scan. Both forward and backward hyper-Raman emission in the 819 nm region were analyzed. We then increased the pump intensity to several milli-Joules to strongly saturate the one-photon transition. Both forward and backward hyper-Raman emission were recorded again and compared with the emission spectra obtained in the unsaturated regime. Special care was taken to ensure that the detection geometry for the forward and backward emissions produced identical detection efficiencies. In both directions two spatial filters (2 mm in diameter) in each arm ensured that only axial emission was injected into the spectrometer for analysis. When the laser was tuned near one-photon resonance with one of the 4p sub-levels in sodium, a difference
255
L. Deng et al. / Optics Communications 142 (IY97J 253-256 frequency field o,, is generated during the time interval in which all three fields (in a given path) are present simultaneously. However, the generated wave-mixing field (3p + 3s) is also strongly reabsorbed. With suitable excitation energy (to ensure the weak pumping) and concentrations, the gain for the ,forward component of third step of the stimulated emission processes will be strongly suppressed [IO]. Such interference involves two pathways leading to the terminal 3p level. The first pathway involves the absorption of one laser photon and the stimulated emissions of one Raman photon and one hyper-Raman photon, terminating on the 3P,,z or 3P,,, state. The second pathway is created by absorption of the internally generated four-wave mixing photon at the difference frequency w,. The two transition probability amplitudes to the 3p level have the same magnitudes but are 180” out of phase, resulting in cancellation of the 3P ,,z,3,z excitation. Fig. 1 shows the energy level diagram. In Fig. 2 we show a typical scan of the stimulated hyper-Raman profile associated with the 4-3-3-3 branch, where the UV pump laser was tuned 5 cm- ’ below the 4P,,, level. In this figure, the upper trace is for backward emission while the lower trace shows the profile for forward emission. When the pump laser was detuned close to the 4P,,, state on the low energy side, we have observed two sharp peaks in the backward emission spectrum. These two peaks are located at about 818.3 nm and 819.5 nm respectively, corresponding to the two emission pathways in the 4-3-3-3 branch, i.e. 4Pj,? + 3D5,?+ 3P,,, (X19.5 nml and 4P,,, + 3D .7/z -j 3P,,, (818.3 nm). The ratio of the two peak heights. however, is strongly dependent upon both laser intensity and the laser detuning from the 4P,,, level because of competition between emissions associated with the two 4p fine structure levels. Although the photon
4P3l2
4p1/2
6 <_t--____. 1
OSRS +-
j
%HRS
WL
Fig.
1. Energy
schemes.
level diagram
3d5f2,3t2
11 o,,,
3p3,2
7-r
3Pu2
showing
relevant
laser coupling
0.12 ,
z 0.10 *g f
T=315”
o.oot 4
818.5
B
’ 819.0
’
’
’ ’ 820.0
’
819.5 Wavelength
j
’
820.5
(nm)
Fig. 2. Scan of the SHRS profiles in the weak pumping regime for the 4P,,, + 3D,,: + 3P,,, branch at T = 315”. Laser was tuned to 5 cm-’ above the 4P,,, level. Upper trace: the forward emission profile; lower trace: the backward emission profile. Notice that the forward component is totally suppressed.
energy is closer to the 4P,,? than to the 4P,,, level, the contribution from the 4P,,, level can be significant due to the fact that the latter transition has twice the oscillator strength of the 4P,,, level. Indeed, when tuned to the low energy side of the 4P,,2 level, we have observed a region where the two peaks have comparable heights. As the laser was tuned further away from the 4P,,, state toward lower energy, the contribution from the 4PX,2 level diminishes quickly, and finally only the 4P,,? + 3D,,, + 3P,,z (818.3 nm) transition can be seen in the backward emission profile. On the other hand, if the laser is detuned to the high energy stde of the 4P,,? level. the transition 4PJ,, ---) 3D,,, + 3P,,2 (819.5 nm) dominates, and we expect to see only one peak located at 819.5 nm (see Fig. 2). In any case, however, no forward emission can be detected. We could reproduce similar spectra even when the laser intensity was varied by a factor of 5 to 8 (for instance, from 10 pJ to 80 FJ for the data shown here), as long as we keep the system from being close to the saturation regime for the given detuning. In another words, as long as the condition for weak pumping is observed, we observed no intensity dependence of the interference effects, just as reported before [6-81. These results are in agreement with the theory on destructive quantum interference encountered in the low pumping regime. When the intensity of the laser was increased significantly so that strong saturation of the one-photon excitation was established, quite different hyper-Raman emission characteristics have been observed. In this situation, the ground state is significantly depleted and large ac Stark shifts (or Autler-Townes splittings) have been introduced into both the ground state and the upper state of the one-photon resonance. A crude way to see why this strong pumping could destroy the quantum interference is to observe the atomic wave function under such strong exci-
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ration were encountered. The observed forward hyper-Raman emission is much stronger and much broader in comparison with the backward hyper-Raman emission. We conclude that quantum interference cannot be effectively established in such strong pumping situation.
Acknowledgements
t.,..,.,,.,,...,....~ 808.5
819
819.5
Wavelength
820
820.5
(urn)
Fig. 3. Same as Fig. 2. except that laser energy was 3 m.l (same beam diameter as in Fig. 2). The intensity was several orders of magnitude above the saturation intensity for the detuning selected, and the transition was strongly saturated. Upper trace: the forward emission profile: lower trace: the backward emission profile. Notice that the forward component is much stronger and broader.
This research was partly sponsored by National Science Foundation Grant PHY-9540854 and by US Department of Energy Office of Health and Environmental Research under contract DE-AC05840R21400 with Lockheed Martin Energy System, Inc. The summer support to L. Deng from Oak Ridge Associated Universities (ORAU)/Oak Ridge Institute of Science and Engineering (ORISE) is gratefully acknowledged and experiments were carried out at the Oak Ridge National Laboratory.
References [5]. One finds that the ac Stark shift will appear in the phase factor of the atomic wavefunction just like the bandwidth of the laser. Also, a large population can appear in the upper state, even when the laser is detuned considerably from resonance. Such large and pulsing ac Stark shifts and the production of an excited state population will unavoidably change the very sensitive phase relations required for establishing the quantum interference. Once the suppression mechanism is defeated we would expect a gain for the forward hyper-Raman emission. Due to the large broad ac Stark shifts induced by strong pumping, the spectrum of the forward directed hyper-Raman emission should be much broader than that of the backward emission. In Fig. 3 we show a scan of the stimulated hyper-Raman profile associated with the 4-3-3-3 branch (4P,,, + 3D5,, + 3P3,>, 819.5 nm), where the UV pump laser was tuned 5 cm-’ above the 4P,,, level. The upper trace is for forward emission while the lower trace shows the profile for backward emission. The energy used for these measurements was typically several milli-Joules (usually 2 to 3 orders of magnitude higher than the saturation intensity at given detuning). Comparing with Fig. 2 we see the reappearance of the forward hyper-Raman emission which is much stronger and much broader than its backward directed counter-part, as expected. We have also observed the similar competition between 4P,,, and 4P,,, levels found in the weak pumping regime when the laser was detuned to the low energy side of the 4P,,, level. Such a competitive behavior exhibited characteristics that are similar to those observed in the weak pumping regime. In conclusion we have observed forward directed hyper-Raman emission in the strong excitation regime where both ground state depletion and one-photon transition satutation
111 E.A. Manykin, A.M. Afanas’ev.
Sov. Phys. JETP 21 (1967) 619; 25 (1967) 828. Dl J.C. Miller, R.N. Compton, M.G. Payne, W.R. Garrett, Phys. Rev. Lett. 75 (1980) 114; M.G. Payne, W.R. Garrett, H.C. Baker, Chem. Phys. Lett. 75 (1980) 468; M.G. Payne, W.R. Garrett, Phys. Rev. A 26 (1982) 356; M.G. Payne, W.R. Garrett, W.R. Ferrell, Phys. Rev. A 26 (1986) 1143. 131 D.J. Jackson, J.J. Wynne, Phys. Rev. Lett. 49 (1983) 543; D.J. Jackson, J.J. Wynne, P.H. Kes, Phys. Rev. A 28 (1983) 781. 141 W.R. Garrett, S.D. Henderson, M.G. Payne, Phys. Rev. A 34 (1986); Phys. Rev. A 35 (1987) 5032. 151M.G. Payne, J.Y. Zhang, W.R. Garrett, Phys. Rev. A 48 (1993) 2334: L. Deng, J.Y. Zhang, M.G. Payne. W.R. Garrett, Phys. Rev. Lett. 73 (1994) 2035. [d M.A. Moore, W.R. Garrett, M.G. Payne. Optics Comm. 68 (1988) 310. 171 R.K. Wunderlich, W.R. Garrett, R.C. Hart, M.A. Moore, M.G. Payne. Phys. Rev. A 41 (1990) 6345. [81 W.R. Garrett, M.A. Moore, R.C. Hart, M.G. Payne, R.K. Wunderlich. Phys. Rev. A 45 (1992) 6687. 191 Y.P. Malakyan, Optics Comm. 69 (1988) 315. There are numerous errors in this paper. For instance. the equations of motion and the inclusion of the ac Stark shift; Y.P. Malakyan, J. Phys. B 23 (1990) 131. 1101W.R. Garrett, R.C. Hart. J.C. Miller, M.G. Payne, J.E. Wray, Optics Comm. 86 (1991) 205. 1111W.R. Garrett, V.W. Bamett, M.A. Moore, M.G. Payne, Optics Lett. 19 (1994) 581. 1121M.G. Payne, L. Deng, W.R. Garrett. a review article to be submitted to Rev. Mod. Phys. 1131M.H. Lu. Y.M. Liu, J. Phys. B 27 (1994) 5089. 1141M.H. Lu. Y.M. Liu, Appl. Phys. B. 57 (1993) 167. 1151M.G. Payne, L. Deng, W.R. Garrett, Forward Continuum stimulated Raman emission with an intense pump laser tuned near a resonance, Phys. Rev. A, submitted.