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Two-photon induced stimulated Raman scattering in cesium vapor
Volume
21, number
I
April 1977
OPTICS COMMUNICATIONS
TWO-PHOTON INDUCED STIMULATED
RAMAN SCATTERING
IN CESIUM VAPOR
Q.H.F. VREHEN and H.M.J. HIKSPOORS Philips Research Laboratories, Eindhoven, Received
10 January
Two-photon
The Netherlands
1977
induced
stimulated
Raman
scattering
has been
and subsequently
nNLfi3(w2,WL
Wl
X
1
lP,,12
A@)31
1
2wL + ws ++ir)(ozl
-
2.q
21/+, I2 - WJ21
- as>
- WL)2
(1)
1’ 2
where pii is a dipole matrix element, wii a transition frequency, N the atomic number density and r the width of the final level 2. In (1) the first term within the square brackets represents the two-photon induced Raman scattering, and the second term the three-photon scattering. In the system to be discussed below the first 127
Volume 21. number 1
OPTICS COMMUNICATIONS 7 S ‘/z ( 18536 cm-‘)
Fig. 2. Relevant part of the energy level scheme in cesium. Hyperfine structure has been neglected. All energies are given in wavenumbers. The levels 6S1/,, 6Pq2 and 7S1/* act as the levels 1,2 and 3 in fig. lb.
term is about ten times larger than the second; the terms have the same sign and interfere constructively. In our experiments we have irradiated cesium vapor with radiation from a Nd : YAG laser at 1.064 pm. The relevant energy levels [6] are sketched in fig. 2, where hypertine structure has been neglected. The levels 1, 2 and 3 correspond respectively to the ground level 6S,,,, and the excited levels 6P3,2 and 7s near two-photon resonance 2:‘2’ -W31=254cm The system has:4 . Two-photon resonant enhaAcem:nt of self-defocusing in the same system was observed by Lehmberg and coworkers [7]. Evidently the cesium atom is not a true three-level system. We have not observed any stimulated scattering to 6P,,,, but the presence of that level enhances the susceptibility (1) for scattering to 6P,,2 by roughly a factor of 2.5. More importantly, the degeneracy of the level 6P3,2 leads to interesting polarization effects. First we notice that the two-photon induced Raman scattering cannot be excited by circularly polarized light since the two-photon transition from 6S1,2 of a unito 7%/2 is forbidden for circular polarization directional excitation beam. On the other hand, threephoton scattering can occur for linearly and for circularly polarized excitation with equal probability. Thus one can distinguish experimentally between the two types of scattering by making observations both for linearly and for circularly polarized excitation. Second, in two-photon induced Raman scattering the polarization of the scattered light can be parallel or perpendicular to that of the exciting light with equal probability, whereas in three-photon scattering the polarization of 128
April 1977
the scattered light is strongly coupled to the polarization of the excitation (parallel linear for linearly polarized excitation and opposite circular for circularly polarized excitation). In principle, the two-photon induced stimulated Raman scattering can occur both in the forward and in the backward direction. However, in the forward direction an additional nonlinear optical process is possible, four-photon parametric generation, as indicated in fig. lc. In this process two laser photons wL are converted into a signal photon ws and an idler photon wi. Since the parametric conversion requires a certain degree of phase matching it does not contribute to the backward scattering. Thus both stimulated Raman scattering and parametric generation contribute to the forward scattering, whereas the backward scattering is solely due to stimulated Raman scattering. We have actually observed the forward scattering and the results will be reported in a separate publication. Here we wish to focus our attention on the two-photon induced stimulated Raman scattering and consequently we restrict ourselves to a discussion of the backward scattering. It is instructive to calculate the expected Raman gain from (1). From the oscillator strengths [8] we find the dipole matrix elements for linear polarization as p21 = 7.0 X lo-” e.s.u. and p32 = 6.6 X 10-l’ e.s.u. At low densities the width r‘ is determined by Doppler broadening, r,/(2n) = 1073 MHz for T= 500 K, corresponding to a saturated vapor pressure of 0.25 torr and a densityN = 4.8 X 10ls cme3; at this density the gain coefficient g has the value g = 1.2 X lo-l8 cm3/W2. At high d ensities the width r is determined by Holtsmark braodening, rH/(2n) = 4.8 X lo-l7 N GHz [9]. Since rH is proportional to the density, the gain coefficient is independent of density when Holtsmark broadening dominates, i.e., for N > 2.0 X 1016 cme3 or p > I torr; for such densities one finds g = 5.4 X lo-l8 cm3/W2. In calculating these gain coeffieients it has been assumed that the bandwidth of the laser radiation is smaller than the width of the transition. As already mentioned the presence of the level 6P, 2 enhances the gain by a factor 2.5, to g = 1.4 X lo- h7 cm3/W2 at high densities. Our experimental apparatus is presented in fig. 3. The laser beam is generated by a Nd : YAG laser oscillator/amplifier system. A pulse of 2 nsec length is cut out of a 30 ns Q-switched pulse by electro-optical means. The output mirror of the laser oscillator is either a two plate sapphire resonant reflector, yielding
Volume 21, number 1 GLPSS
PLATES
OPTICS COMMUNICATIONS CESIUM
HEATPIPE
Fl
Pl
LYlYrL MONITOR
Fig. 3. Schematic diagram of the experimental apparatus. Fl, F2 and F3 filters; P,, P, Polaroid analyzers; D1, Dz, D3 detectors. The monitor stored in a Tektronic
April 1977
displays the input and output Transient Digitizer.
pulse as
a laser linewidth of 0.02 cm-‘, or a dielectric mirror yielding a laser linewidth of 0.4 cm-‘. In both cases the maximum peak power amounts to about 150 MW. With the help of a concave mirror (R = 5 m) the beam is focused into a cesium heat pipe. The cross-sectional area at the focus (0.55 mm2) and divergence angle (full angle 1.55 mrad) indicate the presence of three to four transverse modes in the beam. The heat pipe has a length of 200 cm. The cesium column extends over the central 120 cm. A fraction of the input beam is deflected into a detector for monitoring its pulse shape and amplitude. The laser beam is linearly polarized; a dh plate can be inserted to study the effect of circularly polarized pumping radiation. The scattered light can be studied both in the forward and in the backward direction. The pumping radiation is removed with a suitable filter (a 3 mm silicon plate at an elevated temperature); analyzers allow us to study the polarization of the scattered light, which is spectrally resolved with a monochromator, detected with a germanium avalanche detector (Optitron GA 1) and displayed on the monitor of a Tektronix Transient Digitizer. For two-photon induced backward stimulated Raman scattering we have observed a threshold of about 2.5 GW/ cm2 for linearly polarized pump light. For circularly polarized pump light we have not been able to reach threshold with intensities as high as 10 GW/cm2. This observation clearly proves the overriding importance of the near two-photon resonance, which in the present case of a transition from 6S,,, to 7S contributes only for linearly polarized pump ligh:i2 For pump intensities above 2.5 GW/cm2 stimulated scattering occurs with a laser linewidth of 0.02 cm-’
F3g. 4. by the second duced a peak div.).
Photograph of a typical pulse sequence as displayed monitor. The first pulse is the input laser pulse, the pulse, with opposite polarity, is the two-photon inbackward stimulated Raman pulse. The pump pulse has power of 50 MW, the scattered pulse of 10 kW (2 ns/
for vapor pressures above 0.2 torr and with a laser linewidth of 0.4 cm-’ for vapor pressures between 4 torr and 80 torr. Qualitatively one would expect such behaviour from the dependence of the Raman gain on density and linewidth and from the dependence of the atomic linewidth on the density, as discussed above. Extensive measurements have been made at 0.2 torr, at 10 torr and at 40 torr with essentially the same results. In fig. 4 the pump pulse and the Raman pulse are displayed with opposite polarity; the pulse powers are 60 MW and 10 kW respectively. It can be seen that the backward scattered pulse is short. Apparently, the scattered pulse is not generated over the full 120 cm length of the cesium column (which would require the scattered pulse to be nearly 8 ns long) but only over about 10 cm or less. One might then expect the generation to take place near the focus of the pump beam, which, in the absence of any cesium, lies very close to the center of the heat pipe. However, from the delay time of the backward scattered pulse we conclude that it is generated when the pump pulse propagates through the first few centimeters of the cesium vapor. Probably the laser beam is rapidly defocussed [7], so that the highest intensities occur near the front end of the cesiurn column. Indeed, we have clearly observed self-defocusing at the prevailing intensities and vapor densities. The spectrum of the backward scattered light is presented in fig. 5. Each experimental point is the average for ten shots with pump powers (50 f 7) MW. The cesium pressure was 40 torr, corresponding to a Holtsmark linewidth of the 6P,,, level of 0.9 cm-’ ; the spectral resolution was 1.3 cm-‘, the laser line129
Volume
2 1, number
1
I
POLARIZATION o-0-0
1
x--x--x
II
1 +* k
I
7OLO
7030
wg Icmi’)
‘\ 7050 -
7060 65 112
r;ig. 5. Spectrum of the two-photon induced backward stimulated Raman light. Crosses for polarization parallel to that of the laser radiation, open circles for perpendicular polarization. Each experimental point is the average for 10 shots. Intensity (50 i 7) MW, vapor pressure 40 torr, Holtsmark width of the 6Pq2 level 0.9 cm-‘, spectral resolution of monochromator 1.3 cnl’ A: calculated frequency for scattering to 6P3/, without optical Stark effect; B and C: calculated frequencies for scattering to (6P3j2, +3/2) and (6P,/,, i-1/2) respectively, when optical Stark shifts arc included.
width 0.4 cm-‘. Instead of a single line with a width of about 2 cm-l we observe two broader bands, one for polarization parallel to that of the laser and one for polarization perpendicular. Both bands are shifted from the nominal position A of the 6Pji2 level. We explain the spectrum by taking into consideration the optical Stark shifts of the relevant levels. We have calculated these shifts for the exciting wavelength of 1.064 pm using level energies and oscillator strengths from the literature [6,8]. The results are summarized in fig. 6. The 6Sli2 ground level is shifted downwards, excited level is split into a +$ component the and 6P312 a +z component. More quantitatively, we find for I .064 pm AE,(~S~,~)= AE,(6P3,2,
-10.9
X lo-l2
cm-‘/(V/cm)2,
+5_) = +4.7 X lo-l2
A60(6P3,2, ++)= -3.948
cm-1/(V/cm)2,
X lo-l2
cm-1/(V/cm)2.
To check our calculations we also computed Stark shifts, and we found Aes(6S,,,)=
-1.8 X lo-l2
AE~(~P,,~, +)= 130
April 1977
OPTICS COMMUNICATIONS
-7.6
cm-1/(V/cm)2,
X 1012 cm-1/(V/cm)2,
the DC
-
I ?112 OPTICAL ATOMIC
STARK
SHIFTS
CESIUb’
Fig. 6. Optical Stark effect of the levels 6S1j2, (6P,/,, *3/2) and (6Pq2, *l/2) of atomic sodium. Scattering to (6P3/2, +3/2) and (6P,/,, *l/2) corresponds to perpendicular and parallel polarization respectively. Numerical values arc given in the te\t.
AE~(~P,,~, +j)=
--5.69X
lo-l2
cm-1/(V/cm)2.
These values agree well with published experimental and theoretical results [lo] . In fig. 5 the lines B and C indicate the expected positions of the Raman lines for scattering to (6P3,2, ?f) and (6P3,2, *h) with perpendicular and parallel polarization respectively and for a pump intensity of 3.2 GW/cm2, which is the measured value in these experiments. Good agreement exists with the position of the observed bands. The width of these bands is undoubtedly due to temporal and spatial non-uniformity of the intensity and to variations from shot to shot. With a gain coefficient g= 1.4x lo-l7 cm3/W2 and with a pump intensity I = 3.2 GW/cm2 the threshold condition g12L 2 20 can be met with an interaction length L of only 1 to 2 mm. Over such short distances along the pump beam the pump intensity and the optical Stark shifts are essentially constant. In summary, we have observed two-photon induced stimulated Raman scattering in cesium vapor. To the best of our knowledge this is the first observation of stimulated hyper-Raman scattering in any system. Spontaneous hyper-Raman scattering in molecular SYSterns has been reported before [ 111. In order to distinguish the stimulated hyper-Raman scattering from
Volume
21, number
1
OPTICS COMMUNICATIONS
four-photon parametric generation it is essential to study the backward scattered light. In our system the Raman line is shifted, split, and broadened by the optical Stark effect. This Stark effect combined with selfdefocusing of the laser beam explains the relatively high threshold intensity. The results show that fifth order optical nonlinearities can become important in metal vapors.
References [l]
P.P. Sorokin, N.S. Shiren, J.R. Lankard, E.C. Hammond and T.G. Kazyaka, Appl. Phys. Letters 10 (1967) 44. [2] N.N. Badalyan, V.A. Iradyan, and M.E. Movsesyan, JETP Letters 8 (1968) 316 [ZhETF Pis. Red. 8 (1968) 5181. 131 V.M. Arutyunyan, T.A. Papazyan, Yu.S. Chilingaryan, A.V. Karmenyan, and S.M. Sarkisyan, Sov. Phys. JETP 39 (1974) 243 [Zh. Eksp. Teor. Fiz. 66 (1974) 5091.
April 1977
[4] J.L. Carlsten and A. SzGke, Phys. Rev. Letters 36 (1976) 661. [5] Q.H.F. Vrehen and H.M.J. Hikspoors, IX Intern. Quantum Electronics Conf., Amsterdam, 1976, paper LlO. Published in: Opt. Commun. 18 (1976) 113. [6] C.E. Moore, Atomic Energy Levels, Vol. 3, National Bureau of Standards, circular 467, Washington, 1958. [7] R.H. Lehmberg, J. Reintjes and R.C. Eckardt, Appl. Phys Letters 25 (1974) 374; R.H. Lehmberg, J. Reintjes and R.C. Eckardt, Phys. Rev. Al3 (1976) 1095. [8] P.M. Stone, Phys. Rev. 127 (1962) 1151. ] C.L. Chen and A.V. Phelps, Phys. Rev. 173 (1968) 62. ] A.M. Bench-Bruevich and V.A. Khodovoi, Sot. Phys. Uspekhi 10 (1968) 637 [Usp. Fiz. Nauk 93 (1967) 711. [ll ] R.W. Terhune, P.D. Maker and C.M. Savage, Phys. Rev. Letters 14 (1965) 681; S. Kielich, J.R. Lalanne, and F.B. Martin, Phys. Rev. Letters 26 (1971) 1295; W.Yu and R.R. Alfano, Phys. Rev. Al 1 (1975) 188.
131
21, number
I
April 1977
OPTICS COMMUNICATIONS
TWO-PHOTON INDUCED STIMULATED
RAMAN SCATTERING
IN CESIUM VAPOR
Q.H.F. VREHEN and H.M.J. HIKSPOORS Philips Research Laboratories, Eindhoven, Received
10 January
Two-photon
The Netherlands
1977
induced
stimulated
Raman
scattering
has been
and subsequently
nNLfi3(w2,WL
Wl
X
1
lP,,12
A@)31
1
2wL + ws ++ir)(ozl
-
2.q
21/+, I2 - WJ21
- as>
- WL)2
(1)
1’ 2
where pii is a dipole matrix element, wii a transition frequency, N the atomic number density and r the width of the final level 2. In (1) the first term within the square brackets represents the two-photon induced Raman scattering, and the second term the three-photon scattering. In the system to be discussed below the first 127
Volume 21. number 1
OPTICS COMMUNICATIONS 7 S ‘/z ( 18536 cm-‘)
Fig. 2. Relevant part of the energy level scheme in cesium. Hyperfine structure has been neglected. All energies are given in wavenumbers. The levels 6S1/,, 6Pq2 and 7S1/* act as the levels 1,2 and 3 in fig. lb.
term is about ten times larger than the second; the terms have the same sign and interfere constructively. In our experiments we have irradiated cesium vapor with radiation from a Nd : YAG laser at 1.064 pm. The relevant energy levels [6] are sketched in fig. 2, where hypertine structure has been neglected. The levels 1, 2 and 3 correspond respectively to the ground level 6S,,,, and the excited levels 6P3,2 and 7s near two-photon resonance 2:‘2’ -W31=254cm The system has:4 . Two-photon resonant enhaAcem:nt of self-defocusing in the same system was observed by Lehmberg and coworkers [7]. Evidently the cesium atom is not a true three-level system. We have not observed any stimulated scattering to 6P,,,, but the presence of that level enhances the susceptibility (1) for scattering to 6P,,2 by roughly a factor of 2.5. More importantly, the degeneracy of the level 6P3,2 leads to interesting polarization effects. First we notice that the two-photon induced Raman scattering cannot be excited by circularly polarized light since the two-photon transition from 6S1,2 of a unito 7%/2 is forbidden for circular polarization directional excitation beam. On the other hand, threephoton scattering can occur for linearly and for circularly polarized excitation with equal probability. Thus one can distinguish experimentally between the two types of scattering by making observations both for linearly and for circularly polarized excitation. Second, in two-photon induced Raman scattering the polarization of the scattered light can be parallel or perpendicular to that of the exciting light with equal probability, whereas in three-photon scattering the polarization of 128
April 1977
the scattered light is strongly coupled to the polarization of the excitation (parallel linear for linearly polarized excitation and opposite circular for circularly polarized excitation). In principle, the two-photon induced stimulated Raman scattering can occur both in the forward and in the backward direction. However, in the forward direction an additional nonlinear optical process is possible, four-photon parametric generation, as indicated in fig. lc. In this process two laser photons wL are converted into a signal photon ws and an idler photon wi. Since the parametric conversion requires a certain degree of phase matching it does not contribute to the backward scattering. Thus both stimulated Raman scattering and parametric generation contribute to the forward scattering, whereas the backward scattering is solely due to stimulated Raman scattering. We have actually observed the forward scattering and the results will be reported in a separate publication. Here we wish to focus our attention on the two-photon induced stimulated Raman scattering and consequently we restrict ourselves to a discussion of the backward scattering. It is instructive to calculate the expected Raman gain from (1). From the oscillator strengths [8] we find the dipole matrix elements for linear polarization as p21 = 7.0 X lo-” e.s.u. and p32 = 6.6 X 10-l’ e.s.u. At low densities the width r‘ is determined by Doppler broadening, r,/(2n) = 1073 MHz for T= 500 K, corresponding to a saturated vapor pressure of 0.25 torr and a densityN = 4.8 X 10ls cme3; at this density the gain coefficient g has the value g = 1.2 X lo-l8 cm3/W2. At high d ensities the width r is determined by Holtsmark braodening, rH/(2n) = 4.8 X lo-l7 N GHz [9]. Since rH is proportional to the density, the gain coefficient is independent of density when Holtsmark broadening dominates, i.e., for N > 2.0 X 1016 cme3 or p > I torr; for such densities one finds g = 5.4 X lo-l8 cm3/W2. In calculating these gain coeffieients it has been assumed that the bandwidth of the laser radiation is smaller than the width of the transition. As already mentioned the presence of the level 6P, 2 enhances the gain by a factor 2.5, to g = 1.4 X lo- h7 cm3/W2 at high densities. Our experimental apparatus is presented in fig. 3. The laser beam is generated by a Nd : YAG laser oscillator/amplifier system. A pulse of 2 nsec length is cut out of a 30 ns Q-switched pulse by electro-optical means. The output mirror of the laser oscillator is either a two plate sapphire resonant reflector, yielding
Volume 21, number 1 GLPSS
PLATES
OPTICS COMMUNICATIONS CESIUM
HEATPIPE
Fl
Pl
LYlYrL MONITOR
Fig. 3. Schematic diagram of the experimental apparatus. Fl, F2 and F3 filters; P,, P, Polaroid analyzers; D1, Dz, D3 detectors. The monitor stored in a Tektronic
April 1977
displays the input and output Transient Digitizer.
pulse as
a laser linewidth of 0.02 cm-‘, or a dielectric mirror yielding a laser linewidth of 0.4 cm-‘. In both cases the maximum peak power amounts to about 150 MW. With the help of a concave mirror (R = 5 m) the beam is focused into a cesium heat pipe. The cross-sectional area at the focus (0.55 mm2) and divergence angle (full angle 1.55 mrad) indicate the presence of three to four transverse modes in the beam. The heat pipe has a length of 200 cm. The cesium column extends over the central 120 cm. A fraction of the input beam is deflected into a detector for monitoring its pulse shape and amplitude. The laser beam is linearly polarized; a dh plate can be inserted to study the effect of circularly polarized pumping radiation. The scattered light can be studied both in the forward and in the backward direction. The pumping radiation is removed with a suitable filter (a 3 mm silicon plate at an elevated temperature); analyzers allow us to study the polarization of the scattered light, which is spectrally resolved with a monochromator, detected with a germanium avalanche detector (Optitron GA 1) and displayed on the monitor of a Tektronix Transient Digitizer. For two-photon induced backward stimulated Raman scattering we have observed a threshold of about 2.5 GW/ cm2 for linearly polarized pump light. For circularly polarized pump light we have not been able to reach threshold with intensities as high as 10 GW/cm2. This observation clearly proves the overriding importance of the near two-photon resonance, which in the present case of a transition from 6S,,, to 7S contributes only for linearly polarized pump ligh:i2 For pump intensities above 2.5 GW/cm2 stimulated scattering occurs with a laser linewidth of 0.02 cm-’
F3g. 4. by the second duced a peak div.).
Photograph of a typical pulse sequence as displayed monitor. The first pulse is the input laser pulse, the pulse, with opposite polarity, is the two-photon inbackward stimulated Raman pulse. The pump pulse has power of 50 MW, the scattered pulse of 10 kW (2 ns/
for vapor pressures above 0.2 torr and with a laser linewidth of 0.4 cm-’ for vapor pressures between 4 torr and 80 torr. Qualitatively one would expect such behaviour from the dependence of the Raman gain on density and linewidth and from the dependence of the atomic linewidth on the density, as discussed above. Extensive measurements have been made at 0.2 torr, at 10 torr and at 40 torr with essentially the same results. In fig. 4 the pump pulse and the Raman pulse are displayed with opposite polarity; the pulse powers are 60 MW and 10 kW respectively. It can be seen that the backward scattered pulse is short. Apparently, the scattered pulse is not generated over the full 120 cm length of the cesium column (which would require the scattered pulse to be nearly 8 ns long) but only over about 10 cm or less. One might then expect the generation to take place near the focus of the pump beam, which, in the absence of any cesium, lies very close to the center of the heat pipe. However, from the delay time of the backward scattered pulse we conclude that it is generated when the pump pulse propagates through the first few centimeters of the cesium vapor. Probably the laser beam is rapidly defocussed [7], so that the highest intensities occur near the front end of the cesiurn column. Indeed, we have clearly observed self-defocusing at the prevailing intensities and vapor densities. The spectrum of the backward scattered light is presented in fig. 5. Each experimental point is the average for ten shots with pump powers (50 f 7) MW. The cesium pressure was 40 torr, corresponding to a Holtsmark linewidth of the 6P,,, level of 0.9 cm-’ ; the spectral resolution was 1.3 cm-‘, the laser line129
Volume
2 1, number
1
I
POLARIZATION o-0-0
1
x--x--x
II
1 +* k
I
7OLO
7030
wg Icmi’)
‘\ 7050 -
7060 65 112
r;ig. 5. Spectrum of the two-photon induced backward stimulated Raman light. Crosses for polarization parallel to that of the laser radiation, open circles for perpendicular polarization. Each experimental point is the average for 10 shots. Intensity (50 i 7) MW, vapor pressure 40 torr, Holtsmark width of the 6Pq2 level 0.9 cm-‘, spectral resolution of monochromator 1.3 cnl’ A: calculated frequency for scattering to 6P3/, without optical Stark effect; B and C: calculated frequencies for scattering to (6P3j2, +3/2) and (6P,/,, i-1/2) respectively, when optical Stark shifts arc included.
width 0.4 cm-‘. Instead of a single line with a width of about 2 cm-l we observe two broader bands, one for polarization parallel to that of the laser and one for polarization perpendicular. Both bands are shifted from the nominal position A of the 6Pji2 level. We explain the spectrum by taking into consideration the optical Stark shifts of the relevant levels. We have calculated these shifts for the exciting wavelength of 1.064 pm using level energies and oscillator strengths from the literature [6,8]. The results are summarized in fig. 6. The 6Sli2 ground level is shifted downwards, excited level is split into a +$ component the and 6P312 a +z component. More quantitatively, we find for I .064 pm AE,(~S~,~)= AE,(6P3,2,
-10.9
X lo-l2
cm-‘/(V/cm)2,
+5_) = +4.7 X lo-l2
A60(6P3,2, ++)= -3.948
cm-1/(V/cm)2,
X lo-l2
cm-1/(V/cm)2.
To check our calculations we also computed Stark shifts, and we found Aes(6S,,,)=
-1.8 X lo-l2
AE~(~P,,~, +)= 130
April 1977
OPTICS COMMUNICATIONS
-7.6
cm-1/(V/cm)2,
X 1012 cm-1/(V/cm)2,
the DC
-
I ?112 OPTICAL ATOMIC
STARK
SHIFTS
CESIUb’
Fig. 6. Optical Stark effect of the levels 6S1j2, (6P,/,, *3/2) and (6Pq2, *l/2) of atomic sodium. Scattering to (6P3/2, +3/2) and (6P,/,, *l/2) corresponds to perpendicular and parallel polarization respectively. Numerical values arc given in the te\t.
AE~(~P,,~, +j)=
--5.69X
lo-l2
cm-1/(V/cm)2.
These values agree well with published experimental and theoretical results [lo] . In fig. 5 the lines B and C indicate the expected positions of the Raman lines for scattering to (6P3,2, ?f) and (6P3,2, *h) with perpendicular and parallel polarization respectively and for a pump intensity of 3.2 GW/cm2, which is the measured value in these experiments. Good agreement exists with the position of the observed bands. The width of these bands is undoubtedly due to temporal and spatial non-uniformity of the intensity and to variations from shot to shot. With a gain coefficient g= 1.4x lo-l7 cm3/W2 and with a pump intensity I = 3.2 GW/cm2 the threshold condition g12L 2 20 can be met with an interaction length L of only 1 to 2 mm. Over such short distances along the pump beam the pump intensity and the optical Stark shifts are essentially constant. In summary, we have observed two-photon induced stimulated Raman scattering in cesium vapor. To the best of our knowledge this is the first observation of stimulated hyper-Raman scattering in any system. Spontaneous hyper-Raman scattering in molecular SYSterns has been reported before [ 111. In order to distinguish the stimulated hyper-Raman scattering from
Volume
21, number
1
OPTICS COMMUNICATIONS
four-photon parametric generation it is essential to study the backward scattered light. In our system the Raman line is shifted, split, and broadened by the optical Stark effect. This Stark effect combined with selfdefocusing of the laser beam explains the relatively high threshold intensity. The results show that fifth order optical nonlinearities can become important in metal vapors.
References [l]
P.P. Sorokin, N.S. Shiren, J.R. Lankard, E.C. Hammond and T.G. Kazyaka, Appl. Phys. Letters 10 (1967) 44. [2] N.N. Badalyan, V.A. Iradyan, and M.E. Movsesyan, JETP Letters 8 (1968) 316 [ZhETF Pis. Red. 8 (1968) 5181. 131 V.M. Arutyunyan, T.A. Papazyan, Yu.S. Chilingaryan, A.V. Karmenyan, and S.M. Sarkisyan, Sov. Phys. JETP 39 (1974) 243 [Zh. Eksp. Teor. Fiz. 66 (1974) 5091.
April 1977
[4] J.L. Carlsten and A. SzGke, Phys. Rev. Letters 36 (1976) 661. [5] Q.H.F. Vrehen and H.M.J. Hikspoors, IX Intern. Quantum Electronics Conf., Amsterdam, 1976, paper LlO. Published in: Opt. Commun. 18 (1976) 113. [6] C.E. Moore, Atomic Energy Levels, Vol. 3, National Bureau of Standards, circular 467, Washington, 1958. [7] R.H. Lehmberg, J. Reintjes and R.C. Eckardt, Appl. Phys Letters 25 (1974) 374; R.H. Lehmberg, J. Reintjes and R.C. Eckardt, Phys. Rev. Al3 (1976) 1095. [8] P.M. Stone, Phys. Rev. 127 (1962) 1151. ] C.L. Chen and A.V. Phelps, Phys. Rev. 173 (1968) 62. ] A.M. Bench-Bruevich and V.A. Khodovoi, Sot. Phys. Uspekhi 10 (1968) 637 [Usp. Fiz. Nauk 93 (1967) 711. [ll ] R.W. Terhune, P.D. Maker and C.M. Savage, Phys. Rev. Letters 14 (1965) 681; S. Kielich, J.R. Lalanne, and F.B. Martin, Phys. Rev. Letters 26 (1971) 1295; W.Yu and R.R. Alfano, Phys. Rev. Al 1 (1975) 188.
131