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Gain measurements of stimulated Raman scattering using a tunable dye laser
Volume 5. number 1
April
OPTICS COMMUNICATIONS
GAIN MEASUREMENTS
OF STIMULATED
USING A TUNABLE
RAMAN
1972
SCATTERING
DYE LASER
1. REINHOLD and M. MAIER Physik-Department
der Technischen Received
Universitiit Miinchen, Munich, Germany 14 February
1972
The gain factor of stimulated Raman scattering was measured quantitatively as a function of frequency using a tunable dye laser and a ruby laser as signal and pump light source, respectively. In methanol a gain factor of 4 X lo4 cm/MW and a frequency width of 18 cm-’ was obtained for the strongest Raman line (AvR = 2837 cm-‘).
For quantitative investigations of stimulated scattering processes [ 1,2] direct gain measurements in an oscillator-amplifier experiment have been employed successfully. For instance, accurate values of the gain factor were obtained for stimulated Brillouin scattering (SBS) [3] , stimulated thermal Brillouin scattering [4] , and stimulated thermal Rayleigh scattering [S] . In these experiments a weak signal beam is amplified in the presence of a strong pump beam in an amplifier cell. Investigations of stimulated Raman scattering (SRS) in oscillator-amplifier experiments were limited to a few substances [6,7], where suitable oscillators are available. The reason is twofold: (1) in many substances, especially in liquids, stimulated Brillouin scattering competes successfully with SRS in the oscillator cell because of its higher gain factor; (2) early experiments in liquids have shown that SRS is often generated in “filaments” of small diameter. The Raman signal leaving the oscillator cell has large divergence and short time duration. No quantitative measurements are possible in this case [8] . In this letter a new and widely applicable method is reported where the signal light is generated by a tunable dye laser. In our system the properties of the light beam emitted by the dye laser (frequency width intensity distribution over the cross section, time dependence, and polarization) are well defined and allow quantitative measurements of the absolute value of the Raman gain factor. By tuning the dye laser frequency the gain factor is measured as a function of
frequency and the width of the corresponding Raman line is obtained. Fig. 1 shows the experimental setup. A giant pulse ruby laser emits light pulses with a duration of 15 nsec and a peak power of 300 kW. The intensity distribution over the cross section is approximately gaussian. The pulses are amplified in a ruby amplifier by a factor of 10. Part of the ruby laser pulse (= 20%) is used to pump the dye laser. The active material is a solution of 3,3’diethyl-2,2’-(4,5,4’,5’-dibenzo)-thiatricarbocyanine iodide in acetone [9]. Frequency tuning is performed with a grating [lo] . The dye laser emitted a light pulse of 10 nsec duration, 5 X lOA rad divergence, and 2 cm-’ linewidth. A
0
RUBY AMPLIFIER
RUBY
LASER
Fig. 1. Experimental setup for the determination of the Raman gain in an amplifier cell. PD photodiode, D diaphragm, POL polarizer, F filter, BS beam splittet.
31
Volume 5, number 1
small diaphragm D (diameter 1.5 mm) was used to of the dye laser beam. Its peak power was reduced by D to approximately 1 kW. The polarization of the dye laser and ruby laser pulse were made parallel by a polarizer POL. Signal and pump light beam are recombined by beam splitter BS and focused slightly into the amplifier cell (length 1= 50 cm). The focus is well outside the liquid cell. Special care was given to the exact temporal and spatial overlap of the dye laser and ruby laser beam within the cell. The frequency of the dye laser is monitored by a grating spectrograph via beam splitter BS. Amplification occurs if the frequency difference of both light pulses corresponds to the frequency of the molecular vibration under investigation. The incident and amplified signal power and the pump power are measured by the photodiodes PDl, PD2, and PD3, respectively. The overall risetime of the detection system is 0.5 nsec. Photodiode PD4 monitors the backward scattered light which could arise from stimulated Brillouin scattering. It should be emphasized that no SBS occurred during our Raman gain measurements. According to the theory of SRS [ 11 an exponential amplification limit the diameter
Ia = li exp(glr_ I)
(1)
is obtained, if the amplified signal intensity Ia is small compared to the laser intensity, It. Ii is the incident signal intensity and 1 is the interaction length. For parallel polarization of the signal and pump light the steady state gain factor g is given by [ 1 l] 16rr2c2N da I‘ g=---da ,,r2tAo2’ &+2 ( )
April 1972
OPTICS COMMUNICATIONS
For comparison with experiments we integrate eq. (1) over the cross section F of the beam, because photodiodes measure power values, not intensities. The amplified signal power is given by Pa = JIi exp(gZLI) dF
(3)
F
For small values of gILI, eq. (3) can be integrated for arbitrary intensity distributions over the cross section to give Pa = Pi[ 1 toglL(0)I]
= Pi exp[olglt(0)l],
(4)
where Pi is the incident signal power and IL(O) the pump intensity in the center of the ruby laser beam. The factor (Ydepends on the detailed profiles of the signal and pump beam and their radii rD and r~, respectively. For a narrow signal beam (rD < r~), we obtain CY= 1; usually (Yis smaller than 1. In our experiments the ruby laser light has a gaussian intensity distribution over the cross section, while the dye laser beam had wide wings with an exponentially decreasing intensity. As an example we considered, therefore, a gaussian pump beam and a signal beam having an exponentially decreasing intensity as a function of radial coordinate r. We calculated a value of CY= 0.23 and 0.49 for a ratio of r&D = 1 and 2, respectively. In our experiments the light beams are focused slightly into the liquid cell. The amplification occurs mainly in the region of high intensity at the end of the cell. Focusing can be taken into account by introducing an average laser intensity
(2)
Here c is the velocity of light in vacuum, n the index of refraction, N the number of molecules per cm3; (do/da),, and I are the spontaneous Raman scattering cross section (for parallel polarization of the incident and scattered light) and linewidth, respectively; oL , WS, and AWR are the frequencies of the pump and signal light and the molecular vibration; Ao = WL - ws - AOR is the detuning of the signal frequency. The gain factor g is characteristic for the stimulated scattering process. It depends on (i) the material, (ii) the frequency difference between the two interacting waves, and (iii) the polarization of the two interacting waves. We are especially interested in the absolute value and the frequency dependence of the gain factor. 32
Tt = (l/r)Jr,iO,z)dz 0
into eq. (4). Using our measured intensity distributions of the ruby laser and dye laser beam we calculated a value of (Y= 0.35. The small value of ti is mainly due to the broad wings of the signal beam which are not amplified by the small intensity of the wings of the gaussian pump beam. For a determination of the absolute value of the gain factor the average intensity 7~ must be known. rL was determined by measuring the onset of SBS. If we increased the laser power used in the Raman gain measurements by 15%, Brillouin light was detected by photodiode PD4 (power conversion 1%). Assuming exponential amplification and taking into account the transient behavior of SBS [ 12,131 and the inten-
OPTICS COMMUNICATIONS
Volume 5, number 1
sity distributions over the cross section, a gain gSBSIL nl= 40 is necessary to amplify the spontaneous Briliouin power to 1% of the laser power. The Brillouin gain factor for methanol is known with high accuracy (gsBs = 1.3 X lop3 cm/MW [2]). From these investigations we obtained an average intensity of IJ_ = 53 MW/cm2. This number should be compared with the value of 57 MW/cm2 obtained by a direct measurement as follows: the beam diameters at the entrance and exit of the cell were determined from microdensitometer traces of photographic plates and the absolute power values were measured using a calibrated photodiode, Raman gain measurements have been performed in liquid methanol (T = 20°C). Fig. 2 shows the frequency dependence of the gain factor g of the Raman line of methanol with a frequency shift of 2837 cm-l. The experimental points (open circles) are obtained from the ratio of the amplified and incident signal light P,IPi using eq. (4). The data of fig. 2 were normalized to the peak of the gain curve; in this way the value of (Yand the absolute number of TL do not enter this result. The solid line drawn through the experimental points is’a lorentzian curve [ 141 [see eq. (2)] with a half-width of 18 cm-l *. Our results are
‘do’
April 1972
in good agreement with measurements of spontaneous Raman scattering where a linewidth of 17 cm-l and 19.6 cm-l was reported in refs. [ 151 and [ 161, respectively. We have determined the absolute value of the gain factor g by measuring the (small) amplification in the center of the 2837 cm-l Raman line. Using our value of (Y= 0.35 and the average value of our intensity measurements rL = 55 MW/cm2 we obtain from eq. (4) a gain factor ofg= 4X lop4 cm/MW (+40%). The error is mainly due to the limited accuracy of o(+ 15%) and IL (* 20%). From eq. (2) we calculate a total Raman scattering cross section of (da/da) ,, = 1.25 X 10p30 cm2/molecule sterad or a peak cross section (in the line center) of (up),, = 4.4 X 1O-32 cm3/mo1ecu1e sterad. Within the experimental accuracy our number agrees with the total scattering cross section of 10p30 cm2/molecule sterad obtained from spontaneous Raman scattering [ 16]**. In conclusion it should be emphasized that the accuracy of the reported method can be improved further. If focusing of the light beams is avoided by applying higher pump power, the error in determining absolute gain factors is reduced considerably. In addition, a reduction of the frequency width of the signal light allows the measurement of narrow Raman lines (< low2 cm-l). The authors would like to thank Professor Dr. W. Kaiser for valuable discussions and Dr. M.J. Colles for sending a preprint of his paper. * The dye laser line (width 2 cm-‘) has rapidly decreasing Wings (approximately gaussian frequency profile); no correction is therefore required to the measured width of the Raman line (width 18 cm-‘). ** The scattering cross section of methanol is corrected for the ruby laser frequency according to the W$ dependence and the presence of an absorption band at approximately 62000 cm-‘.
oC10
FREQUENCY
References
lO
0
l A’j
kmiil
Fig. 2. Normalized gain factor g/g,, for the Raman line of methanol with a frequency shift of 2837 cm-‘.
[ 1) N. Bloembergen, Am. J. Phys. 35 (1967) 989. [ 21 W. Kaiser and M. Maier, Stimulated Rayleigh, Brillouin, and Raman spectroscopy, Laser Handbook, Vol. 2 (North-Holland, Amsterdam) to be published. [3] D. Pohl and W. Kaiser, Phys. Rev. Bl(I970) 31; M. Denariez and G. Bret, Phys. Rev. 17 l(1968) 160.
33
Volume
5, number
1
OPTICS COMMUNICATIONS
[4] D. Pohl, I. Reinhold and W. Kaiser, Phys. Rev. Letters 20(19681 1141. [5] W. Rother, H. Meyer and W. Kaiser, Z. Naturforsch. 25a (1970) 1136. [6] N. Bloembergen, G. Bret, P. Lallemand, A. Pine and P. Simova, IEEE J. Quantum Electron. 3 (1967) 197. [7] G. Bisson and G. Mayer, Compt. Rend. Acad. Sci. (Paris) 265 (1967) 397; J. Phys. (Paris) 29 (1968) 97. [8] N. Bloembergen and P. Lallemand, in: Physics of quantum electronics, eds. P.L. Kelley, B. Lax and P.E. Tannenwald (McGraw-Hill, New York, 1966) p. 137. [9] Y. Miyazoe and M. Maeda, Appl. Phys. Letters 12 (1968) 206. [IO] B.H. Soffer and B.B. McFarland, Appl. Phys. Letters 10 ( 1967) 266.
34
April
1972
[ 1 l] M. Maier, W. Kaiser and J.A. Giordmaine, Phys. Rev. 177 (1969) 580. [ 121 R.L. Carman, F. Shimizu, C.S. Wang and N. Bloembergen, Phys. Rev. A2 (19701 60; S.A. Akhmanov, K.N. Drabovich, A.P. Sukhorukov and A.S. Chirkin, Soviet Phys. JETP 32 (1971) 266. [ 131 M. Maier and G. Renner, Opt. Commun. 3 (1971) 301. [ 14) N.N. Belyaeva and M.A. Novikov, Opt. Spectry. 30 (1971) 135. [ 151 R.L. Carman, M.E. Mack, F. Shimizu and N. Bloembergen, Phys. Rev. Letters 23 (1969) 1327. (161 M.J. Colles and J.E. Griffiths, J. Chem. Phys., to be published.
April
OPTICS COMMUNICATIONS
GAIN MEASUREMENTS
OF STIMULATED
USING A TUNABLE
RAMAN
1972
SCATTERING
DYE LASER
1. REINHOLD and M. MAIER Physik-Department
der Technischen Received
Universitiit Miinchen, Munich, Germany 14 February
1972
The gain factor of stimulated Raman scattering was measured quantitatively as a function of frequency using a tunable dye laser and a ruby laser as signal and pump light source, respectively. In methanol a gain factor of 4 X lo4 cm/MW and a frequency width of 18 cm-’ was obtained for the strongest Raman line (AvR = 2837 cm-‘).
For quantitative investigations of stimulated scattering processes [ 1,2] direct gain measurements in an oscillator-amplifier experiment have been employed successfully. For instance, accurate values of the gain factor were obtained for stimulated Brillouin scattering (SBS) [3] , stimulated thermal Brillouin scattering [4] , and stimulated thermal Rayleigh scattering [S] . In these experiments a weak signal beam is amplified in the presence of a strong pump beam in an amplifier cell. Investigations of stimulated Raman scattering (SRS) in oscillator-amplifier experiments were limited to a few substances [6,7], where suitable oscillators are available. The reason is twofold: (1) in many substances, especially in liquids, stimulated Brillouin scattering competes successfully with SRS in the oscillator cell because of its higher gain factor; (2) early experiments in liquids have shown that SRS is often generated in “filaments” of small diameter. The Raman signal leaving the oscillator cell has large divergence and short time duration. No quantitative measurements are possible in this case [8] . In this letter a new and widely applicable method is reported where the signal light is generated by a tunable dye laser. In our system the properties of the light beam emitted by the dye laser (frequency width intensity distribution over the cross section, time dependence, and polarization) are well defined and allow quantitative measurements of the absolute value of the Raman gain factor. By tuning the dye laser frequency the gain factor is measured as a function of
frequency and the width of the corresponding Raman line is obtained. Fig. 1 shows the experimental setup. A giant pulse ruby laser emits light pulses with a duration of 15 nsec and a peak power of 300 kW. The intensity distribution over the cross section is approximately gaussian. The pulses are amplified in a ruby amplifier by a factor of 10. Part of the ruby laser pulse (= 20%) is used to pump the dye laser. The active material is a solution of 3,3’diethyl-2,2’-(4,5,4’,5’-dibenzo)-thiatricarbocyanine iodide in acetone [9]. Frequency tuning is performed with a grating [lo] . The dye laser emitted a light pulse of 10 nsec duration, 5 X lOA rad divergence, and 2 cm-’ linewidth. A
0
RUBY AMPLIFIER
RUBY
LASER
Fig. 1. Experimental setup for the determination of the Raman gain in an amplifier cell. PD photodiode, D diaphragm, POL polarizer, F filter, BS beam splittet.
31
Volume 5, number 1
small diaphragm D (diameter 1.5 mm) was used to of the dye laser beam. Its peak power was reduced by D to approximately 1 kW. The polarization of the dye laser and ruby laser pulse were made parallel by a polarizer POL. Signal and pump light beam are recombined by beam splitter BS and focused slightly into the amplifier cell (length 1= 50 cm). The focus is well outside the liquid cell. Special care was given to the exact temporal and spatial overlap of the dye laser and ruby laser beam within the cell. The frequency of the dye laser is monitored by a grating spectrograph via beam splitter BS. Amplification occurs if the frequency difference of both light pulses corresponds to the frequency of the molecular vibration under investigation. The incident and amplified signal power and the pump power are measured by the photodiodes PDl, PD2, and PD3, respectively. The overall risetime of the detection system is 0.5 nsec. Photodiode PD4 monitors the backward scattered light which could arise from stimulated Brillouin scattering. It should be emphasized that no SBS occurred during our Raman gain measurements. According to the theory of SRS [ 11 an exponential amplification limit the diameter
Ia = li exp(glr_ I)
(1)
is obtained, if the amplified signal intensity Ia is small compared to the laser intensity, It. Ii is the incident signal intensity and 1 is the interaction length. For parallel polarization of the signal and pump light the steady state gain factor g is given by [ 1 l] 16rr2c2N da I‘ g=---da ,,r2tAo2’ &+2 ( )
April 1972
OPTICS COMMUNICATIONS
For comparison with experiments we integrate eq. (1) over the cross section F of the beam, because photodiodes measure power values, not intensities. The amplified signal power is given by Pa = JIi exp(gZLI) dF
(3)
F
For small values of gILI, eq. (3) can be integrated for arbitrary intensity distributions over the cross section to give Pa = Pi[ 1 toglL(0)I]
= Pi exp[olglt(0)l],
(4)
where Pi is the incident signal power and IL(O) the pump intensity in the center of the ruby laser beam. The factor (Ydepends on the detailed profiles of the signal and pump beam and their radii rD and r~, respectively. For a narrow signal beam (rD < r~), we obtain CY= 1; usually (Yis smaller than 1. In our experiments the ruby laser light has a gaussian intensity distribution over the cross section, while the dye laser beam had wide wings with an exponentially decreasing intensity. As an example we considered, therefore, a gaussian pump beam and a signal beam having an exponentially decreasing intensity as a function of radial coordinate r. We calculated a value of CY= 0.23 and 0.49 for a ratio of r&D = 1 and 2, respectively. In our experiments the light beams are focused slightly into the liquid cell. The amplification occurs mainly in the region of high intensity at the end of the cell. Focusing can be taken into account by introducing an average laser intensity
(2)
Here c is the velocity of light in vacuum, n the index of refraction, N the number of molecules per cm3; (do/da),, and I are the spontaneous Raman scattering cross section (for parallel polarization of the incident and scattered light) and linewidth, respectively; oL , WS, and AWR are the frequencies of the pump and signal light and the molecular vibration; Ao = WL - ws - AOR is the detuning of the signal frequency. The gain factor g is characteristic for the stimulated scattering process. It depends on (i) the material, (ii) the frequency difference between the two interacting waves, and (iii) the polarization of the two interacting waves. We are especially interested in the absolute value and the frequency dependence of the gain factor. 32
Tt = (l/r)Jr,iO,z)dz 0
into eq. (4). Using our measured intensity distributions of the ruby laser and dye laser beam we calculated a value of (Y= 0.35. The small value of ti is mainly due to the broad wings of the signal beam which are not amplified by the small intensity of the wings of the gaussian pump beam. For a determination of the absolute value of the gain factor the average intensity 7~ must be known. rL was determined by measuring the onset of SBS. If we increased the laser power used in the Raman gain measurements by 15%, Brillouin light was detected by photodiode PD4 (power conversion 1%). Assuming exponential amplification and taking into account the transient behavior of SBS [ 12,131 and the inten-
OPTICS COMMUNICATIONS
Volume 5, number 1
sity distributions over the cross section, a gain gSBSIL nl= 40 is necessary to amplify the spontaneous Briliouin power to 1% of the laser power. The Brillouin gain factor for methanol is known with high accuracy (gsBs = 1.3 X lop3 cm/MW [2]). From these investigations we obtained an average intensity of IJ_ = 53 MW/cm2. This number should be compared with the value of 57 MW/cm2 obtained by a direct measurement as follows: the beam diameters at the entrance and exit of the cell were determined from microdensitometer traces of photographic plates and the absolute power values were measured using a calibrated photodiode, Raman gain measurements have been performed in liquid methanol (T = 20°C). Fig. 2 shows the frequency dependence of the gain factor g of the Raman line of methanol with a frequency shift of 2837 cm-l. The experimental points (open circles) are obtained from the ratio of the amplified and incident signal light P,IPi using eq. (4). The data of fig. 2 were normalized to the peak of the gain curve; in this way the value of (Yand the absolute number of TL do not enter this result. The solid line drawn through the experimental points is’a lorentzian curve [ 141 [see eq. (2)] with a half-width of 18 cm-l *. Our results are
‘do’
April 1972
in good agreement with measurements of spontaneous Raman scattering where a linewidth of 17 cm-l and 19.6 cm-l was reported in refs. [ 151 and [ 161, respectively. We have determined the absolute value of the gain factor g by measuring the (small) amplification in the center of the 2837 cm-l Raman line. Using our value of (Y= 0.35 and the average value of our intensity measurements rL = 55 MW/cm2 we obtain from eq. (4) a gain factor ofg= 4X lop4 cm/MW (+40%). The error is mainly due to the limited accuracy of o(+ 15%) and IL (* 20%). From eq. (2) we calculate a total Raman scattering cross section of (da/da) ,, = 1.25 X 10p30 cm2/molecule sterad or a peak cross section (in the line center) of (up),, = 4.4 X 1O-32 cm3/mo1ecu1e sterad. Within the experimental accuracy our number agrees with the total scattering cross section of 10p30 cm2/molecule sterad obtained from spontaneous Raman scattering [ 16]**. In conclusion it should be emphasized that the accuracy of the reported method can be improved further. If focusing of the light beams is avoided by applying higher pump power, the error in determining absolute gain factors is reduced considerably. In addition, a reduction of the frequency width of the signal light allows the measurement of narrow Raman lines (< low2 cm-l). The authors would like to thank Professor Dr. W. Kaiser for valuable discussions and Dr. M.J. Colles for sending a preprint of his paper. * The dye laser line (width 2 cm-‘) has rapidly decreasing Wings (approximately gaussian frequency profile); no correction is therefore required to the measured width of the Raman line (width 18 cm-‘). ** The scattering cross section of methanol is corrected for the ruby laser frequency according to the W$ dependence and the presence of an absorption band at approximately 62000 cm-‘.
oC10
FREQUENCY
References
lO
0
l A’j
kmiil
Fig. 2. Normalized gain factor g/g,, for the Raman line of methanol with a frequency shift of 2837 cm-‘.
[ 1) N. Bloembergen, Am. J. Phys. 35 (1967) 989. [ 21 W. Kaiser and M. Maier, Stimulated Rayleigh, Brillouin, and Raman spectroscopy, Laser Handbook, Vol. 2 (North-Holland, Amsterdam) to be published. [3] D. Pohl and W. Kaiser, Phys. Rev. Bl(I970) 31; M. Denariez and G. Bret, Phys. Rev. 17 l(1968) 160.
33
Volume
5, number
1
OPTICS COMMUNICATIONS
[4] D. Pohl, I. Reinhold and W. Kaiser, Phys. Rev. Letters 20(19681 1141. [5] W. Rother, H. Meyer and W. Kaiser, Z. Naturforsch. 25a (1970) 1136. [6] N. Bloembergen, G. Bret, P. Lallemand, A. Pine and P. Simova, IEEE J. Quantum Electron. 3 (1967) 197. [7] G. Bisson and G. Mayer, Compt. Rend. Acad. Sci. (Paris) 265 (1967) 397; J. Phys. (Paris) 29 (1968) 97. [8] N. Bloembergen and P. Lallemand, in: Physics of quantum electronics, eds. P.L. Kelley, B. Lax and P.E. Tannenwald (McGraw-Hill, New York, 1966) p. 137. [9] Y. Miyazoe and M. Maeda, Appl. Phys. Letters 12 (1968) 206. [IO] B.H. Soffer and B.B. McFarland, Appl. Phys. Letters 10 ( 1967) 266.
34
April
1972
[ 1 l] M. Maier, W. Kaiser and J.A. Giordmaine, Phys. Rev. 177 (1969) 580. [ 121 R.L. Carman, F. Shimizu, C.S. Wang and N. Bloembergen, Phys. Rev. A2 (19701 60; S.A. Akhmanov, K.N. Drabovich, A.P. Sukhorukov and A.S. Chirkin, Soviet Phys. JETP 32 (1971) 266. [ 131 M. Maier and G. Renner, Opt. Commun. 3 (1971) 301. [ 14) N.N. Belyaeva and M.A. Novikov, Opt. Spectry. 30 (1971) 135. [ 151 R.L. Carman, M.E. Mack, F. Shimizu and N. Bloembergen, Phys. Rev. Letters 23 (1969) 1327. (161 M.J. Colles and J.E. Griffiths, J. Chem. Phys., to be published.