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Efficient stimulated Raman scattering in silicon
Volume 30, number 2
OPTICS COMMUNICATIONS
August 1979
EFFICIENT STIMULATED RAMAN SCATTERING IN SILICON H.-P. GRASSL * and Max MAIER Fachbereich Physik der UniversitatRegensburg, Regensburg, Germany Received 10 April 1979
Stimulated Raman scattering in silicon was investigated at liquid helium temperatures. A Q-switched single m o d e N d : YAG laser was used to generate Stokes radiation at 1.127/zm. Time resolved measurements give a maximum power conversion efficiency of 20%. The effects of intensity induced losses axe discussed.
1. Introduction Stimulated Raman scattering (SRS) in silicon with pump lasers at 1.06/am is attractive for efficient Raman Stokes light generation and phonon excitation. Experiments with Q-switched Nd:YAG [ 1] and Nd:glass [2-4] lasers at temperatures of 77 K and 200 K have been reported. Short sample lengths ranging between 0.2 cm and 4 cm as well as short focal lengths between 2.3 and 20 cm were used in previous experiments [ 1 - 4 ] . Strong absorption and surface damage occurred at high laser intensities. The observed powers of stimulated Stokes radiation were very small and in no case exceeded the spontaneous Raman scattering power by more than a few orders of magnitude. However, the calculated gain factor g = 0.19 cm/MW [ 1] is quite large indicating the possibility of high conversion efficiencies at low pump intensities. In this letter we report on experiments with a Q-switched single mode Nd:YAG laser where power conversion efficiencies up to 20 per cent were achieved without damaging the crystal. The silicon crystal was 13 cm long and had nearly parallel end faces. The long sample length and the feedback from the end surfaces allowed to reduce the pump intensity necessary for efficient Raman light generation below the damage threshold of the material. The ex* Present address: Siemens AG, Forschungslaboratorium, Munich, Germany.
periments were carried out at liquid helium temperatures. At these temperatures the linear absorption of pump laser and Stokes light is negligibly small even for very long crystals [5]. The effects of twophoton absorption [6,7] and free carrier absorption [8] will be discussed.
2. Experimental The experimental setup is shown in fig. 1. A Qswitched Nd:YAG laser oscillator-amplifier system emits light pulses with a duration of approximately 17 ns (fwhm) and an energy of up to 80 mJ. The light pulses consist of single longitudinal modes with nearly gaussian temporal and spatial shape. The linewidth of the light pulses was approximately 0.003
~j"
PD3
I Nd:YAG Laser
i
,
He-cryostat
A
un O
\
PD1 Fig. 1. Schematic diagram of the experimental setup. L1, L2 lenses; PD1 to PD3 photocells; F1 to F3 f'flters; BS beamsplitter; M mirror; ODL optical delay line.
253
Volume 30, number 2
OPTICSCOMMUNICATIONS
cm -1. The laser light is focussed with lens L1 (focal length f = 115 cm) to a diameter of 1.1 mm (fwhm) at the surface of the sample. The distance between lens L1 and the crystal is 80 cm. The silicon sample is a dislocation free single crystal with a resistivity of 50 ~ cm. The laser beam enters the sample at normal incidence and propagates along the [ 111 ] direction. The end faces of the sample are nearly parallel forming an angle of 1.3 mrad. The sample is immersed in superfluid helium providing efficient cooling and a clear optical path. The transmitted laser light and the generated Stokes light were separated with mirror M which reflects 99.5% of the laser light and transmits 45% of the first Stokes component (~'S 1 = 1.127 pro). For further wavelength discrimination interference filters and a 5 mm thick silicon plate which absorbs laser light at room temperature (T -~ 0.5% at 1.064 #m and T ~ 9.8% at 1.127/am) were used. The incident and transmitted laser power was measured with photocell PD 1 (risetime < 0.5 ns). A fraction of the incident laser power was separated with beam splitter BS and reached PD 1 via a 50 ns optical delay line ODL. The forward and backward scattered Raman Stokes light was detected by photocells PD 2 and PD 3, respectively. The photodetector signals were recorded by two fast transient digitizers which were interfaced to a computer for data storage and evaluation. For absolute energy measurements the photocells were replaced by calibrated thermopiles or pyroelectric energy meters.
3. Results and discussion
A typical example of our time resolved measurements is shown in fig. 2. The incident and transmitted laser powers, PL and PT respectively, and the forward Raman Stokes power PSF are plotted versus time t (solid lines). The peak power of the incident laser pulse was 0.65 MW giving a peak intensity of 46 MW/ cm 2. The broken line represents the transmitted laser power PLT which is measured when the focusing lens L1 is removed. In this case the laser intensity is so small that no SRS is observed and intensity induced losses can be neglected. The reduction of the transmitted laser pulse PLT compared to the incident laser pulse PL is due to reflection losses at the surfaces o f the silicon crystal (refractive index n ~ 3.5). 254
August 1979
I 0.6 g rw t.l.J
t1 t2 b I I ~
I -
--
/Z' / J' \~/------~
0
t3
1
PT
..o 0..
I
10
20 TIME
\~ \.
30
40
50
[nsl
Fig. 2. Oscilloscope traces of the incident laser power PL, the transmitted laser power PT, and the forward Raman Stokes power PSF (solid lines). The broken line corresponds to the transmitted laser power PLT without focusing lens LI (for details see text). Four different time intervals are to be considered in fig~ 2: i) t < t 1 : SRS is below the detection limit. PT (with lens L1) is slightly smaller than PET (without LI). The difference is due to the influence of twophoton absorption, which has been observed in silicon [6,7]. ii) t 1 < t < t2: The strong onset of SRS sharply reduces the transmitted laser power PT" We define the threshold power PTh of SRS as the incident laser power, where the Ralnan power exceeds our detection limit. From fig. 2 we find a value OfPTh = 0.33 MW 9 at time t = t 1), which corresponds to an intensity OflTh = 23 MW/cm 2. PTh was found to be rather independent of laser risetime and peak power. The threshold intensity ITh of stimulated Raman scattering is estimated from the known numbers of the Raman gain factor g and the crystal length 1. Since the end faces of the crystal are not exactly parallel, two limiting cases are considered: a) a traveling wave system (Raman generator) and b) a feedback system (Raman oscillator). a) For the generator system we assume that the threshold occurs at a Raman gain G T h = giTh l ~ 25. Using a gain factor o f g = 0.19 cm/MW [1] and a crystal length o f / = 13 cm we calculate a value of iTb t = 10 MW/cm 2 inside the Si crystal, corre. sponding to an incident intensity value OflTh = 15 MW/cm 2.
Volume 30, number 2
OPTICS COMMUNICATIONS
b) The feedback for the Raman oscillator is provided by the end surfaces of the Si crystal with a reflectivity R = 0.31. For tile calculation of the threshold intensity of the Raman oscillator the differential equation for the Stokes intensity was solved (see eq. (1.12) in [9] ). Using our measured laser pulse of fig. 2 we calculate a threshold intensity of 13 MW/cm 2. When the influence of two-photon absorption is taken into account in the estimates slightly higher values for the threshold intensities are found. It should be noted that the measured threshold intensity and the value for the Raman gain factor are of limited accuracy. Considering this fact both the generators and oscillator estimates give the correct order of magnitude for the threshold value. However, there is experimental evidence that feedback from the crystal surfaces is effective at least in the saturation range of SRS. When the crystal was tilted a few degrees with respect to the laser beam marked drop in Raman conversion was observed, indicating the ilnportance of feedback from the end surfaces for high conversion efficiency. iii) t 2 < t < t 3 : Strong depletion of the laser power due to SRS and nonlinear absorption is observed. Stokes radiation is emitted both in the forward and backward direction. The peak power conversion efficiency of the forward Raman Stokes light is PSF/PL 0.2. The power of the backward scattered Stokes ] light was measured to be approximately one half of PSF or less. The forward Stokes emission occurred in a circular cone (half angle aperture 14 mrad) superimposed on a continuous intensity distribution. The divergence of the transmitted laser light is 3 mrad from the beginning of the pulse up to time t 2. Its value is determined by focussing lens LI. The divergence was observed to increase from 3 mrad at t 2 ~ 17 ns to a maximum value of 7 mrad at t 3 ~ 34 ns. These observations indicate that changes in the refractive index occur, which may be caused e.g. by heating of the interaction volume, by mobile carriers or by shifts of the band gap induced by the strong light fields. At high pump intensities stimulated emission of second order Stokes light is detected using a PbS photoconductive cell. No anti-Stokes light could be detected above the stray light level of the laser line using a 60 cm monochromator with a 6001/mm grating° The absence of anti-Stokes light can be un-
August 1979
derstood from the strong absorption at the anti-Stokes wavelength ?'AS = 1.008/lm which lies above the absorption edge of silicon (c~AS = 4.3 cm -1 [5]). Analysis of any backward scattered or reflected light near the laser wavelength yielded no evidence of stimulated Brillouin scattering. iv) t > t 3 : The transmission of the laser pulse is less in the tail of the pulse than at the leading part. Stimulated Raman scattering cannot account for this loss in transmitted laser power. We believe that twophoton absorption and stepwise absorption processes by free electrons and holes [6-8] which have been created by two-photon absorption and possibly by absorption of anti-Stokes light are responsible for the reduction of laser power.
4. Conclusions We have observed stimulated Raman scattering in silicon with first and second order Stokes generation. The first Stokes light was emitted with high conversion efficiency. The efficiency of stimulated Raman scattering was enhanced by feedback from the end surfaces of the crystal. There is experimental evidence for tile occurrence of competing processes, Cog. two-photon absorption and free carrier absorption.
Acknowledgements We are indebted to Dr. W. Keller of the Siemens Forschungslaboratorium for donating the silicon crystals, to professor Dr. A. Penzkofer for a critical reading of the manuscript and valuable discussions, to H. Wetzel for supplementary measurements, and to T. Ascherl for skillful polishing of the Si crystal.
References [1] J.M. Ralston and ILK. Chang, Phys. Rev. B2 (1970) 1858. [2] L Kitazima and H. Iwasawa, Japan. J. Appl. Phys. 11 (1972) 599. [3] L Kitazima and H. lwasawa, Optics Comm. 5 (1972) 18. [4] I. Kitazima and H. Iwasawa, Japan. J. Appl. Phys. 12 (1973) 758. [5] G. G. Macfarlane, T.P. McLean, J.E. Quarrington and V. Roberts, Phys. Rev. 111 (1958) 1245. 255
Volume 30, number 2
OPTICS COMMUNICATIONS
[6] J.F. Reintjes and J.C. McCroddy, Phys. Rev. Lett. 30 (1973) 901. [7] J. Sevin and G. Mayer, C.R. Acad. Sci., Ser. B 264 (1967) 1369. [8] J.M. Ralston and R.K. Chang, AppL Phys. Lett. 15 (1969) 164.
256
August 1979
[9] A.Z. Grasyuk, in: P.N. Lebedev Physics Institute, VoL 76, ed. N.G. Basov (Consultants Bureau, New York, 1976) p. 73.
OPTICS COMMUNICATIONS
August 1979
EFFICIENT STIMULATED RAMAN SCATTERING IN SILICON H.-P. GRASSL * and Max MAIER Fachbereich Physik der UniversitatRegensburg, Regensburg, Germany Received 10 April 1979
Stimulated Raman scattering in silicon was investigated at liquid helium temperatures. A Q-switched single m o d e N d : YAG laser was used to generate Stokes radiation at 1.127/zm. Time resolved measurements give a maximum power conversion efficiency of 20%. The effects of intensity induced losses axe discussed.
1. Introduction Stimulated Raman scattering (SRS) in silicon with pump lasers at 1.06/am is attractive for efficient Raman Stokes light generation and phonon excitation. Experiments with Q-switched Nd:YAG [ 1] and Nd:glass [2-4] lasers at temperatures of 77 K and 200 K have been reported. Short sample lengths ranging between 0.2 cm and 4 cm as well as short focal lengths between 2.3 and 20 cm were used in previous experiments [ 1 - 4 ] . Strong absorption and surface damage occurred at high laser intensities. The observed powers of stimulated Stokes radiation were very small and in no case exceeded the spontaneous Raman scattering power by more than a few orders of magnitude. However, the calculated gain factor g = 0.19 cm/MW [ 1] is quite large indicating the possibility of high conversion efficiencies at low pump intensities. In this letter we report on experiments with a Q-switched single mode Nd:YAG laser where power conversion efficiencies up to 20 per cent were achieved without damaging the crystal. The silicon crystal was 13 cm long and had nearly parallel end faces. The long sample length and the feedback from the end surfaces allowed to reduce the pump intensity necessary for efficient Raman light generation below the damage threshold of the material. The ex* Present address: Siemens AG, Forschungslaboratorium, Munich, Germany.
periments were carried out at liquid helium temperatures. At these temperatures the linear absorption of pump laser and Stokes light is negligibly small even for very long crystals [5]. The effects of twophoton absorption [6,7] and free carrier absorption [8] will be discussed.
2. Experimental The experimental setup is shown in fig. 1. A Qswitched Nd:YAG laser oscillator-amplifier system emits light pulses with a duration of approximately 17 ns (fwhm) and an energy of up to 80 mJ. The light pulses consist of single longitudinal modes with nearly gaussian temporal and spatial shape. The linewidth of the light pulses was approximately 0.003
~j"
PD3
I Nd:YAG Laser
i
,
He-cryostat
A
un O
\
PD1 Fig. 1. Schematic diagram of the experimental setup. L1, L2 lenses; PD1 to PD3 photocells; F1 to F3 f'flters; BS beamsplitter; M mirror; ODL optical delay line.
253
Volume 30, number 2
OPTICSCOMMUNICATIONS
cm -1. The laser light is focussed with lens L1 (focal length f = 115 cm) to a diameter of 1.1 mm (fwhm) at the surface of the sample. The distance between lens L1 and the crystal is 80 cm. The silicon sample is a dislocation free single crystal with a resistivity of 50 ~ cm. The laser beam enters the sample at normal incidence and propagates along the [ 111 ] direction. The end faces of the sample are nearly parallel forming an angle of 1.3 mrad. The sample is immersed in superfluid helium providing efficient cooling and a clear optical path. The transmitted laser light and the generated Stokes light were separated with mirror M which reflects 99.5% of the laser light and transmits 45% of the first Stokes component (~'S 1 = 1.127 pro). For further wavelength discrimination interference filters and a 5 mm thick silicon plate which absorbs laser light at room temperature (T -~ 0.5% at 1.064 #m and T ~ 9.8% at 1.127/am) were used. The incident and transmitted laser power was measured with photocell PD 1 (risetime < 0.5 ns). A fraction of the incident laser power was separated with beam splitter BS and reached PD 1 via a 50 ns optical delay line ODL. The forward and backward scattered Raman Stokes light was detected by photocells PD 2 and PD 3, respectively. The photodetector signals were recorded by two fast transient digitizers which were interfaced to a computer for data storage and evaluation. For absolute energy measurements the photocells were replaced by calibrated thermopiles or pyroelectric energy meters.
3. Results and discussion
A typical example of our time resolved measurements is shown in fig. 2. The incident and transmitted laser powers, PL and PT respectively, and the forward Raman Stokes power PSF are plotted versus time t (solid lines). The peak power of the incident laser pulse was 0.65 MW giving a peak intensity of 46 MW/ cm 2. The broken line represents the transmitted laser power PLT which is measured when the focusing lens L1 is removed. In this case the laser intensity is so small that no SRS is observed and intensity induced losses can be neglected. The reduction of the transmitted laser pulse PLT compared to the incident laser pulse PL is due to reflection losses at the surfaces o f the silicon crystal (refractive index n ~ 3.5). 254
August 1979
I 0.6 g rw t.l.J
t1 t2 b I I ~
I -
--
/Z' / J' \~/------~
0
t3
1
PT
..o 0..
I
10
20 TIME
\~ \.
30
40
50
[nsl
Fig. 2. Oscilloscope traces of the incident laser power PL, the transmitted laser power PT, and the forward Raman Stokes power PSF (solid lines). The broken line corresponds to the transmitted laser power PLT without focusing lens LI (for details see text). Four different time intervals are to be considered in fig~ 2: i) t < t 1 : SRS is below the detection limit. PT (with lens L1) is slightly smaller than PET (without LI). The difference is due to the influence of twophoton absorption, which has been observed in silicon [6,7]. ii) t 1 < t < t2: The strong onset of SRS sharply reduces the transmitted laser power PT" We define the threshold power PTh of SRS as the incident laser power, where the Ralnan power exceeds our detection limit. From fig. 2 we find a value OfPTh = 0.33 MW 9 at time t = t 1), which corresponds to an intensity OflTh = 23 MW/cm 2. PTh was found to be rather independent of laser risetime and peak power. The threshold intensity ITh of stimulated Raman scattering is estimated from the known numbers of the Raman gain factor g and the crystal length 1. Since the end faces of the crystal are not exactly parallel, two limiting cases are considered: a) a traveling wave system (Raman generator) and b) a feedback system (Raman oscillator). a) For the generator system we assume that the threshold occurs at a Raman gain G T h = giTh l ~ 25. Using a gain factor o f g = 0.19 cm/MW [1] and a crystal length o f / = 13 cm we calculate a value of iTb t = 10 MW/cm 2 inside the Si crystal, corre. sponding to an incident intensity value OflTh = 15 MW/cm 2.
Volume 30, number 2
OPTICS COMMUNICATIONS
b) The feedback for the Raman oscillator is provided by the end surfaces of the Si crystal with a reflectivity R = 0.31. For tile calculation of the threshold intensity of the Raman oscillator the differential equation for the Stokes intensity was solved (see eq. (1.12) in [9] ). Using our measured laser pulse of fig. 2 we calculate a threshold intensity of 13 MW/cm 2. When the influence of two-photon absorption is taken into account in the estimates slightly higher values for the threshold intensities are found. It should be noted that the measured threshold intensity and the value for the Raman gain factor are of limited accuracy. Considering this fact both the generators and oscillator estimates give the correct order of magnitude for the threshold value. However, there is experimental evidence that feedback from the crystal surfaces is effective at least in the saturation range of SRS. When the crystal was tilted a few degrees with respect to the laser beam marked drop in Raman conversion was observed, indicating the ilnportance of feedback from the end surfaces for high conversion efficiency. iii) t 2 < t < t 3 : Strong depletion of the laser power due to SRS and nonlinear absorption is observed. Stokes radiation is emitted both in the forward and backward direction. The peak power conversion efficiency of the forward Raman Stokes light is PSF/PL 0.2. The power of the backward scattered Stokes ] light was measured to be approximately one half of PSF or less. The forward Stokes emission occurred in a circular cone (half angle aperture 14 mrad) superimposed on a continuous intensity distribution. The divergence of the transmitted laser light is 3 mrad from the beginning of the pulse up to time t 2. Its value is determined by focussing lens LI. The divergence was observed to increase from 3 mrad at t 2 ~ 17 ns to a maximum value of 7 mrad at t 3 ~ 34 ns. These observations indicate that changes in the refractive index occur, which may be caused e.g. by heating of the interaction volume, by mobile carriers or by shifts of the band gap induced by the strong light fields. At high pump intensities stimulated emission of second order Stokes light is detected using a PbS photoconductive cell. No anti-Stokes light could be detected above the stray light level of the laser line using a 60 cm monochromator with a 6001/mm grating° The absence of anti-Stokes light can be un-
August 1979
derstood from the strong absorption at the anti-Stokes wavelength ?'AS = 1.008/lm which lies above the absorption edge of silicon (c~AS = 4.3 cm -1 [5]). Analysis of any backward scattered or reflected light near the laser wavelength yielded no evidence of stimulated Brillouin scattering. iv) t > t 3 : The transmission of the laser pulse is less in the tail of the pulse than at the leading part. Stimulated Raman scattering cannot account for this loss in transmitted laser power. We believe that twophoton absorption and stepwise absorption processes by free electrons and holes [6-8] which have been created by two-photon absorption and possibly by absorption of anti-Stokes light are responsible for the reduction of laser power.
4. Conclusions We have observed stimulated Raman scattering in silicon with first and second order Stokes generation. The first Stokes light was emitted with high conversion efficiency. The efficiency of stimulated Raman scattering was enhanced by feedback from the end surfaces of the crystal. There is experimental evidence for tile occurrence of competing processes, Cog. two-photon absorption and free carrier absorption.
Acknowledgements We are indebted to Dr. W. Keller of the Siemens Forschungslaboratorium for donating the silicon crystals, to professor Dr. A. Penzkofer for a critical reading of the manuscript and valuable discussions, to H. Wetzel for supplementary measurements, and to T. Ascherl for skillful polishing of the Si crystal.
References [1] J.M. Ralston and ILK. Chang, Phys. Rev. B2 (1970) 1858. [2] L Kitazima and H. Iwasawa, Japan. J. Appl. Phys. 11 (1972) 599. [3] L Kitazima and H. lwasawa, Optics Comm. 5 (1972) 18. [4] I. Kitazima and H. Iwasawa, Japan. J. Appl. Phys. 12 (1973) 758. [5] G. G. Macfarlane, T.P. McLean, J.E. Quarrington and V. Roberts, Phys. Rev. 111 (1958) 1245. 255
Volume 30, number 2
OPTICS COMMUNICATIONS
[6] J.F. Reintjes and J.C. McCroddy, Phys. Rev. Lett. 30 (1973) 901. [7] J. Sevin and G. Mayer, C.R. Acad. Sci., Ser. B 264 (1967) 1369. [8] J.M. Ralston and R.K. Chang, AppL Phys. Lett. 15 (1969) 164.
256
August 1979
[9] A.Z. Grasyuk, in: P.N. Lebedev Physics Institute, VoL 76, ed. N.G. Basov (Consultants Bureau, New York, 1976) p. 73.