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Investigation of parameters controlling stimulated Raman scattering in InSb around 5 μm
Volume
4, number 3
OPTICS COMMUNICATIONS
INVESTIGATION
CF
RAMAN
PARAMETERS
SCATTERING
November
CONTROLLING IN InSb
AROUND
STIMULATED 5 urn
R. G. MELLISH, R. B. DENNIS and R. L. ALLWOOD of Physics, Heriot-Watt University, Edinburgh,
Department
Received
27 September
1971
UK
1971
Raman-laser light with a peak power of 2 W and continuously tunable with magnetic field from 5.24 to 5.62 pm has been obtained using a Q-switched CO2 laser as a primary source, the frequency being first doubled by phase matched second harmonic generation in tellurium and then shifted by the stimulated spin-flip process in InSb. The dependence of the output on input power, magnetic field, sample temperature and input focussing parameters has been investigated and theoretically interpreted. The Raman laser has been used to obtain high-resolution absorption spectra of atmospheric water vapour, over a range of N 20 resolvable lines.
A previous communication has described the use of 5.3 pm radiation obtained by second har manic generation (SHG) in tellurium with a Qswitched CO2 laser as the primary source, as a pump for stimulated spin-flip magneto-Raman scattering in InSb [l]. The work has now been extended by selecting a number of wavelengths of operation of the CO2 laser, thus increasing the tuning range of the Raman laser, and by making further experimental and theoretical investigation of the conditions which determine the final output power. The Raman scattering took place in a sample of n-type InSb, which contained 9.7 x 1015 donors cm- 3, and which was mounted inside a superconducting solenoid. The pump light propagating in the Voigt configuration, was polarised parallel to the magnetic field. The input and output pulses were observed simultaneously with copper -doped germanium photoconductive de tectors, which were calibrated by comparison with a photon drag detector. This device exploits the transfer of momentum from a beam of photons to the electrons in a crystal of p-type Ge, and the consequent movement of carriers, on average, towards one end of the crystal. It is calibrated for direct measurement of powers up to 10 MW at 10.6 urn, and has a response time of less than 1 nsec. Since the previous work was described more has been learnt about the process of SHG in Te. Hammond [2] has continued the work of Gandrud and Abrams [3], investigating the efficiency of conversion to second harmonic and the details of
the process which limits the output power. In Te, when some harmonic has been generated, a photon of the harmonic and a photon of the fundamental are simultaneously absorbed and excite an electron across the energy band gap. Free carriers produced in this way then absorb more light, principally at the fundamental frequency, and prevent the generation of more harmonic once a certain power level has been reached. Thus, a firm limit is placed on the harmonic power obtainable from a given active volume of the tellurium defined by the spot size of the laser beam. To obtain more harmonic power one must use a greater fundamental power spread over a larger beam diameter. This limiting process determines that the pulse rises rapidly at the start of the laser pulse, and then falls back to zero long before the end of the laser pulse. The CO2 laser produced pulses of = 20 kW peak and 300 nsec full-width-at-half -modulus (fwhm). The light was focussed onto a 6 mm thick crystal of Te set at the phase match angle. The maximum intensity was = 107 W cm-2, which is the highest which can be used if the damage threshold is not to be exceeded. Even at this intensity damage spots were produced occasionally, probably when the beam landed at a point of the crystal where the surface was not clean. Second harmonic pulses emerging from the Te were of peak power = 400 W and = 140 nsec fwhm. The pump radiation was focussed onto the InSb sample by an NaCl lens of 20 cm focal 249
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length, residual 10.6 pm light being blocked by a piece of MgO. The 5.3 pm power entering the Raman sample was = 50 W. In the Te, because the fundamental propagates as an extraordinary ray, there is an angle of approximately 50 between its k-vector and its Poynting vector. The harmonic generated at each point in the crystal has both vectors parallel to the fundamental kvector, and so it propagates in a direction which takes it away from the fundamental ray. This process, known as walk off, also limits the conversion efficiency. The harmonic output from the end face of the crysial therefore was not a circular beam but had an asymmetrical profile. Measurements with an accurately trackable pinhole showed that the focal spot on the InSb was also irregular, but approximated to a gaussian distribution of 250 pm radius. This gives a maximum intensity at the centre of the beam of 5 x lo4 W cm-2. At a field of 30 kG, where the Raman oscillation was strongest, the pump power was eight times above threshold. This implies that the threshold intensity was about 6 x lo3 W cm-2. This figure is in moderate agreement with previously quoted values of Smith et al. [4], and of Mooradian et al. [ 51, the latter being measured with a cw CO laser; but it is significantly higher than the value obtained by Irslinger et al. [6]. Fig. 1 shows typical pulse shapes of the various beams, obtained at a field of 46 kG. The conditions were such that the limiting process in
November
19 il
the Te was just occurring. The Stokes pulses, typically of 2 W peak power, were only a little shorter than the pump pulses (- 100 nsec and 240 nsec fwhm, respectively). Because of the saturation in the Te the harmonic output had less pulse-to-pulse instability than the laser. The scattered radiation also was observed to occur consistently, and to vary by only some 5% from pulse to pulse, in contrast to that from the identical system pumped with 10.6 pm light. A diffraction grating which formed part of the CO2 laser cavity was used to select, in turn, several wavelengths in the 10.6 and the 10.2 pm bands. With each pump wavelength the Raman output wavelength was measured as a function of field. Fig. 2 shows the tuning ranges obtained. In the case of 5.15 pm pump, intense Raman scattering ceased at 15 kG; at lower fields stimulated recombination radiation @RR) was observed. Previous measurements of SRR using optical pumping [7] and electrical excitation [8,9] both show two distinct tuning characteristics. These can be accurately correlated with the interband transitions and polarization selection rules of Pidgeon and Brown [lo]. In this experiment SRR has an octput power N 100 mW, the same as the spin flip power near threshold. SRR occurs at the observed wavelengths independent of the precise pumping wavelength, but it is very sensitive to changes in temperature which shift the band gap.
5.7r
(b) /\
I
/
A /
1 division
Fig. 1. Typical oscilloscope
(cl SRR L
I
=
I
100 ns
tracings for
CO2 laser pulse, (b) the SEIG from the (c) the stimulated scattered output -
(a) the tellurium,
input and
illustrating the narrowing at each stage of the conversion process.
250
Fig. 2. The observed tuning ranges for stimulated Stokes scattering for three different pump wavelengths at 5.296, 5.276, and 5.152 pm. Stimulated recombination radiation at low magnetic fields is also shown.
Volume 4, number 3
November 1971
OPTICS COMMUNICATIONS
The threshold for Raman oscillation in InSb with a pump of around 5.3 pm is low because the denominator of the scattering cross section resonates when tip, the energy of a pump photon, is close to the energy of the first virtual transition, from the valence band to the upper spin state in the conduction band. The value of the cross section varies rapidly with magnetic field as this energy moves away from the pump energy; but precise investigation of the fielddependence is rendered difficult by several factors. Firstly, the number of electrons available for Raman scattering is also a function of the field. At low fields, the Fermi level lies above the bottom of the second Landau level (rz= 0, spin down). Electrons near kZ = 0 are therefore unable to take part in Raman scattering, since what would be the final state is already occupied. The effect, where virtual transitions are blocked, has been discussed by Wherrett and Harper [ll], for the case of a sharp Fermi level. Only for fields above the quantum condition, when EF < liw,f (where i?wsf is the spin-flip energy), are all the electrons available to take part in scattering. The critical field is 26 kG for the present doping. At finite temperatures the boundary between the two regimes is not sharp and the effective number of electrons becomes a complicated function of the field. If, on the other hand, the temperature is very low, the number of free carriers may be reduced by magnetic freeze-out at high fields [12]. Secondly, the resonance depends critically on the precise size of the band gap which is in turn dependent on the temperature, not of the bulk sample, but of the radiated filament where the scattering is taking place. This region is illuminated by the pump beam, and its temperature can only be estimated. Taking a figure of 300K gives a zero-field band gap of 1886 cm-l. At 20 kG the valence-tospin-down-conduction transition has reached With the laser operating at 10.59 1974 cm-l. pm, the pump is at 1888 cm-l; and with the laser operating at 10.30 pm, the pump is at 1941 cm-l. Thus the latter pump is much closer to resonance. It was observed that oscillations ceased at 20 kG with the lower energy pump but continued to lower fields with the higher energy pump; even though the blocking effect strongly reduces the scattering cross section for fields below 26 kG. At 60 kG the transition produced by the pump photon is far from resonance, and a small change of pump frequency would be expected to have little effect. It was in fact observed that the high-field limit of oscillation was
60 kG for all pump frequencies. This limit may be determined in part by variation of the spontaneous scattering linewidth with field. The dependence of this linewidth on various factors is being investigated. At a field of 46 kG, well inside the range of oscillation, the relationship between input and output powers was studied. The input was monitored by reflecting a portion of the beam off a KRS5 plate onto a second detector. The power was varied by rotating the Te crystal away from the phase-matching angle. It was observed that there was little fluctuation of Stokes power from pulse to pulse, even when the pump power was reduced to only just above threshold. This is in contrast to the behaviour of the same system with a 10.6 km pump, when the Stokes pulses become very erratic near threshold 1131. Fig. 3 shows output/input curves both for the best pulses, at a given setting of the tellurium, and for the power averaged over many pulses, but because the statistical variations of the pulses were essentially the same at all levels the curves are identical. Mention has been made of the saturation process in the Te, and of the irregular shape of the focal spot of the harmonic beam. As the Te was moved away from phase-match the distribution of power over the spot, as well as the total power, changed; and so one cannot give a precise theory relating Stokes output to pump input. Nevertheless, the experimental results fit the following simple theory fairly well. It is assumed’that, because the gains and losses in the Raman sample are both so high, the usual concept of cavity modes is not really valid; and that the distribution of oscillating power is determined primarily by that of pump power, which is assumed to be gaussian. Diffusion of
3r (P)
o- Peak input power
01
Average input power
Fig. 3. Comparison of the experimentally observed points (0) and the theoretical expression (solid line), in arbitrary units, for the output/input dependence of both the peak pulse powers (left) and average powers (right). 251
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carriers out of the active region, and spin-relaxation during the pulse, are neglected. Suppose that, in a given region of the crystal, the pump intensity is at some instant a factor A above threshold. When a fractionf of the spins have flipped, the excess population in the lower energy level is reduced to a fraction (1 - Zf) of the original number. The threshold in that region is thereby raised to l,‘(l -2,f) times its original value, as the Raman gain is proportional to the excess population of electrons in the lower spin state. We assume that Raman scattering goes on, and the local threshold rises until it has become equal to the intensity actually present; whereupon oscillation ceases, and no more spins flip until the input power rises further. Then A (1 - 2s) = 1, or f = :(l - 1 ‘A). At the peak of the input pulse let the power be filth, where Pth is the threshold power. At a distance rfrom the centre of the spot the intensity is then given by I = Pith exp (-4’20~) where Ith is the threshold intensity and 2cr (- ((‘) is the gaussian beam radius. Then A = p exp ( -$‘2a2), and the fraction of the spins that have flipped is ~2/2$)). The output energy dE, 4 {l - (l/fi)exp( produced up to this time from an annular element of the crystal between 7. and I’+ dr is dE = $ (1 - (l/p) where is the length of the to be
exp (~~;‘2a~))N~w~
2;; L rdr ,
N is the free carrier concentration, xws energy of a Stokes photon, and L is the of the crystal. Integrating over the area active region we find the total energy, E,
E = Ntiw,
.02L(loge
$J - 1 + 1 ‘fi) .
When the maximum pump intensity is well above threshold, a small change of spot size should have little effect on the output, as the changes in CTand p largely cancel. It was indeed found that with a field of 46 kG, when p was 3.5, the Stokes output power was insensitive to longitudinal movement of the focussing lens. According to the theory the cancellation should be perfect near p = 5, and the output power should then be a maximum. Fig. 3 shows curves calculated from this theory, which closely agree with the experimental points. This further indicates that spin-relaxation and diffusion are negligible, since they would lead to a more complex energy relationship. It has been observed that Raman oscillation with a 10.6 pm pump is strongly dependent on 252
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1971
the bulk temperature of the sample, disappearing when it is heated to around 400K [4]. With the 5.3 pm pumped system, the effect of the sample temperature was measured when the input power was 3.5 times above threshold. The Raman output was found to be roughly constant up to a bulk temperature of 200K and then to fall off rapidly, ceasing entirely at about 300K. This effect can be explained on three counts. Firstly, the thermal excitation of electrons from the spin-up to the spin-down conduction band state reduces the number of electrons available to scatter. At the temperatures and fields in question this should account for a variation of less than 10% and is not expected to be the dominant mechanism. Secondly, the spin-lattice relaxation time decreases with increasing temperature, lowering the Raman gain. The primary cause, however, is thought to be the lowering of the energy gap with temperature. At 5.3 pm this leads to increased absorption of the pump beam; and at 10.6 pm it leads to a finite probability of two-photon absorption. Even a small absorption coefficient for either process will yield a significant number of free conduction electrons, which will give increased blocking and free carrier absorption. Intense collinear scattering at the secondStokes and anti-Stokes frequencies was first reported by Allwood et al. 1141, using a 10.6 pm pump. Thus far we have failed to see any second-Stokes output in any of our experiments with a pump of around 5 pm, with the collection optics set for observation of either collinear or transverse emission. The limit of sensitivity was set by the level of stray pump light, transmitted through the sample or scattered within it. The filtering system had a total rejection of N 105; so any second-Stokes output must have been weaker than the stray pump radiation by at least this factor. The mechanisms, both microscopic and maof the production of second-Stokes croscopic, radiation are still under discussion. If it is produced by a genuine Raman scattering process it can only occur where there is a sufficient excess population of spins in the lower energy level; and this excess is unlikely to exist in a region of the crystal where stimulated Stokes radiation has already been produced. A geometry in which the Stokes oscillation occurred in a bouncing-ball mode would therefore be the most conducive to the production of second-Stokes oscillation. The theory of which kind of cavity mode is excited under any given experimental conditions has been given by Smith et al. [4].
Volume 4, number 3
OPTICS COMMUNICATIONS
Mooradian et al. [5] and Pate1 [15] have observed second-Stokes output at around 5 urn in systems in which the Stokes and pump beams were not collinear. If second-Stokes output arises through a parametric interaction involving the pump radiation it would be expected that much less would appear with a 5 urn pump than with a 10 ,um pump; both because the pump is weaker and because the phase mismatch is much greater in the former case when all the frequencies involved are near the band gap where the dispersion is large and nonlinear. Also the interaction may involve anti-Stokes radiation. This has certainly been present in the experiments with a 10.6 pm pump, but in the present case the antiStokes frequency falls in a region where the material absorbs strongly. and the level of antiStokes radiation is therefore extremely low. While second-Stokes emission provides an extension of the tuning range of the Raman laser, it appears that this may be more satisfactorily obtained in a practical wide-range Raman spec trometer by the use of various pump wavelengths and by mixing of the Stokes frequency with other laser frequencies. A transversely excited atmospheric pressure (TEA) laser can be made to operate with a number of gases, e.g., CO, C02, H20, and HF, giving many pump wavelengths in the range 5-30 ,um. Sum frequency mixing has already been observed by Pidgeon et al. [16], using phase matched tellurium. We have shown that the range can be increased considerably by the simple expedient of selecting different lines from the primary CO2 laser. Using only Stokes output with a single CO2 laser line, a useful tuning range of 70 cm-l is available. Fig. 4 shows a typical water vapour spectrum, obtained with an atmospheric path Magnetic 60 -~--VP1
Field 40
(kG) 20
s .-
T z
b
07
9
I
1760
Fig.
4.
sorption
I
1
1600 Wavenumber
I
I
1620 (cm-‘)
I
1640
The observed atmospheric water vapour abspectrum in the region of 1800 cm-l using the tunable scattered output as source.
November
1971
length of 4 m. The pump wavelength was 5.2956 pm. Some twenty lines are visible. It can be seen that some are considerably broader than others. This indicates that the observed linewidths are real, and are determined by pressure broadening and the long path length and not by the spectral resolution of the Raman laser, which must therefore be better than 0.5 cm-l. Other evidence suggests that its actual linewidth is less than 0.03 cm-l [17]. Measurements of the positions of the water vapour lines determine a reproducibility and resettability of the Raman output frequency of one part in 104. At present these limits are set by lack of accurate magnetic field homogeneity and calibration. These results demonstrate the value of stimulated spin-flip scattering for high-resolution spectroscopy around 5 urn. We wish to thank the Science Research Council for financial support and Professor S. D. Smith for providing the laboratory facilities. We also acknowledge valuable experimental and theoretical assistance from Dr. R. A. Wood. Mr. W. J. Firth, and Mr. A. McNeish.
REFERENCES [l] R. L. Allwood. R. B. Dennis. R. G. Mellish, S. D. Smith, B. S. Wherrett nnd R. A. Wood, J. Phys. C (Solid State Phgs.) 4 (1971) L 126. I21. C.Hammond, Univ. of Southampton, Dept.of Electronic Engineering, internal report (1971). .131 W. B. Gandrud and R. L. Abrams, Appl. Phvs. Letters 17 (1970) 302. [4] S.D. Smith, R. L. Allwood, R. B. Dennis, W. J. Firth, B. S. Wherrett, Ii. A. Wood and II. G. Hafele, Proc. Intern. Conf. on Light Scattering in Solids, Paris (1971). [5] A. Mooradian, S. H. J. Brueck and F. A. Btum, Appl. Phys. Letters 17 (1970) 481. [6] C. Irslinger, R. Grisar, II. Wachernig, H. G. H%fele and S. D. Smith, Phys. Stat. Sol., to be published. [7] R. Grisar, C. Irslinger. II. Wachernig and H. G. HBfele, Opt. Commun. 3 (1971) 415. [8] R. J. Phelan, A. R. Calawa, R. II. Rediker, 1~.J. Keyes and B. Lax, Appl. Phys. Letters 3 (1963) 143. [9] R. L. Bell and K. T. Rogers, Appl. Phys. Letters 1 (1964) 9. [lo] C. R. Pidgeon and R. N. BroLvn, Phys. Rev. 146 (1966) 575. [ll] B. S. Wherrett and P. G. Harper, Phys. Rev. 183 (1969) 692. [12] R.Kaplan, Proc. Intern. Conf. on the Physics of Semiconductors. Kvoto (19GG) P. 249. [13] R. L. Allwood, S: D:Devine, R.-G. Mellish, S. D. Smith and R.A.Wood, J. Phys. C (Solid State Phys.) 3 (1970) L18G.
253
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h’ovember 19’71
OPTICS COMMUNICATIOKS
[14] R. L. Allwood, R.B.Dennis, S.D. Smith, B. S. Wherrett and R. A. Wood, J. Phys. C. (Solid State Phys.) 4 (1971) L63. [15] C.K. N. Patel, Appl. Phys. Letters 18 (1971) 274.
[16] C. R. Pidgeon, B. Lax, R. L. Aggarwal, C. E. Chase and F. Brown, Appl. Phys. Letters, to be published. [17] C.K. N. Patel, E. D. Shaw and R. J. Kerl, Phys. Rev. Letters 25 (1970) 8.
ERRATUM
F. C. Strome Jr. and S. A, Tuccio,
Triplet quenching and continuous laser action in three fluorescein dyes, Opt. Commun. 4 (1971) 58.
The dye concentration given in the last sentence second paragraph should be 2 X 10s4 M.
254
of the
4, number 3
OPTICS COMMUNICATIONS
INVESTIGATION
CF
RAMAN
PARAMETERS
SCATTERING
November
CONTROLLING IN InSb
AROUND
STIMULATED 5 urn
R. G. MELLISH, R. B. DENNIS and R. L. ALLWOOD of Physics, Heriot-Watt University, Edinburgh,
Department
Received
27 September
1971
UK
1971
Raman-laser light with a peak power of 2 W and continuously tunable with magnetic field from 5.24 to 5.62 pm has been obtained using a Q-switched CO2 laser as a primary source, the frequency being first doubled by phase matched second harmonic generation in tellurium and then shifted by the stimulated spin-flip process in InSb. The dependence of the output on input power, magnetic field, sample temperature and input focussing parameters has been investigated and theoretically interpreted. The Raman laser has been used to obtain high-resolution absorption spectra of atmospheric water vapour, over a range of N 20 resolvable lines.
A previous communication has described the use of 5.3 pm radiation obtained by second har manic generation (SHG) in tellurium with a Qswitched CO2 laser as the primary source, as a pump for stimulated spin-flip magneto-Raman scattering in InSb [l]. The work has now been extended by selecting a number of wavelengths of operation of the CO2 laser, thus increasing the tuning range of the Raman laser, and by making further experimental and theoretical investigation of the conditions which determine the final output power. The Raman scattering took place in a sample of n-type InSb, which contained 9.7 x 1015 donors cm- 3, and which was mounted inside a superconducting solenoid. The pump light propagating in the Voigt configuration, was polarised parallel to the magnetic field. The input and output pulses were observed simultaneously with copper -doped germanium photoconductive de tectors, which were calibrated by comparison with a photon drag detector. This device exploits the transfer of momentum from a beam of photons to the electrons in a crystal of p-type Ge, and the consequent movement of carriers, on average, towards one end of the crystal. It is calibrated for direct measurement of powers up to 10 MW at 10.6 urn, and has a response time of less than 1 nsec. Since the previous work was described more has been learnt about the process of SHG in Te. Hammond [2] has continued the work of Gandrud and Abrams [3], investigating the efficiency of conversion to second harmonic and the details of
the process which limits the output power. In Te, when some harmonic has been generated, a photon of the harmonic and a photon of the fundamental are simultaneously absorbed and excite an electron across the energy band gap. Free carriers produced in this way then absorb more light, principally at the fundamental frequency, and prevent the generation of more harmonic once a certain power level has been reached. Thus, a firm limit is placed on the harmonic power obtainable from a given active volume of the tellurium defined by the spot size of the laser beam. To obtain more harmonic power one must use a greater fundamental power spread over a larger beam diameter. This limiting process determines that the pulse rises rapidly at the start of the laser pulse, and then falls back to zero long before the end of the laser pulse. The CO2 laser produced pulses of = 20 kW peak and 300 nsec full-width-at-half -modulus (fwhm). The light was focussed onto a 6 mm thick crystal of Te set at the phase match angle. The maximum intensity was = 107 W cm-2, which is the highest which can be used if the damage threshold is not to be exceeded. Even at this intensity damage spots were produced occasionally, probably when the beam landed at a point of the crystal where the surface was not clean. Second harmonic pulses emerging from the Te were of peak power = 400 W and = 140 nsec fwhm. The pump radiation was focussed onto the InSb sample by an NaCl lens of 20 cm focal 249
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length, residual 10.6 pm light being blocked by a piece of MgO. The 5.3 pm power entering the Raman sample was = 50 W. In the Te, because the fundamental propagates as an extraordinary ray, there is an angle of approximately 50 between its k-vector and its Poynting vector. The harmonic generated at each point in the crystal has both vectors parallel to the fundamental kvector, and so it propagates in a direction which takes it away from the fundamental ray. This process, known as walk off, also limits the conversion efficiency. The harmonic output from the end face of the crysial therefore was not a circular beam but had an asymmetrical profile. Measurements with an accurately trackable pinhole showed that the focal spot on the InSb was also irregular, but approximated to a gaussian distribution of 250 pm radius. This gives a maximum intensity at the centre of the beam of 5 x lo4 W cm-2. At a field of 30 kG, where the Raman oscillation was strongest, the pump power was eight times above threshold. This implies that the threshold intensity was about 6 x lo3 W cm-2. This figure is in moderate agreement with previously quoted values of Smith et al. [4], and of Mooradian et al. [ 51, the latter being measured with a cw CO laser; but it is significantly higher than the value obtained by Irslinger et al. [6]. Fig. 1 shows typical pulse shapes of the various beams, obtained at a field of 46 kG. The conditions were such that the limiting process in
November
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the Te was just occurring. The Stokes pulses, typically of 2 W peak power, were only a little shorter than the pump pulses (- 100 nsec and 240 nsec fwhm, respectively). Because of the saturation in the Te the harmonic output had less pulse-to-pulse instability than the laser. The scattered radiation also was observed to occur consistently, and to vary by only some 5% from pulse to pulse, in contrast to that from the identical system pumped with 10.6 pm light. A diffraction grating which formed part of the CO2 laser cavity was used to select, in turn, several wavelengths in the 10.6 and the 10.2 pm bands. With each pump wavelength the Raman output wavelength was measured as a function of field. Fig. 2 shows the tuning ranges obtained. In the case of 5.15 pm pump, intense Raman scattering ceased at 15 kG; at lower fields stimulated recombination radiation @RR) was observed. Previous measurements of SRR using optical pumping [7] and electrical excitation [8,9] both show two distinct tuning characteristics. These can be accurately correlated with the interband transitions and polarization selection rules of Pidgeon and Brown [lo]. In this experiment SRR has an octput power N 100 mW, the same as the spin flip power near threshold. SRR occurs at the observed wavelengths independent of the precise pumping wavelength, but it is very sensitive to changes in temperature which shift the band gap.
5.7r
(b) /\
I
/
A /
1 division
Fig. 1. Typical oscilloscope
(cl SRR L
I
=
I
100 ns
tracings for
CO2 laser pulse, (b) the SEIG from the (c) the stimulated scattered output -
(a) the tellurium,
input and
illustrating the narrowing at each stage of the conversion process.
250
Fig. 2. The observed tuning ranges for stimulated Stokes scattering for three different pump wavelengths at 5.296, 5.276, and 5.152 pm. Stimulated recombination radiation at low magnetic fields is also shown.
Volume 4, number 3
November 1971
OPTICS COMMUNICATIONS
The threshold for Raman oscillation in InSb with a pump of around 5.3 pm is low because the denominator of the scattering cross section resonates when tip, the energy of a pump photon, is close to the energy of the first virtual transition, from the valence band to the upper spin state in the conduction band. The value of the cross section varies rapidly with magnetic field as this energy moves away from the pump energy; but precise investigation of the fielddependence is rendered difficult by several factors. Firstly, the number of electrons available for Raman scattering is also a function of the field. At low fields, the Fermi level lies above the bottom of the second Landau level (rz= 0, spin down). Electrons near kZ = 0 are therefore unable to take part in Raman scattering, since what would be the final state is already occupied. The effect, where virtual transitions are blocked, has been discussed by Wherrett and Harper [ll], for the case of a sharp Fermi level. Only for fields above the quantum condition, when EF < liw,f (where i?wsf is the spin-flip energy), are all the electrons available to take part in scattering. The critical field is 26 kG for the present doping. At finite temperatures the boundary between the two regimes is not sharp and the effective number of electrons becomes a complicated function of the field. If, on the other hand, the temperature is very low, the number of free carriers may be reduced by magnetic freeze-out at high fields [12]. Secondly, the resonance depends critically on the precise size of the band gap which is in turn dependent on the temperature, not of the bulk sample, but of the radiated filament where the scattering is taking place. This region is illuminated by the pump beam, and its temperature can only be estimated. Taking a figure of 300K gives a zero-field band gap of 1886 cm-l. At 20 kG the valence-tospin-down-conduction transition has reached With the laser operating at 10.59 1974 cm-l. pm, the pump is at 1888 cm-l; and with the laser operating at 10.30 pm, the pump is at 1941 cm-l. Thus the latter pump is much closer to resonance. It was observed that oscillations ceased at 20 kG with the lower energy pump but continued to lower fields with the higher energy pump; even though the blocking effect strongly reduces the scattering cross section for fields below 26 kG. At 60 kG the transition produced by the pump photon is far from resonance, and a small change of pump frequency would be expected to have little effect. It was in fact observed that the high-field limit of oscillation was
60 kG for all pump frequencies. This limit may be determined in part by variation of the spontaneous scattering linewidth with field. The dependence of this linewidth on various factors is being investigated. At a field of 46 kG, well inside the range of oscillation, the relationship between input and output powers was studied. The input was monitored by reflecting a portion of the beam off a KRS5 plate onto a second detector. The power was varied by rotating the Te crystal away from the phase-matching angle. It was observed that there was little fluctuation of Stokes power from pulse to pulse, even when the pump power was reduced to only just above threshold. This is in contrast to the behaviour of the same system with a 10.6 km pump, when the Stokes pulses become very erratic near threshold 1131. Fig. 3 shows output/input curves both for the best pulses, at a given setting of the tellurium, and for the power averaged over many pulses, but because the statistical variations of the pulses were essentially the same at all levels the curves are identical. Mention has been made of the saturation process in the Te, and of the irregular shape of the focal spot of the harmonic beam. As the Te was moved away from phase-match the distribution of power over the spot, as well as the total power, changed; and so one cannot give a precise theory relating Stokes output to pump input. Nevertheless, the experimental results fit the following simple theory fairly well. It is assumed’that, because the gains and losses in the Raman sample are both so high, the usual concept of cavity modes is not really valid; and that the distribution of oscillating power is determined primarily by that of pump power, which is assumed to be gaussian. Diffusion of
3r (P)
o- Peak input power
01
Average input power
Fig. 3. Comparison of the experimentally observed points (0) and the theoretical expression (solid line), in arbitrary units, for the output/input dependence of both the peak pulse powers (left) and average powers (right). 251
\‘olume
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carriers out of the active region, and spin-relaxation during the pulse, are neglected. Suppose that, in a given region of the crystal, the pump intensity is at some instant a factor A above threshold. When a fractionf of the spins have flipped, the excess population in the lower energy level is reduced to a fraction (1 - Zf) of the original number. The threshold in that region is thereby raised to l,‘(l -2,f) times its original value, as the Raman gain is proportional to the excess population of electrons in the lower spin state. We assume that Raman scattering goes on, and the local threshold rises until it has become equal to the intensity actually present; whereupon oscillation ceases, and no more spins flip until the input power rises further. Then A (1 - 2s) = 1, or f = :(l - 1 ‘A). At the peak of the input pulse let the power be filth, where Pth is the threshold power. At a distance rfrom the centre of the spot the intensity is then given by I = Pith exp (-4’20~) where Ith is the threshold intensity and 2cr (- ((‘) is the gaussian beam radius. Then A = p exp ( -$‘2a2), and the fraction of the spins that have flipped is ~2/2$)). The output energy dE, 4 {l - (l/fi)exp( produced up to this time from an annular element of the crystal between 7. and I’+ dr is dE = $ (1 - (l/p) where is the length of the to be
exp (~~;‘2a~))N~w~
2;; L rdr ,
N is the free carrier concentration, xws energy of a Stokes photon, and L is the of the crystal. Integrating over the area active region we find the total energy, E,
E = Ntiw,
.02L(loge
$J - 1 + 1 ‘fi) .
When the maximum pump intensity is well above threshold, a small change of spot size should have little effect on the output, as the changes in CTand p largely cancel. It was indeed found that with a field of 46 kG, when p was 3.5, the Stokes output power was insensitive to longitudinal movement of the focussing lens. According to the theory the cancellation should be perfect near p = 5, and the output power should then be a maximum. Fig. 3 shows curves calculated from this theory, which closely agree with the experimental points. This further indicates that spin-relaxation and diffusion are negligible, since they would lead to a more complex energy relationship. It has been observed that Raman oscillation with a 10.6 pm pump is strongly dependent on 252
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the bulk temperature of the sample, disappearing when it is heated to around 400K [4]. With the 5.3 pm pumped system, the effect of the sample temperature was measured when the input power was 3.5 times above threshold. The Raman output was found to be roughly constant up to a bulk temperature of 200K and then to fall off rapidly, ceasing entirely at about 300K. This effect can be explained on three counts. Firstly, the thermal excitation of electrons from the spin-up to the spin-down conduction band state reduces the number of electrons available to scatter. At the temperatures and fields in question this should account for a variation of less than 10% and is not expected to be the dominant mechanism. Secondly, the spin-lattice relaxation time decreases with increasing temperature, lowering the Raman gain. The primary cause, however, is thought to be the lowering of the energy gap with temperature. At 5.3 pm this leads to increased absorption of the pump beam; and at 10.6 pm it leads to a finite probability of two-photon absorption. Even a small absorption coefficient for either process will yield a significant number of free conduction electrons, which will give increased blocking and free carrier absorption. Intense collinear scattering at the secondStokes and anti-Stokes frequencies was first reported by Allwood et al. 1141, using a 10.6 pm pump. Thus far we have failed to see any second-Stokes output in any of our experiments with a pump of around 5 pm, with the collection optics set for observation of either collinear or transverse emission. The limit of sensitivity was set by the level of stray pump light, transmitted through the sample or scattered within it. The filtering system had a total rejection of N 105; so any second-Stokes output must have been weaker than the stray pump radiation by at least this factor. The mechanisms, both microscopic and maof the production of second-Stokes croscopic, radiation are still under discussion. If it is produced by a genuine Raman scattering process it can only occur where there is a sufficient excess population of spins in the lower energy level; and this excess is unlikely to exist in a region of the crystal where stimulated Stokes radiation has already been produced. A geometry in which the Stokes oscillation occurred in a bouncing-ball mode would therefore be the most conducive to the production of second-Stokes oscillation. The theory of which kind of cavity mode is excited under any given experimental conditions has been given by Smith et al. [4].
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OPTICS COMMUNICATIONS
Mooradian et al. [5] and Pate1 [15] have observed second-Stokes output at around 5 urn in systems in which the Stokes and pump beams were not collinear. If second-Stokes output arises through a parametric interaction involving the pump radiation it would be expected that much less would appear with a 5 urn pump than with a 10 ,um pump; both because the pump is weaker and because the phase mismatch is much greater in the former case when all the frequencies involved are near the band gap where the dispersion is large and nonlinear. Also the interaction may involve anti-Stokes radiation. This has certainly been present in the experiments with a 10.6 pm pump, but in the present case the antiStokes frequency falls in a region where the material absorbs strongly. and the level of antiStokes radiation is therefore extremely low. While second-Stokes emission provides an extension of the tuning range of the Raman laser, it appears that this may be more satisfactorily obtained in a practical wide-range Raman spec trometer by the use of various pump wavelengths and by mixing of the Stokes frequency with other laser frequencies. A transversely excited atmospheric pressure (TEA) laser can be made to operate with a number of gases, e.g., CO, C02, H20, and HF, giving many pump wavelengths in the range 5-30 ,um. Sum frequency mixing has already been observed by Pidgeon et al. [16], using phase matched tellurium. We have shown that the range can be increased considerably by the simple expedient of selecting different lines from the primary CO2 laser. Using only Stokes output with a single CO2 laser line, a useful tuning range of 70 cm-l is available. Fig. 4 shows a typical water vapour spectrum, obtained with an atmospheric path Magnetic 60 -~--VP1
Field 40
(kG) 20
s .-
T z
b
07
9
I
1760
Fig.
4.
sorption
I
1
1600 Wavenumber
I
I
1620 (cm-‘)
I
1640
The observed atmospheric water vapour abspectrum in the region of 1800 cm-l using the tunable scattered output as source.
November
1971
length of 4 m. The pump wavelength was 5.2956 pm. Some twenty lines are visible. It can be seen that some are considerably broader than others. This indicates that the observed linewidths are real, and are determined by pressure broadening and the long path length and not by the spectral resolution of the Raman laser, which must therefore be better than 0.5 cm-l. Other evidence suggests that its actual linewidth is less than 0.03 cm-l [17]. Measurements of the positions of the water vapour lines determine a reproducibility and resettability of the Raman output frequency of one part in 104. At present these limits are set by lack of accurate magnetic field homogeneity and calibration. These results demonstrate the value of stimulated spin-flip scattering for high-resolution spectroscopy around 5 urn. We wish to thank the Science Research Council for financial support and Professor S. D. Smith for providing the laboratory facilities. We also acknowledge valuable experimental and theoretical assistance from Dr. R. A. Wood. Mr. W. J. Firth, and Mr. A. McNeish.
REFERENCES [l] R. L. Allwood. R. B. Dennis. R. G. Mellish, S. D. Smith, B. S. Wherrett nnd R. A. Wood, J. Phys. C (Solid State Phgs.) 4 (1971) L 126. I21. C.Hammond, Univ. of Southampton, Dept.of Electronic Engineering, internal report (1971). .131 W. B. Gandrud and R. L. Abrams, Appl. Phvs. Letters 17 (1970) 302. [4] S.D. Smith, R. L. Allwood, R. B. Dennis, W. J. Firth, B. S. Wherrett, Ii. A. Wood and II. G. Hafele, Proc. Intern. Conf. on Light Scattering in Solids, Paris (1971). [5] A. Mooradian, S. H. J. Brueck and F. A. Btum, Appl. Phys. Letters 17 (1970) 481. [6] C. Irslinger, R. Grisar, II. Wachernig, H. G. H%fele and S. D. Smith, Phys. Stat. Sol., to be published. [7] R. Grisar, C. Irslinger. II. Wachernig and H. G. HBfele, Opt. Commun. 3 (1971) 415. [8] R. J. Phelan, A. R. Calawa, R. II. Rediker, 1~.J. Keyes and B. Lax, Appl. Phys. Letters 3 (1963) 143. [9] R. L. Bell and K. T. Rogers, Appl. Phys. Letters 1 (1964) 9. [lo] C. R. Pidgeon and R. N. BroLvn, Phys. Rev. 146 (1966) 575. [ll] B. S. Wherrett and P. G. Harper, Phys. Rev. 183 (1969) 692. [12] R.Kaplan, Proc. Intern. Conf. on the Physics of Semiconductors. Kvoto (19GG) P. 249. [13] R. L. Allwood, S: D:Devine, R.-G. Mellish, S. D. Smith and R.A.Wood, J. Phys. C (Solid State Phys.) 3 (1970) L18G.
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OPTICS COMMUNICATIOKS
[14] R. L. Allwood, R.B.Dennis, S.D. Smith, B. S. Wherrett and R. A. Wood, J. Phys. C. (Solid State Phys.) 4 (1971) L63. [15] C.K. N. Patel, Appl. Phys. Letters 18 (1971) 274.
[16] C. R. Pidgeon, B. Lax, R. L. Aggarwal, C. E. Chase and F. Brown, Appl. Phys. Letters, to be published. [17] C.K. N. Patel, E. D. Shaw and R. J. Kerl, Phys. Rev. Letters 25 (1970) 8.
ERRATUM
F. C. Strome Jr. and S. A, Tuccio,
Triplet quenching and continuous laser action in three fluorescein dyes, Opt. Commun. 4 (1971) 58.
The dye concentration given in the last sentence second paragraph should be 2 X 10s4 M.
254
of the