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Resonant and small volume non-resonant cells as infrared-acoustic detectors for laser spectroscopy
00m91i81/060337-05 Pngsmon
RESONANT CELLS
so2 ooio Rnr Ltd
AND SMALL VOLUME NON-RESONANT AS INFRARED-ACOUSTIC DETECTORS FOR LASER SPECTROSCOPY H. G. KRAFT* and J. W. BEVAN
Chemistry Department, Texas A & M University. College Station. Texas 77843. U.S.A. (Received 9 April 1981) Abstract--Resonant and non-resonant opto-acoustic cells constructed as infrared high resolution laser spectroscopic detectors have been investigated. Sensitivity studies involving the lyb i +-00 0 rotational-vibrational spectrum of CO, with a color center laser (RbCI:Li) have been completed to evaluate the most appropriate design. The small volume non-resonant infrared-acoustic cell is shown to be most sensitive for this purpose.
INTRODUCTION The availability of powerful infrared lasers as optical excitation sources has offered the opportunity of a wide variety of physically-related investigations using the opto-acoustic effect. Measurement of atmospheric pollutants at ppb level, determination of gas absorption coefficients as low as 10-‘” m-‘, collisional radial energy transfer processes, represent only a few of the applications studied. (‘) Optimization of infrared-acoustic cell design especially for detection involving ultra-low concentrations of pollutants has been the subject of intense investigation from both a theoretical and experimental standpoint.‘2-6’ A majority of such studies involve total gas pressures of about 1 atm. inside the acoustic cell. Relatively few studies however exist involving infrared-acoustic techniques at pressures of 50 torr or less (‘*‘) where spectroscopic high resolution gas phase investigations are usually performed. The advent of commercially available, broad-band tunable cw infrared lasers such as Spin Flip Raman”‘, or color center”” lasers, offers the opportunity of routine application of the infrared-acoustic technique to high resolution rotational-vibrational spectroscopy. Laser powers in excess of one mW and line widths in the range 3 to 10e4 GHz combine to indicate potential applications of such detectors, not only in spectroscopic analysis but also as a very convenient method of spectral frequency calibration using reference gases. Although some gas phase spectroscopic applications of infrared-acoustic detection have been made”‘, no studies have reported design optimization of resonant relative to small volume non-resonant acoustic cells for this specific purpose at pressures of 50 torr or less. Significant differences in the signal characteristics for resonant and non-resonant cells have been observed in the pressure range 760 to 75 torr and rapid decreases have been observed below the latter pressure. (11) These results indicate the necessity of design optimization of such acoustic cells for low pressure spectroscopic purposes. The present work concerns the spectroscopic applications of infrared-acoustic detection using tunable color center lasers. Specifically investigations of a small volume nonresonant cell and a resonant acoustic cell involving electret-type miniature microphones have been studied. The relative sensitivity of these cells is reported for the pressure range 760-l torr CO2 in order to determine experimentally which of the cells considered is most appropriate for general purpose laser spectroscopy. Such an evaluation is necessary to ascertain whether practically attainable Q values and response of the resonant cell are sufficient to overcome the advantages of the optimized response from the small volume non-resonant acoustic cell. l
Robert A. Welch Post-doctoral Fellow. 337
H. G. KRAFT and J. W. BEVAN
338
REFERENCE 1
Kr+ Laser
I
I)
I
Crystal chombw Fig. I. Schematic for recording photo-acoustic spectra using a color center laser.
EXPERIMENTAL
The basic experimental arrangement is shown in Fig. 1. A color center laser (Burleigh FCL-10, RbCI:Li color center crystal) is pumped with the chopped beam of the 6471 A line in a Spectra-Physics 171 Kr+ laser. A continuous variation of the chopper frequency up to 5000 Hz with a quoted stability of _+0.2% was possible using a PARC Model 192 variable speed chopper. The chopper frequency was monitored continuously with a HP5246 L electronic counter showing a stability of _+1 Hz during measurements. The laser was used in multi-mode operation for broad-band scanning with a 0.05 cm-’ linewidth and 1.5 mm beam diameter, output powers of 1 mW being used in the experiments described in this paper. Laser beams were directed through the centers of the extracavity acoustic cells and monitored with PbS detectors. Both acoustic cells were enclosed in vacuum boxes with CaFz windows and maintained on vibration damping supports, thus minimizing both extraneous acoustic and mechanical noise. As a result these acoustical and mechanical sources of noise were negligible relative to the electrical noise. The acoustic signal was amplified by a PARC HR-8 lock-in amplifier. Two basically different cell designs were investigated for most sensitive acoustic response, these being: (a) a small volume non-resonant cell, and (b) a resonant cell. An optimum design was chosen for both cells. For the non-resonant cell the volume was minimized to maximize the signal,“) and in the resonant case the cell design’“’ was chosen to have a Q comparable to the best currently available. Knowles BT 1834 miniature electret microphones (sensitivity 10 mV/Pa) with built in FET preamplifier were used in all acoustic cells to enable a comparison of acoustic signals. Small volume non-resonant cell The small volume cell constructed is shown drawn to scale in Fig. 2. Fabricated from a stainless steel block the cell has 0.4~~ gas volume. (the latter being 2.Ocm long and 0.5 cm in diameter). Metal disks with 2.0 mm orifice enable transmission of the laser beam through CaFz windows. The Knowles BT 1834 microphone is mounted in the cell wall. The upper section of the cell contains the necessary electrical connections and battery for the microphone sealed from the sample area. Modulation frequencies of 50 and 500 Hz were used in recording spectra. Electrical noise on the lock-in amplifier with 3 s time constant was f 18 nV and f 4 nV respectively at 760 torr pressure of COZ.
Infrared-acoustic detectors for laser spectroscopy
339
TEFLDN ROD MICROPHONE
Fig. 2. Small volume non-resonant infrared-acoustic cell. 0.4 cm’.
Resonant Cell The basic resonant cell design was similar to that previously used by Gerlach and Amer.” t, The carefully polished copper interior had 9.94 cm diameter and 10 cm length with the microphone inserted in the cell wall. For a cylindrical cell the acoustical resonant frequencies are given by Morse (13)
f&,,, being the frequency of the acoustical modes. Eigenvalues p. m, and n refer to the longitudinal, azimuthal and radial modes respectively, r is, the radius of the cavity and 1 its length. u, is the velocity of sound and a, the nth derivative of the Bessel function dJ, (na)/da. The strongest resonance mode for CO2 at 760 torr pressure, 28°C temperature, the radial (001) mode occurred at 3301 Hz with a Q of 470 (Q defined as resonant frequency divided by half width at half power). Operated at resonant frequency the electrical noise on the lock-in amplifier with a 3 s time constant was & 1.5 nV. The {yi i +OO”O spectrum of carbon dioxide was recorded in the range 2.7702.780pm to enable a comparison to be made between the photoacoustic signals of the different cells at a series of pressures from 760 to 1 torr with a 3s time constant under comparable conditions. At higher pressures spectral transition overlap occurred as a consequency of pressure broadening. The signal magnitudes were corrected assuming a Lorentzian lineshape.
RESULTS
A comparison of the relative signals and signal/noise ratios for the two cells is given in Fig. 3. The signals were measured base to peak for both cells at a series of pressures from 760 to 1 torr to facilitate the comparison under the same conditions. Signal magnitudes were corrected for rotational transition overlap. Although the small volume non-resonant cell provided a spectrum at 1 torr pressure no spectrum could be recorded for the resonant cell under these conditions. The first radial mode (001) of the resonant cell was found to be the strongest and was used for all subsequent measurements. Significant differences in the signal characteristics for the resonant and small volume non-resonant cells are evident in Fig. 3. It is apparent from Fig. 3 that the small volume non-resonant cell signal is significantly greater than that observed for the resonant cell by a factor varying from 1.07 x 10’ to 1.16 x lo’, over the pressure range 760-5 torr. As the width of a collision-broadened spectral line is closely proportional to pressure and the integral of the absorption cross-section over the line is constant, the signal magnitude INF. 21/b-n
340
H. G. KRAFTand J. W. BEVAN
Non-resonant
Non-resonant
Resonant cell (b)
2
w
I
P(torr)
Fig. 3. Infrared-acoustic results for $ 1 +OO’O bands of C02. Logarithm of (a) signal magnitude (0) in arbitary absolute units. and (b) signal to noise ratio (A) versus logarithm of total pressure in Torr. Modulation frequency 50Hz for non-resonant cell. estimated error of signal intensity i 5% and signal/noise ratios < loo/,.
can be expected to be constant at high pressures. Results for the small volume non-resonant cell reflect the influence of this latter effect at higher pressures. The resonant cell also exhibits a decrease in the rate of signal magnitude increase with pressure at higher pressures, which correlates with a decrease in Q value.” I) In the low pressure region the signal of the small volume non-resonant cell is proportional to a power of the pressure of about 2.5 as reported for non-resonant cells by Farrow and Richton.“’ The signal of the resonant cell in the low pressure region is proportional to a power of the pressure raised to only 1.3. The first radial mode (001) causes a higher gas density along the axis of the cell and therefore the absorbed laser power and signal correspond to an imaginary higher pressure. Although for low pressures the decrease of signal magnitude is more rapid for the small volume non-resonant cell than for the resonant cell, the former cell is still preferable for spectroscopic purposes due to its greater sensitivity under comparable conditions.
Infrared-acoustic detectors for laser spectroscopy
341
A comparison of the equaiiy important relative signal to noise ratios indicates that in the pressure range of most importance for high resolution spectroscopy the sensitivity of the small volume cell is greater by a factor of between 10 and 37 over the pressure range 100-5 torr. At higher pressures we were unable to determine this ratio with adequate accuracy to warrant any comment. At very low pressures, about 1 torr, the relative magnitudes of signal to noise resulted in practical limitations in the optimization of the phase of the lock-in amplifier. An improvement in signal/noise ratio between 2 to 5 was possible in the pressure range l-10 torr, using an increase in modulation frequency to 500 Hz. This was primarily attributed to a decrease in l/f noise and a better optimization of a lock-in amplifier at the higher frequency despite a decrease in absolute signal. CONCLUSIONS A comparison of both signal and signal to noise has been made for a small volume and a resonant acoustic cell with a Q comparable to the best currently available. The small volume non-resonant ceil is shown to be significantly more sensitive than the resonant cell, for the pressure range (l-50 torr) of particular interest in high resolution spectroscopy. Although the sensitivity of acoustic detection decreases substantially using lower total cell pressures the signals observed can be maximized using a small volume non-resonant acoustic ceil. The infrared-acoustic detection technique does have distinct advantages, for certain purposes, over conventional low pressure high resolution absorption studies, which potentially makes it a powerful technique. Its insensitivity to source noise, the absence of background associated with the laser output profile-often a problem in iaserrelated absorption studies-and its small volume requirement for expensive or highly toxic samples make it a particularly attractive technique in these cases. The small volume requirements also make it extremely useful for recording frequencies of reference spectra needed for calibration in such spectroscopic studies. From a practical spectroscopic viewpoint the small volume non-resonant ceil poses fewer problems than the resonant ceil. The stringent dependence of the resonant acoustic frequency on sample conditions results in many problems when recording spectra. In addition the small volume acoustic cell used in these experiments was found to be relatively insensitive to extraneous acoustical interference. As a consequence, spectra were usually recorded without use of the vacuum box previously mentioned. It is highly probable that the sensitivity of the small volume infrared-acoustic detectors described here can be significantly improved. Utilization of miniature microphones with a smaller active area (Knowles BT 1759) and focusing the laser beam into a smaller volume ceil can be used with subsequent increase in sensitivity, particularly in the case of molecules where saturation effects are not significant. Acknowledgemenrs-We would like to express our appreciation to the National Science Foundation (Grant CHE 79-23237), the Robert A. Welch Foundation (Grant A-747) and the Research Corporation (Cottrell Research Grant) for supporting this research.
REFERENCES 1. ROSENCWAIG, A. Adc. electronic Elecrron Phys, 46. 207 (1978) (and included references). 2. ROSENGRAN L. G.. Appl. Opr., 14, 1960 (1075). 3. KAMMR. B., J. Appl. Phys., 47 3550 (1976). 4. KREUZER L. B., 1. Appl. Phys.. 42 2934 (1971). 5. DEWEY C. F., Jr.. R. D. KAMM,& C. E. HACKETT,Appl. Phys. Lerrs., 23, 633 (1973). 6. NODOV E., Appl. Opt.. 17, I IO (1978). 7. a) BUTCHERR. J., R. B. DENNIS & S. D. SMITH,Proc. Roy. Sot. A, 344, 541 (1975). b) PATEL C. K. N. & R. J. KERR Opt Commun. 24, 294 (1978). 8. FARROW L. A. & R. E. RICHTON,J. Appl. Phys., 48 (12), 4962 (1977). 9. PATEL C. K. N. & E. D. SHAW, Php. Rec.. 33, 127 (1971). IO. BEIGANCR., G. LITFIN & H. WELLING, Opr. Commun. 22, 269 (1977). 11. GERLACHR. & N. M. AMER. Appl. fhys. Lerr., 32, 228 (1978). 12. THOMAS L. J., M. J. KELLEY & N. M. AMER, Appl. PhJs. Lerr., 32, 736 (1978). 13. MORSEP. M.. Vibrarion and Sound. McGraw-Hill. New York (1948).
RESONANT CELLS
so2 ooio Rnr Ltd
AND SMALL VOLUME NON-RESONANT AS INFRARED-ACOUSTIC DETECTORS FOR LASER SPECTROSCOPY H. G. KRAFT* and J. W. BEVAN
Chemistry Department, Texas A & M University. College Station. Texas 77843. U.S.A. (Received 9 April 1981) Abstract--Resonant and non-resonant opto-acoustic cells constructed as infrared high resolution laser spectroscopic detectors have been investigated. Sensitivity studies involving the lyb i +-00 0 rotational-vibrational spectrum of CO, with a color center laser (RbCI:Li) have been completed to evaluate the most appropriate design. The small volume non-resonant infrared-acoustic cell is shown to be most sensitive for this purpose.
INTRODUCTION The availability of powerful infrared lasers as optical excitation sources has offered the opportunity of a wide variety of physically-related investigations using the opto-acoustic effect. Measurement of atmospheric pollutants at ppb level, determination of gas absorption coefficients as low as 10-‘” m-‘, collisional radial energy transfer processes, represent only a few of the applications studied. (‘) Optimization of infrared-acoustic cell design especially for detection involving ultra-low concentrations of pollutants has been the subject of intense investigation from both a theoretical and experimental standpoint.‘2-6’ A majority of such studies involve total gas pressures of about 1 atm. inside the acoustic cell. Relatively few studies however exist involving infrared-acoustic techniques at pressures of 50 torr or less (‘*‘) where spectroscopic high resolution gas phase investigations are usually performed. The advent of commercially available, broad-band tunable cw infrared lasers such as Spin Flip Raman”‘, or color center”” lasers, offers the opportunity of routine application of the infrared-acoustic technique to high resolution rotational-vibrational spectroscopy. Laser powers in excess of one mW and line widths in the range 3 to 10e4 GHz combine to indicate potential applications of such detectors, not only in spectroscopic analysis but also as a very convenient method of spectral frequency calibration using reference gases. Although some gas phase spectroscopic applications of infrared-acoustic detection have been made”‘, no studies have reported design optimization of resonant relative to small volume non-resonant acoustic cells for this specific purpose at pressures of 50 torr or less. Significant differences in the signal characteristics for resonant and non-resonant cells have been observed in the pressure range 760 to 75 torr and rapid decreases have been observed below the latter pressure. (11) These results indicate the necessity of design optimization of such acoustic cells for low pressure spectroscopic purposes. The present work concerns the spectroscopic applications of infrared-acoustic detection using tunable color center lasers. Specifically investigations of a small volume nonresonant cell and a resonant acoustic cell involving electret-type miniature microphones have been studied. The relative sensitivity of these cells is reported for the pressure range 760-l torr CO2 in order to determine experimentally which of the cells considered is most appropriate for general purpose laser spectroscopy. Such an evaluation is necessary to ascertain whether practically attainable Q values and response of the resonant cell are sufficient to overcome the advantages of the optimized response from the small volume non-resonant acoustic cell. l
Robert A. Welch Post-doctoral Fellow. 337
H. G. KRAFT and J. W. BEVAN
338
REFERENCE 1
Kr+ Laser
I
I)
I
Crystal chombw Fig. I. Schematic for recording photo-acoustic spectra using a color center laser.
EXPERIMENTAL
The basic experimental arrangement is shown in Fig. 1. A color center laser (Burleigh FCL-10, RbCI:Li color center crystal) is pumped with the chopped beam of the 6471 A line in a Spectra-Physics 171 Kr+ laser. A continuous variation of the chopper frequency up to 5000 Hz with a quoted stability of _+0.2% was possible using a PARC Model 192 variable speed chopper. The chopper frequency was monitored continuously with a HP5246 L electronic counter showing a stability of _+1 Hz during measurements. The laser was used in multi-mode operation for broad-band scanning with a 0.05 cm-’ linewidth and 1.5 mm beam diameter, output powers of 1 mW being used in the experiments described in this paper. Laser beams were directed through the centers of the extracavity acoustic cells and monitored with PbS detectors. Both acoustic cells were enclosed in vacuum boxes with CaFz windows and maintained on vibration damping supports, thus minimizing both extraneous acoustic and mechanical noise. As a result these acoustical and mechanical sources of noise were negligible relative to the electrical noise. The acoustic signal was amplified by a PARC HR-8 lock-in amplifier. Two basically different cell designs were investigated for most sensitive acoustic response, these being: (a) a small volume non-resonant cell, and (b) a resonant cell. An optimum design was chosen for both cells. For the non-resonant cell the volume was minimized to maximize the signal,“) and in the resonant case the cell design’“’ was chosen to have a Q comparable to the best currently available. Knowles BT 1834 miniature electret microphones (sensitivity 10 mV/Pa) with built in FET preamplifier were used in all acoustic cells to enable a comparison of acoustic signals. Small volume non-resonant cell The small volume cell constructed is shown drawn to scale in Fig. 2. Fabricated from a stainless steel block the cell has 0.4~~ gas volume. (the latter being 2.Ocm long and 0.5 cm in diameter). Metal disks with 2.0 mm orifice enable transmission of the laser beam through CaFz windows. The Knowles BT 1834 microphone is mounted in the cell wall. The upper section of the cell contains the necessary electrical connections and battery for the microphone sealed from the sample area. Modulation frequencies of 50 and 500 Hz were used in recording spectra. Electrical noise on the lock-in amplifier with 3 s time constant was f 18 nV and f 4 nV respectively at 760 torr pressure of COZ.
Infrared-acoustic detectors for laser spectroscopy
339
TEFLDN ROD MICROPHONE
Fig. 2. Small volume non-resonant infrared-acoustic cell. 0.4 cm’.
Resonant Cell The basic resonant cell design was similar to that previously used by Gerlach and Amer.” t, The carefully polished copper interior had 9.94 cm diameter and 10 cm length with the microphone inserted in the cell wall. For a cylindrical cell the acoustical resonant frequencies are given by Morse (13)
f&,,, being the frequency of the acoustical modes. Eigenvalues p. m, and n refer to the longitudinal, azimuthal and radial modes respectively, r is, the radius of the cavity and 1 its length. u, is the velocity of sound and a, the nth derivative of the Bessel function dJ, (na)/da. The strongest resonance mode for CO2 at 760 torr pressure, 28°C temperature, the radial (001) mode occurred at 3301 Hz with a Q of 470 (Q defined as resonant frequency divided by half width at half power). Operated at resonant frequency the electrical noise on the lock-in amplifier with a 3 s time constant was & 1.5 nV. The {yi i +OO”O spectrum of carbon dioxide was recorded in the range 2.7702.780pm to enable a comparison to be made between the photoacoustic signals of the different cells at a series of pressures from 760 to 1 torr with a 3s time constant under comparable conditions. At higher pressures spectral transition overlap occurred as a consequency of pressure broadening. The signal magnitudes were corrected assuming a Lorentzian lineshape.
RESULTS
A comparison of the relative signals and signal/noise ratios for the two cells is given in Fig. 3. The signals were measured base to peak for both cells at a series of pressures from 760 to 1 torr to facilitate the comparison under the same conditions. Signal magnitudes were corrected for rotational transition overlap. Although the small volume non-resonant cell provided a spectrum at 1 torr pressure no spectrum could be recorded for the resonant cell under these conditions. The first radial mode (001) of the resonant cell was found to be the strongest and was used for all subsequent measurements. Significant differences in the signal characteristics for the resonant and small volume non-resonant cells are evident in Fig. 3. It is apparent from Fig. 3 that the small volume non-resonant cell signal is significantly greater than that observed for the resonant cell by a factor varying from 1.07 x 10’ to 1.16 x lo’, over the pressure range 760-5 torr. As the width of a collision-broadened spectral line is closely proportional to pressure and the integral of the absorption cross-section over the line is constant, the signal magnitude INF. 21/b-n
340
H. G. KRAFTand J. W. BEVAN
Non-resonant
Non-resonant
Resonant cell (b)
2
w
I
P(torr)
Fig. 3. Infrared-acoustic results for $ 1 +OO’O bands of C02. Logarithm of (a) signal magnitude (0) in arbitary absolute units. and (b) signal to noise ratio (A) versus logarithm of total pressure in Torr. Modulation frequency 50Hz for non-resonant cell. estimated error of signal intensity i 5% and signal/noise ratios < loo/,.
can be expected to be constant at high pressures. Results for the small volume non-resonant cell reflect the influence of this latter effect at higher pressures. The resonant cell also exhibits a decrease in the rate of signal magnitude increase with pressure at higher pressures, which correlates with a decrease in Q value.” I) In the low pressure region the signal of the small volume non-resonant cell is proportional to a power of the pressure of about 2.5 as reported for non-resonant cells by Farrow and Richton.“’ The signal of the resonant cell in the low pressure region is proportional to a power of the pressure raised to only 1.3. The first radial mode (001) causes a higher gas density along the axis of the cell and therefore the absorbed laser power and signal correspond to an imaginary higher pressure. Although for low pressures the decrease of signal magnitude is more rapid for the small volume non-resonant cell than for the resonant cell, the former cell is still preferable for spectroscopic purposes due to its greater sensitivity under comparable conditions.
Infrared-acoustic detectors for laser spectroscopy
341
A comparison of the equaiiy important relative signal to noise ratios indicates that in the pressure range of most importance for high resolution spectroscopy the sensitivity of the small volume cell is greater by a factor of between 10 and 37 over the pressure range 100-5 torr. At higher pressures we were unable to determine this ratio with adequate accuracy to warrant any comment. At very low pressures, about 1 torr, the relative magnitudes of signal to noise resulted in practical limitations in the optimization of the phase of the lock-in amplifier. An improvement in signal/noise ratio between 2 to 5 was possible in the pressure range l-10 torr, using an increase in modulation frequency to 500 Hz. This was primarily attributed to a decrease in l/f noise and a better optimization of a lock-in amplifier at the higher frequency despite a decrease in absolute signal. CONCLUSIONS A comparison of both signal and signal to noise has been made for a small volume and a resonant acoustic cell with a Q comparable to the best currently available. The small volume non-resonant ceil is shown to be significantly more sensitive than the resonant cell, for the pressure range (l-50 torr) of particular interest in high resolution spectroscopy. Although the sensitivity of acoustic detection decreases substantially using lower total cell pressures the signals observed can be maximized using a small volume non-resonant acoustic ceil. The infrared-acoustic detection technique does have distinct advantages, for certain purposes, over conventional low pressure high resolution absorption studies, which potentially makes it a powerful technique. Its insensitivity to source noise, the absence of background associated with the laser output profile-often a problem in iaserrelated absorption studies-and its small volume requirement for expensive or highly toxic samples make it a particularly attractive technique in these cases. The small volume requirements also make it extremely useful for recording frequencies of reference spectra needed for calibration in such spectroscopic studies. From a practical spectroscopic viewpoint the small volume non-resonant ceil poses fewer problems than the resonant ceil. The stringent dependence of the resonant acoustic frequency on sample conditions results in many problems when recording spectra. In addition the small volume acoustic cell used in these experiments was found to be relatively insensitive to extraneous acoustical interference. As a consequence, spectra were usually recorded without use of the vacuum box previously mentioned. It is highly probable that the sensitivity of the small volume infrared-acoustic detectors described here can be significantly improved. Utilization of miniature microphones with a smaller active area (Knowles BT 1759) and focusing the laser beam into a smaller volume ceil can be used with subsequent increase in sensitivity, particularly in the case of molecules where saturation effects are not significant. Acknowledgemenrs-We would like to express our appreciation to the National Science Foundation (Grant CHE 79-23237), the Robert A. Welch Foundation (Grant A-747) and the Research Corporation (Cottrell Research Grant) for supporting this research.
REFERENCES 1. ROSENCWAIG, A. Adc. electronic Elecrron Phys, 46. 207 (1978) (and included references). 2. ROSENGRAN L. G.. Appl. Opr., 14, 1960 (1075). 3. KAMMR. B., J. Appl. Phys., 47 3550 (1976). 4. KREUZER L. B., 1. Appl. Phys.. 42 2934 (1971). 5. DEWEY C. F., Jr.. R. D. KAMM,& C. E. HACKETT,Appl. Phys. Lerrs., 23, 633 (1973). 6. NODOV E., Appl. Opt.. 17, I IO (1978). 7. a) BUTCHERR. J., R. B. DENNIS & S. D. SMITH,Proc. Roy. Sot. A, 344, 541 (1975). b) PATEL C. K. N. & R. J. KERR Opt Commun. 24, 294 (1978). 8. FARROW L. A. & R. E. RICHTON,J. Appl. Phys., 48 (12), 4962 (1977). 9. PATEL C. K. N. & E. D. SHAW, Php. Rec.. 33, 127 (1971). IO. BEIGANCR., G. LITFIN & H. WELLING, Opr. Commun. 22, 269 (1977). 11. GERLACHR. & N. M. AMER. Appl. fhys. Lerr., 32, 228 (1978). 12. THOMAS L. J., M. J. KELLEY & N. M. AMER, Appl. PhJs. Lerr., 32, 736 (1978). 13. MORSEP. M.. Vibrarion and Sound. McGraw-Hill. New York (1948).