- Email: [email protected]
Accurate measurements for cyanic laser wavelengths using resonator interferometry
Volume
OPTICS
4, number 6
ACCURATE LASER
COMMUNICATIONS
MEASUREMENTS
WAVELENGTHS
USING
February/March
FOR
RESONATOR
1972
CYANIC INTERFEROMETRY
W. J. SCHADE Jr. Electronic
Materials
Sciences
Division,
Naval
Electronics
Received
Laboratory
3 December
Center,
San Diego,
California
92152, USA
1971
Accurate measurements are described for resonant wavelengths at 311 /.un and 337 pm in the HCN laser using resonator interferometry. Analysis of the theoretical and experimental conditions for laser resonator interferometry indicates that the resonant wavelengths correspond to the medium in which the scanning mirror is displaced.
1. INTRODUCTION Laser resonator interferometry (LRI) has been used by many investigators to analyse the far infrared resonant spectra of cyanic and watervapor lasers [l-3]. In general, laser emission at selected wavelengths was recorded as a function of the length of the optical resonator. The wavelength of the laser transition was computed from the measured displacement of a resonator mirror between longitudinal modes at common points on the spectral power turning curves (SPTC) for a common transverse mode. Previous measurements were restricted to about 1 part in lo3 because of limitations in the methods for calibrating the mirror displacement and recording the laser emission. This communication describes methods for increasing the accuracy of measurements for resonant wavelengths in far infrared gas lasers using LRI. A Michelson interferometer and radiation at 633 nm from a He-Ne laser are used to calibrate the displacement of a scanning resonator mirror. The accuracy of this technique is about 2 parts in lo5 with reference to computed vacuum wavelengths at 311 grn and 337 Fm. Analysis of the theoretical and experimental conditions for LRI measurements indicates that a stable laser medium does not cause a systematic error, which is in contradiction to previous statements [2,3]; however, a correction is necessary for the index of refraction of the medium in which the resonator mirror is scanned. 2. RESONANCE CONDITIONS The fundamental
postulate
that the phase change of a mode of oscillation must be an integer multiple of 2n radians after a round trip between the resonator mirrors. Most theoretical analyses of optical resonators treat them as passive structures immersed in a homogeneous, isotropic medium [4]. For the purpose of LRI, it is necessary to specify the various optical path lengths through the resonator. A practical laser resonator generally contains several optical materials which can be described by a spatially and temporally dependent index of refraction, n(x, y, z, t). This expresses the index of refraction at the time t and cartesian coordinates (x,y,z). The optic axis of the laser resonator is collinear with the z axis of the coordinate system. Attention is restricted to the axial dependence of the refractive index at a specific time 7 (which corresponds to the experimental conditions for the following section), where n(O,O, z, T) = n(z). For standing waves in the optical resonator, the resonance condition can be expressed by twice the single-pass phase change, 277 ,” [d&(z)] - P(L) = (q + l)r, (1) 0 where dz is an element of length along the axis, h(z) is the resonant wavelength in the medium between z and z + dz, L is the geometrical length of the resonator, p(L) is the phase shift associated with the mirror curvature [4] and the integer q is the longitudinal mode order or the number of axial nodes. For the optical resonator described in the next section, 6(L) is given by 141
for resonance
is
p(L)
= 3(2p+ I+ 1) arccos
[l - (2L/R)]
,
(2) 399
in which p and 1 are respectively the radial and azimuthal order numbers for a transverse mode and R is the radius of curvature of the concave mirror. To interpret accurately the measurements usually made in far infrared LRI. the line integral of eq. (1) must be evaluated. This can be simplified in many cases when there are more or less definable boundaries aiong the optical path. In many far infrared gas lasers, measurements for resonant wavelengths are made by scanning an internal mirror in an inactive background gas which is uniform throughout the displacement while all other conditions in the laser are maintained constant (either continuously or periodically reproducible). This condition is described by eq.(l) as 21 s
Li
dz,‘hi (z) +
'0
-(Yj+1)+i3(Lj)/n
Lj
J Li I
dz/‘$,,(z)
/
_. (3)
in which Li is the length of the optical path that remains constant, Xi(z) is the resonant wavelength along that path. h,,(z) is the resonant wavelength in the medium where the displacement occurs. and Lj is length of the resonator for the qj th longitudinal mode. When eq.(3) is used for the two resonator lengths at the first and last observed longitudinal modes (j = 1 and 2) for the same ho (in vacua). the difference between them is
L2 If Am (z) does not vary along the displacement path, eq. (4) becomes u
= (::+O)h,/2
.
(5)
where the displacement U = L 1 - L2, R=41-Y2 and h = [J(Ll) - $(L2)\/7i. Eq. (5) is used to compute the resonant wavelength with the measured displacement and computed values for g and h. Attention is directed to the fact that the measured displacement between longitudinal modes corresponds to the resonant wavelength in the medium where the mirror is moved, as stated explicitly in eq.(5). This is in contrast with previous statements [2,3] that the index of refraction of the plasma or active medium introduces a systematic error in the measurements for resonant wavelengths. Typically, the background gas pressure in far infrared lasers is about 1 torr; consequently, h, will differ from h0 by about 10m6 as indicated in recent measurements for the refractive index of nitrogen and water400
vapor at 337 pm and 311 ,um[ij]. The effects of the background gas can be eliminated by using :I suitable window to separate the active medium from the scanning milror chamber jvhich c*ould be evacuated. Eq. (1) has also been used in other LRI mrasurements such as those for transverse mode separations, spectral separations within the SPTC and changes in optical path lengths in the laser. Such measurements will be reported elsewhere.
3. EXPERIMENTAL
CONDITIONS
The laser apparatus and equipment for production of data are shown in the diagram of fig.1. The laser medium is produced by dc excitation of natural gas (about 90 mole percent methane) and nitrogen which flow through a conductively cooled 161 Pyrex tube. 76 mm id, the ends of which are joined to vacuum enclosures containing the mirrors for the optical resonator. The electrodes are 153 cm apart. The total operating gas pressure was about 0.7 torr as measured with a Hastings DV-GM thermocouple gauge. The discharge current was 0.4 A. The optical resonator is formed by a circular plane mirror and a circular concave mirror with a 30m radius of curvature. Both reflecting surfaces are opaque gold films on glass substrates. The plane mirror is stationary with a 2 mm diameter hole in the center for output coupling. The concave mirror is mounted on a translation stage which is pushed by turning a screw with a variable speed motor outside the vacuum enclosure. The resonator mirrors are separated by 195 cm which is variable to * 1.27 cm. A Michelson interferometer is used continuously to measure the displacement of the scanning resonator mirror. The calibration mirror is mounted on the translation stage behind the concave tuning mirror inside the vacuum enclosure so they move through the same distance simultaneously. The calibration source is a Spectra-Physics Model 119, He-Ne laser tuned to the center of the transition for 633 nm radiation. The filtered output of the HCN laser was detected with a thermistor bolometer at 20 Hz chopping frequency, synchronously amplified, and displayed on a two channel strip chart recorder simultaneously with a calibration interferogram for the change in length of the optical resonator. In contrast with previous measurements j l-31, this method of calibration avoids
Volume 4, number 6
-PTICS COMMUNICATIONS
February/March1972
FOLDING AND
OUTPUT MIR
LASER SPECTRUM CALIBRATION
TRACE
Fig. 1. A scanning laser resonator with interferometric calibration for the mirror displacement. any errors resulting from independent accelerations in the scanning laser mirror and the chart recorder. Data for resonant wavelengths were obtained by scanning the resonator continuously through more than 100 consecutive longitudinal modes which required from 2 to 30 minutes, depending on the velocity of the scanning mirror. Only the first and last SPTC’s were traced with the calibration patterns for each run. Between these two traces, the calibration interference maxima were recorded with an electronic counter while the scanning mirror was moved at higher velocity with the power supply for the far infrared laser turned off to avoid spurious counts from discharge noise.
4. MEASUREMENTS The mirror displacement, D, is measured with the calibration interferogram, D = s&./2, where A, is the calibration wavelength and s is the total number of interference units, h,/2. This number is the sum of an integer and two fractions, s = u + f0 + fr, in which u is the whole number of interference maxima between the centers of the two recorded SPTC’s and f0 and _fr are the fractional units to the corre-
sponding centers. Generally, linear interpolations for the fractions are sufficiently accurate. Resonant wavelengths are computed with eq. (5) and the approximation b = 0. This is a good approximation for the present measurements since b = 5.6 X 10m4, with p = 1 = 0, for a displacement of 2.5 cm which covers about 148 mode intervals of the 337 wrn transition so that b/g x 3.7 x 10-6. When several measurements are made for the same resonant A, the method of least squares is used to compute the slope, X,, of the best fit of a straight line through the origin for the equation D =gXd2. The value of g is taken as the integer nearest the value computed from D and the vacuum wavelength at the center of the SPTC (a preliminary measurement for the separation between adjacent longitudinal modes is also satisfactory in this computation); this obviates the need to count each longitudinal mode or maintain the laser discharge while the length of the resonator is scanned rapidly. The accuracy of this technique was examined by making simultaneous measurements for the HCN transitions at 311 nm and 337 urn. Absolute frequency measurements [i’] were used to compute the vacuum wavelengths at the centers of these transitions. Applying eq. (5) (with b = 0), ~1 -s2 = (glX1 -g2X2)/Ac, with SI and s2 as the 401
Volume 4, number 6
OPTICS COMMUNICATIONS
number of calibration units, /X,/2, for the two displacements. For a scan throughgl = 144 and g2 = 133 mode intervals and with vacuum wavelengths for hl = 310.8870 pm, h2 = 336.5578 pm, and h, = 0.633 Frn *, the computed difference is sl -s2 = 8.75 which is to be compared with a measured value of 10. This discrepancy is within the uncertainty f 1.5 in locating the centers of the SPTC’s. The comparison indicates an accuracy of about 2 parts in lo5 for a single scan through s N 70 x lo3 calibration units. The two major sources of experimental errors are in locating the center of the laser transition and changes in the reference path of the calibration interferometer during a scan. The systematic errors are similar to those reported recently in accurate vacuum wavelength measurements for far infrared laser transitions [9]. Error caused by angular misalignment of the optic axes for the calibration mirror and the resonator tuning mirror was estimated to be less than 10T7. Variations of Xc in the source or in the refractive index of the calibration optical path were estimated to be of the order of 5 X 10b7. The long-term stability of the far infrared laser was examined with water vapor as the active medium. For a period t = 1 hour, after a stabilizing period of about 2 hours, the range of variations in the laser intensity indicated a relative change, AX, in the resonant wavelength at 78 pm, of the order Ah/ht < 10s6/hr. The change in the intensity distribution of the calibration interference pattern indicated a drift error of about hc/2 per hour. Several improvements can be made to increase the precision of these measurements. Faster scanning through larger (possibly folded) displacements will add a significant figure for each factor of 10 in the displacement; however, the effect of b in eq. (5) must also be considered. Shorter scanning time reduces the uncertainty in the background drift of the interferometer. The calibration wavelength of the He-Ne laser can be compared with the 86Kr standard wavelength which sets the limit of accuracy.
February/March
19’i2
also be made for resonant bandwidths, radiative bandwidths, mode structure and optical path changes. Calibration with a Michelson interferometer and a stable He-Ne laser provides measurements with precision and accuracy that compare favorably with those reported from any other method. In measurements for laser wavelengths, a reported accuracy of about 1 part in 106 was obtained with a vacuum Michelson interferometer in which far infrared and 633 nm laser wavelengths were compared over a 4-meter path difference [9]. Comparable accuracy could be achieved with LRI by evacuating the space in which the scanning mirror is moved; however, in LRI, the instabilities of the laser resonator and calibration interferometer are independent and require separate stabilization controls. Here again, the time required for the measurements becomes an important parameter. Absolute frecluency measurements provide data for computing vacuum wavelengths with the speed of light [7,9,10]. However, these measurements have been restricted to the highest power radiation from lasers 3 to 8 meters in length because of the responsivity of the point-contact diodes. In contrast, LRI can be used to measure any observable laser transition with comparable accuracy (for comparable spectral profiles). The present limitation on the accuracy of absolute frequency and wavelength measurements is in specifying the center of the laser transition.
ACKNOWLEDGMENTS It is a pleasure to acknowledge the support provided by R. F. Potter and W. L. Eisenman during the developmental stages of this work. Many design features and most of the laser apparatus and instrumentation were expertly constructed by J. Kupecz whose efforts were essential. D. D. Kirk and W. M. Worrell made valuable contributions in constructing the apparatus. Discussions with S. A. Miller regarding analysis of the data and the loan of an electronic counter from C. J. Gabriel are greatly appreciated.
5. CONCLUSION The preceding results and discussions demonstrate the utility of LRI for analyzing the spectral characteristics of far infrared gas lasers. With a single optical instrument, measurements can * This value is sufficiently accurate for the computation: higher accuracy is given in ref. [S]. 402
REFERENCES [I] H. Steffen and F.K.Kneubuhl, J.Quantum Electron. QE-4 (1968) 992 and references therein. [2] A. Minoh, T. Shimizu, S. Kobayashi and K. Shimoda, Jap. J. Appt. Phvs. 6 (1961) 921. [3] O.M. Staffsudd; F. A.‘Haak and K. Radisavljevic, J.Quantum Electron. QE-3 (1967) 618.
Volume
4, number
6
OPTICS COMMUNICATIONS
[4] H. Kogelnik and T. Li, Appl. Opt. 5 (1966) 1550; H. Kogelnik, in: Lasers, ed. A. K. Levine (Dekker, New York, 1966) p.295. [5] C. C. Bradley and H. A. Gebbie, Appl. Opt. 10 (1971) 755. [6] W. J. Schade Jr., Gaseous Laser Cooling System, US Patent No. 3,554,275, issued January 12, 1971. [7] L. 0. Hacker and A. Javan, Phys. Letters 25A (1967) 469.
February/March
1972
[8] K. D. Mielenz, K. F. Nefflen, K. E. Gillilland, R. B. Stephens and R. B. Zipin, Appl. Phys. Letters 7 (1967) 277. [9] V. Daneu, L. 0. Hacker, A. Javan, D. Ramachandra Rao, A. Szoke and F. Zernike, Phys. Letters 29A (1969) 319. [lo] K. M. Evenson, J. S. Wells, L. M. Matarrese and L. B. Elwell, Appl. Phys. Letters 16 (1970) 159.
403
OPTICS
4, number 6
ACCURATE LASER
COMMUNICATIONS
MEASUREMENTS
WAVELENGTHS
USING
February/March
FOR
RESONATOR
1972
CYANIC INTERFEROMETRY
W. J. SCHADE Jr. Electronic
Materials
Sciences
Division,
Naval
Electronics
Received
Laboratory
3 December
Center,
San Diego,
California
92152, USA
1971
Accurate measurements are described for resonant wavelengths at 311 /.un and 337 pm in the HCN laser using resonator interferometry. Analysis of the theoretical and experimental conditions for laser resonator interferometry indicates that the resonant wavelengths correspond to the medium in which the scanning mirror is displaced.
1. INTRODUCTION Laser resonator interferometry (LRI) has been used by many investigators to analyse the far infrared resonant spectra of cyanic and watervapor lasers [l-3]. In general, laser emission at selected wavelengths was recorded as a function of the length of the optical resonator. The wavelength of the laser transition was computed from the measured displacement of a resonator mirror between longitudinal modes at common points on the spectral power turning curves (SPTC) for a common transverse mode. Previous measurements were restricted to about 1 part in lo3 because of limitations in the methods for calibrating the mirror displacement and recording the laser emission. This communication describes methods for increasing the accuracy of measurements for resonant wavelengths in far infrared gas lasers using LRI. A Michelson interferometer and radiation at 633 nm from a He-Ne laser are used to calibrate the displacement of a scanning resonator mirror. The accuracy of this technique is about 2 parts in lo5 with reference to computed vacuum wavelengths at 311 grn and 337 Fm. Analysis of the theoretical and experimental conditions for LRI measurements indicates that a stable laser medium does not cause a systematic error, which is in contradiction to previous statements [2,3]; however, a correction is necessary for the index of refraction of the medium in which the resonator mirror is scanned. 2. RESONANCE CONDITIONS The fundamental
postulate
that the phase change of a mode of oscillation must be an integer multiple of 2n radians after a round trip between the resonator mirrors. Most theoretical analyses of optical resonators treat them as passive structures immersed in a homogeneous, isotropic medium [4]. For the purpose of LRI, it is necessary to specify the various optical path lengths through the resonator. A practical laser resonator generally contains several optical materials which can be described by a spatially and temporally dependent index of refraction, n(x, y, z, t). This expresses the index of refraction at the time t and cartesian coordinates (x,y,z). The optic axis of the laser resonator is collinear with the z axis of the coordinate system. Attention is restricted to the axial dependence of the refractive index at a specific time 7 (which corresponds to the experimental conditions for the following section), where n(O,O, z, T) = n(z). For standing waves in the optical resonator, the resonance condition can be expressed by twice the single-pass phase change, 277 ,” [d&(z)] - P(L) = (q + l)r, (1) 0 where dz is an element of length along the axis, h(z) is the resonant wavelength in the medium between z and z + dz, L is the geometrical length of the resonator, p(L) is the phase shift associated with the mirror curvature [4] and the integer q is the longitudinal mode order or the number of axial nodes. For the optical resonator described in the next section, 6(L) is given by 141
for resonance
is
p(L)
= 3(2p+ I+ 1) arccos
[l - (2L/R)]
,
(2) 399
in which p and 1 are respectively the radial and azimuthal order numbers for a transverse mode and R is the radius of curvature of the concave mirror. To interpret accurately the measurements usually made in far infrared LRI. the line integral of eq. (1) must be evaluated. This can be simplified in many cases when there are more or less definable boundaries aiong the optical path. In many far infrared gas lasers, measurements for resonant wavelengths are made by scanning an internal mirror in an inactive background gas which is uniform throughout the displacement while all other conditions in the laser are maintained constant (either continuously or periodically reproducible). This condition is described by eq.(l) as 21 s
Li
dz,‘hi (z) +
'0
-(Yj+1)+i3(Lj)/n
Lj
J Li I
dz/‘$,,(z)
/
_. (3)
in which Li is the length of the optical path that remains constant, Xi(z) is the resonant wavelength along that path. h,,(z) is the resonant wavelength in the medium where the displacement occurs. and Lj is length of the resonator for the qj th longitudinal mode. When eq.(3) is used for the two resonator lengths at the first and last observed longitudinal modes (j = 1 and 2) for the same ho (in vacua). the difference between them is
L2 If Am (z) does not vary along the displacement path, eq. (4) becomes u
= (::+O)h,/2
.
(5)
where the displacement U = L 1 - L2, R=41-Y2 and h = [J(Ll) - $(L2)\/7i. Eq. (5) is used to compute the resonant wavelength with the measured displacement and computed values for g and h. Attention is directed to the fact that the measured displacement between longitudinal modes corresponds to the resonant wavelength in the medium where the mirror is moved, as stated explicitly in eq.(5). This is in contrast with previous statements [2,3] that the index of refraction of the plasma or active medium introduces a systematic error in the measurements for resonant wavelengths. Typically, the background gas pressure in far infrared lasers is about 1 torr; consequently, h, will differ from h0 by about 10m6 as indicated in recent measurements for the refractive index of nitrogen and water400
vapor at 337 pm and 311 ,um[ij]. The effects of the background gas can be eliminated by using :I suitable window to separate the active medium from the scanning milror chamber jvhich c*ould be evacuated. Eq. (1) has also been used in other LRI mrasurements such as those for transverse mode separations, spectral separations within the SPTC and changes in optical path lengths in the laser. Such measurements will be reported elsewhere.
3. EXPERIMENTAL
CONDITIONS
The laser apparatus and equipment for production of data are shown in the diagram of fig.1. The laser medium is produced by dc excitation of natural gas (about 90 mole percent methane) and nitrogen which flow through a conductively cooled 161 Pyrex tube. 76 mm id, the ends of which are joined to vacuum enclosures containing the mirrors for the optical resonator. The electrodes are 153 cm apart. The total operating gas pressure was about 0.7 torr as measured with a Hastings DV-GM thermocouple gauge. The discharge current was 0.4 A. The optical resonator is formed by a circular plane mirror and a circular concave mirror with a 30m radius of curvature. Both reflecting surfaces are opaque gold films on glass substrates. The plane mirror is stationary with a 2 mm diameter hole in the center for output coupling. The concave mirror is mounted on a translation stage which is pushed by turning a screw with a variable speed motor outside the vacuum enclosure. The resonator mirrors are separated by 195 cm which is variable to * 1.27 cm. A Michelson interferometer is used continuously to measure the displacement of the scanning resonator mirror. The calibration mirror is mounted on the translation stage behind the concave tuning mirror inside the vacuum enclosure so they move through the same distance simultaneously. The calibration source is a Spectra-Physics Model 119, He-Ne laser tuned to the center of the transition for 633 nm radiation. The filtered output of the HCN laser was detected with a thermistor bolometer at 20 Hz chopping frequency, synchronously amplified, and displayed on a two channel strip chart recorder simultaneously with a calibration interferogram for the change in length of the optical resonator. In contrast with previous measurements j l-31, this method of calibration avoids
Volume 4, number 6
-PTICS COMMUNICATIONS
February/March1972
FOLDING AND
OUTPUT MIR
LASER SPECTRUM CALIBRATION
TRACE
Fig. 1. A scanning laser resonator with interferometric calibration for the mirror displacement. any errors resulting from independent accelerations in the scanning laser mirror and the chart recorder. Data for resonant wavelengths were obtained by scanning the resonator continuously through more than 100 consecutive longitudinal modes which required from 2 to 30 minutes, depending on the velocity of the scanning mirror. Only the first and last SPTC’s were traced with the calibration patterns for each run. Between these two traces, the calibration interference maxima were recorded with an electronic counter while the scanning mirror was moved at higher velocity with the power supply for the far infrared laser turned off to avoid spurious counts from discharge noise.
4. MEASUREMENTS The mirror displacement, D, is measured with the calibration interferogram, D = s&./2, where A, is the calibration wavelength and s is the total number of interference units, h,/2. This number is the sum of an integer and two fractions, s = u + f0 + fr, in which u is the whole number of interference maxima between the centers of the two recorded SPTC’s and f0 and _fr are the fractional units to the corre-
sponding centers. Generally, linear interpolations for the fractions are sufficiently accurate. Resonant wavelengths are computed with eq. (5) and the approximation b = 0. This is a good approximation for the present measurements since b = 5.6 X 10m4, with p = 1 = 0, for a displacement of 2.5 cm which covers about 148 mode intervals of the 337 wrn transition so that b/g x 3.7 x 10-6. When several measurements are made for the same resonant A, the method of least squares is used to compute the slope, X,, of the best fit of a straight line through the origin for the equation D =gXd2. The value of g is taken as the integer nearest the value computed from D and the vacuum wavelength at the center of the SPTC (a preliminary measurement for the separation between adjacent longitudinal modes is also satisfactory in this computation); this obviates the need to count each longitudinal mode or maintain the laser discharge while the length of the resonator is scanned rapidly. The accuracy of this technique was examined by making simultaneous measurements for the HCN transitions at 311 nm and 337 urn. Absolute frequency measurements [i’] were used to compute the vacuum wavelengths at the centers of these transitions. Applying eq. (5) (with b = 0), ~1 -s2 = (glX1 -g2X2)/Ac, with SI and s2 as the 401
Volume 4, number 6
OPTICS COMMUNICATIONS
number of calibration units, /X,/2, for the two displacements. For a scan throughgl = 144 and g2 = 133 mode intervals and with vacuum wavelengths for hl = 310.8870 pm, h2 = 336.5578 pm, and h, = 0.633 Frn *, the computed difference is sl -s2 = 8.75 which is to be compared with a measured value of 10. This discrepancy is within the uncertainty f 1.5 in locating the centers of the SPTC’s. The comparison indicates an accuracy of about 2 parts in lo5 for a single scan through s N 70 x lo3 calibration units. The two major sources of experimental errors are in locating the center of the laser transition and changes in the reference path of the calibration interferometer during a scan. The systematic errors are similar to those reported recently in accurate vacuum wavelength measurements for far infrared laser transitions [9]. Error caused by angular misalignment of the optic axes for the calibration mirror and the resonator tuning mirror was estimated to be less than 10T7. Variations of Xc in the source or in the refractive index of the calibration optical path were estimated to be of the order of 5 X 10b7. The long-term stability of the far infrared laser was examined with water vapor as the active medium. For a period t = 1 hour, after a stabilizing period of about 2 hours, the range of variations in the laser intensity indicated a relative change, AX, in the resonant wavelength at 78 pm, of the order Ah/ht < 10s6/hr. The change in the intensity distribution of the calibration interference pattern indicated a drift error of about hc/2 per hour. Several improvements can be made to increase the precision of these measurements. Faster scanning through larger (possibly folded) displacements will add a significant figure for each factor of 10 in the displacement; however, the effect of b in eq. (5) must also be considered. Shorter scanning time reduces the uncertainty in the background drift of the interferometer. The calibration wavelength of the He-Ne laser can be compared with the 86Kr standard wavelength which sets the limit of accuracy.
February/March
19’i2
also be made for resonant bandwidths, radiative bandwidths, mode structure and optical path changes. Calibration with a Michelson interferometer and a stable He-Ne laser provides measurements with precision and accuracy that compare favorably with those reported from any other method. In measurements for laser wavelengths, a reported accuracy of about 1 part in 106 was obtained with a vacuum Michelson interferometer in which far infrared and 633 nm laser wavelengths were compared over a 4-meter path difference [9]. Comparable accuracy could be achieved with LRI by evacuating the space in which the scanning mirror is moved; however, in LRI, the instabilities of the laser resonator and calibration interferometer are independent and require separate stabilization controls. Here again, the time required for the measurements becomes an important parameter. Absolute frecluency measurements provide data for computing vacuum wavelengths with the speed of light [7,9,10]. However, these measurements have been restricted to the highest power radiation from lasers 3 to 8 meters in length because of the responsivity of the point-contact diodes. In contrast, LRI can be used to measure any observable laser transition with comparable accuracy (for comparable spectral profiles). The present limitation on the accuracy of absolute frequency and wavelength measurements is in specifying the center of the laser transition.
ACKNOWLEDGMENTS It is a pleasure to acknowledge the support provided by R. F. Potter and W. L. Eisenman during the developmental stages of this work. Many design features and most of the laser apparatus and instrumentation were expertly constructed by J. Kupecz whose efforts were essential. D. D. Kirk and W. M. Worrell made valuable contributions in constructing the apparatus. Discussions with S. A. Miller regarding analysis of the data and the loan of an electronic counter from C. J. Gabriel are greatly appreciated.
5. CONCLUSION The preceding results and discussions demonstrate the utility of LRI for analyzing the spectral characteristics of far infrared gas lasers. With a single optical instrument, measurements can * This value is sufficiently accurate for the computation: higher accuracy is given in ref. [S]. 402
REFERENCES [I] H. Steffen and F.K.Kneubuhl, J.Quantum Electron. QE-4 (1968) 992 and references therein. [2] A. Minoh, T. Shimizu, S. Kobayashi and K. Shimoda, Jap. J. Appt. Phvs. 6 (1961) 921. [3] O.M. Staffsudd; F. A.‘Haak and K. Radisavljevic, J.Quantum Electron. QE-3 (1967) 618.
Volume
4, number
6
OPTICS COMMUNICATIONS
[4] H. Kogelnik and T. Li, Appl. Opt. 5 (1966) 1550; H. Kogelnik, in: Lasers, ed. A. K. Levine (Dekker, New York, 1966) p.295. [5] C. C. Bradley and H. A. Gebbie, Appl. Opt. 10 (1971) 755. [6] W. J. Schade Jr., Gaseous Laser Cooling System, US Patent No. 3,554,275, issued January 12, 1971. [7] L. 0. Hacker and A. Javan, Phys. Letters 25A (1967) 469.
February/March
1972
[8] K. D. Mielenz, K. F. Nefflen, K. E. Gillilland, R. B. Stephens and R. B. Zipin, Appl. Phys. Letters 7 (1967) 277. [9] V. Daneu, L. 0. Hacker, A. Javan, D. Ramachandra Rao, A. Szoke and F. Zernike, Phys. Letters 29A (1969) 319. [lo] K. M. Evenson, J. S. Wells, L. M. Matarrese and L. B. Elwell, Appl. Phys. Letters 16 (1970) 159.
403