with a spacing of approximately 26.5 mK (800 Mc/sec) between adjacent components, in rough agreement with earlier results. ... striking contrast to the noble gas ion lasers,3 -' which typically .... plate, there is no reason to suspect that the inter-.
1598
R. L. POWELL
AND K. A. STETSON
not be too great in amplitude or the vibration information becomes impossible to detect. Each successive peak in the image reconstruction becomes weaker as the amplitude of the vibration increases. This difficulty may be alleviated by holography with longer wavelengths. The stability of the rest position of the object is also critical, as mentioned in the opening section of this paper. This may cause difficulties when freely suspended subjects are examined. It is of historical importance to contrast this method of vibration analysis with that reported in Ref. 6, cited in the mathematical analysis preceding this section. In this reference, Osterberg reported the use of an interferometer to study the vibration modes of piezoelectric quartz crystals. The crystals are polished and then used as one of the mirrors of the interferometer. Once a simple set of straight line fringes has been obtained, the crystal is excited by an alternating electric field. The resonances of the crystal are detected by the change in visibility and phase reversal of the fringes. In this case, visual persistence serves to integrate the vibrating fringe pattern and modify its visibility ac-
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA
Vol. 55
cording to the same zero-order Bessel function of the vibration amplitude we have described. This technique operates in real time, since visual persistence may be used, at the price of having to optically polish the subject, which, in the case of the peizoelectric crystal, is not necessarily a disadvantage. It is hoped that this paper, nonetheless, will stimulate new interest in the Osterberg process. ACKNOWLEDGMENTS The authors would like to acknowledge the interest of A. Kozma in the process, which led to his setting forth the interpretation of statistical motions presented in this paper. Also, we would like to acknowledge con-
versations with H. Osterberg which have helped further an understanding of the basic similarities of the two processes. Finally, we would like to acknowledge the help of E. Leith and J. Upatnieks in clarifying our understanding of the two-beam hologram process, and particularly J. Upatnieks for proposing in the summer of 1964 the use of hologram for analysis of vibrationspof objects.
VOLUME 55, NUMBER 12
DECEMBER 1965
Laser Emission in Ionized Mercury: Isotope Shift, Linewidth, and Precise Wavelength* R. L. BYERI W. E. BELL, E. HODGES,AND A. L. BLOOM Spectra-Physics, Inc., 1255 Terra Bella Avenue, Mowntain View, California 94041 (Received 29 April 1965) The 6150-A laser transition in Hg II generated in a pulsed hollow cathode discharge, has been studied under high resolution. The line shows structure corresponding to the expected shifts from the even isotopes, with a spacing of approximately 26.5 mK (800 Mc/sec) between adjacent components, in rough agreement with earlier results. The fullwidth at half-maximum of each component has been measured as 500 Mc/sec. The wavelength has been compared to that of thorium secondary wavelength standards and it has been determined that the vacuum wavelength of the "02Hgcomponent is 6151.1650 .. The possibility of the mercury hollow cathode laser as a laboratory wavelength standard is pointed out.
I. INTRODUCTION
LASER action from gaseous ions was first observed 2
in a pulsed mercury-helium discharge." Although many other types of ion lasers have been discovered, mercury is still of interest because the large atomic weight implies narrower emission profile linewidths than might be obtained from other ions. In this paper we report the results of interferometric measurements on the hyperfine structure of the visible laser transition 7p'P 1-7s2S 1, at 6150 A. We have found that the ex*
Work supported il part by the U. S. Arny Signal Corps.
t Present address: Dept. of Applied Physics, Stanford Univer-
sity, Stanford, California 94305. 'W. E. Bell, Appl. Phys. Letters 4, 34 (1964). 2 A. L. Bloom, W. E. Bell, and F. 0. Lopez, Phys. Rev. 135, A578 (1964).
pected isotope structure is clearly resolved and that the linewidth of each component of the emission spectrum is 500 Mc/sec, the width to be expected from mercury near room temperature. It is about one-third the Doppler width in a helium-neon laser and is in striking contrast to the noble gas ion lasers,3 -' which typically have widths of the order of 0.1 cm-l (3000 Mc/sec). II. APPARATUS AND TECHNIQUE The laser that was used in these experiments is shown in Fig. 1. The tube was filled with helium to a pressure
I W.
B. Bridges, Appl. Phys. Letters 4, 128 (1964).
4 E. I. Gordon, E. F. Labuda, and W. B. Bridges, Appl. Phys.
Letters 4, 178 (1964). 5W. B. Bridges, Proc. IEEE 52, 843 (1964).
December 1965
LASER EMISSION
IN IONIZED
of 1-2 torr and operated from a pulser at a repetition rate of approximately 1000/sec with 5 kV pulses approximately 2-,usec long. Both anodes were flashed simultaneously, although operation at somewhat lower gain could be obtained from one anode alone. Strong emission of the 6150-A radiation was observed to take place from within the cathode tube, and laser action took place during the pulse, starting approximately 2 ,usecafter initiation of the pulse and decaying at the end of the pulse (Fig. 2). Peak powers were of the order of 2-3 W.
Since laser emission takes place from within the cathode region of the discharge, we have designated this structure as a hollow cathode laser. It differs from previous pulsed mercury-helium lasers, consisting of ordinary glow discharge tubes, in several respects: (1) the laser action takes place during the pulse, rather than in the afterglow, (2) the only visible transition observed is the orange line at 6150 A (the green line at 5677
A which is obtained easily in the glow discharge
tube has not been observed in this structure), and (3) in the wavelength region below lu the only other laser transition observed by us in the hollow cathode is the
A, i.e., the line 7p'Pt`-7s'S2
doublet companion to 6150
MERCURY
1599
I
FIG. 2. Oscillogram of the current pulse (above) and laser output (below), time scale 1 ,usec/div. Ez
1
1
__1
1
-
I
%_.. -
1 I 1 -1 - I __ I
spectral lines from a thorium halide electrodelessVdischarge lamp' used as a secondary standard 7 and the output of a 6328 A helium-neon laser operating at the center of the power dip8 of the emission profile. The helium-neon laser was not used as a wavelength standard in these experiments because this laser employs enriched 20Ne whereas the laser used in a recent wavelength determination at the U. S. National Bureau of Standards 9 employed neon with the natural isotopic constitution. It was intended, instead, that the heliumneon laser provide an accurate check on the alignment and focus of the spectrometer and also to give a direct measure of the resolution of the interferometer at each spacing. However, it turned out, surprisingly, that the lines from the mercury laser were sharper than those from the helium-neon laser. This is discussed in more detail in Sec. VI of this paper.
at 7945 A. Laser action at this wavelength had not been reported previously. 2
III. LINEWIDTH MEASUREMENTS
Interferometric studies of the laser output at 6150 A were performed with conventional Fabry-Perot interferometers and photographic recordings. The initial measurements were made in our laboratory with an air Fabry-Perot having a spacing of 35 mm. These measurements were used primarily for the linewidth determinations. For the wavelength measurements the laser, operating with a smaller pulser and at somewhat lower gain, was taken to the University of California, at Berkeley, where photographic plates were taken using a vacuum Fabry-Perot crossed with a 3-m plane grating spectrometer. Three interferometer spacers with lengths of 25, 34, and 75 mm were used in the Berkeley experiment. The exposures taken for the wavelength determination included, besides the mercury laser output,
VACUUM SYSTEM
ANODEI
FIG. 1. Hollow cathode laser. The cathode is a Kovar tube 2.5
cm in diameter and 30-cm long.
Figure 3 shows an uncorrected densitometer trace of the observed line structure when the laser is operated at high gain. At this gain level the weak contribution from 2041Hgis distinctly visible as a fourth component and the other three lines appear to overlap slightly; however, in all cases all components are clearly resolved from each other. The analysis of structure in laser emission is somewhat different from that in ordinary spontaneous emission because of the existence of a well-defined threshold for
oscillation. The particular laser shown in Fig. 1 employed 3-m-radius mirrors spaced 135 cm apart and the resonator diameter was 1.5 cm, limited only by the aperture of the Brewster windows. Under these circumstances, the laser was operating simultaneously in a very large number of modes and covering almost a continuum of resonant frequencies under the Doppler linewidth. When a line is well-saturated in this manner, the saturation behavior is essentially that of a homogeneously broadened line,'0 and under these circumstances that power output per unit frequency range is proportional to"
tW(v)=(t/s)[g(v)/(a+t)]-1, 6 A. Davison, A. Giacchetti, and R. W. Stanley, J. Opt. Soc. Am. 52, 447 (1962). 7 W. F. Meggers and R. W. Stanley, J. Res. Natl. Bur. Std. (U. S.) 69A, 109 (1965). 8 W. E. Lamb, Jr., Phys. Rev. 134, A1429 (1964). ' K. D. Mielenz, H. D. Cook, K. E. Gillilland, and R. B. Stephens, Science 146, 1672 (1964). '"A. D. White, E. I. Gordon, and J. D. Rigden, ADDI. Phys. Letters 2, 91 (1963). " W. W. Rigrod, J. Appl. Phys. 34, 2602 (1963).
BYER, BELL, HODGES, AND BLOOM
1600
V
FIG. 3. Densitometer
trace of the Hg ii laser line at 6150 A, showing estimated height of threshold.
Vol. 55
densitometer. Actually, the Doppler width observed in the laser beam is determined by velocities along the axis and does not necessarily represent the mean speeds of the ions; furthermore, in a hollow cathode structure the ion accelerations are expected to be at right angles to the laser axis. If this is indeed the case, then the measured Doppler width probably corresponds fairly closely to the true gas temperature at the instant of emission, and the results are not inconsistent with a room-temperature Doppler width of 450 Mc/sec. IV. WAVELENGTH DETERMINATIONS
THRESHOLD
The wavelength determination experiment employed a vacuum Fabry-Perot interferometer and three sources, as described in Sec. II. The two lasers (Hg and He-Ne) were operated simultaneously and their beams where W(v) is the energy density at frequency v within were combined through a combination of a beam the laser, g(v) is the corresponding single pass gain, I splitter, slit, and predispersing prism optics. The slit is the transmittance through the output mirror, a images, not the laser source images, were focused at the represents all other losses, and s is a saturation paslit of the grating spectrometer, special care being taken rameter whose numerical value is of no importance here that the slit images of the two lasers were as nearly but is assumed to be constant for all isotopes and all coincident as possible. The thorium source was infrequency ranges. As a consequence the laser output troduced via a flip mirror; it was located so that its profile is expected to be simply the spontaneous emis- position and physical dimensions were optically equivasion profile minus a constant "pedestal" corresponding lent to the slit used in defining the laser beams. In to threshold. This relationship should hold throughout order to reduce exposure time on the thorium, the the line profile except possibly for regions near the edges predisperser was not used, instead a red-orange filter whose widths are of the order of the inverse lifetime was inserted in the optical path so that only spectrum of the lower state (perhaps several megacycles wide and lines between 6100 and 6400 A were recorded. well below resolution of the interferometer). If the relaThe grating was used at the blaze angle in the 9th tive height of the pedestal can be determined compared order giving a plate factor of 1.1 A/mm and permitting to the center of the line, then, under the assumption that a 600-,4slitwidth. This large slitwidth insured that the the line has a Gaussian profile, the remainder of the centers of the fringe systems were always present on the profile can be easily reconstructed and the half-power plates and could be located for densitometer profiling. points determined. The procedure was to adjust the interferometer and We have indicated in Fig. 3 our best estimate of let it stand at constant temperature until stable (at the threshold height compared to the output maxima least two hours), then evacuate. After final adjustments of the interferometer two exposures were made on the of the 202Hg and 204 Hg lines. The density of the film was not high and no correction has been applied for density photographic plate; on one, the thorium was exposed flattening of the peaks; therefore, this estimate is only for 5 min, on the other the thorium was exposed for approximate. However, it should be noted that the 1 min. In between these exposures the laser lines strong components rise high enough above threshold were superimposed with exposures of 1-2 sec. Figures that small errors in the estimate of threshold and peak 4 and 5 show portions, around each laser line, of the heights do not seriously affect the linewidth measure- 34-mm-spacer 1-min thorium exposure. The time rement. The estimates are also supported by the observed quired to switch from thorium to laser sources and back again was a few seconds and, in view of the gains and fixed losses in the laser. The total loss (a+t) was fairly high-about 10% per double pass. The gain reproducibility of fringes in the two exposures on each of the strongest component, however, was sufficient to plate, there is no reason to suspect that the interferometer moved appreciably during the process. allow several pieces of lossy glass to be placed within the cavity without quenching all oscillation, and agreed The plates were measured by means of a comparator roughly with the projected gain of about 40% per equipped with punched card output. Each standard double pass (2.2 dB/m in single pass). line was measured four separate times on each plate. The The Doppler linewidth determined from these fringe pattern was measured by using an oscilloscope measurements is 500ti50 Mc/sec, fullwidth at half- split image coincidence and also directly by eye, with maximum. This width includes corrections for an instru- ten fringes set for each pattern. The output cards remental width of about 100 Mc/sec determined by the corded the comparator setting for each successive finesse of the Fabry-Perot and by the resolution of the fringe in the pattern. These data were then reduced with
LASER EMISSION
December 1965
IN IONIZED TABLE
MERCURY
I. Wavelengths and isotope splittings for the 6150 A line of Hg II.
Isotope
Xvac,A
g
200H26.4
202Hg Et
'54
mK
Splittings Mc/sec
6151.1851
198119
5iZ
1601
04H96151.153
6151.1750 6151.1650
792±~15 26.8 31 31
805±--15 92013 920-430
spacer thicknesses related, through the computation and the thorium wavelengths, to the primary length standard, while the remainder comes from uncertainties in the fringe measurements. This probable error also agrees with the internal consistency of results obtained from different plates and exposures. The uncertainties in determining the centers of the Hg fringes are of the order of 4-0.0002 A, somewhat greater than the available resolution because of overexposure of some of the
FIG. 4. Portion of spectrograph plate taken with 75-mm spacer, showing Hg II laser line at 6150 A (line with sharp fringes and structure) and adjacent Th lines.
the aid of a computer
Hg lines; this is the limiting uncertainty in determining the separation between isotopes. The flattening of the profiles caused by overexposure can also produce systematic errors, but these are thought to be small because of the sharpness of the entire fringe system. The wavelength for 114Hg is an estimate based primarily upon Fig. 3.
program" 2 which, from least-
squares-adjusted fringe diameters, computed the fractional orders E, from which were obtained the true interferometer spacings and the phase shift corrections for the dielectrically coated interferometer plates.' 3 The rms deviations in e were typically of the order of 0.02 for the thorium standards and 0.001 for sharply defined Hg fringes, corresponding to distances of about 1 /u on the comparator. As a final check on the spacing and phase shift determination the thorium wavelengths were computed and compared with the input values.7 For the 19 lines between 6100 and 6360 A that were used,
the mean deviation was +0.0003 A and on nine lines the agreement was better than 4t0.0001 A. V. RESULTS
The final results are presented in Table I, which gives the vacuum wavelengths of the four observed even isotopes, as well as the isotope separations in mK and Mc/sec. The probable error on all absolute wave4 lengths except that of "1 Hg is estimated to be +0.0005 A. Of this, +-0.0002 A reflects uncertainties in the
u L. C. Marquet, thesis, University of California, Berkeley, California 1964 (unpublished). 13Further details of the data reduction, including the thorium wavelengths used, are given in Report No. 3, contract DA-28-043AMC-00194(E) (unpublished), copies of which are available from the authors.
FIG. 5. Portion of same plate used for Fig. 4 showing Ne laser line at 6328 A. Note the secondary interference pattern and extreme intensity changes in the fringes, analogous to the "scintillation" characteristic of highly coherent light.
1602
BYER, BELL, HODGES, AND BLOOM
The total "IHg-19 8Hg shift is somewhat less than that of 6445 mK obtained by Shorthill and Fowles'4 with separated isotopes, and we have investigated the possibility of biases caused by the simultaneous presence of several isotopes. Photographic bias in fringes as
Vol. 55
our suggestion is, surprisingly, the fact that the mercury laser, when operated as described here, is not as coherent a source as the helium-neon laser. Unlike other types of gas lasers, the hollow cathode laser appears to operate most efficiently when its bore diameter is relatively large compared to the mirror separation, thus making it sharply defined as those of Fig. 4 should be negligible. If the emission profiles of each isotope are truly Gauss- relatively simple to operate simultaneously in a very ian, and the lines have their stated width and separation, large number of spatial and temporal modes. Such a then shifts in apparent peak position due to their mutual source may be considered to be intermediate in coproximity cannot be more than 2X 10-A. One re- herence between a single-mode laser and a truly inmaining possibility is that of buried contributions from coherent source. On the other hand, the clear definition odd isotopes. The absence of any promninentcontribution of the truncated Doppler profile defines the Doppler from the odd isotopes is not surprising since with their center wavelength to high accuracy without requiring lower abundances and manifold hyperfine structure stabilization of the cavity length. The difference bethey would not be expected to give a contribution above tween the single-mode and multimode lasers was illusthreshold unless, by accident, one of these hyperfine trated strongly in our experiments and can be seen to components coincided within about one Doppler width some extent in the photographs of Figs. 4 and 5. The with that of an even isotope. According to Mrozowskill fringes from the helium-neon laser, although superthe hyperfine constant for "19 Hg in this line is approxi- ficially sharp, turn out in fact to be obscured by unmately ten times greater than the isotope effect, so that wanted interferences between widely separated surfaces accidental coincidences between even and odd isotopes in the optical system, caused by the high degree of coare not very likely. We have not, however, calculated herence, which made these fringes less well-defined under the expected positions of odd isotope hyperfine com- close examination than those of the mercury laser. This ponents to determine whether or not any coincidences may be regarded as a "mismatch" between the laser output and the spatial passbands of a spectrometer, might exist. Should biases nevertheless exist, we feel that the which has been developed over the years to be matched wavelength that reflects most accurately the result as closely as possible to incoherent sources. Thus, withfor an individual isotope is probably "'1Hg. Subsequent out wishing to disparage the single-mode laser for use to the work described in Sec. IV, a laser was prepared in optical systems designed for its characteristics (long with enriched "'1Hg(> 90% enrichment), and the fringes distance fringe counting, for example) we feel that a from it and from the "'1Hg component of natural Hg highly multimode laser with relatively narrow Doppler width may be a better source for use in experiments were intercompared visually in a 50-cm Fabry-Perot. No shift as large as a tenth of a fringe (0.0004 A) was where coherent and incoherent sources have to be seen, although shifts of this order of magnitude should employed simultaneously. have been easily detectable. Ultimately, the usefulness of a spectroscopic source as a wavelength standard depends also on its reproduciVI. APPLICATION TO WAVELENGTH bility. A laser source employing standing wave cavity STANDARD modes is, by its nature, immune to Doppler shifts since The Doppler width given here is by far the narrowest motions of ions can only broaden the line symmetrically of any known laser transition in the visible, and this and cannot shift the line center. Shifts from the Stark suggests the possibility that the mercury ion laser may effect are expected to be negligible in the hollow cathode make a convenient secondary standard for use in structure, particularly in view of the simple alkali-like applications where its pulsed operation is not a hin- nature of the terms responsible for this laser transition.' drance. For this purpose, it would obviously be de- Pressure shifts remain a possible source of difficulty, sirable to use an enriched isotope, with the result not particularly from the helium. Preliminary experiments only that the full narrowness of the Doppler line is intercomparing two lasers have failed to uncover shifts achieved but also that the gain per pass is increased by as great as 0.0004 A, when the helium pressure was a factor of three. An enriched isotope laser, operating raised from the usual 1 or 2 torr to 7 torr. Nevertheless, multimode, has given sharp fringes in a Fabry-Perot it is clear that further work needs to be done on this with a 1-m separation. point; it would also be highly desirable to compare The reader may wonder why we suggest the hollow the wavelengths of separated isotopes with primary cathode mercury laser as a wavelength standard, in standards. view of the demonstrated capabilities of the stabilized ACKNOWLEDGMENT single-wavelength helium-neon laser.' The reason for We are indebted to Sumner P. Davis for permission 11R. W. Shorthill and G. R. Fowles, J. Opt. Soc. Am. 48, 459 (1958). to use the spectrographic equipment of the University " S. Mrozowski, Phys. Rev. 61, 605 (1942). of California Physics Department and for many helpful 16T. S. jaseja, A. Javan, and C. H. Towvnes,Phys. Rev. Letters 10, 165 (1963).
suggestions.
