Volume 17, mmber 3
DISTRIBUTION OF STIM*ULATED EMISSION IN LIQUIDS
15 July 1965
E. GARMIRE Physics
Two independent classes of higher-order stimulated Ramaii emission with strikingly different properties have been identified in liquids. Class I radiation follows closely an expected angular distribution. That is, the wave vectors of the nth order anti-Stokes radiation, kn, and the first-order Stokes radiation, k_ 1, which produces it, obey the phase matching criteria: k, +k,_l = k-1 +kn, where k. is the wave vector of the exciting laser radiation [e.g. 11. Such behaviour is observed in calcite , but liquids have presented a number of anomalous features . For the first time, class I radiation ha8 been identified in liquids, giving close numerical agreement with the above equation. Apparently class I radiation had not been observed in most previous experiments because of insufficient Stokes radiation at the requisite angles. Independently of the class I radiation at phasematching angles, liquids also produce another class of radiation with a different emission pattern and a number of different properties. The emission cones of this class II radiation may be multiple or diffuse and often vary in size and number in a seemingly random manner. The simplest such patterns may differ from class I radiation in angle as much as 30 percent. Class II radiation is usually quite intense and produces the cones of stimulated Raman light which have been .most commonly observed and studied in the past. Stimulated Raman scattering was generated by parallel light from a 10 Mwatt giant pulse ruby laser 1 Cc/s wide. In order to enhance Stokes radiation near the phase matching direction, a 10 cm liquid cell with glass ends aligned parallel W&Xtilted at a variable angle 0 with respect to the laser beam. A portion of the Stokes radiation at the angle 0 was fed back by reflection from the * Work supported in part by NASA, Grant NSG-330, and in part by the Air Force Cambridge Research Laboratories, Office of Aerospace, USAF, under Contract AF19(626)-4011.
22 June 1965
glass-to-air interface which allowed a factor of 104 increase of Stokes intensity in this direction. A typical angular distribution of radiation from such a cell of benzene is shown in fig. 1. The two examples of Stokes radiation (b) demonstrate the enhancement of first-order Stokes in the direction of cell-reflection and exhibit its absorption rings, lYn, corresponding to the generation of emission rings of class I phase-matching radiation. The class I second-order Stokes emission ring is lshelled 0-2. The anti-Stakes radiation (a) of class I is labelled 8, and appears on the opposite side of the laser beam from the corresponding Stokes, as expected from the wave vector equation. The class II anti-Stokes cones, cpm are full circles, generally larger than the class I angles, and observed to be independent of the Stokes enhancement. Circularly symmetric class I radiation can be produced by aligning the axis of the liquid celI parallel to the laser beam, or by using a long (25 cm) cell and no apparent reflections. Table 1 gives theoretical and observed valuesinradiansof0,,rp,,u,foranumberof liquids and on, angles calculated for total transverse mismatch. Under multimode laser excitation, off-axis Stokes radiation was enhanced only 102, and usually no class I radiation was observed. Acetone appeared to be an exception, producing class I as well as class II, without any reflections. In this
Fig. 1. 251
Volume 17, number 3
-2 1 2 3
0.055 0.0257 0.0506 0.0750
15 July 1965
en (Exp) 0.054 0.0258 0.051 0.073
&4% f 1% &4% It 3%
0.042 0.031 0.056 0.085
0.023 0.0295 0.0324 0.0354
0.023 + 8% 0.030 f 8% 0.032 k 8%
1 2 3
0.0235 0.0464 0.0688
0.022 + 9% 0.047 + 4% 0.072 +3%
0.050, 0.061 0.078
0.0340 0.0583 0.0814
0.0417 f 2%
0.064 k 3%
case, the class II radiation was broadened in frequency the order of 50 cm-l, while no broadening was observed for class I. Under single mode excitation, both classes had similar linewidths. Class II radiation is evidently generated from very small filaments of the laser beam, for the emission cones are unaffected when produced by a 10 cm cylindrical lens, while the class I cones become ellipses . Class I intensity increased, and class II decreased in benzene when the 10 cm cell was replaced by a 25 cm cell. While the mechanism for the generation of class I radiation is generally understood, class II radiation is evidently generated by a different process, as yet unexplained. Since enhancement of the Stokes radiation at angles does not appear to affect the intensity of class II radiation, these cones may result from coupling to the much more intense Stokes radiation at smaller angles. The small filaments which produce class II may allow significant generation of radiation which is not entirely phase-matched transverse to the laser beam. Thus anti-Stokes would occur at angles larger than the phase-matching values, as ob-
0.040 0.0377 0.0642 0.0923 0.0379
served, and couple to Stokes at smaller angles. The angle a, is the limiting value of such considerations . The author wishes to thank Dr. C. H. Townes for his constant guidance, Dr. R. Y. Chiao for helpful discussions and Dr. F. DeMartini for help with experiments.
1. E.Garmire, F. Pandarese and C.H.Townes. Phys. Rev.Letters 11 (1963) 160. 2. R. Chiao, B. P.Stoicheff, Phys.Rev. Letters 12 (1964) 290. (1964) 490; 3. E.Garmire, Bull.Am.Phys.Soc.9 R. W. Hellwarth. F. J. McClung, W. G. Wagner, D. Weiner, Bull.Am.Phys.Soc.9 (1964) 490; R. W. Terhune, P.D.Maker, Phye.Rev. 137 (1965) A816. Both B . P . Stoicheff and F. J . McChmg pointed out the importance of single mode pumping at the Gordon Conference on Non-Linear Optics, September, 1964. (1964) 490; 4. C.f. A.Sz&e, Bull.Am.Phys.Soc.9 Y. R. Shen and N .Bloembergen, Phys . Rev. 137 (1965) 1787. 5. R. Tepper, senior thesis, M. I.T. (1965).
J. A. HOWE Bell
Received 8 June 1965
As various authors have pointed out, cf. Polanyi [l] and Pate1 [Z], it is possible to obtain stimulated emission in the rotational P branch of a vibrational band given that Tvib >> Trot, With 252
neither T having a “negative” value. Recently, however, we have reported laser oscillation on six members of the R branch of the CO2 OO”lloo0 band , a situation which requires Tvib < 0.