416 IEEE JOURNAL ELECTRONICS,OF QUANTUM VOL. W-7>NO. 8: AUGUST 1971 pulsed xenon ,” AppZ. Phys. Lett., vol. 17, 1970, pp. 305- [91 W. B. Gandrud and R. L. Abrams, “Reduction in SHG effi- 306. ciency in telluriumby photoinduced carriers,” dppl. Phys. [SI W. F. Krupke, “Passive &-switching of a COa laser using a Lett., vol. 17,1970, pp. 302-305. mixture of SF, and GFsC1 gases,” Appl. Phys. Lett., vol. 14, [lo] R. S. Caldwell and H. Y. Fan, “Optical properties of tellur- 1969, p. 221. and ium selenium,” Phys. Rev.,1959, vol. 114, p. 664.

Nonlinear Effects in Inorganic Liquid

R. R. ALFANO, ALEXANDER LEMPICKI, AND STANLEY L. SHAPIRO

Abstract-Inorganic liquids,phosphorous, andselenium oxy- man or Brillouin scattering can lead to a power limita- chlorides, used as solvents for Nd, exhibit a number of nonlinear tion while self-focusing may cause the deterioration of properties, which may reflect in the performance of liquid lasers. the beam quality and thus limit the usefulness of the Spontaneous and stimulated Raman scattering have been studied. Measuredcross sections and gains indicate that upto power liquid laser. Another effect which is particularly easy to levels of a fewhundred megawatts per squarecentimeter the observe in liquid lasers is’thatof self-&-switching. So far effect on laserand amplifierproperties are negligible. No self- no adequate explanation of its mechanism hasbeen given, focusing has been observed. Under mode-locked conditions sub- but the suggestion [4] that it may be due to’ stimulated stantialconversion to Ramanfrequencies have been obtained. Brillouin scattering is not borne out by the present in- No connection has beenfound between stimulated Brillouin scattering and the phenomenon of self-&-switching. vestigation. In general, the type of effects described here have ob- I. INTRODUCTION vious pertinence to all liquid laser media, including dyes. This paper, however, is limited to the investigation of ECENTLY inorganicliquid lasersoperating at Raman scat.tering, Brillouin scatt.ering, and self-focusing high output energies and powers have been con- in inorganic liquid lasers only. structed [ 11. Solutions of Nd in selenium oxy- chloride (SeO’Cl2) or phosphorousoxychloride (POC13) 11. MATERIALS have been operated in &-switched, self-&-switched, and Inorganic laser solutions are multicomponent systems. mode-locked regimes [ 21 [ 71. Under these conditions - They consist of a salt of Kd (chloride or fluoroacetate) the power available inside a liquid laser cavity can be dissolved ineither seleniumoxychloride (SeOC12) or as high as in conventional glass or ruby lasers. Since the phos,phorous oxychloride (P0Cl3) acidified with a Lewis active medium is a liquid, however, many of the non- acid such as tin tetrachloride (SnC14) or zirconium oxy- linear effects associated with the third-order susceptibil- chloride (ZrCI4) [3]. In addition,depending upon the ity can be expected to occur and to affect the laser out- Nd salt and solvent used, some reaction products can be put. present in solution. In the most commonly used solution, The nonlinear effects associatedwith liquids are us- Nd+3:POC1, :ZrC14, Nd is introduced as a fluoroacetate ually investigated by using high peak power solid-state (Nd (CF,COO),). The composition of the solution is lasers. Thus the first observation of stimulated Raman (in moles per liter) : Nd-0.3; ZrCI4-0.45’; P0Cl3-9; re- scattering was made by placing the nitrobenzene Kerr adion product (dimer) F2O3Cl4-0.9. The most abundant cell inside the lasercavity to Q switch theruby 18.1. component is the oxychloride solvent, and one would ex- Also, saturable absorber liquids are used in &-switched pect thatthe main contribution to nonlinear effects and modelocked lasers [9], andanisotropic molecular should thereforebe determined from the properties of liquids can be used to couple modes’ of solid-state lasers SeOC12 or POC1,. It should be noted that both of these through the optical Kerr effect [lo],[ 111. Our case dif- molecules are highlyanisotropic having symmet,ries of fers in that the entire active medium is a liquid and the C, and CZv,respect.ively, and highlypolarizable [E]. effects may become “self-generated.” Onecan expect therefore that nonlinearitiesassociated The specific problems that are of interest concern lim- with molecular orientation in strong optical fields may itations imposed by nonlinearities on the output of liquid play a role. lasers. Thus, for instance, generation of stimulated Ra- 111. SPONTAKEOUSRAMAN SCATTERIKG Manuscript received February25, 1971. The study of spontaneous Raman scattering has ob- ’ The authors are with the Bayside Research Center, GTE Lab- oratories, Bayside, N. Y. vious pertinence to our problem since a measurement of ALFANO et al.: NONLINEAR EFFECTS IN LIQUID LASERS 417

VERTICAL I L Y SCATTERED LIGHT

HORl ZONTAL

/' INCIDENT .q LIGHT

Fig. 1. Geometry of the spontaneousRaman scattering experi- ment.

589 thescattering crosssection can lead to atheoretical d k I297 estimake of the stimulated . A comparison of calcu- lated and measured gain can in turn shed light on the occurrence of self-focusing.Since data onoxychlorides in the literature[ 131, [ 141 are rather qualitative,a quan- I1 titative experiment had to be performed. Spontaneous scattering spectra were obtained by using the geometry shown in Fig. 1. Excitation was provided by the 4880-A line of - laser with 501 mW power out,put and a vert.ically polarized beam. Radiation scat- tered at 90" was focused into the slit of a $-m Jarrell- Ash spectrometer, and detected by an RCA 1P21 photo- multiplier, Keithley ammeter, and strip chart recorder. Vertically or horizontally polarizedcomponents of the scatteredlight could be selected byan analyzer. The I I I II II spectrometer resolution was 0.5 A or 1.5 cm-l, sufficient 158 b 158 246 272 346386 to measure the much broader Raman lines of P0Cl3 and v (ern-') SeOC12. To providecomparison between the scattering (b) of different liquids, solutions could be placed in identical Fig. 2. (a) Raman spectrum of pure POCI,. (b) Raman spectrum cells. of pure SeOCb. Spontaneous Raman spectra of pure POCI3 and pure SeOClz are shorn in Fig. 2. The most intense lines are I C5.2-4 I themetal-halogen vibrations at 488 cm-l (POC13) and 386cm-l (SeOC12). The 488 cm-l POC13 lineis shown underhigh resolution inFig. 3 (a). The FWHM was measured to be 5.2 t 0.8 cm-l. A large fraction of this width is presumablydue tothe presence of different chlorine isotopes. The line is almost completely polarized vertically with anextinction ratio >30. Upon addition of the Nd ion and Lewis acid, several h changes occur in the spectra of the pure solvents. The 488 cm-l line of POlC13 is reduced in intensity by about 10 percent and a new line appears some 5 cm-l to the red of the 488 cm-l line. This newline, shown in Fig. 3 (b), appears to be caused by the addition of the Lewis acid since it isalso presentin solutions containing no Nd ion. The intensity of the 1297 cm? line is substan- tially reduced upon the addition of Nd presumably be- cause it coincides with an absorption dueto the ion when 488 589 Y (cm") the exciting wavelengthis 4880 A. The most intense feature of the SeOCl,2Raman spectra (b) is the 386 cm-l S+C1 vibration. Its lineshape in the pure Fig.3. (a) 488 ern-1 vibrational line of POCL under high reso- lution. (b) 488 em-1 line at a faster scan speed showing extra solution a,nd in laser solutions with different Nd3+ con- band in laser solution. 418 IEEE JOURNAL OF QUANTUM ELECTRONICS, AUGUST 1971 centrations is shown under high resolution in Fig. 4. In a pure SeOCl, solution t,he 386 cm-l line has a complex structure ~18cm-l wide and is polarized vertically. In the lasersolution of Nd3+ SeOC12, as in P0Cl3, a new line appears shifted to the red of the 386 cm-l line by sz 5 cm-l. When Nd"' is removed from the laser solution, the extra line is still present indicating that the ionic complex is not responsible for this new line. At thehigh- estmolar concentrations studied molar), the red shifted line is nearly as intense as the main Raman line. For the calculation of gain in stimulated Raman scat- I I tering, it is necessary to know the magnit,ude of the for- I ward spontaneous scattering cross section per molecule, per unit solid angle (dr/dn),, 8 = 1800. This quantity is rather difficult to measure absolutely but insome special casescan be deduced from comparativemeasurements performed at 90". Such a special case arises if we com- parethe 488 cm- and 386 cm-l lines of P0Cl3and SeOC12 with the 656 cm-l Raman line of CS,. All of these Fig. 4. (a) Raman spectrum of SeOCL line at 3S6 em-1.

*= TAV__- Av 1 2' (1) dv [%I "=Yo 2 27r (v - VJ2 + ($) From the linewidth of CS2 measured by Clements and We can integrate t'he differential cross section over the Stoicheff [19], its cross section takenas 3.8 X linewidth AV and volume and obtain cm2 [20], and our measurement.s of intensity ratios (6) and linewidth, we can obtain the cross sections for the oxychlorides at 4880 A. These, together with other per- tinent data, are given in Table I. Toobtain cross sections (2) for other exciting wavelengths, we can use the relation- ship [21] Using theparameter K,,,, defined byMcClung a,nd Weiner [ 181, we obtain

where vl, V, are the wave number frequencies of the ex- citing radiation and vs1, vS~are the corresponding fre- The cross sectionper molecule is obtainedfrom (2) quencies of the Stokes lines. and (3) Iv. STIMULATED RAhtAN AND BRILLOXTINSCATTERING Stimulatedscattering in liquid laser media,was ob- where N is the number densityof the substance. tained in two differentways. For the measurement of ALFANO et al.: NONLINEAR EFFECTS IN LIQUID LASERS 419 TABLE I STIMULATEDRAMAN SCA~ERINQ DATAFOR OXYCHLORIDES

POClS SeOClz

Raman shift vE 488 cm-X 356 cm-l Linewidth AvR 5.2 cm-1 18 cm-I Forward szattering cross section (du/dQ): 4550 4 3.05 X cm2 9.6 X cm2 6940 $ 0.86 X cm2 2.7 x 10-29cmz 10 600 A 0.16 X cm2 0.49 X cmz Gain coefficient (calculated):b 6940 d 2.44 X cm/MW 2.63 X 10-3 cm/MW 10 600 A 1.6 X loq3 cm/MW 1.6 X cm/MW Gain coeffizient (measured): 6940 A 2.6 X lo-* cm/MW

Calculated from a Calculated (7). I b Calculated from (1) and (7). spectral shifts and energy conversion, an external laser source (ruby or Nd glass) was used and its output passed through a cell containing the liquid (Sections A and B). In a second set of experiments the ouput of a liquid laser MONITOR itself was shown to contain stimulated Raman emission PHOTC internally generated (Section C). A. Threshold and Energy Conversion. A singleA transverseand longitudinal (Korad) was used for most measurements of energy con- I I version intostimulated Raman scattering (SRS) and I stimulated Brillouin scattering (SBS) . The experimental arrangement is shown in Fig. 5. The Korad laser con- sists of a sapphire etalon output reflector, a 1-mm aper- Fig. 5. Experimentalarrangement for investigatingstimulated Raman and Brillouin scattering. ture, a 4-in ruby rod, a Kodak &-switch dye cell anti- reflection coated atthe ruby wavelength, and a 100 percent reflectivity rear-output reflector. measured by comparing the pulse heights on the scope. Theruby laser output pulse duration was 15 ns as Theforward Raman beam wasobserved byplacing measured by a TRG detector connected to a Tektronix Corning 7-69 filters infront of tube 1, andthe back 519 scope (0.5-ps risetime).Independent measurements Brillouin beam was observed by placing a narrow-band of the laser out,put power with an EGG radiometer and filter in frontof tube 2. a TRG calorimeter yielded a valueof 1 MW. An inverted Most of the stimulated Raman scattering experiments werecarried out with POC13-based laser solutions. In telescope reduced the beam area size to 0.5 mm2 acrossl the Raman cell, which was 50 cm long. The outputpower order to separate the nonlinear effects of the main com- entering the cell was typically 0.7 MW, thus giving a ponent (P0Cl3)from possiblecontributions of NC3, power per unit area of =140 MW/cm2. The Raman cell Lewis acid and reaction products, experiments were car- was several meters from the laser and tilted to minimize ried out on pure POcl3,a mixture of P0Cl3 andP203C14,1 optical feedback. Glass microscope slides were placed in and in standard laser solution with theNC3 ion replaced the laser beam to vary thepower. The beampolarization by Eu'~.This replacement was necessary because Ng3 was perpendicular to the table. The laser output power has a strong absorption band at the rubyfrequency. The was monitored before and after the Raman cell as was use of a different rare-earthion was not believed to the forward and backward SRS and SBS. Glass wedges change any of the relevant propertiesof the material. with surfaces parallel to the laser polarization reflected The curve of SRS versus the ruby laser intensity for thelight upon MgO reflectors. The diffused scattered pure Poc13 is plotted in Fig. 6. Only forward Raman light fromt.he MgO plates thenfell upon RCA 922 photo- scatteringwas observedfrom POC13. BackwardSRS tubes (S1 response) whose outputs were displayed on a from POcl3 was measured to be 50.01 of the forward 555 Tektronix oscilloscope. Attenuators were placedin front of the tubes so that they operated in a linear re- 1 Thismixture was prepared by dissolving Nd(qF?COO), in sponse region. The phot.otube responses were calibrated pure POCL and filtering out the Nd contaming preclpltates. The remainder is believed to contain a mixture of POCL and PsOSL by conventional techniques. Conversion efficiencies were in proportion occurring in standard laser solutionC22l. 420 IEEE JOURNAL OF QUaNTUM ELECTRONICS, AUGUST 1971 In another series of experiments picosecond pulse ex- MATERIAL : PURE POCI, LENGTH: 50 crn citation wasused to produce stimulated scattering. Under RUBY LASER 0.3 these conditionsBrillouin scatteringusually does, not occur and one can expect more efficient conversion into Raman scatOering [24].The experimental set up was similar to that used for observations of self-phase modu- lation in liquids and solids [25]. It consisted of a mode- locked Nd:glass laser whose output wasconverted to the second harmonic and the bean1 collimated to a di- MWIcrn' ameter of 1.2mm. The energyper pulse was -5 mJ, Fig. 6. Stimulated Raman andBrillouin sca.t.tering in POCL pulse duration -4 ps, and peak power -1 GW/cm2. The versus ruby laser intensity. output from the cell was passed through a 10-cm focal length lens pla'ced at thefocal distance from a2-cm-high scattering at the power levels of the experiment. Theo- slit of ag-m Jarrell-Ash spectrograph, and recorded retically[23], the forward-to-backward rat.io isone, photographically on Polaroid 3000 speedfilm. Corning under steady-stat.e condit., but this valueis computed filters 5-60 and 5-61 mere used to attenuate the funda- in the absence of backward SBS, which, if present, can mental frequency and Dass the ant,i-Stokes shifted light. compete against the backSRS' light. For observation of Stokes shifted light a 3-67 Corning As seenfrom Fig. 6, substantialRaman conversion filter was used.The exposed film containing both spectral occurs over a length of 50 cm at powers of ~100MW/ and angular [24], [25] information is shown in Fig. 7. cm2. From the initial rising portion of the SIRS curve, As much as eight anti-Stokes and five Stokes' stimulated we can calculat,e the gain of the stimulated process by lines could be detected. In all probability thedecreasing using the expression sensitivity of t.he Polaroid film limits t,he number of ob- servable St'okes lines. In addition to the Raman lines a substantial amount of self-phase-modulated emission is IB 0~ IL exp (g14 (8) seen to form a spectrallycontinuous and spatially diverg- where Ix is the Raman int.ensity as itleaves the cell and ing background. IL is the intensity of the laser. We obt.ain g(POG1,) = No attempts were made to estimate the energy con- 2.6 x (cmJMW) . version into Raman and self-phase-modulated radiation The Brillouin-scatteringcurve shows that alarge under this type of excitation. The results indicate, how- amount of laser conversion to SBS takes place at -20 ever, that the use of liquid lasersfor amplification of MW/cm2. At powers where substantial Raman conver- very-high-intensity picosecond pulses may lead to a sionbegins, approximately 20 percent of the laser has very complex output. been depleted into backward Brillouin scattering. At the highest laser powers in this experiment, as much as 40 B. Frequ.en.cy Shifts Due to SBS percent of the laser beam is converted to SBS and 30 The frequency shift due toSBS was measured in order percent toSRS light. to elucidate t,he possible connection of this phenomenon The curves of the Raman andBrillouin intensities ver- withthe self-&-switchingproperties of the aprot.ic sus laser po,wer reach saturation regions at high powers laser [4]. The experimental arrangement used for these because of laser depletion into, f3R.S and SBS. The laser measurements was similar to that described by Brewer depletion was furtherverified by observing that thelaser andShapero [26] and is shown inFig. 8,. A TRG 104 beam intensity transmitted through t\he cell decreased as ruby las'er Q switched by a rotating prism and crypto- the SBS and SRS,built up. cyanine dye was used as a source. A resonant reflector For solutionscontaining amixture of POCI, and consisting of two sapphire plates produced a single longi- P203C14the only difference in Raman scattering was an tudinal-mode output. increase of threshold by approximately 20 percent. This The peak power of the pulse was measured by an ITT corresponds roughly t80the volume decrease of pure POCI, planar photodiode TI. Part of the signal reflected from caused by the presence of the dimer. When pure P0Cl3 beamsplitter B2 waspassed twice through a quarter- was doped with its dimer plus europium, the threshold wave plat,e, rotatingits polarization by 90°, and was. for Raman scattering increased still further. These re- thendirected tothe Fabry-Perot interferometer. The sults show that at laserpowers used in these experiments, major part of the signal was focused by a 100-mm focal- pure P0Cl3 is primarily responsible for SRS, and that length lens L into a 150.-mm cell containing the liquid rare-earthions and additional liquidcomponents act under study. like inactive participants. This lenswas used to increase the power density of To ascertain if SRS, isassociated with self-focusing, the ruby radiation, which otherwise was' insufficient to photographs of SRS light were taken at the end of the produce SBS inNd-containing solution. As previously cell. No filaments could be detected at the power levels noted, an absorption at the ruby frequencymade this used. necessary. The back-scatteredradiation from the cell ALF.4NO et al. : NOKLINEAR EFFECTS IN LIQum'LASERS 421

PURE POCI, SeOCI, L

8 765 4 3 2 I L IS ANTI-STOKES (a) Av =0.178 cm-'

S LI 234 5 STOKES POCI- S

Fig. 7. Angular emission from pure POCL under picosecond laser excitation. (a) Anti-Stokes emission. (b) Stokes emission.

aV= 0.117cm-'

L

S

LA

FP Av 10.19ern-'

-POLAROID+ QUADRANT -FILM L Fig. 5. Experimental arrangement for the measurement of stimu- Fig. 9. Interferograms of the incident (L)and scattered (5) lated Brillouinshifts. L-ruby laser; TI,7'-planar photodi- radiation. Inter-order spacing for SeOClz0.494 cm-'; POCk odes; B,, Bz, &-beam splitters; PI,F-filters; L-lens. 0.27 cm-1; Kd+3:SeOCL:SnCl&-0.494 cm-1. was detected by the photodiode T,, and part of it was of the phenomenon resides in the formation of refractive allowed to enter the Fabry-Perot interferomet.er. To dis- index gratings recentlydiscussed by Keyet al. [27]. tinguishbetween the incident andscattered radiation, which, upon arrival at the interferometer, are polasized C. Stimulated Rama.n Scattering: Self-Generated at right angles,, a quadrant of sheet polarizers was placed The internalgeneration of Raman scattering ina liquid in frontof the film.. laser has been briefly reported by Alfano and Shapiro[ 71 Typical interferograms of the incident and back-scat- and by Landet al. [28,]. tered radiation are shown in Fig. 9. Table TI gives the The experimental set up in the present work is shown measured shifts AV for a number of solutions. From AV on Fig. 10. It consisted of a 25-cm cell of 1 cm2 cross and the refractive index (n)at the rubyfrequency V, the section placed in a. dual elliptical cavity. Up to 2500 J velocity of sound can be calculated by using the ex- v, could be discharged through two flashlamps. The cavity pression wasformed by a10-m radius, fully reflect.ing mirror, Av = 2vv,n/c. sin 012 (9) and a 50 percent reflecting flat mirror separated by 70 cm. The external surfaces of cell windowswere cut at where 0 = 180". This is also tabulated in Table 11. As- the Brewster angle, and the output mirror was wedged suming no dispersion in the velocity of sound, one can to reduce subsidiary resonances in the cavity. Since the also calculate the Brillouin shift at the Nd-laser wave- refractiveindices of quartz (1.45) andNd3+: POC13 length of 1.06 p by using the appropriate refractive in- (1.452) match quite well, no reflection is obtained from dex in (9).These values are given in the last column of the quartz-solutioninterfaces; as a consequence, the Table 11. innersurfaces of the windows canbe pasallel to each No correlation was found between these shifts and the other, greatly simplifying thecell construction. spacing of linesoccurring in thespectra of se1f-Q- The laser could be operated in three different regimes: switched outputs.On this basis one cantherefore rule Q switched by a saturable absorber (Kodak 9860 dye) ; out stimulated Brillouin scatteringas the mechanism re- mode locked by suitably adjusting the concentration of sponsible for self-&-switching. A more likely explanation the sa.me dye; and self-&-switched by removing the dye 422 ' IEEE JOURNAL OF QUANTUM ELECTRONICS, AUGUST 1971 TABLE I1 BRILLOUINSHIFTS, REFRACTIVE INDICES, AND VELOCITY OF SOUNDIN LASERSOLUTIONS

Au(6942) V, Av(10600) Material (cm-l) 69; A 106gO A (cm/s) (cm-l)

SeOCll 0.178 1.6396 1.6249 1130 0.115 POCL- 0.117 1.4559 1.4501 837 0.076 SnClr 0.116 1.5042 1.4952 SO3 0.075 SeOClS:SnC14 0.178 1.6416 1.6268 1129 0.114 POCl,:SnC14 0.147 1.457" 1.452* 1050 0.096 SeOC12:SnCle:Nd+3b 0.19 1.6650 1.6499 1188 0.123 Poc13 :SnCl4: Ndf3 0.18 1.480. 1.475" 1266 0.117

a Estimated values based on increase of refractive index of SeOClz upon addition of SnCL and xd. 0.3 molar concentration of neodymium.

I1 LASER 488cm-' MI Tc =75ns (a) Fig. 10. Schematic arrangement of a mode-locked liquid laser. cell and repla,cing theouput reflector by an uncoated quartz wedge. The output of the laser was directed into t- either a2-m Bausch andLomb or a 8-mJarrell-Ash (b) spectrograph and recorded on sensitized Kodak 12 plates Fig. 11. (a) Mode-locked Nd:POCL laser out,put showing stimu- or Polaroid 57 film. A planar photodiode and Tektronix lated Raman line. (b) Time output on a 'Tektronix 519 oscillo- 519 oscilloscope was used to monitor the timedependence scope. of the output. The Nd3+:POCls lasershowed stimulated Raman scat- tained. Spectra and oscilloscope traces obtained in the tering in all three modes, of operation. Figs. 11 and 12 self-@switched mode of operation are shown in Fig. 13. show a spectrum and an oscilloscope trace obtained with In thiscase SR,Sappeared only on the most intense shots a mode-locked laser that had a pulse duration of 3 ps butcontrary to the mode-locked casecontained anti- and produced Raman scat,teringwit,h every shot. The Stokes lines as well. stimulated first Stokes line at 488 cm-l is clearly visible. With Nd+3Se08Cl,2 solutionswe were able to obtain Ra- In other spectrograms the second Stokesline was also man generation only in the mode-locked regime. An ex- sometimes detected. The lasting band of about 100 ern-l ample is given in Fig. 14. When regular trains of pulses width is devoid of any structure except for a sharp line wereemitted (arather exceptionalcase with SeOC1,2) of about 2 cm-l width, positioned to t,he left of the center the first and sometimes the second St,okes lines (386 of the band. The SRS lines were also struct.ureless a'nd cn1-l) were detected. The laser and Raman emission both. of about the same 100 cm-l width. The position of the occurred over a narrow band of approximately 6 em-l. center of the Raman emission shifts within 10 cm-l from The pulse duration measured by two-photon fluorescence shot to shot with respect to thecenter of the lasing band. was 6 ps. The narrower bandwidth and longer pulse dura- Since not all thepulses in the mode-locked t,rain produce tion can be attributed to thepresence of reflections at the Raman scattering there should not necessarily be exact parallel liquid-window interfaces, which is larger than for agreement between the laser bandwidth, which contains POC13 because of poorer refractive index matching the spectrum of all the pulses,, and the SR,S bandwidth, (SeOC12-1.67; quartz-1.45). The presence of parallel re- which contains the spectrum of only some of t'hem. The flecting surfaces in the ca,vity is known to cause band- Raman conversion to first St,okes was measured by plac- width narrowing and pulse lengthening[ 71. ing neutral density filters over the film at thelocation of the laser line and attenuating it until itreached the same V. DIS~USSION intensity as the Raman line. By calibratingfilm the spec- The measurements of spontaneous Raman cross sec- tral response with a lamp at conversion of ap- tions reported in Section I11 can be used to calculate the proximately 12 percent(into the first Stokes) was ob- gain of the stimulated process that in turn can be com- ALFANO et al.: NONLINEAR EFFECTS IN LIQum LASERS 423

10522H 3529.43i 488 ern-' ’ ird ORDER 1 I PDCl, LINE 3519.29i 5350.46; 3rd ORDER 2nd ORDER Fig. 12. Spectra of mode-locked Nd :POCL liquid laser. Two shots show =IO0 cm-1 central band and Raman shifted light.

the performance of liquid amplifiers. The question that we would like to answer is how much of the signal that isfed into an amplifier is likely tobe converted into Raman scattering at the output of the device. Since we assume that the stimulated scattering will be generated from noise in the amplifier medium (the input does not conta$n any Stokes radiation), an accurate calculation is far from trivial and in fact cannot be obtained with- out approximat.ions in an analytic form. To obtain an estimate, let us refer to Fig. 15, which shows a cell of length I and cross-sectional area A, filled m7it.h the liquid t- U-20 ns lasermedium andtraversed by abeam from another (b) laser. The amount of Raman flux produced in the ele- Fig. 13. (a) Seif-&-switched spectrumshowing Stokes and anti- ment dx and directed so that it will pass through the Stokes Raman scattering. (b) Time output on a Tektronix 519 right window of the cell can be written as oscilloscope.

Since Raman flux generated near the entrance window (left) will experience the greatest gain, we can replace x by I in the solid angle (A/z2).Upon integration we ob-

LASER __c 1st STOKES tain 1.06~ x - 388 cm-‘ Fig. 14. StimulatedRaman scattering from Nd+3:SeOCE:SnCL laser Q switched with a dye. Using quantities characteristic of the experiment that pared with the directly measured va,lues of the gain. The lead to Fig. 6 (I = 50 cm, A - 1 cm2, A ,= 6940 A) and an gain coefficient g defined by (8) is given by [29] input IL = 100 MW/cm2, we obtain Ix % 2 X MWJ cm2, which is about three orders of magnitude less than what is observed. This result leads us to believe that the relatively high SRS output shorn in Fig. 6 is the result where ,usis the angular frequency of t.he first Stokes line of residual feedback that changes the cell from a Ranmn and the other symbols have their usualmeanings. noise amplifier to a multiple-pass oscillator.2 This possi- Using (10) we can calculate the gain coefficient g for bility makes it very important to eliminate optical feed- P0Cl3. The measured and calculatedvalues are tabu- back whenever a liquid is used as an amplifier. This is, lated in Table I. We see that they agree within ten per- of course, standard practice even if no, SRS is generated. cent. This close agreementconstitutes a strong proof With good design, SRS fromliquid amplifiers should that at the power levels used inSRS (150 MW/cm2) not impose any limitations at power inputs in the 100- there is no evidence for self-focusing. This confirms the 200 MWJcm2 range. earlierresult (Section III), whichshowed absence of Self-generation of ‘SRSin liquid laser oscillators will filaments on photographs, and indicates thaf the beam be governed by similar consideration. Here the problem quality of liquid lasers is not likely to deteriorate from issomewhat more critical since it imposes’ acondition self-focusing-at least up to thesepower levels. A knowledge of the gain for SRS’permits us to make 2 An alternativeexplanation would be that self-focusing does occur in the cell. This, however, would contradict the remarkable an est.imate of the limitation imposed by scattering on agreement between calculated and measured gains cited above. 424 IEEE JOURNAL OF QUANTUM ELECTRONICS, AUGUST 1971

ing of Nda+:SeOCLliquid laser,” J. Appl. Phys., VO~. 38, 7’- 1968, 61154116. n pp. .-__ [71 R. R. Alfano and S. L. Shapiro, “Picosecond pulse emission ... , _I.., ... ’. ...’, ,.,r : , . , ,/ ._”_ ,I . , --__ froma mode-locked Nd3+ POCb liquid laser,” Opt. Com- 1L I, IL mun., vol. 2,1970, pp. 90-92. I81 G. Eckhardt, R. Hellwarth, F. J. McClung, S. E. Schwarz, dx7i Lx -_1 IR D. Weiner, and E. J. Woodbury, “Stimulated Raman scatter- ing from organic liquids,” vol. 9,1962, pp. Fig. 15. Geometryleading to (11). Laserbeam of intensity 11. Phys. Rev. Lett., traverses a cell of length 1 and cross sectionalarea A, and 455-457. I91 A. J. DeMaria, D. A. Stetser, and H. Heynau, “Self-mode- produces a single-pass Raman outputIR. locking of laser with saturable absorbers,” Awl. Phys. Lett., vol. 8, 1966, pp. 174-176. 1101 J. P. Laussade and A. Yariv, “Mode-locking and ultra-short on the resonator mirrors to have optimum reflectivity for laserpulses by anisotropicmolecular liquids,” AppL Phys. the fundamental and essent.ially zero reflectivity for the Lett., vol. 13, 1968, pp. 65-66. [111 J. Comly, E. Garmire, J. P. Laussade, and A. Yariv, “Ob- Raman frequencies. The difficulty in observing Ramaa servation of mode-locking and ultrashort optical pulses in- emission under Q-switchedconditions indicates, how- duced by anisotropicmolecular liquids,” Awl. Phys. Lett., vol. 13, 196S, pp. 176-178. ever, that no serious loss due to SRS does occur at power 1121 G.Nagarajan and A. Muller,“Thermodynamische funk- levels of 100 MW/cm2. tionenand molekulare polarisierbarkeiten von thionyl und seleninylhalogeniden,” 2. Naturjorsch., A, vol. 216,1966, pp. A somewhat different picture is presented in the case 612417. of very high-peak-power picosecond pulseswhere SRS 1131 H. Gerding, E. Smit, and R. Westrik,“Die ramanspektren unddie molekulstrukturen des selenoxychloridsund des emission accompanies every shot and conversion efficien- thionylchlorids,” Rec. Truv. Chim., vol. 60, 1941, pp. 514-522. cies to SRS of 12 percent have been measured. Quanti- E141 D. Kato, “Raman in the SeOCkSnCL liquid,” J. Phys. SOC.Jup., vol. 29, 1970, p. 1103. tative estima,tes of the conversion would require the use 1151 G. Herzberg, Mobcular Spectra and Molecular Structure 11 of transient gain equations E301 and a knowledge of dis- Infraredand RamanSpectra of PolyatomicMolecules. Princeton, A’. J. : Van Nostrand, 1968: p. 277. persion effects. Additional da,ta on thresholds and gains [161 T. @. Damen, R. C. C. Leite, and. S. P. S. Porto, “Angular would be neededto warrantsuch treatment. dependence of the Ray,an scattermg from benzeneexcited by the He-Ne cw laser, Phys. Rev. Latt., vol. 14,1965, pp. In conclusion, we would like to emphasize that re- 9-1 1. sultspresented in this paper wereobtained using sta- 1171 L. Nafie, P.Stern, B. Fanconi, and W.-L. Peticolas, “Angu- lar dependence of Ramanscattering mtensity,” J. Chem. tionary(not flowing) liquidlaser media. Thenatural Phys., VOI.52, 1970, pp. 1584-1588. regime of operation of these devices is inthe flowing [181 F. J. McClungand D. Weiner,“Measurement of Raman scattering cross-section for use in calculating stimulated mode,which greatly improves the reproducibility of Raman scattering effects,” J. Opt. Soe. Amer., vol. 54,1964, results. The technology of flowing Nd liquid lasers only pp. 641-644. 1191 W. R. L. Clement8 and B. P. Stoicheff, “Raman linewidth recently has been developed, and as their levels of per- for stimulated thresho,ld and gain calculations,” Appl. Phys. formance climbs to higher values, the effects of nonlinear Lett., vol. 12, 1968,‘~~.246-248. 1201 E. M. Garmire, iln investigation of stimulatedRaman properties of the medium will become more clearly de- emission:” PhD. dissertation,Mass. Inst. Technol.,Cam- fined. bridge, Mass., 1965. 1211 R. H. Pantell and H. E. Puthoff, Fundamentals of &ua?ztz~m Electronrcs. New York: Wlley, 1969, p. 240. ACKNOWLEDGMENT [221 K. French, private communication. C231 N. Bloembergen, “The stimulated Raman effect,” Amer. J. The authors wish to express their tha,nks t,o K. French Phys., ~01.35,1967,pp: 989-1023. for providing liquid laser solutions and information on I241 S. L. Shapiro, J. A. Glordmalne, and K. W. Wecht, “Stimu- lated Raman and Brillouin scattering with picosecond light theirchemistry, to C. Fallier who tookmost dataon pulses,” Phys. Rev. Lett.,vol. 19, 1967, pp. 1093-1095. Brillouin scattering, and to T. Illing and8. Hussain who [251 R. R. Alfano and S. L. Shaniro,“Emission in the region 4000. to 7000 A via four-photon coupling in glass,” Phys. 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