Pumping of stimulated Raman scattering by stimulatedBrillouin scattering within a single liquid droplet: input
laser linewidth effects
Jian-Zhi Zhang, Gang Chen, and Richard K. Chang
Department of Applied Physics, Yale University, New Haven, Connecticut 06520
Received May 15,1989; accepted September 5,1989
The intensity threshold for stimulated Raman scattering (SRS) with a single-mode laser beam is noted to be -3times lower than that with a multimode beam. The intensity threshold for stimulated Brillouin scattering (SBS)from droplets is lower than that for SRS. The temporal profiles of the laser pulse, SRS, and SBS are simultaneouslymeasured with a streak camera (100-psec resolution). The first SBS pulse always occurs earlier than the first SRSpulse. In addition, the subsequent series of SBS and SRS pulses is temporally correlated; i.e., the minimum of the(n + 1)th SBS pulse occurs when the nth SRS pulse reaches a maximum. The second-harmonic beam of a single-mode or multimode Q-switched Nd:YAG laser is tightly focused at the center of the droplet's illuminated face in
order to avoid excitation of any morphology-dependent resonances of a droplet. We conclude that, for single-modelaser excitation of droplets, the internal SBS pumps the SRS.
INTRODUCTION
Competition between stimulated Raman scattering (SRS)and stimulated Brillouin scattering (SBS) has been observedfrom liquids in an optical cell.1"2 Based on small-signal gainmeasurements, the steady-state gain coefficient for the Bril-louin process is considerably larger than that for the Ramanprocess. Thus the SBS threshold is reached before the SRSthreshold, and the backward-propagating SBS dominatesthe SRS when a Q-switched laser pulse (nanoseconds induration) propagates through several centimeters of the liq-uid cell. In fact, at high input intensities, the stimulatedBrillouin process can reflect a large portion of the incidentwave within the first few millimeters of the cell and therebyprevent the Raman waves from being further amplified inthe cell; i.e., the SRS is suppressed by the generation ofintense SBS.'
The competition between SBS and SRS is dependent onwhether the laser pulse duration is shorter than the acousticor vibrational mode lifetime. The steady-state Brillouin(Raman) gain is reached only when the laser pulse durationexceeds the acoustic (vibrational) mode lifetime. The life-time of the acoustic phonons for most liquids is -1 nsec,except for CS2, which has an exceptionally long lifetime of-2.5 nsec. The lifetime of the vibrational modes is usually inthe picosecond range. Thus, for most liquids, the steady-state regime for SBS and SRS can be considered to bereached during the initial portion of a Q-switched laser pulseof 5-15-nsec duration. However, for CS2 during the first fewnanoseconds of the rising portion of the laser pulse, the SRSis already fully established (in the steady-stage regime),while the acoustic phonon population is still increasing (inthe transient regime).3 Once the Brillouin gain has in-creased to its steady-state value in the CS2 cell, the acousticwave is so intense that it reflects the subsequent portion ofthe laser pulse within a few millimeters of the cell, and theSRS can no longer be sustained. The gain for stimulatedBrillouin and Raman processes is dependent on the phase
and amplitude fluctuations of the laser.4 When a single-mode and a multimode laser pulse have the same energy, thehigh-intensity picosecond spikes associated with multimodebeating provide more SRS gain and less SBS gain, becauseonly the steady-state Raman gain can be established for eachof the picosecond spikes.5 Consequently, with liquids in acell, the SRS intensity threshold is lower and the SBS inten-sity is higher for a multimode laser beam than for a single-mode beam.
In the frequency domain, the gain for SRS and SBS in anoptical cell depends on the laser linewidth AXL relative to thespontaneous Raman linewidth AXR (typically 10 cm-') andthe spontaneous Brillouin linewidth AXB (typically 0.02cm-'). For SBS, the Brillouin gain decreases when AXL >
A\B. For SRS, since AXL is generally less than AXR, theRaman gain, in principle, is less dependent on the laserlinewidth.
For liquid droplets, it is generally assumed that all thenonlinear-optical effects (e.g., lasing,6 7 SRS,8 9 and SBS10 )observed thus far from single droplets are initiated by theinternal intensity of the incident laser radiation. This as-sumption is usually made without any exceptions, because,for transparent droplets with a radius much larger than thelaser wavelength, the internal intensity just within the drop-let shadow face is enhanced by at least 2 orders of magnitudeas a result of the focusing effect of the spherical droplet-illuminated face.'1 Even greater enhancement of the inter-nal intensity just within the droplet rim is expected when theincident wavelength matches that of one of the denselyspaced morphology-dependent resonances (MDR's) of asphere,12-' 4 particularly a MDR with a narrow linewidth or ahigh Q factor.
Our present studies to determine whether the SRS fromsingle droplets is pumped by the input laser or by the SBShave been motivated chiefly by the possibility of using SRSspectra to identify the chemical composition of droplets in aspray of multicomponent fluids.'5 Before the SRS spectracan be used as a quantitative molecular species probe for
Zhang et al.Vol. 7, No. 1/January 1990/J. Opt. Soc. Am. B 109
sprays, more information is needed on the competition be-tween SBS and SRS and on the dependence of the Ramangain on ZAL, particularly that commonly available from amultimode or a single-mode (injection-seeded) Q-switchedNd:YAG laser.
The present investigation indicates that, when a single-mode laser is used, the first-order Stokes SRS is pumped bythe SBS rather than by the internal intensity of the incidentlaser beam, whether or not L is on an input resonance. Inseveral different experiments, the pumping of a nonlinear-optical wave by the internal intensity of another nonlinearwave has been observed within liquid droplets. The inter-nal intensity of a lasing droplet containing dye can in turnpump the SRS."" 6 The internal intensity of the first-orderStokes SRS can pump another first-order Stokes SRS,which in turn can pump another first-order Stokes SRS,leading to multiorder Stokes SRS as high as the 14th order.' 7
The time delay of the multiorder Stokes SRS relative to theinput laser pulse has recently been reported.18Y1 9
The generation of nonlinear waves within the droplet re-quires detailed consideration of the internal distribution ofthe pump radiation and the spatial overlap between thepumping radiation and the resultant stimulated radiation.In particular, when considering whether SRS within a drop-let is pumped by the internal intensity of the incident laseror by the internal intensity of some other nonlinearly gener-ated radiation, it is essential to know the pumping fielddistribution and its spatial overlap with the SRS radiationconfined just within the droplet rim.
When a focused laser beam is directed along the dropletprincipal axis [hereafter referred to as focused center illumi-nation; see Fig. 1(a)], the internal field distribution occurs atthe focal region just within the droplet shadow face, wherethe internal intensity of the incident radiation is high wheth-er or not the input resonance is satisfied. 20 21 For focusedcenter illumination, no rays graze the droplet interface.Therefore no incident rays can launch a MDR.9
,22 The SBS
and SRS, which need optical feedback in order to lower theiroscillation thresholds, are always on a MDR.9 Consequent-ly the internal field distribution of these nonlinear waves isconfined at the droplet rim. The spatial overlap betweenthe internal laser wave and the nonlinear wave is confined tothe focal region of the internal laser wave. However, thespatial overlap between one nonlinear wave serving as thepump and another nonlinear wave being amplified or stimu-lated is along the entire droplet circumference, as both thesewaves are confined just within the droplet rim. Conse-quently, with focused center illumination, the spatial over-lap between two types of nonlinear wave, both of which arecircumnavigating the droplet rim, is considerably largerthan that between the nonlinear wave and the internal laserfields, regardless of the droplet size parameter (x = 27ra/XL,where a is the droplet radius).
When the focused input wave is imaged along the dropletedge [hereafter referred to as focused edge illumination; seeFig 1(b)] and the input resonance condition is not satisfied,the internal field distribution is localized mainly in a regionwithin the droplet shadow face. 20'2' However, when theincident wavelength or the droplet radius is tuned to aninput resonance, the spatial distribution of the incident ra-diation is then confined along the droplet rim; i.e., thoseincident rays that graze the droplet rim can launch a travel-ing wave that circumnavigates the droplet rim,22 as is the
(a) Focused Center Illumination
(b) Focused Edge Illuminatioi
(c) Input Resonance
k SBS
1
kS BS
k SBS
Nz~:-:~z4 kLFig. 1. Geometric-optics schematics of the k vector of the incidentlaser beam (with an angular spread kL + kL) and of the SBS (ksBs)for (a) focused center illumination, (b) focused edge illumination,and (c) the input resonance. In order for the droplet to provideoptical feedback at SBS, kSBs must be tangent to the droplet inter-face, and the SBS must travel around the droplet rim (shown in thecounterclockwise direction). With focused center illumination (a),no rays graze the droplet interface, and thus no input resonance canbe excited, regardless of the laser wavelength or droplet radius.When the droplet rim is illuminated (c), the input resonance can beexcited for specific ratios of the droplet radius and L. The internalradiation at XL is shown traveling around the droplet rim in theclockwise direction.
case for the stimulated Brillouin and Raman waves [see Fig.1(c)]. With focused edge illumination, which is on an inputresonance, the spatial overlap between the incident laserbeam and the internal nonlinear wave is comparable withthe spatial overlap between two internal nonlinear waves.Furthermore, because x is tuned to a MDR, the energy con-tained in the incident rays near the droplet interface can beaccumulated within the droplet during the cavity lifetime = Q, where is the angular frequency of the radiation and
Zhang et al.110 J. Opt. Soc. Am. B/Vol. 7, No. 1/January 1990
Q is the quality factor for the particular MDR. 23 Since themeasured r can be as long as 15 nsec, comparable with orlonger than the laser pulse duration,23 the internal energyaround the droplet rim is accumulated throughout the dura-tion of the laser pulse. With focused edge illumination andwith x tuned to a MDR, the internal intensity should beconsiderably larger than that with focused center illumina-tion, whether x is tuned on or off a MDR.2 0'2' Consequently,the pumping of a nonlinear wave (such as SBS or SRS) bythe laser (with focused edge illumination and XL at an inputresonance) is extremely effective, because of the combina-tion of the greatly enhanced field at XL confined around therim and the good spatial overlap between the internal fieldat XL and the nonlinear wave.
When a large-diameter beam illumination (beam radius >a) is used, similar considerations apply. The large beam canbe grouped into rays that can launch waves around thedroplet rim if XL is tuned to an input resonance (as is the casefor focused edge illumination) and rays that are focused bythe droplet's illuminated face (as is the case for focusedcenter illumination).24
To date, no experimental evidence exists of the lowering ofthe intensity threshold necessary to achieve lasing, SRS, orSBS when the incident wavelength XL or the droplet radius ais tuned in order to reach the appropriate x that matches aMDR. In this research we chose to use the focused centerillumination configuration that enables us to investigate thegain dependence on AXL and the competition between theSBS and SRS without the additional complications associat-ed with having XL on or off an input resonance.
We report here the increase of the input intensity thresh-old of SRS when AXL is increased and when an input reso-nance is not excited by using the focused center illuminationof droplets. For single-mode laser pumping (AXL < AXB), wereport the first observation, to our knowledge, that SRSwithin a single droplet is not directly pumped by the laserradiation but is pumped by the SBS, which is generatedwithin the droplet by the single-mode laser radiation. Con-trary to the cell results, the SRS intensity threshold of drop-lets irradiated by a single-mode laser beam is -3 times lowerthan that irradiated by a multimode laser beam. By simul-taneously measuring the time profiles of the single-modeinput laser pulse, SRS, and SBS, we noted the following: (1)the SBS threshold is reached before the SRS threshold be-cause of the higher Brillouin gain and (2) the growth of SRSis correlated with the decay of SBS because the Brillouinwave is pumping the Raman wave. Further supporting evi-dence on the correlation of SBS and SRS is found in thephotographs that display the spatial distribution of SRS andSBS within the droplets. However, when multimode laserpulses (AXL > AXB) are used, the SRS in droplets is directlypumped by the laser, and the SBS threshold need not bereached.
EXPERIMENTAL SETUP
A linear stream of monodispersed liquid droplets (a 45,im) is produced by a Berglund-Liu vibrating orifice genera-tor. The second harmonic of a Nd:YAG laser (XL = 0.532gM) provides the incident radiation with AXL - 0.006 cm-1
at 0.532 Am when the injection seeder is on (single-modecase) and with /AXL 0.4 cm-1 at 0.532gum when the injectionseeder is off (multimode case). In order to avoid exciting
any droplet MDR, focused center illumination is used; i.e.,the laser beam is focused on the droplet with a spot size withradius - (1/3)a and aimed along the principal diameter of thedroplet.2' With focused center illumination, the incidentbeam is further focused by the spherical droplet's illuminat-ed face, and an even tighter focal spot occurs just within thedroplet shadow face. The radiation from SBS and SRS iscollected at 90° relative to the droplet flow axis and to thelaser propagation direction. The nonlinear radiation fromSBS and SRS is imaged onto a 35-mm camera, a Fabry-Perot interferometer, or a streak camera.
RESULTS AND DISCUSSION
PhotographsFigures 2(a) and 2(b) are photographs of an ethanol droplettaken with single-mode laser pumping through a green filterand a red filter, respectively. The green incident laser beamis propagating from left to right, and the photographs aretaken at 900 to the laser beam and the droplet flow direction.The green image [Fig. 2(a)] consists of the following: (1) twoarcs associated with SBS generated within the droplet, (2)one elastic scattering dot associated with the focus spot(labeled fs) of the incident radiation just within the dropletshadow face, and (3) one larger spot resulting from the spec-ular reflection (labeled sr) from a plane tangent to the drop-let equator and oriented at 450 relative to the laser propaga-tion direction. The red image [Fig. 2(b)] consists of only twoarcs, which are associated with the SRS generated within thedroplet. The attenuation of the red filter is sufficient toblock the green radiation from the fs and the sr. .
For the single-mode case, above a certain input intensitylevel (-0.3 GW/cm 2), the red and green arcs are alwayssimilar in length, implying that the SBS and SRS are spa-tially correlated. Between -0.1 and -0.3 GW/cm 2, only thegreen image appears and the red image is undetectable,implying that the SBS threshold is reached but not the SRSthreshold. Below -0.1 GW/cm 2, only the two green dots (fsand sr) exist, indicating that the red and green arcs have aninput intensity threshold and that the two green spots (fsand sr in Fig. 2) are of linear optics origin.
The converse is true for multimode laser pumping. Above-1 GW/cm2, only the red image and the two green spots (fsand sr) appear, and the green arcs are undetectable, imply-ing that the SRS threshold is reached but not the SBSthreshold. The lengths of the red arcs with multimodepumping are shorter than those with single-mode pumping(for nearly equal fluences for both the single-mode and mul-timode cases), suggesting that the SRS gain with multimodepumping is less than with single-mode pumping. At inputlaser intensities below 1 GW/cm2 , only the two green dots(fs and sr) can be detected, again indicating that the red arcshave an input intensity threshold and that the two greenspots do not.
SBS and SRS ThresholdsBy using the presence of the red arcs as a criterion that theSRS threshold is reached, the dependence of the SRS inten-sity threshold on AXL iS investigated with focused centerillumination by turning the injection seeder within theNd:YAG laser on and off. For both water and ethanol drop-lets, the input intensity needed to reach the SRS threshold
Zhang et al. Vol. 7, No. 1/January 1990/1J. Opt. Soc. Am. B 111
SBS Arcs
(specular reflection
(sr)(b)
Laser
I)focalspot(f s)
Red ImageSRS Arcs
YAG Laser
SBS SpectraA Fabry-Perot interferometer is used to verify that thegreen arcs, such as those shown in Fig. 2(a), are of SBSorigin. The experimental configuration used to measure theSBS spectra is shown in Fig. 3(a). A circular aperture isaligned to pass the radiation from a portion of the green arcsnear the droplet shadow face. Furthermore, this aperture isaligned to block most of the radiation from the focal spot [fsin Fig. 2(a)] and all the radiation from the specularly reflect-ed spot [sr in Fig. 2(a)]. A narrow segment of the Fabry-
(a)Aperture F-P Slit
0Intensified
Diode Array
Readout
F-P Rings and Slit(Front View)
Fig. 2. Photographs of ethanol droplets (a 45 m) irradiatedwith a single-mode laser beam (propagating from left to right at -1GW/cm 2) focused along the principal diameter of the droplet [re-ferred to as focused center illumination; see Fig. 1(a)]. (a) Thegreen image consists of two SBS arcs, one elastic scattering dot atthe focal spot (fs) of the internal laser radiation and one elasticscattering dot resulting from specular reflection (sr) of the incidentradiation. (b) The red image consists of two SRS arcs. The SBSand SRS arc lengths are always equal, and both arcs lengthen andshorten as the input intensity increases and decreases, respectively.Below the SBS intensity threshold, the SBS and SRS arcs are notobservable; only the two green dots (fs and sr) are detectable.
with single-mode pumping is 3 times lower than that withmultimode pumping. If we assume that the SRS is pumpedby the laser radiation, this decrease in the SRS intensitythreshold with single-mode pumping is somewhat surprisingbecause AXL<< AXR, whether the laser is operating in singlemode or in multimode. Thus the SRS threshold is expectedto be only weakly dependent on AL if the SRS is directlypumped by the laser. In fact, the SRS threshold is expectedto be lower for the multimode case because the picosecondspikes, which are unavoidably superimposed upon the 7-nsec Q-switched pulse, provide a larger effective gain for theRaman process.5 The observed increase of the SRS intensi-ty threshold with multimode laser pumping is consistentwith our other experimental evidence, which suggests thatpumping of the SRS by the laser is less efficient than pump-ing by SBS, which is suppressed because AXL > AXB for themultimode laser.
(b)
(C)
Center FSR FSR -Illumination O.435cm 1
SBS
EdgeIllumination
- elastic
Fig. 3. (a) The experimental configuration used to determine thewavelength shift of the green arcs. The aperture passes a portion ofthe green arc onto the Fabry-Perot interferometer (F-P). A greenfilter (not shown) blocks the red SRS from reaching the interferom-eter. The slit passes a strip of the Fabry-Perot rings (see the insetfor a front view) onto an intensified photodiode array. TypicalFabry-Perot interferometer outputs are shown for (b) focused cen-ter illumination of methanol droplets (a 45 ,m) and for (c) focusededge illumination. The unavoidable elastic scattering serves as aconvenient fiducial marker for the elastic wavelength and as a cali-brator of the interferometer linewidth. The free spectral range(FSR) is 0.435 cm-'.
Green Image(a)
LasersMMMMMMMMM1MMM-_
112 J. Opt. Soc. Am. B/Vol. 7, No. 1/January 1990
Perot rings passes through a horizontal slit [see Fig. 3(a)]and is imaged onto an intensified photodiode array.
Three orders of free spectral range (labeled FSR and cor-responding to 0.435 cm-') are simultaneously displayed inFigs. 3(b) and 3(c). Some of the elastic scattering from thefocal spot [fs in Fig. 2(a)] serves as a fiducial marker for theincident wavelength and enables us to determine the finesseof the interferometer, which gives rise to a measuredlinewidth of -0.02 cm-' (by neglecting AXL 0.006 cm-').
With focused center illumination of methanol droplets (a- 45 Am), Fig. 3(b) shows that the linewidth of the SBS peakis AXSBS - 0.04 cm-'. The measured AXSBS is a convolutionof the interferometer linewidth and the linewidth of theparticular MDR within the spontaneous Brillouin linewidth.The spontaneous Brillouin linewidth in a droplet is deter-mined by the inverse of the acoustic phonon lifetime (-0.025cm-') and by the angular spread of the k vector of the inputwave (kL + AkL) introduced by the curved illuminated face[see Fig. 1(a)].10
For methanol droplets with focused center illumination,the measured SBS Brillouin shift AWSBS = 0.16 cm-' [see Fig.3(b)]. The scattering angle 0 between the k vectors of theinput laser radiation (kL) and the SBS (kSBS) can be deducedfrom the measured AWSBS. At any 0, AWSBS is related toAwmax as follows25: AwSBS = Aaomax[sin (0/2)], where Awmx isthe maximum Brillouin shift at 0 = 1800. From the sponta-neous Brillouin measurements2 5 of methanol in an opticalcell at 0 = 1800, the measured Awmax = 0.185 cm-'. Thus,from the measured ACOSBS from droplets, we deduce that 0 -118°. From geometric-optics considerations,0 0 900 is ex-pected if kSBS is assumed to be tangent to the shadow facebecause SBS is always on a MDR [see Fig. 1(a)]. Further-more, based on geometric-optics considerations, the factthat the measured 0 1180 is reasonable because the inci-dent beam radius is -(1/3)a, and the spherical illuminatedface causes a spread in the k vector of the input radiation[see Fig. 1(a)].
To verify that 0 can be deduced from the measured AWSBS,the droplets are illuminated with focused edge illumination[see Fig. 1(b)]. The kSBS still has to be tangent to thedroplet rim in order that this wave be on a MDR that pro-vides the necessary optical feedback for SBS. In Fig. 3(c),the Brillouin shift in the SBS spectrum for methanol drop-lets with focused edge illumination is larger than with fo-cused center illumination, i.e., AWISBS = 0.18 cm'1 versusAWSBS = 0.16 cm-' [compare Figs. 3(b) and 3(c)]. The scat-tering angle deduced from AwSBS is 0 # 1530. From thegeometric-optics considerations shown in Fig. 1(b), therewill be a range of scattering angles, with the largest angle 0 -1400 between the kSBS and kL of the incident ray refracted atthe droplet interface. The fact that the measured AWtSBS <
Awmax implies that, even with focused edge illumination, noinput resonance is reached. If an input resonance werereached, the internal laser radiation would circumnavigatethe droplet equator and generate a counterpropagating SBSwave with 0 1800 [see Fig. 1(c)]. By varying the dropletradius, we observed AwSBS Awmax in the SRS spectrumfrom droplets only occasionally, implying that the inputresonance condition is difficult to find.2 6
In Fig. 3(c), the linewidth of the SBS peak observed withfocused edge illumination is AXSBS 0.06 cm-', which islarger than that observed with focused center illumination(AXSBS 0.04 cm-'). The wider AXSBS with focused edge
illumination is caused by the larger AkL associated with thisform of illumination [compare Figs. 1(a) and 1(b)].
Time ProfilesFigure 4 shows the experimental configuration for simulta-neously measuring the temporal profiles of the incident laserand of the SRS and SBS generated in the droplets. Thegreen and red images shown in Figs. 2(a) and 2(b) are rotated900 by the dove prism placed after the collection lens (la-beled Lens 1). After the dove prism are two color filters, oneon top of the other. The top half passes one green spot (fs)and one green arc located near the droplet shadow face. Thebottom half passes one red arc located near the droplet'silluminated face. The imaging lens (Lens 2) inverts thissplit color image, causing the green arc to be focused on thebottom half of the streak-camera slit and the red arc to befocused on the top part of the slit. Lens 2 is adjustedlaterally to position a portion of the green and red arcs ontothe vertical slit of the streak camera and to position thebright green dot [fs in Fig. 2(a)] outside the slit. An opticalfiber is used to channel a portion of the laser beam to the
Streak Camera
red (SRS)
green (SBS)
Lens 2
greene
red - Color Filters
Dove Prism
Lens 1OpticalFiber
Droplet
Laser Beam
Fig. 4. Schematic of the experimental configuration used to mea-sure simultaneously the time profiles of the laser pulse, one red SRSarc, and one green SBS arc. The dove prism rotates the imagesshown in Fig. 2 by 900. The green filter passes part of the greenimage (one arc and the fs dot near the droplet shadow face in Fig. 1),and the red filter passes part of the red image (one arc near thedroplet's illuminated face). Lens 2 focuses this split color imageonto the vertical streak-camera slit, which blocks most of the elasticradiation from the fs dot. An optical fiber channels a portion of thelaser beam onto the very top of the streak-camera slit.
Mhang et al.
Vol. 7, No. 1/January 1990/J. Opt. Soc. Am. B 113
very top of the streak-camera slit. The temporal profile ofthe input green laser radiation can, therefore, be simulta-neously measured with the time profiles of the red arc (SRS)and the green arc (SBS).
Figure 5 shows the temporal profiles of the input laser,SRS, and SBS, which are simultaneously measured for threeseparate laser shots, all with input intensity at -1 GW/cm 2.The three-dimensional curves shown in Fig. 5 display thetime on one horizontal axis, the position along the streakcamera slit on the vertical axis, and the relative intensitieson the third axis orthogonal to the time and position axes.
With focused center illumination of ethanol droplets (a45 m; input intensity, -1 GW/cm 2), the following can beobserved from the three time profiles: (1) the first SBSpulse occurs a few nanoseconds after the beginning of thelaser pulse, consistent with the fact that the Brillouin waveneeds to make many trips around the droplet rim and manytraversals through the high-intensity focal spot of the inputlaser before the spontaneous Brillouin noise is greatly ampli-fied; (2) the first SRS pulse is delayed relative to the firstSBS pulse, consistent with the optical cell results, indicatingthat the SRS gain is less than the SBS gain; (3) the SBS andSRS pulses are temporally correlated, implying that thedecay of the SBS is related to the growth of the SRS; (4) therelatively smooth portion of the SBS time profile closelyresembles the input laser time profile, indicating that theelastic radiation from the focal spot [fs in Fig. 2(a)] is nottotally blocked by the streak-camera slit and is detected bythe lower portion of the streak camera; and (5) the absence ofa relatively smooth portion of the SRS time profile indicatesthat all the green elastic scattering from the droplet isblocked by the red filter. Similar time profiles were alsoobserved for focused edge illumination of ethanol droplets.
The temporal correlation between the pulses of SRS andSBS from ethanol droplets can be illustrated even moreclearly by plotting the time profiles of the laser, SRS, andSBS without displaying the position information along thevertical streak-camera slit. Figure 6(a) replots the simulta-neously detected time profiles of the laser, SRS, and SBS forthe same data displayed in Fig. 5(b). Figures 6(b) and 6(c)are the time profiles for two other laser shots (input intensi-ty, 1 GW/cm 2). In the three curves shown in Fig. 6, thefirst SBS pulse always occurs earlier than the first SRSpulse, consistent with the fact that the Brillouin gain islarger than the Raman gain, and thus the SBS threshold isreached before the SRS threshold.
The observation that the first SBS pulse precedes the SRSpulse in the case of ethanol droplets is consistent with ourcurrent investigation of many liquids (including ethanol) ina 10-cm-long optical cell. Based on our optical cell results, itis not surprising that, when ethanol droplets are illuminatedby a single-mode laser beam, the first SBS peak precedes thefirst SRS peak (see Figs. 5 and 6). We noted that in anoptical cell, when the single-mode laser is used (AXL < AXB),the backward-traveling SBS threshold is reached before theSRS threshold. In fact, we also found that, when the cell isilluminated by higher input intensities, SRS is totally sup-pressed as a result of the reflection of the single-mode laserradiation by the intense acoustic wave that accompanies thedetected SBS. However, the opposite was observed fordroplets. On increasing the single-mode laser intensity tothe laser-induced breakdown threshold for ethanol droplets,we observed no instance in which the intense SBS prevented
(a)
.t_
n
0)
(b)
0)0
C
._
0
a-
(c)co
C
:tV°._
(C
0C
0.4-,
-
._CL
uC)
:t!
5 nsec Time
5 nsec
Input
SRS
SBS
Input
SRS
SBS
Time
Input
- SRS
- SBS
5 nsec TimeFig. 5. Three-dimensional plots of the time profiles of the laserbeam, SRS (red arc), and SBS (green arc) for focused center illumi-nation of ethanol droplets (a 45 jim). The single-mode laserintensity is 1 GW/cm 2 for all three laser shots [(a)-(c)]. Time isalong the horizontal axis, the position along the streak-camera slit isalong the vertical axis, and the relative intensity is displayed alongthe axis orthogonal to the time and position axes.
the appearance of SRS, as was observed in the case ofethanol in an optical cell.3 When the multimode laser isused (Xo > AIB) to illuminate an optical cell, we note thatthe converse is true; i.e., the SRS intensity threshold isreached, while no SBS is detected. Based on our optical cellresults, it is not surprising that, when ethanol droplets areirradiated by a multimode laser beam, SRS can be detectedwithout generating SBS.
What is surprising is that the SRS intensity threshold ofethnol droplets irradiated with the single-mode laser beam is-3 times lower than that with the multimode laser beam,while the SRS intensity threshold of ethanol in a cell cannotbe reached with a single-mode beam. In addition, it is
Mhang et al.
114 J. Opt. Soc. Am. B/Vol. 7, No. 1/January 1990
(a)
-A 5 nsec H- Time
(b)
(c)
SBS
-- A 5 nsec i- Time
Laser
SRS
SBS
- 5 nsec - TimeFig. 6. Similar to Fig. 5 except that the position along the streak-camera slit is not displayed. The three-dimensional curve shown inFig. 5(b) is replotted in (a). Time profiles from two different lasershots (at -1 GW/cm 2) are shown in (b) and (c). Note that the SRSand SBS pulses in all three curves are correlated; i.e., the decay ofthe first SBS pulse is followed by the growth of the first SRS pulse,and the regrowth of the (n + 1)th SBS pulse occurs after the decay ofthe nth SRS pulse.
surprising that the SRS and SBS peaks are temporally cor-related; i.e., the growth of SRS occurs when SBS decays, andthe growth of SBS occurs when SRS is at a minimum (seeFigs. 5 and 6 for five different laser shots at ;1 GW/cm 2).
The observed temporal correlation of the SBS and SRSpulses is strongly suggestive that SBS is pumping the SRS.In particular, we believe that the following sequence of
events is occurring in the droplets: (1) the first SBS pulse,which is pumped by the single-mode laser beam at the focalspot just with the droplet shadow face, is depleted on pump-ing the first SRS pulse; (2) the first SRS pulse, which ispumped by the first SBS pulse, is depleted on pumpinganother first-order Stokes SRS17, 23; (3) the second SBS pulseis pumped by the remaining portion of the single-mode laserpulse; (4) the second SRS pulse is pumped by the secondSBS pulse after the first SRS pulse is depleted; and (5) thesequence repeats for the subsequent SBS and SRS pulsesuntil the laser pulse is shut off and can no longer continue topump the (n + 1)th SBS pulse after the nth SRS pulse isdepleted.
The growth and decay of the SBS and SRS pulses can bephenomenologically described as follows:
(-a + aB)IEB12 = (AIEL12 - BERI2)IEB12,
(G- a + aR)IER12 = (CIEBI2
+ DIEL12 - EIE2Ri
2)!ER1
2,
(TI )IELI2 = -(FIEBI 2 + GIERI2)IELI2,
where a60 corresponds to the Brillouin or Raman radiation(with intensity IEBI2 or IERI2) traveling around the dropletrim and where 6z corresponds to the laser radiation (IELI2)traveling along the principal diameter. Coefficients A-Gare proportional to the imaginary part of X(
3) for the various
four-wave-mixing processes. The growth of the SBS pulse(IEBI2) results from amplification by the internal laser radia-tion of the spontaneous Brillouin scattering (AIEL12). Thedecay of the SBS pulse results from the intensity-dependentdepletion on pumping SRS (BIER12) and to a lesser extentfrom leakage from the droplet interface (aB). The growth ofthe SRS pulse (IERI2) results from amplification of the spon-taneous Raman scattering by the internal SBS (CIEBI2) andlaser radiation (DIELI2). At high intensities, the decay of theSRS pulse results predominantly from the intensity-depen-dent depletion on pumping another first-order Stokes SRS(EIE2R12) and to a lesser extent from leakage from the dropletinterface (aR). The depletion of SBS associated with pump-ing another first-order Stokes SBS is ruled out because high-er-order Stokes SBS has never been observed.1 0 The laserradiation (IELI2) traveling along the droplet principal diame-ter is depleted by the generation of SBS (FIEBI2) and SRS(GIER1
2).
If there were no temporal correlation between the SBSand SRS pulses, instead only a mere time delay between thefirst SBS pulse and the first SRS pulse, we would be able toconclude that the Brillouin gain is larger than the Ramangain in droplets (as in the case for the optical cell). Thetemporal correlation of the SBS and SRS pulses stronglysuggests that SRS within the droplets is pumped by theinternal radiation of the SBS and not by the internal radia-tion of the single-mode laser pulse.
CONCLUSIONS
The internal field strength and spatial distribution can begreatly altered, depending on whether the input resonance isexcited. In this experiment, a focused single-mode or multi-mode laser beam is directed along the principal diameter ofdroplets in order to prevent excitation of any input reso-
Laser
SRS
Mhang et al.
Vol. 7, No. 1/January 1990/J. Opt. Soc. Am. B 115
nance (regardless of x). When a single-mode laser is used,photographs of SBS and SRS from single ethanol dropletsreveal that the green SBS arcs and the red SRS arcs havesimilar spatial distributions within the droplet rim. AFabry-Perot interferometer was used to verify that the radi-ation emerging from the green arcs observed from methanoldroplets is Brillouin shifted by AWSBS from the incident laserfrequency. The scattering angle 0 between kL and kSBS isdeduced from the measured AWSBS. From the simulta-neously measured time profiles of the laser, SRS, and SBS,we have observed that the first pulse from ethanol dropletsoccurs before the first SRS pulse. Furthermore, we havefound that all the SRS and SBS pulses are temporally corre-lated; i.e., the maximum of the SRS pulse is preceded by theminimum of the SBS pulse, and the regrowth of the SBSpulse occurs after the SRS pulse is depleted.
We have also used the focused edge illumination configu-ration to irradiate the droplets. The a and the observed SBSlinewidth from droplets with focused edge illumination arelarger than those with focused center illumination, consis-tent with the geometric-optics picture shown in Figs. 1(a)and 1(b). Even with focused edge illumination of methanoland ethanol droplets, we rarely observed AWSBS = Awmax,implying that the input resonance condition shown in Fig.1(c) is satisfied only occasionally.
From these observations, we conclude that the followingprocesses can occur within droplets that are irradiated witha focused single-mode laser beam (AXL < AXB) directed alongthe droplet principal diameter: (1) the droplet's illuminat-ed face further focuses the incident beam to a focal regionjust within the droplet shadow face; (2) spontaneous Bril-louin scattering and spontaneous Raman scattering are cre-ated in this focal region; (3) spontaneous Brillouin scatter-ing, with kSBs tangent to the droplet interface ( 90°), hasan overall AXB (determined by the acoustic phonon lifetimeand the angular spread of kL + AkL), which is broad enoughto span one of the numerous MDR's needed to provide opti-cal feedback; (4) the SBS threshold is exceeded when theBrillouin gain at the focal region of the incident beam islarger than the round-trip loss around the droplet rim; (5)spontaneous Raman scattering (created by the internal laserradiation) has a linewidth (determined by the vibrationalmode lifetime) that is broad enough to span one or severalMDR's needed to provide optical feedback; (6) spontaneousRaman scattering is amplified more efficiently by the inter-nal intensity of SBS, which is distributed around the dropletrim, than by the localized incident laser intensity; (7) theSRS threshold is achieved when the round-trip gain provid-ed by the SBS exceeds the round-trip loss of the SRS aroundthe droplet circumference; (8) the first SBS pulse is depletedby pumping the first SRS pulse; (9) the first SRS pulse isdepleted by the parametric generation of the Raman signalat the second-order Stokes and by further amplification ofthis second-order Stokes'8 ; (10) the second SBS pulse needsto be repumped by the remaining single-mode laser pulse;(11) the second SRS pulse needs to be repumped by thesecond SBS pulse; and (12) for the third SBS and third SRSpulses, the previous sequences are repeated.
When a multimode laser (AXL > AXB) is used, the incidentlaser beam provides more gain for SRS than for SBS, and theSRS is directly pumped by the internal intensity of the
multimode laser beam. By switching the laser from multi-mode to single-mode operation, the input intensity neededto achieve the SRS threshold in ethanol droplets is -3 timeslower. This decrease implies that the internal SBS is moreefficient in pumping SRS than the highly focused incidentbeam (with narrow or wide AXL) because of the greater spa-tial overlap between the SBS and SRS waves, which are bothon MDR's of a sphere.
ACKNOWLEDGMENTS
We gratefully acknowledge helpful discussions with ShirishChitanvis and the partial support of this research by the U.S.Air Force Office of Scientific Research (grant 88-0100).
The authors are also with the Yale University Center forLaser Diagnostics.
REFERENCES
1. M. Maier, W. Kaiser, and J. A. Giordmaine, Phys. Rev. Lett. 17,1275 (1966).
2. M. Maier, W. Kaiser, and J. A. Giordmaine, Phys. Rev. 177,580(1968).
3. D. Pohl, M. Maier, and W. Kaiser, Phys. Rev. Lett. 20, 366(1968).
4. M. Trippenbach, K. Rzazewski, and M. G. Raymer, J. Opt. Soc.Am. A 1, 671 (1984).
5. N. Bloembergen and Y. R. Shen, Phys. Rev. Lett. 13,720 (1964).6. H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, Opt.
Lett. 9, 499 (1984).7. H.-B. Lin, A. L. Huston, B. J. Justus, and A. J. Campillo, Opt.
Lett. 11, 614 (1986).8. J. B. Snow, S.-X. Qian, and R. K. Chang, Opt. Lett. 10,37 (1985).9. R. K. Chang, S.-X. Qian, and J. H. Eickmans, in Methods of
Laser Spectroscopy, Y. Prior, A. Ben-Reuven, and M. Rosen-bluh, eds. (Plenum, New York, 1986), p. 249.
10. J.-Z. Zhang and R. K. Chang, J. Opt. Soc. Am. B 6,151 (1989).11. D. S. Benincasa, P. W. Barber, J.-Z. Zhang, W.-F. Hsieh, and R.
K. Chang, Appl. Opt. 26, 1348 (1987).12. P. Chylek, J. D. Pendleton, and R. G. Pinnick, Appl. Opt. 24,
3941 (1985).13. S. C. Hill and R. E. Benner, J. Opt. Soc. Am. B 3, 1509 (1985).14. S. C. Hill and R. E. Benner, in Optical Effects Associated with
Small Particles, P. W. Barber and R. K. Chang, eds. (WorldScientific, Singapore, 1988), p. 3.
15. M. Golombok and D. B. Pye, Chem. Phys. Lett. 151, 161 (1988).16. W.-F. Hsieh, H.-M. Tzeng, and R. K. Chang, in Special Issue of
the Annual Report of the Institute of Physics, Academia Sin-ica (Taiwan), (Academia Sinica, Taiwan, 1986), Vol. 16, p. 1.
17. S.-X. Qian and R. K. Chang, Phys. Rev. Lett. 56, 926 (1986).18. W.-F. Hsieh, J.-B. Zheng, and R. K. Chang, Opt. Lett. 13, 497
(1988).19. R. G. Pinnick, A. Biswas, P. Chylek, R. L. Armstrong, H. Latifi,
E. Creegan, V. Srivastava, M. Jarzembski, and G. Fernandez,Opt. Lett. 13,494 (1988).
20. B. Maheu, G. Brehan, and G. Bouesbet, Appl. Opt. 26,23 (1987).21. J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys.
64, 1632 (1988).22. T. Baer, Opt. Lett. 12, 392 (1987).23. J.-Z. Zhang, D. H. Leach, and R. K. Chang, Opt. Lett. 13, 270
(1988).24. R. K. Chang, D. H. Leach, and J.-Z. Zhang, in Proceedings of the
U.S.-Mexico Workshop on Electrodynamics of Interfaces andComposite Systems, Taxco, Mexico, August 10-14,1987, R. G.Barrera and W. L. Mochan, eds. (World Scientific, Singapore,1988), p. 373.
25. P. A. Fleury and R. Y. Chiao, J. Acoust. Soc. Am. 39,751 (1966).26. S. M. Chitanvis and C. D. Cantrell, J. Opt. Soc. Am. B 6, 1326
