Coherent Raman mixing and coherent anti-Stokes Ramanscattering from individual micrometer-size droplets
Shi-Xiong Qian,* Judith B. Snow, and Richard K. Chang
Section of Applied Physics and Center for Laser Diagnostics, Yale University, New Haven, Connecticut 06520
Received May 20, 1985; accepted July 9, 1985
The coherent Raman mixing spectra from individual micrometer-sized droplets of ethanol and of water consist ofregularly spaced peaks that correspond to the morphology-dependent resonances of a spherical droplet. In con-trast, the coherent anti-Stokes Raman scattering spectra from droplets exhibit no morphology-dependent peaks.Both results are explained by the spatial overlap of thematching conditions associated with the droplet.
Laser emission and stimulated Raman scattering(SRS) from individual monodisperse liquid droplets(with radii a in the 20-40-pum range) flowing in a linearstream have recently been reported. 1' 2 These two ob-servations are associated with the morphology-depen-dent resonances (MDR's) of a sphere.3 At specificvalues of the parameter x (x = 27ra/X, where X is theoptical wavelength and a is the radius), the droplet in-terface can significantly enhance the internal field atspecific incident wavelengths (input resonance)4' 5
and/or can efficiently provide optical feedback for theinternally generated wave at specific fluorescence orRaman-shifted wavelengths (output resonance).1' 2
Calculations have been reported that pertain to co-herent Raman scattering in spheres, assuming thatperfect phase matching is maintained throughout thesphere and that x values do not correspond to anyMDR's (i.e., are nonresonant). 6' 7 Experimental ob-servation of coherent anti-Stokes Raman spectroscopy(CARS) from H2 gas contained within a glass micro-balloon has previously been reported, although the ef-fects of the spherical interface were not discussed.8
We report the first experimental observation to ourknowledge of four-wave mixing processes [CARS andcoherent Raman mixing (CRM)] from individualdroplets. Our CRM, CARS, and SRS results havedemonstrated that both chemical speciation and sizedetermination of individual micrometer-sized dropletsare possible.
Highly monodisperse droplets (1 part in 104) weregenerated by a modified Berglund-Liu vibrating orificeaerosol generator. For the CRM experiment, a Q-switched Nd:YAG laser provided the incident radiationat COIR (1064 nm) and at c, (532 nm). For the broad-band CARS experiment, a dye laser provided thebroadband radiation ("2) centered at the Stokeswavelength (w, - w1,), where xv is the molecular vi-brational frequency. The detection system consistedof a computer-controlled silicon-intensified-target(SIT) vidicon camera/spectrograph system.
In order further to clarify the connection between
enhanced internal field distributions and by the phase-
CRM and SRS, using the present notation one of thefour standard small-amplitude growth equations forplane waves incident upon an extended medium can bewritten as follows9 :
a E( 1 -c,) < XXME*(WIR)E(WIR - cv)E(Wi)eiAkZ
+ x jsIE(wj)|2E(wi - w)), (1)
where X3VM and X3s are the third-order susceptibilitiesand Ak is the wave-vector mismatch among the fourwaves. When the electric fields of the input wave at WIR
and of the resultant SRS wave at (WIR - co,) are intense,then by the four-wave mixing (FWN) process additionalgain is coherently added to the SRS. Optimum gainfrom the FWM term occurs when Ak = 0. CRM is alsocommonly referred to as biharmonic pumping.9
The CRM spectrum at (w, - w,) from H20, shownin Fig. 1(a), consists of spectrally narrow peaks that aresimilar to the SRS spectrum at (co, - w) from slightlylarger droplets shown in Fig. 1(b). The SRS has beenpreviously explained 2 as a consequence of the wave-length-selective optical feedback provided by the liq-uid-air interface at MDR's for specific wavelengthswithin the bandwidth of the spontaneous Ramanspectrum of H20 [see Fig. 1(d) for H2 0 in a 1-cm opticalcell]. The radius of the droplet can be accurately de-termined from the wavelength spacing of these SRS andCRM peaks.10 The broadband CARS spectrum at (2w,- (° 2 )) from H20 droplets is shown in Fig. 1(c). Thefrequency range of the broadband CARS spectrum islimited by the spectral bandwidth of the broadbanddye-laser emission. The small irregular peaks super-imposed upon the much smoother line shape cannot beattributed to MDR's but are associated with the spectralfluctuations in the broadband dye-laser emission.Similar CRM and CARS results were observed formonodisperse ethanol droplets.
To demonstrate that the CRM process effectivelylowers the SRS threshold, we determined the intensitydependence of one of the CRM peaks on I(col) at severalI(WIR) values for monodisperse ethanol droplets with
Fig. 1. Spectra from monodisperse H2o droplets with-30-sam radius undergoing (a) CRM, (b) SRS, and (c) CARS.The spontaneous Raman spectrum of H20 in a 1-cm opticalcell is shown in (d). The Raman-shift region corresponds tothe 0-H stretching mode of water.
a 30 gm (see Fig. 2). Thresholds for coherentemission at (c 1 - wv) are lowered when I(WIR) is in-creased from 0 to 580 MW/cm 2 , indicating that addi-tional Raman gain is provided by the FWM process [seeEq. (1)]. The CRM signal becomes the SRS signalwhen I(WIR) = 0-
We investigated the dependence of CRM and CARSintensities from both H20 and ethanol droplets on therelative angle 4' between the two input beams, i.e., be-tween I(c 1 ) and I(WIR) for CRM and between 1(wj) andI((W 2 )) for CARS. For the 1-cm optical cell case, theCARS intensity decreased symmetrically and steeplyas 4' was detuned by as little as +0.20 from lpm (4 ' pm= 2.30 for H2 0 and 4' pm = 3.40 for ethanol). In con-trast, for the droplet case, the CARS intensity decreasedbroadly as 4' was detuned by as much as +20 from 4 '
pm.
Furthermore, the detuning curve was asymmetric, i.e.,the CARS intensity for the collinear configuration (4'= 0) is higher than the intensity at 4b = 2(bpm.
The spectral features and intensity of CRM and SRSwere noted to be sensitive to varying the droplet radiusto satisfy the input resonance at w1. However, theCRM emission was insensitive to the input resonanceat wIR. Surprisingly, the CARS intensity was inde-pendent of radius as it was continuously varied over theinput MDR's at co1. The input resonance is alwayssatisfied for the input Stokes radiation since thebroadband (wO2 ) spans several MDR's for a fixed radius.Moreover, the output resonance condition is alwayssatisfied since the broadband CARS spectrum in the(2col - (wO2 )) range also always spans several MDR's.
We believe that these observations can be explainedqualitatively by considering the incident wave distri-bution within the droplets and the Stokes growth ex-pression shown in Eq. (1). At a MDR, one of the in-ternal field coefficients becomes large, resulting ingreatly enhanced fields near the spherical interface3-5[schematically shown in Fig. 3(a)]. All the other in-ternal field coefficients remain small and give rise to adistribution that can be essentially described by geo-metric optics [shown in Fig. 3(b)], i.e., focusing of theincident wave near the forward portion of thesphere.4 ' 5
When E(COIR) = 0, optical gain for the SRS wave at(G1 - co) is provided by the last term in Eq. (1). Atspecific wavelengths corresponding to output reso-nances within the (c1 - wx) bandwidth, increased op-tical feedback occurs, resulting in spectrally narrow SRSpeaks with regular wavelength spacing within the (X1- co,) bandwidth. When E(GIR) is intense, the expo-nential growth of the SRS wave at (WIR - wV) can pro-vide additional gain to the SRS wave at (w1 - w,)through the FWM process [see the second term of Eq.(1)]. This additional gain is optimized when Ak = 0,i.e., for 4' - 4'pm* Because the MDR's are narrow andwidely spaced, tuning the droplet radius so that inputresonance is satisfied for both waves at WIR and co1 ishighly improbable. Figure 2 shows the results for val-ues of COIR and co1 that do not satisfy the input resonancecondition. The optimum angle between the COIR and co,
103
a,CE
Lia,1-
I--zI-0.D.0cc
'-4
12
10
100 200I (w1 ) MW/cm2
300
Fig. 2. The intensity dependence of a CRM peak as a func-tion of 1(w1) at different values of I(WIR) for an ethanol dropletwith - 4 2 -sm radius. The dominant CRM peaks are withinthe spontaneous Raman profile associated with the C-Hstretching mode (2930 cm'1) of ethanol. The CRM processbecomes the SRS process when I(WIR) = 0.
Fig. 3. Schematic representation of the internal field dis-tribution in a plane containing the propagation direction. (a)The summation of nonresonant terms and the internal fieldcan be approximated by geometric-optics ray tracing of aplane wave (k). A spread in propagation vector occurs withinthe medium (km + A km). (b) The resonant term coefficientgives rise to a symmetric field distribution confined near thecircumference.
waves is determined primarily by the spatial overlapamong the three waves [E*(wOIR)E(wIR - w,)E(coj]rather than by the usual phase-matching condition.The large gain of the (WIR - W,) Stokes wave (GIR) di-minishes the importance of the wave-vector mismatch(Ak). As long as at least one of the two input waves,E(WIR) or E(w1 ), is not in resonance, the additional gainto the SRS wave at (co, - o) is localized in the focalregion.
Phase matching and spatial overlap between the twoinput waves are important for the CARS process. Ini-tially, we expected the CARS signal to be largest whenE(w1 ) and selected portions of E((wO2)) were enhancedat the MDR's for these two waves. However, the eiAkzterm is vanishingly small for path integrals around thecircumference. In contrast, when 4' 'bpm, the eiAkzterm is significant for path integrals along the propa-gation direction, and the spatial overlap of the twononresonant localized fields is still large, although notso large as in the collinear geometry, i.e., 4' = 0. Theinsensitivity of the experimental CARS results to inputMDR's suggests that the four-wave parametric processfavors the nonresonant terms over the resonantterms.
The considerably broadened phase-matching curveobserved for CARS is consistent with the fact that theinteraction length is localized in a small region near theforward portion of the droplet as well as with the factthat the spherical interface induces a spread in km afterthe plane wave enters the droplet. A spread in km byan amount Aks causes a spread in the phase-matching
angle, i.e., 4'pm for extended medium becomes 4 'pm +A4'pm for a droplet. The collinear geometry results inthe largest triple product overlap for E2 (wi)E*(( A2)),since the two input waves are both localized [see Fig.3(b)]. The asymmetry in the phase-matching curve isconsistent with the fact that this triple product favorsthe collinear configuration (4' = 0) while the phase-matching condition favors 4' = Ppm* At 4' = 24bpm, theoverlap of the fields is considerably less than that for 4'= 0; hence the asymmetrical curve as a function of 4'.
In principle, the output resonances should slightlyincrease the broadband CARS signal at specific wave-lengths within the anti-Stokes bandwidth (2w1 - (O2)).Small peaks (with regular wavelength spacing) super-imposed upon the much smoother broadband CARSspectrum were not observed [see Fig. 1(c)]. The ab-sence of these peaks implies a poor coupling efficiencybetween the coherently generated phase-matched wavepropagating along the droplet diameter and the MDR'sconfined near the circumference.
In conclusion, for individual liquid droplets under-going coherent nonlinear processes that exhibitthreshold behavior (e.g., lasing and SRS), the existenceof MDR's increases the internal fields of the input waveand provides optical feedback. For nonlinear para-metric processes (e.g., CARS), our results indicate thatthe phase-matching requirement is still important eventhough the phase-matching angle is broadened by thespherical interface.
We gratefully acknowledge the partial support of thisresearch by the U.S. Army Research Office (contract no.DAAG29-85-K-0063), the U.S. Air Force Office of Sci-entific Research (contract no. F49620-85-K-0002), andthe Donors of the Petroleum Research Fund, adminis-tered by the American Chemical Society.
* On leave from the Department of Physics, FudanUniversity, Shanghai, China.
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