Photon lifetime within a droplet: temporal determination ofelastic and stimulated Raman scattering
Jian-Zhi Zhang, David H. Leach, and Richard K. Chang
Section of Applied Physics and Center for Laser Diagnostics, Yale University, New Haven, Connecticut 06520
Received October 26, 1987; accepted January 20, 1988
Time profiles of the elastically scattered and stimulated Raman scattered radiation from single ethanol dropletsilluminated by 100-psec mode-locked pulses were measured with a streak camera. The Q factor of the droplet,which acts as an optical cavity, was deduced from the decay time of the internally trapped radiation. Based on theintensity dependence of time profiles, it is also deduced that the photon lifetime is limited by the depletion of the in-ternal intensity in generating nonlinear-optical radiation.
Both experiments and Lorenz-Mie theory' indicatethat a single transparent droplet with a large size pa-rameter (X = 27ra/X, where a is the droplet radius andX is the wavelength) exhibits peaks in the various mea-sured spectra and calculated quantities when X of theincident radiation or of the internally generated wave-length-shifted radiation satisfies the morphology-de-pendent resonances (MDR's) of a sphere. Lasing andstimulated Raman scattering (SRS) experiments withsingle droplets2 -5 suggest that at a specific X corre-sponding to a MDR, the droplet can be envisioned asan optical cavity that provides the necessary feedbackfor the amplified fluorescence and spontaneous Ra-man radiation traveling within the droplet rim.
The Q factor of a droplet cavity depends on themode number n and the mode order I of the MDR thatexists at Xnj. The Q factors of various MDR's can becalculated from real and imaginary parts of the polesof the far-field scattering or internal-field coeffi-cients, 6 i.e., Q = Re(Xn,1)/Im(Xn,1), which can be >1020.From the measured optical levitation,7 spontaneousRaman,8 lasing,2 and SRS4 spectra, the largest Q factorcan be deduced from the narrowest MDR peak locatedat X with an intensity half-width AX, i.e., Q = V/AX -105 in the visible range, since X - 2 X 104 cm-' and AX- 0.1 cm'1, which is generally limited by the spectrom-eter or tunable-dye-laser resolution. An estimate of Q_ 105 was also deduced from the enhancement of ener-gy transfer between two different types of dye mole-cule embedded in a droplet. 9
We present results on the radiation lifetime of theelastically scattered radiation trapped within a liquiddroplet when the pulsed incident radiation with fre-quency co is coupled with a MDR located within thelinewidth of the incident radiation. Even after theincident pulse is shut off, the internal radiation shouldcontinue circulating within the ethanol droplet andshould decay with a lifetime rela that is directly relatedto the droplet-cavity Q factor, i.e., Q = Tela X coo. Fromthe growth of the SRS radiation, we deduce that theRaman gain is provided by the internally circulatingradiation at wo. From the decay time of the SRSradiation (rSRS) with frequency w,, we confirm the
premise that the droplet provides feedback by partic-ular MDR's within a broad spontaneous Ramanlinewidth.
A linear stream of monodispersed ethanol dropletswith a - 45 /im was produced by a Berglund-Liugenerator at a rate of 50 kHz. The incident radiationfrom a Q-switched mode-locked Nd:YAG laser has thefollowing characteristics: X0 = 0.5324 im, each pulseis -100 psec with an estimated Fourier-limitedlinewidth AX0 = 0.3 cm-', it is mode locked at 75.6MHz, the Q-switched pulse duration is -230 nsec andthere is a train of 17 mode-locked pulses within eachQ-switched burst, and the average energy is -200 IAJper Q-switched burst. The Q-switched pulses of 1kHz were synchronized with the oscillator driving thedroplet generator.
Figure 1 shows that the collection optics, aligned at90° relative to the incident laser direction, contained acolor filter to pass either the elastic scattering at X0 orthe SRS radiation at XSRS and imaged a portion of thedroplet (with 1oX magnification) onto the lower partof the streak-camera entrance slit. The streak camera(Hadland Photonics Imacon 500) with a time resolu-tion of 2 psec was operated in a synchroscan moderelative to the laser mode-locker signal. An opticalfiber channeled some of the incident radiation ontothe upper part of the streak-camera entrance slit.
To increase the coupling of the incident radiationwith a MDR, the incident beam was tightly focused toa spot diameter of -15 gm and irradiated along thedroplet equator at the W or E edge [see top view inFigs. 1(a) and 1(b)]. When the W edge is illuminatedand viewed at 90° to the laser beam, a bright spotappears at spot A of the droplet, corresponding totransmitted rays that have undergone two refractionsat the droplet-air interface [see Figs. 1(a) and 1(c)].When the E edge is illuminated, a bright spot appearsbetween edges A and B, corresponding to rays thathave been specularly reflected by a tangent plane onthe droplet illuminated face [see Figs. 1(b) and 1(d)].
These two bright spots dominated the streak-cam-era output, and their temporal profiles were identicalto that of the input laser, i.e., -100 psec (see the input
Fig. 1. Schematic of the experimental configuration. Therelative directions of the laser and the collection optics withrespect to the droplet are shown in the top portion. In thelower portion, the top view shows the illumination of thedroplets by the focused beam in (a) and (b). At X0, thebright spots due to the refracted and reflected rays are de-noted in the side view by larger solid dots in (c) and (d). Themuch dimmer radiation from the edges is denoted by smalleropen dots in (c) and (d). At XSRS, the red spots at edges Aand B appeared equally bright [see the smaller solid dots inside views (e) and (f)]. The position of the streak camera slitrelative to the droplet is shown in (c)-(f).
curve in Fig. 2). The time scale of the streak camerawas calibrated by detecting the transmitted signalthrough a Fabry-Perot interferometer with a d = 4.5cm mirror spacing (see Fig. 2).
To avoid the bright spots, the collection optics im-aged the dimmer part of the droplet onto the streak-camera slit. Figure 1(c) shows that, with illuminationat the W edge, elastic radiation from the B edge isimaged onto the streak-camera slit. Figure 1(d)shows the case for edge A with edge E illumination.The elastic radiation from these much dimmer edges ismainly from the leakage of the internally trapped radi-ation and is, therefore, related to the lifetime of theinternally trapped radiation.
Figure 2 shows the time profile of the elastic scatter-ing measured from the dim A edge with illumination atthe E edge [see Figs. 1(b) and 1(d)]. The intensitymaximum is reached at the end of the input pulse,indicating that the internal field continues to growduring the entire input pulse. After the input pulse isshut off, the elastic scattering starts to decay with Tela
= 130 psec or Q - 5 X 105. Similar results wereobtained for the elastic scattering from the dim B edgewith illumination near the W edge [see Figs. 1(a) and1(c)]. Based on the Lorenz-Mie calculation with X =470 and m = 1.36 (where m is the refractive index ofethanol), a MDR with n = 487 and 1 = 23 has Q = 6 X105. However, theory predicts10 that MDR's will beseparated by -0.5 cm-' and will have much higher Qvalues, e.g., Q = 7 X 1022 for n = 534 and 1 = 13.Within the 0.3-cm'l-input linewidth, we do not knowthe n and 1 values of the MDR that is excited.
The SRS signal from ethanol droplets of this samesize was passed through a red filter in the collectionoptics. With irradiation by a tightly focused beamlocalized at edge W or edge E, the SRS radiation isnoted to be confined around the equator. The twoSRS red spots at XSRS were of nearly equal intensity atthe A and B edges when viewed at 90° to the laser-beam direction [see Figs. 1(e) and 1(f)] and were muchbrighter than the two dim A and B edges radiating atX0. No SRS was observed when the focused beam wasdirected along the center of the droplet (i.e., at point Bon the circumference in Fig. 1) since the MDR withinthe input pulse is less efficiently coupled in this config-uration.
The time profile of the first-order SRS from ethanoldroplets (with a Raman shift of 2940 cm-1) is alsoshown in Fig. 2. The maximum intensity is reachedslightly after the input pulse is shut off, and the inten-sity decays with TSRS = 210 psec, corresponding to Q =6 X 105. The time profile of the second-order SRS(with a Raman shift equal to 2 X 2940 cm-') is also
I I I.
0 300 600 900 1200
TIME DELAY (psec)
Fig. 2. The time profiles of the following signals were de-tected by the streak camera: (1) transmission through aFabry-Perot interferometer; (2) the input laser radiationchanneled to the streak camera by an optical fiber; (3) elasticscattering from the dimmer spot shown in Fig. 1(d); (4) first-order SRS from edge A shown in Fig. 1(f); and (5) second-order SRS from edge A shown in Fig. 1(f).
272 OPTICS LETTERS / Vol. 13, No. 4 / April 1988
/ ~~~~~~~~~I max
0.651 max
0.581,ma
0.44 max
0.30 max
0 300 600 900 1200
TIME DELAY (psec)
Fig.3. Time profiles of the input and the first-order SRS asa function of input intensity. With 0U3Imax, the SRS signaldrifts toward the right-hand edge of the streak camera wherethe sensitivity is low, and the intensity droop is, therefore, anartifact of this measurement. With 0.44Imax and 0.3lmax, theSRS decay time is longer than the 6.5-nsec streak-cameraretrace, and thus the baselines rise at times before and afterthe 0-psec time delay.
shown in Fig. 2. Its maximum intensity is reachedeven later than that of the first-order SRS, consistentwith the previous observation that the multiorder SRSis pumped by the internal intensity of the preceding-order SRS.11 The decay time for the second-orderSRS is longer, T SRS = 400 psec, corresponding to Q = 1X 106.
The input intensity dependence of the SRS rise anddecay times is shown in Fig. 3. At the maximum inputintensity (Imax 100 GW/cm 2 for the largest of the 17mode-locked pulses), the temporal profile of the first-order SRS shown in Fig. 3 is shorter than that shown inFig. 2, which was measured at slightly lower intensity.Figure 3 shows that, as the intensity is decreased to0.3lmax, the rise time and decay time for the SRS radia-tion become longer. The rise time with 0. 441max i5 50long that the SRS intensity reaches a maximum after1000 psec. Furthermore, the decay times with 0.3Imaxand 0.44Imax are so long that, during the 6.5-nsec re-trace of the streak camera (in the synchroscan mode),SRS is still present, and there is, therefore, an appar-ent rise in the baseline for time delays of <0 psec inFig. 3. For 0 3 1max, TSRS > 5 nsec, which translates toQ > 2 X 107. Even at 0.3lmax, the generation of sec-ond- and higher-order SRS is possible, and the deple-tion of the SRS internal intensity can decrease TSRS-The results for higher intensities can be summarizedas follows: for 0.SSImax, TSRS = 1500 psec (Q = 5 X106); for 0.65Imax, TSRS = 600 psec (Q = 2 X 106); and forImax, T SRS = 130 psec (Q = 5 X 105).
From the intensity dependence of the SRS timeprofiles shown in Fig. 3, conclusions can be drawn
about the lifetime of the internally trapped radiationat X0. The Tela is limited either by the leakage rate ofthe particular MDR (TMDR) or by the depletion rate ofthe nonlinear Raman process (TNL) that can convertthe radiation at Xo to XSRS, i.e., 1/Tela = 1/TMDR + 1/TNL-As long as internally trapped radiation at X0 is avail-able to provide the pumping, the amplified spontane-ous Raman emission can continue to increase. Thefact that the time delay for the SRS to reach themaximum intensity lessens with increased input in-tensity suggests that the internally trapped radiationat X0 is depleted by the generation of SRS.
Similarly, the radiation lifetime of the first-orderSRS within the droplet is limited either by the leakageassociated with MDR's within the spontaneous Ra-man linewidth10 or by the depletion of the SRS radia-tion due to the generation of the second-order Stokes.The progressively shorter rSRS as the input intensity isincreased implies that the internally trapped radiationat XSRS is depleted by the generation of the second-order SRS rather than by the leakage associated withMDR's. The TSRS for the second-order SRS (see Fig.2) could also be limited by intensity depletion in gen-erating the third-order SRS.
At input intensities below the SRS threshold, thedroplet-cavity lifetime should be much longer thanour measurements indicate. Ultimately, Tela shouldbe limited by the natural leakage of a particular MDRwith the highest Q, by the inhomogeneity in the liquidrefractive index, by shape distortions due to surround-ing air traveling at a nonzero velocity.'2
We thank S. C. Hill of Clarkson University for theQ-factor calculations and gratefully acknowledge thepartial support of this research by the U.S. Air ForceOffice of Scientific Research (contract no. F49620-85-K-0002) and the U.S. Army Research Office (contractno. DAAL03-87-0076).
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