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Optics Letters

Phase-modulation-broadened line shapes from micrometer-size CS_2 droplets

Shixiong Qian, Richard K. Chang

Published Jun 1, 1986• 20 citations
Publisher

Abstract

Asymmetrically broadened line shapes observed in the stimulated Raman and elastically scattered spectra from a CS(2) droplet are manifestations of phase modulation by means of the intensity-dependent index of refraction. Unique features of the droplet morphology in enhancing the internal fields at the input and Stokes wavelengths and in prolonging the decay time of the waves within the droplet, which acts as an optical cavity, are discussed.

DOI
10.1364/ol.11.000371

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Asymmetrically broadened line shapes observed in the stimulated Raman and elastically scattered spectra from a CS(2) droplet are manifestations of phase modulation by means of the intensity-dependent index of refraction. Unique features of the droplet morphology in enhancing the internal fields at the input and Stokes wavelengths and in prolonging the decay time of the waves within the droplet, which acts as an optical cavity, are discussed.
The regular structure in frequency broadening spectrum of the self-trapped laser and Raman radiations is produced by the phase-modulation of light waves propagating in the filament with intensity-dependent index of refraction. A quantum-mechanical calculation of double quantum transition in a three-level system is shown to explain the process of self-modulation and the production of picosecond pulses in the Raman process. Coherent coupling of the laser and the Stokes waves produces mutual modulation of large amplitude, if the optical field is strong and the vibrational relaxation time is long. Numerical evaluation for CS2 gives a modulation frequency of about 1011 Hz, when an optical power of 10 kW is trapped in a filament of 2 µm radius. Besides, the effect of self-modulation on the spatial distribution of anti-Stokes emission along the filament is discussed and shown to agree with the experimental results observed by Stoicheff and his co-workers.
Stimulated Brillouin scattering in a micrometer-sized liquid droplet is treated theoretically using recently developed techniques, with emphasis on the doubly resonant case, in which the frequencies of both the laser field and the scattered Brillouin field fall within a morphology-dependent resonance, leading to input and output enhancement. An important difference from a bulk medium is the replacement of the selection rules based on momentum conservation by those based on angular momentum conservation, with the latter most conveniently expressed through the spherical wave modes. Special attention is paid to the eigenvalue equation defining the gains and Brillouin shifts, in particular to the difference between small and large droplets. For large droplets, and for given angular momenta of the laser field and the scattered field, there is only one allowed shift with a positive gain. Numerical results for gain and threshold are shown for a droplet of size parameter about 30, and a simple approximate analytic formula for the gain is presented.
Continuous-wave stimulated Raman scattering was observed in 11-13-microm-diameter benzene and toluene microdroplets at pump intensities as low as 8 and 24 kW/cm(2), respectively. Low thresholds were achieved by exploiting simultaneous pump and Stokes wave resonance in the droplets and Raman gains that were cavity QED enhanced ~50 times with respect to bulk liquid values. Based on a photon-state conservation argument, the cavity gain enhancement factor may be approximated by the ratio of the spectral spacing between resonant modes of the same order to that of the homogeneous Raman linewidth. This relation appears to be consistent with the relative experimental behavior of benzene, ethanol, and toluene.
A variety of stimulated nonlinear optical processes are observed under relatively low intensity cw excitation in droplet spherical microcavities. These include stimulated Raman and Rayleigh-wing scattering as well as four-wave parametric oscillation. The low thresholds for these stimulated processes are accounted for by all waves being in resonance with high-QQQ droplet modes and by the existence of a significant cavity QED enhancement (> 100 times) in the nonlinear gain coefficients.
A Stokes shifted superbroadening stimulated scattering has been studied in a CS2{\mathrm{CS}}_{2}CS2​ liquid-core hollow fiber system with a long gain length (2.5 m) by using \ensuremath{\approxeq}10-ns laser pulses with a pump intensity range of (106{10}^{6}106--5\ifmmode\times\else\texttimes\fi{}108{10}^{8}108 W/cm2{\mathrm{cm}}^{2}cm2). The salient features of this stimulated scattering are that the spectral broadening range is very large (\ensuremath{\ge}700 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) and no detectable shift of the spectral maximum or periodical modulation structure is observed. In order to interpret our experimental results, various possible mechanisms and processes are discussed. A model based on stimulated Kerr scattering of anisotropic molecules in liquid is suggested to explain the observation. This model assumes a single-step reorientation of anisotropic molecules induced by an intense optical field.