Heuristic model for the growth and coupling of nonlinear processes in droplets

Standard one-dimensional nonlinear-wave equations are modified to accommodate the growth and coupling of nonlinear waves in droplets. The propagation direction of the nonlinear waves along the length of an optical cell is changed so that it is along the droplet rim. The model includes radiation losses because of nonzero absorption, leakage from the droplet, and depletion in generating other nonlinear waves. For multimode-laser input, the growth and decay of the first- through fourth-order Stokes stimulated Raman scattering (SRS) are calculated as a function of the phase matching of the four-wave mixing process and the model-dependent Raman gain coefficient. The Raman gain coefficient determines the delay time of the first-order SRS, while the phase matching determines the correlated temporal profiles of the multiorder SRS. Both the Raman gain and the phase matching are found to be enhanced in the droplet. The spatial distribution of the internal input-laser intensity is calculated by using the Lorenz–Mie formalism. The temporal profile of the input-laser intensity used in the calculations is identical to the experimentally observed laser time profile. The delay time and the correlated growth and decay of nonlinear waves resulting from the numerical simulation compare favorably with those of the experimental observations. Similar calculations are made for single-mode-laser input for which the stimulated Brillouin scattering (SBS) achieves its threshold before the SRS does and subsequently pumps the SRS.

[1]  J. Stone,et al.  Measurements of the Absorption of Light in Low-Loss Liquids , 1972 .

[2]  Yufen Li,et al.  Comparison between the temporal characteristics of picosecond SRS from the cell and SRO from the droplet , 1990 .

[3]  H. M. Lai,et al.  Dielectric microspheres as optical cavities: Einstein A and B coefficients and level shift , 1987 .

[4]  Richard K. Chang,et al.  Pumping of stimulated Raman scattering by stimulated Brillouin scattering within a single liquid droplet: input laser linewidth effects , 1990 .

[5]  Z. Kam,et al.  Absorption and Scattering of Light by Small Particles , 1998 .

[6]  H. Haus.  Waves and fields in optoelectronics , 1983 .

[7]  R. G. Pinnick,et al.  Stimulated Raman scattering in micrometer-sized droplets: time-resolved measurements. , 1988, Optics letters.

[8]  Steven C. Hill,et al.  Light scattering by particles , 1990 .

[9]  R. Chang,et al.  Photon lifetime within a droplet: temporal determination of elastic and stimulated Raman scattering. , 1988, Optics letters.

[10]  Robert E. Benner,et al.  Morphology-Dependent Resonances , 1988 .

[11]  Chew.  Radiation and lifetimes of atoms inside dielectric particles. , 1988, Physical review. A, General physics.

[12]  H. M. Lai,et al.  Dielectric microspheres as optical cavities: thermal spectrum and density of states , 1987 .

[13]  R. Chang,et al.  Stimulated Raman scattering from individual water and ethanol droplets at morphology-dependent resonances. , 1985, Optics letters.

[14]  James G. Fujimoto,et al.  Time-resolved measurements of picosecond optical breakdown , 1989 .

[15]  R. Chang,et al.  Time dependence of multiorder stimulated Raman scattering from single droplets. , 1988, Optics letters.

[16]  G. M. Hale,et al.  Optical Constants of Water in the 200-nm to 200-microm Wavelength Region. , 1973, Applied optics.

[17]  R. Rockafellar.  The multiplier method of Hestenes and Powell applied to convex programming , 1973 .

[18]  W. Kiefer,et al.  Structural resonances observed in the Raman spectra of optically levitated liquid droplets. , 1985, Applied optics.

[19]  J. Whinnery,et al.  New thermooptical measurement method and a comparison with other methods. , 1973, Applied optics.

[20]  Lin,et al.  Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets. , 1991, Physical review letters.

[21]  T. Lettieri,et al.  Observation of sharp resonances in the spontaneous Raman spectrum of a single optically levitated microdroplet , 1985 .

[22]  P. A. Fleury,et al.  Dispersion of Hypersonic Waves in Liquids , 1966 .

[23]  J Z Zhang,et al.  Spatial distribution of the internal and near-field intensities of large cylindrical and spherical scatterers. , 1987, Applied optics.

[24]  Yaochun Shen.  Principles of nonlinear optics , 1984 .

[25]  E. Purcell,et al.  Resonance Absorption by Nuclear Magnetic Moments in a Solid , 1946 .

[26]  A. Laubereau,et al.  High intensity Raman interactions , 1979 .

[27]  D. Linde,et al.  Quantitative Investigations of the Stimulated Raman Effect Using Subnanosecond Light Pulses , 1969 .