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.
© 1992 Optical Society of America
Ali Serpengüzel, Gang Chen, Richard K. Chang, and Wen-Feng Hsieh, "Heuristic model for the growth and coupling of nonlinear processes in droplets," J. Opt. Soc. Am. B 9, 871-883 (1992)