Nonlinear pulse propagation in a single- and a few-cycle regimes with Raman response

Abstract

The propagation equation for a single-and a few-cycle pulses was derived in a cubic nonlinear medium including the Raman response. Using this equation, the propagation characteristics of a single-and a 4-cycle pulse, at 0.8 μm wavelength, were studied numerically in one spatial dimension. It was shown that Raman term does influence the propagation characteristics of a single-as well as a few-cycle pulses by counteracting the self-steepening effect.Keywords. Few-cycle pulse; nonlinear pulse propagation; Raman effect. PACSNos 42.50.Md; 42.65.Tg; 42.65.SfDuring the last few years, remarkable developments have taken place in experimental techniques for generating ultrashort pulses [1][2][3][4], which led to high-intensity optical pulses with pulse durations equal to one period of the optical cycle or less. Such ultrashort pulses have found applications [5][6][7][8][9][10][11] in diverse areas of physics and technology including nonlinear optical devices, all-optical communication, medical diagnostics and imaging, controlled manipulation of chemical reactions and bond formation, and coherent quantum control of microscopic dynamics. As a result, presently, there is a great deal of interest in the study of propagation characteristics of a single-and a few-cycle pulses in linear as well as nonlinear media.In 1997, Brabec and Krausz [12] presented a novel model for nonlinear pulse propagation in the single-cycle regime in which they showed that, for such pulses, the concept of an envelope could be generalized in terms of the invariance of the central frequency of the pulse under a phase shift of the electric field. Based on this, they derived a nonlinear pulse evolution equation that represents a generalization of the well-known nonlinear Schroedinger equation. This model equation has been successfully used by several authors [13][14][15][16][17] in various studies including nonlinear propagation dynamics of an ultrashort pulse in a hollow waveguide [13], supercontinuum generation by filamentation of a few-cycle pulses [14], estimation of the critical power for self-focussing in bulk media and in hollow waveguides [15], 501