Time-transformation approach to pulse propagation in nonlinear dispersive media: Inclusion of delayed Raman nonlinearity

Abstract

We extend our time-transformation technique to include the delayed Raman response and use it to study propagation of ultrashort, few-cycle, optical pulses inside a dispersive nonlinear medium. Our technique deals directly with the electric field associated with an optical pulse and can be applied to pulses of arbitrary widths, as it does not make use of the slowly varying envelope approximation. We apply it to optical pulses containing several optical cycles and launched such that they form a third-order optical soliton. We vary the number of optical cycles within the pulse from 1 to 10 and study how the features such as soliton fission, intrapulse Raman scattering, and dispersive-wave generation depend on pulse width and soliton order. We find that for a fixed soliton order, the Raman-induced frequency shift becomes smaller, while the fraction of energy transferred to the dispersive wave increases, as pulse width is reduced. In the special case of a single-cycle pulse, the most dominant effect is self-steepening and it leads to dramatically different features in both the shape and spectrum of output pulses.