Propagation of few-cycle pulses in nonlinear Kerr media: harmonic generation

We apply our recently developed time-transformation method for studying the propagation of few-cycle optical pulses inside a nonlinear Kerr medium after taking into account that changes in the refractive index vary with the electric field as E2 and not by its average over an optical cycle. Our technique correctly predicts carrier-wave shocking and generation of odd-order harmonics inside a Kerr medium, the two features found earlier with directly solving Maxwell's equations using the finite-difference time-domain (FDTD) methods. We extend our method to study the impact of a finite response of the Kerr nonlinearity on harmonic generation and to include chromatic dispersion that cannot be ignored for ultrashort pulses. We show that nonlinear effects can help in controlling the width of an ultrashort pulse, even though it cannot propagate as a fundamental soliton. Our time-transformation method provides an alternative to the FDTD technique, as it deals with the electric field directly but does not require step size to be a small fraction of the wavelength, resulting in much faster computation speeds.