Abstract

In the slowly varying envelope approximation, a quasi-monochroma tic light wave of central angular frequency ω_o propagates through a dispersive material at the group velocity. This approximation fails in the case of ultrashort pulses for which the temporal frequency components of the envelope are of the same order as ω_o. The concept of group velocity cannot be used in this case since the signal envelope suffers a strong distortion. To describe the propagation of such pulses, we propose a mathematical time-frequency decomposition of the incident light amplitude into elementary components of same duration τ_a′ each centered at a frequency Ω lying in the Fourier spectral range of the original pulse. Each wavelet component F(Ω, t) is given by the convolution between the Ω Fourier component and an analyzing Gaussian function, whose spectral width will determine its duration. The original pulse is retrieved by integrating F(Ω, t) over the frequency. This method is applied to a representation of the propagation of a 3 fs light pulse through a quartz plate. We will study the deformation and the time enlargement of the pulse versus τ_a and the thickness of the plate, taking into account the strong dispersion of the group time characterizing each wavelet.

© 1992 Optical Society of America