Linear Pulse Propagation

Abstract

This chapter gives a comprehensive introduction to linear pulse propagation in dispersive media. The wave equation in the spectral domain is introduced (i.e., the Helmholtz equation) using Fourier transforms. Basic principles are discussed, such as the superposition principle for linear propagation, allowing the Fourier components of the short laser pulse to propagate as plane waves in the frequency domain and obtaining the final pulse through superposition and Fourier transform into the time domain. Linear system theory is introduced to explain why a short photon pulse in vacuum does not change with propagation (in contrast to an electron wave packet) and why the spectral power does not change for linear propagation in a dispersive medium. None of this applies for nonlinear propagation. Ultrashort pulses are described by a photon wave packet, with a pulse envelope, a time–bandwidth product, and new concepts such as the slowly-varying envelope and slowly-evolving-wave approximation, first, second, and higher order dispersion, group velocity, group index, dispersive pulse broadening, and group delay dispersion are discussed from the first principles introduced in Chap. 1. Applications are covered such as optical communication and superluminal pulse propagation.