Sampling rules in the frequency domain for numerical propagation of ultrashort pulses through linear dielectrics

An efficient numerical algorithm is presented for the numerical modeling of the propagation of ultrashort pulses with arbitrary spatial and temporal characteristics through linear homogeneous dielectrics. The consequence of proper sampling of the spectral phase in pulse propagation and its influence on the efficiency of computation are discussed in detail. The numerical simulation presented here is capable of analyzing the pulse in the space-frequency domain and its on- and off-axis evolution in the space-time domain in any arbitrary plane. As an example, pulse propagation effects such as temporal and spectral shifts, pulse broadening effects, asymmetry, and chirping in dispersive media are demonstrated for axial and off-axial time evolution of a TEM01 pulse. Snapshots of dynamic pulse evolution are presented at various planes transverse to the direction of propagation. The pulse profiles at arbitrary points in the transverse planes are also obtained as a function of time. © 2006 Optical Society of America.