RAY-PULSE MATRICES - A RATIONAL TREATMENT FOR DISPERSIVE OPTICAL-SYSTEMS

We present a new formalism to describe beam propagation in paraxial optical systems with dispersive elements, including both spatial and temporal variations in the propagating signal. This new formalism makes use of 4 × 4 “ray-pulse” matrices which take account of dispersive effects up to quadratic phases in both spatial coordinates (as in the usual paraxial ABCD matrix approach) and in the temporal domain. We show how to use these matrices to write a space-time integral analogous to a generalized Huygens integral, and derive propagation laws for Gaussian ray pulses which are space- and time-varying analogs of the conventional results for Gaussian beams. This new formalism should be very useful in analyzing dispersive optical systems such as prism beam expanders, femtosecond pulse compression systems, and dispersive mode-locked laser cavities. © 1990 IEEE