Ray-pulse matrices: a rational treatment for dispersive opticalsystems

A new formalism to describe beam propagation in paraxial optical systems with dispersive elements, including both spatial and temporal variations in the propagating signal, is presented. This 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. How to use these matrices to write a space-time integral analogous to a generalized Huygens integral is shown, and propagation laws for Gaussian ray pulses which are space- and time-varying analogs of the conventional results for Gaussian beams are derived. The formalism should be useful for analyzing dispersive optical systems such as prism beam expanders, femtosecond pulse compression systems, and dispersive mode-locked laser cavities