Matrix method for calculations on the propagation of coherent laser pulses

A new method is proposed for carrying out calculations on the propagation of coherent pulses through optical systems which contain dispersive elements, modulators, and regions of a dispersive medium. In this method, a matrix analogous to a ray matrix in the optics of Gaussian beams is associated with each element of the optical system. A multiplication of the matrices of the individual elements of the system yields the matrix of the overall system. The latter matrix can be used to construct an integral relation which describes the propagation of a coherent pulse through an optical system of a general type. This relation can be used to construct an algorithm for analyzing the propagation of coherent pulses through optical systems. This algorithm is analogous to the method of Gaussian beams. It substantially simplifies the analysis and makes it more graphic. The method is illustrated by several examples.