Analysis of Optical Pulse Propagation with ABCD Matrices

We review and extend the analogies between Gaussian pulse propagation and Gaussian beam diffraction. In addition to the well-known parallels between pulse dispersion in optical fiber and CW beam diffraction in free space, we review temporal lenses as a way to describe nonlinearities in the propagation equations, and then introduce further concepts that permit the description of pulse evolution in more complicated systems. These include the temporal equivalent of a spherical dielectric interface, which is used by way of example to derive design parameters used in a recent dispersion-mapped soliton transmission experiment. Our formalism offers a quick, concise and powerful approach to analyzing a variety of linear and nonlinear pulse propagation phenomena in optical fibers.