Markov-Airy description of optical scattering, waveguides, and resonators

Representing the reflection and transmission of light by multilayer dielectric structures in terms of Markov chains provides an intuitive, precise, and computationally efficient framework for calculating the dispersive properties (group delay, group delay dispersion, and higher order phase derivatives) of ultrafast laser mirrors and other broadband optical components. The theoretical basis for the Markov-Airy formalism is described, and its ability to precisely determine the dispersive characteristics of multilayer dielectric structures is demonstrated here. Exact expressions for the three lowest order phase derivatives for a dielectric mirror and waveguide are derived, and Markov-Airy-based numerical simulations of specific mirror designs are compared with results obtained with the conventional transition matrix formalism.