The passage of light through slowly varying nonuniform photonic crystal structures is treated using Hamiltonian optics. The approach allows the inverse design of complex and highly compact optical elements as well as providing insight and an appealing physical picture. It can also be used to treat the trapping and deflection of light at distributed defects in one- and two-dimensional (2-D) crystals, and to study the frequency-dependent time delay in chirped one-dimensional (1-D) fiber Bragg gratings (FBG's).
P. St. J. Russell and T. A. Birks, "Hamiltonian Optics of Nonuniform Photonic Crystals," J. Lightwave Technol. 17, 1982- (1999)