Parity, time-reversal and group delay for inhomogeneous dielectric slabs: Application to pulse propagation in finite, one-dimensional, photonic bandgap structures

The author considers the symmetries associated with the group-velocity delay of pulse transmission and reflection in a one-dimensionally inhomogeneous, planar, dielectric structure. From the principles of energy and parity conservation - as well as time-reversal symmetry - he derives the generalised Stokes reciprocity relations for such a slab. From these relations, he obtains very general equations relating the group delays and phases of the transmitted and reflected pulses. These results have important applications to pulse propagation through one-dimensional photonic bandgap structures.