Field transformation approach to photonic band structure calculations

A field transformation method is introduced for the calculation of photonic band structures in periodic lattices of dielectrics. The method has the advantage of avoiding the complications due to matching boundary conditions at the interface of the constituents in a composite medium. The formalism is presented for propagation modes in which the electric field is parallel to the interfaces in both one-dimensional and two-dimensional periodic dielectric structures. Numerical calculations using the present formalism involve typically a matrix of size much smaller than that of using standard plane wave expansions.