Approximate analysis and design of rectangular-lattice photonic crystals.

We present a theoretical analysis of wave propagation in rectangular- and square-lattice photonic crystals by approximating the arbitrary refractive-index function with a staircase profile. This profile has a number of tunable parameters that allow one to fit the band structures of the staircase and the desired structure over a large frequency range. The staircase profile is such that its corresponding two-dimensional wave equation decomposes into two one-dimensional equations by means of a constant decoupling parameter. We show that basic features of the band structure and Bloch waves in photonic crystals can be analyzed theoretically through this simple approximation.