An approximate effective index model for efficient analysis and control of beam propagation effects in photonic crystals

Propagation of optical beams through a photonic crystal (PC) is analyzed and modeled. It is shown that the propagation effects for beams with slow spatial variations can be effectively modeled by diffraction behavior obtained directly from band structure. In particular, we present here an approximate model based on defining an effective index for the PC that can be used to analyze the propagation of optical beams inside the PC using the well-known analytic formulas for wave propagation in bulk media. The model presented here allows for considerable reduction in computation time and complexity. It also allows us to obtain more intuitive and design-oriented information about beam propagation effects inside PCs. We apply this model to several practical cases and show that its results agree very well with direct (time-consuming) numerical simulations.