Modeling the propagation of optical beams in three-dimensional photonic crystals

We show that the propagation effects of optical beams in three-dimensional photonic crystal structures can be modeled using a direction-dependent effective diffractive index model. The parameters of the model (i.e., the effective diffractive indices) can be calculated using the curvatures of the band structure of the photonic crystal at the operation point. After finding these indices, the wave propagation inside the photonic crystal can be analyzed using simple geometrical optics formulas. We show that the model has good accuracy for most practical applications of photonic crystals. As an example, the application of the model for diffraction compensation in a tetragonal woodpile photonic crystal is demonstrated. © 2008 Optical Society of America OCIS codes: 050.1940, 160.5298, 070.7345.