We present an approximate analytical method for fast calculations of complex-shaped two-dimensional photonic crystals. Both E and H polarizations are analyzed. Useful analytical formulas, for calculating the dispersion relations are developed. First, we present the zero order analytic approximation. Then we improve upon it by using perturbation theory, which reduce the relative error significantly.

The accuracy of the approximation is tested against accurate numerical calculations, and a good agreement is found for quite a wide range of photonic crystal parameters.

The presented analytical approach and the derived expressions, not only provide a fast way of calculating the photonic band structure, but also yield a physical insight into the problem.