Variational expression for the analysis of photonic crystal devices

Variational expressions of the eigenfrequencies for photonic crystals are presented. We demonstrate that, by combining the expression with the conventional FDTD algorithm, the features of photonic band structures can be obtained efficiently. The proposed method can also be applied to the dispersion curves of photonic crystal waveguides. By employing the Rayleigh-Ritz method, anti-crossing features of the dispersion curves caused by the coupling of eigenmodes can be also successfully treated.