Out-of-plane diffraction of a two-dimensional photonic crystal with finite dielectric modulation

We present a generalized picture of out-of-plane diffraction in a two-dimensional photonic crystal using the concept of photonic bands and employing a three-dimensional, equal-frequency-surface analysis. We show that the discrete spots of diffraction pattern in a weakly modulated photonic crystal, including those of conventional diffraction gratings, become continuous when the dielectric modulation becomes finite. Furthermore, in a finite-modulated photonic crystal, the diffraction can take place even in the region prohibited by Bragg's law: there are available states for the incident light, which are evanescent in the case of a diffraction grating (weakly modulated photonic crystal).