Coupled-wave theory of reflective phase-shift keyed Bragg grating

Kogelnik’s theory of coupled waves is commonly used to describe the diffraction from a simple volume grating. We present the generalization of this theory for the case of the grating comprising several cells along the direction of light propagation. All the cells have the same period and amplitude, but different phases of the grating. By choosing a set of phases of the cells, the theory enables us to synthesize a grating with the desired wavelength transfer function. We demonstrate a various set of gratings, that are suitable for WDM applications.