Mode coupling in tilted planar waveguide gratings

Three different grating tilting formulas for predicting the optimum grating tilt angle for strong mode coupling in planar waveguide gratings are derived. The optimum tilt angles obtained by the ray-optics approach deviate ~1 degrees for transmissive mode coupling and ~1.5 degrees for reflective mode coupling from those computed by the coupled-mode approach. The coupled-mode analysis and ray-optics analysis of the tilted planar waveguide gratings show that the transmissive planar waveguide gratings should be tilted more than 84 degrees for strong TE(0)-to-TE(mu) mode coupling near 1550 nm.