Design of planar waveguide concave diffraction gratings

In order to design a Planar Waveguide Concave Diffraction Gratings (PW-CDG) accurately, especially a special grating structure, a design method named Modified Recursive Definition of Facet Positions (MRD) was presented. The central position of grating facets could be obtained by two constraint functions, and its numerical solution was derived from a recursive formula approach. To improve the accuracy of computation, a Newton iteration procedure was introduced in the recursive approach to compute each facet position. Two typical design examples, a flat-fieled mount and a flat-top mount, were given to assess the necessity adopting Newton iteration procedure subsequently. Simulation adopting different design methods were compared with each other, comparison indicates that computed results by MRD are identical with that by Power-series Expansion of Light Path Function (PS) with higher power, both of them are more accurate than that of traditional Recursive Definition of Facet Position (RD). It comes a conclution that the modification is crucial for the accurate definition of grating facet positions.