Enlarging applicability domain of the C method with piecewise linear parameterization: gratings of deep and smooth profiles

Abstract

We present two piecewise linear parameterization schemes for the parameterized coordinate transformation method (the C method) to enable it to model gratings of deep and smooth grooves. This work generalizes and elaborates our previous work [Opt. Lett. 39(23), 6644 (2014)]. The previous bilinear transformation is replaced with a general multi-linear transformation. This gives us flexibility to handle more general grating profiles while retaining the simplicity of the linear transformation. We give some general, simple, and empirical rules on composing the piecewise linear transformation function. Both enlarged convergence range and increased groove depth-to-period ratio, which can be at least 10, are achieved with the parameterized C method for a wide class of smooth grating profiles.