Improvement of Fourier Modal Methods by Means of Non Conventional Coordinate Systems

The Fourier modal method has recently been improved with the idea of adaptive spatial resolution . By using a non-uniform sampling scheme that places more sampling points around the permittivity discontinuities, the total number of spatial harmonics required to achieve a given accuracy is significantly reduced. The idea of stretching thinner the space around the discontinuities is not entirely new in the larger context of rigorous numerical methods. What is new in our parametric approach as applied to gratings is that Maxwell´s equations are written in the stretched coordinates under the covariant form.