Restrictions

Fourier Modal Method restrictions

The Fourier Modes Method, also known as RCWA, has not any restriction on grating depth.
The method problem is an electromagnetic field discontinuity at interfaces of different permittivity. Theoretically for infinite number of modes the fields at interfaces are matched correctly. For dielectric structures always there is a smooth convergence with the truncated number of modes increasing but the convergence rate depends on permittivity discontinuity contrast - the less contrast the larger convergence rate. The implementation of NV-field approach increases the convergence rate dramatically.
The largest convergence problems arise for highly conductive metal gratings. In this case the permittivity changes sign at discontinuity interfaces and as a result there are two consequences. First, so called plasmon modes may exist. As usual, these modes field has very sharp coordinate dependence leading to the convergence rate decreasing. And second, the modes propagation constants spectrum became irregular – the effect analogous to the spurious modes generation by truncation the number of modes in the case of one dimensional gratings⁷. In some cases the suggested in this paper modes filtering (also implemented in present code) may help.

Despite the problems described above this method gives practically acceptable results (accuracy is not less than fraction of percent) for moderate number of modes taken for calculation.