Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution

The lamellar grating problem is reformulated through the concept of adaptive spatial resolution. We introduce a new coordinate system such that spatial resolution is increased around the discontinuities of the permittivity function. We derive a new eigenproblem that we solve by using Fourier expansions for both the field and the coefficients of Maxwell’s equations. We provide numerical evidence that highly improved convergence rates can be obtained.