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

The lamellar grating problem is reformulated through the concept of adaptiv e spatial resolution. We introduce a new coordinate system such that spatia l resolution is increased around the discontinuities of the permittivity fu nction. We derive a new eigenproblem that we solve by using Fourier expansi ons for both the field and the coefficients of Maxwell's equations. We prov ide numerical evidence that highly improved convergence rates can be obtain ed. (C) 1999 Optical Society of America [S0740-3232(99)00910-2].