Reformulation of the coordinate transformation method through the concept of adaptive spatial resolution. Application to trapezoidal gratings

We reformulate the coordinate transformation method for profiles represente d by parametric equations. Numerically, the eigenvalue problem is solved by expanding both the electromagnetic field and the periodic coefficients of Maxwell's equations into Fourier series. For trapezoidal gratings, it is sh own that the convergence of the method is closely related to the representa tion of the profile. A proper choice of the representation permits handling profiles that previously had been out of reach owing to their sharp edges. From a practical point of view, we are now able to analyze gratings with t wo vertical facets by using the coordinate transformation method. (C) 2001 Optical Society of America.