We reformulate the coordinate transformation method for profiles represented 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 shown that the convergence of the method is closely related to the representation 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 two vertical facets by using the coordinate transformation method.
© 2001 Optical Society of America
Original Manuscript: November 10, 2000
Revised Manuscript: March 6, 2001
Manuscript Accepted: March 6, 2001
Published: September 1, 2001
Gérard Granet, Jean Chandezon, Jean-Pierre Plumey, and Karyl Raniriharinosy, "Reformulation of the coordinate transformation method through the concept of adaptive spatial resolution. Application to trapezoidal gratings," J. Opt. Soc. Am. A 18, 2102-2108 (2001)