Fourier Modal Method and Its Applications to Inverse Diffraction, Near-Field Imaging, and Nonlinear Optics

Abstract

The Fourier Modal Method (FMM) is perhaps the most popular numerical technique for rigorous analysis of diffraction gratings and other diffractive structures. The method has its roots in late 1960’s, in the work of Burckhardt on sinusoidally modulated volume gratings [1], and it is similar in nature as the so-called Rigorous Coupled-Wave Approach [2]. The method is applicable to dielectric, metallic, and semiconductor grating profiles of quite arbitrary shape, and the materials can be anisotropic. The convergence problems that long persisted for metallic gratings in TM polarized illumination were solved in mid-1990’s by introduction of correct Fourier factorization rules to deal with abrupt discontinuities in permittivity [3]. The FMM is also applicable to two-dimensionally periodic (crossed) gratings with complex permittivity variations in the nominal propagation direction of light [4]. Further, non-periodic structures can be analyzed by introducing so-called perfectly matched layers and nonlinear coordinate transformations. A comprehensive coverage of FMM can be found in Ref. [5].