Modal analysis and suppression of the Fourier modal method instabilities in highly conductive gratings.

The Fourier modal method (FMM), often also referred to as rigorous coupled-wave analysis (RCWA), is known to suffer from numerical instabilities when applied to low-loss metallic gratings under TM incidence. This problem has so far been attributed to the imperfect conditioning of the matrices to be diagonalized. The present analysis based on a modal vision reveals that the so-called instabilities are true features of the solution of the mathematical problem of a binary metal grating dealt with by truncated Fourier representation of Maxwell's equations. The extreme sensitivity of this solution to the optogeometrical parameters is the result of the excitation, propagation, coupling, interference, and resonance of a finite number of very slow propagating spurious modes. An astute management of these modes permits a complete and safe removal of the numerical instabilities at the price of an arbitrarily small and controllable reduction in accuracy as compared with the referenced true-mode method.

Modal method in deep metal-dielectric gratings: the decisive role of hidden modes.

The modal method is well adapted for the modeling of deep-groove, high-contrast gratings of short period, possibly involving metal parts. Yet problems remain in the case of the TM polarization in the presence of metal parts in the corrugations: whereas most of the diffraction features are explained by the interplay of an astonishingly small number of true propagating and low-order evanescent modes, the exact solution of the diffraction problem requires the contribution of two types of evanescent modes that are usually overlooked. We investigate the nature and the role of these modes and show that metal gratings can be treated exactly by the modal method.

Narrowband, polarization-independent free-space wave notch filter.

A two-dimensional-corrugated-slab-waveguide add/drop filter providing 100% resonant reflection at 1.55 microm wavelength for both TE and TM polarizations with identical FWHM is designed. The fabricated device exhibits a reflectivity spectrum of more than 95% peak reflection for both polarizations at 1.537 microm. The coupling scheme involves the TE0 guided mode only; it is made relatively tolerant by means of a double-sided crossed grating.