The Fourier modal method equipped with the concept of adaptive spatial resolution (FMMASR) is shown to be naturally more stable than the classical Fourier modal method toward spurious modes that appear with metallic structures. It is demonstrated that this stability can be further improved by reformulating the eigenvalue problem of the FMMASR. (C) 2009 Optical Society of America

A numerical improvement of the Fourier modal method with adaptive spatial resolution is obtained. It is shown that the solutions of all the eigenvalue problems corresponding to homogeneous regions can be deduced straightforwardly from the solution of one of these problems. Numerical examples demonstrate that computation time saving can be substantial.

We investigate resonant cavitylike modes in dielectric photonic crystals made of collections of subwavelength cylinders with high permittivity. A large number of collective modes appear for TE polarization (where magnetic fields are oriented along the cylinder axis), which possess similar features of resonant cavity modes that occur in polaritonic structures. These modes are dispersionless in nature and intensively gathered around an asymptotic frequency that depends on the subwavelength cylinders. The typical resonant cavitylike modes are illustrated with the magnetic field distributions at the resonant frequencies. In particular, the field pattern in the building block shows a close resemblance to TEnm mode of an isolated waveguide. The respective cutoff frequency at large oscillation orders serves as the asymptotic frequency of resonant cavitylike modes.

It is now well known that the homogenization of a periodic array of parallel dielectric fibers with suitably scaled high permittivity can lead to a possibly negative frequency dependent effective permeability. However this result based on a two-dimensional micro resonator problem on the section of the fibers holds merely in the case of polarized magnetic fields, reducing thus its applications to infinite cylindrical obstacles. In this Note we propose a full 3D extension of previous asymptotic analysis based on a new averaging method for the magnetic field. We evidence a vectorial spectral problem on the periodic cell which accounts for micro-resonance effects and leads to a 3D negative effective permeability tensor. This suggests that periodic bulk dielectric inclusions could be an efficient alternative to the very popular metallic split-ring structure proposed by Pendry.

In this paper, the authors conduct a study of artificial magnetism and anticrossing interaction that arise in photonic crystals and split-ring structures. The magnetic activity comes from localization of fields in photonic crystals with large dielectric contrast as well as in split-ring structures with the defectlike resonance. Both structures exhibit similar dispersion features near the resonance, whose effective permeability can be described in terms of the Lorentz-type oscillators. In particular, strong magnetic response is accompanied with the anticrossing interaction between the two fundamental frequency branches. This feature is characterized by a simple dynamic model which incorporates the coupling between a free and a localized photon state and illustrated with the transition of mode patterns where the fields mutually exchange their localization nature as the wave number changes.

Wave propagation in thin nanostructured films in the low frequency regime was studied. By means of a two-scale analysis, the medium can be homogenized, i.e. described by effective electromagnetic parameters. The effective permeability and permittivity were obtained from a set of partial differential equations. A numerical approach based on the Fourier Modal Method was devised in order to solve these equations.