Brahim Guizal

Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization

A new implementation of the coupled-wave method for TM polarization is proposed. We use a second-order differential operator established by Neviere together with a scattering-matrix approach. Thus we obtain for metallic gratings a convergence rate as quick as that in TE polarization.

Enhanced confined light transmission by single subwavelength apertures in metallic films

The diffraction of light that emerges from a metallic circular aperture is studied. Near- and far-field results are presented. Spectral angular transmitted intensities are performed versus the incident wavelength for four kinds of aperture. It is shown that, for a definite configuration, a large enhancement of transmission--compared with the basic case of a single hole--occurs combined with a spectacular angular confinement of light. Such effects are, for example, of great interest in optical near-field microscopy for which the probe is a nanosource.

Coordinate transformation method as applied to asymmetric gratings with vertical facets

The differential formalism introduced by J. Chandezon during the seventies has been successfully applied to the study of waveguides and to diffraction problems. Until now it was believed that the method could be applied only if the interfaces between media were described by graphs of functions. We show that an eigenoperator formulation of the method allows one to solve a larger set of profiles. This theoretical result is applied to gratings having a vertical facet.

Modal method based on subsectional Gegenbauer polynomial expansion for nonperiodic structures: complex coordinates implementation

In this paper we present an extension of the modal method by Gegenbauer expansion (MMGE) [J. Opt. Soc. Am. A28, 2006 (2011)], [Progress Electromagn. Res.133, 17 (2013)] to the study of nonperiodic problems. The nonperiodicity is introduced through the perfectly matched layers (PMLs) concept, which can be introduced in an equivalent way either by a change of coordinates or by the use of a uniaxial anisotropic medium. These PMLs can generate strong irregularities of the electromagnetic fields that can significantly alter the convergence and stability of the numerical scheme. This is the case, e.g., for the famous Fourier modal method, especially when using complex stretching coordinates. In this work, it will be shown that the MMGE equipped with PMLs is a robust approach because of its natural immunity against spurious modes.

Spatial dispersion in an array of metallic nanorods

The homogeneous and transport properties of a set of metallic fibers were studied. The existence of a plasma frequency was deduced and a precise formula for it was derived. A homogenized system for finite length ohmic wires was derived. Some numerical simulations were made to study the influence of disorder. The persistence of a low-frequency band gap was demonstrated numerically even in the case of a strong disorder. The existence of localized modes was explained in terms of the statistical properties of the medium.

Homogenization of a metallic metamaterial and electrostatic resonances

The homogenization of arrays of metallic rods was studied. Using standard homogenization theory, the effective permittivity was obtained. The onset of resonances was evidenced and showned to be linked with the negative sign of the real part of the permittivity. Numerical computations were performed to test the homogeneous model.

ADVANCES IN IMAGING AND ELECTRON PHYSICS

The purpose of this chapter is to present a unified theory for the numerical implementation of modal methods for the analysis of electromagnetic phenomena with specific boundary conditions. All the fundamental concepts that form the basis of our study will be detailed. In plasmonics and photonics in general, solving Maxwell equations involving irregular functions is common. For example, when the relative permittivity is a piecewise constant function describing a dielectric–metal interface, the eigenmodes of the propagation equation are solutions of Maxwells equations subject to specific boundary conditions at the interfaces between homogenous media. Prior knowledge about the eigenmodes allows one to define more appropriate expansion functions, and the rate of convergence of the numerical scheme will depend on the choice of these functions. In this chapter, we present and explain, a unified numerical formalism that allows one to build, from a set of subsectional functions defined on a set of subintervals, expansion functions defined on a global domain by enforcing certain stresses deduced from electromagnetic field properties. Then numerical modal analysis of a plasmonic device, such as a ring resonator, is presented as an example of an application.Abstract The purpose of this chapter is to present a unified theory for the numerical implementation of modal methods for the analysis of electromagnetic phenomena with specific boundary conditions. All the fundamental concepts that form the basis of our study will be detailed. In plasmonics and photonics in general, solving Maxwell equations involving irregular functions is common. For example, when the relative permittivity is a piecewise constant function describing a dielectric–metal interface, the eigenmodes of the propagation equation are solutions of Maxwells equations subject to specific boundary conditions at the interfaces between homogenous media. Prior knowledge about the eigenmodes allows one to define more appropriate expansion functions, and the rate of convergence of the numerical scheme will depend on the choice of these functions. In this chapter, we present and explain, a unified numerical formalism that allows one to build, from a set of subsectional functions defined on a set of subintervals, expansion functions defined on a global domain by enforcing certain stresses deduced from electromagnetic field properties. Then numerical modal analysis of a plasmonic device, such as a ring resonator, is presented as an example of an application.

Strong coupling of plasmons with confined modes in a quantum metamaterial

The strong coupling between a mode confined in a dielectric waveguide and a surface plasmon was demonstrated. It was shown that the strong and weak coupling regime can coexist. The strong coupling allows the spatial exchange of energy and opens a way towards the quantum control of plasmon, i.e. quantum plasmonics.

Crucial influence of evanescent waves on the electromagnetic properties of metamaterials

The recent interest in the imaging possibilities of photonic crystals (superlensing, superprism, optical mirages, etc.) call for a detailed analysis of beam propagation inside a finite periodic structure. An answer to the following question was sought: Where does the beam emerge? We found that, contrary to common knowledge, it is not always true that the shift of a beam is given by the normal to the dispersion curve. This phenomenon can be explained in terms of evanescent waves and a renormalized diagram yields the correct direction.

Effective properties of resonant arrays of rods

The effective electromagnetic properties of a metamaterial made of nanorods are investigated. It is found that near inner resonances there is a effective magnetic behavior. The domain of validity of the effective permeability model is determined with respect to the wavelength and the filling ratio by means of rigorous numerical computations. It is concluded that the relative dielectric constant should be higher than 32 and the filling ratio lower than 1/2.