Analytical model of the optical response of periodically structured metallic films: Comment.

A comparison is made between rigorous numerical results and a recently proposed analytical method for modeling light diffraction by lamellar diffraction gratings. The conclusion is that the analytical model is quite restrained in its applicability and can be misleading in determining the behavior of the grating efficiencies.

Resonant optical transmission through thin metallic films with and without holes.

Using a rigorous electromagnetic analysis of two-dimensional (or crossed) gratings, we account, in a first step, for the enhanced transmission of a sub-wavelength hole array pierced inside a metallic film, when plasmons are simultaneously excited at both interfaces of the film. Replacing the hole array by a continuous metallic film, we then show that resonant extraordinary transmission can still occur, provided the film is modulated. The modulation may be produced in both a one-dimensional and a two dimensional geometry either by periodic surface deformation or by adding an array of high index pillars. Transmittivity higher than 80% is found when surface plasmons are excited at both interfaces, in a symmetric configuration.

T matrix of the homogeneous anisotropic sphere: applications to orientation-averaged resonant scattering.

We illustrate some numerical applications of a recently derived semianalytic method for calculating the T matrix of a sphere composed of an arbitrary anisotropic medium with or without losses. This theory is essentially an extension of Mie theory of the diffraction by an isotropic sphere. We use this theory to verify a long-standing conjecture by Bohren and Huffman that the extinction cross section of an orientation-averaged anisotropic sphere is not simply the average of the extinction cross sections of three isotropic spheres, each having a refractive index equal to that of one of the principal axes.

Plasmon surface waves and complex-type surface waves: comparative analysis of single interfaces, lamellar gratings, and two-dimensional hole arrays.

The similarities and differences between two types of surface waves that can exist on a plane metal-lossless dielectric interface, on the one hand, and on a plane lossy-lossless dielectric interface, on the other hand, are analyzed numerically. They both can lead to total absorption of light by surface relief gratings and show different behavior in transmission by lamellar gratings.

Single-scattering theory of light diffraction by a circular subwavelength aperture in a finitely conducting screen.

A perturbation theory based on a single-scattering approximation is developed from the rigorous differential theory of diffraction in cylindrical coordinates. It results in analytical formulas in the inverse space for the field amplitudes providing results that are in quantitative agreement with the results of the rigorous method, in both the near- and far-field regions, when a proper correction to the incident field inside the aperture is made by using the renormalized Born approximation. When working in reflection by a screen having permittivity high in modulus, the method proposes an equivalence with the simple model consisting of the emission by a single magnetic dipole excited inside the pierced layer, emission that is then transferred back into the cladding following the Fresnel's coefficients of transmission from the layer into the cladding. The theory predicts a directivity of the radiation pattern that increases for smaller values of modulus of permittivity, both for dielectrics and metals, thus independently of the possibility of plasmon surface wave excitation along the interface. The theory can take into account such surface wave resonances, as well as the waveguide supported by a dielectric slab, but cannot implicitly recognize the modes carried out by the cylindrical waveguide corresponding to the aperture. This fact limits its domain of validity when used in transmission, although the far- and near-field maps can be reconstructed sufficiently well within a multiplicative factor corresponding to the enhanced transmission due to the excitation of these modes.

Mie scattering by an anisotropic object. Part I. Homogeneous sphere.

Establishing a vector spherical harmonic expansion of the electromagnetic field propagating inside an arbitrary anisotropic medium, we extend Mie theory to the diffraction by an anisotropic sphere, with or without losses. The particular case of a uniaxial material leads to a simpler analysis. This work opens the way to the construction of a differential theory of diffraction by a three-dimensional object with arbitrary shape, filled by an arbitrary anisotropic material.

Mie scattering by an anisotropic object. Part II. Arbitrary-shaped object: differential theory.

The differential theory of diffraction by an arbitrary-shaped body made of arbitrary anisotropic material is developed. The electromagnetic field is expanded on the basis of vector spherical harmonics, and the Maxwell equations in spherical coordinates are reduced to a first-order differential set. When discontinuities of permittivity exist, we apply the fast numerical factorization to find the link between the electric field vector and the vector of electric induction, developed in a truncated basis. The diffraction problem is reduced to a boundary-value problem by using a shooting method combined with the S-matrix propagation algorithm, formulated for the field components instead of the amplitudes.

Diffraction theory of an anisotropic circular cylinder.

A fully analytical theory is developed to derive the field diffracted by an infinitely long circular cylinder made of an arbitrary anisotropic homogeneous material, illuminated by an arbitrary plane wave.

Diffraction theory: application of the fast Fourier factorization to cylindrical devices with arbitrary cross section lighted in conical mounting.

The differential theory of diffraction by arbitrary cross-section cylindrical objects is developed for the most general case of an incident field with a wave vector outside the cross-section plane of the object. The fast Fourier factorization technique recently developed for studying gratings is generalized to anisotropic and/or inhomogeneous media described in cylindrical coordinates; thus the Maxwell equations are reduced to a first-order differential set well suited for numerical computation. The resolution of the boundary-value problem, including an adapted S-matrix propagation algorithm, is explained in detail for the case of an isotropic medium. Numerical applications show the capabilities of the method for resolving complex diffraction problems. The method and its numerical implementation are validated through comparisons with the well-established multipole method.

Simulation of two-dimensional Kerr photonic crystals via fast Fourier factorization.

We present an adaptation of the fast Fourier factorization method to the simulation of two-dimensional (2D) photonic crystals with a third-order nonlinearity. The algorithm and its performance are detailed and illustrated via the simulation of a Kerr 2D photonic crystal. A change in the transmission spectrum at high intensity is observed. We explain why the change does not reduce to a translation (redshift) but rather consists in a deformation and why one side of the bandgap is more suited to a switching application than the other one.

Field enhancement in single subwavelength apertures.

A peak of the detected fluorescence rate per molecule has recently been observed in experiments of fluorescence correlation spectroscopy carried out on subwavelength apertures in metallic screens, a phenomenon that appears at a diameter-to-wavelength ratio below the fundamental mode cutoff. Although the origin of the resonant transmission through a subwavelength aperture has been well explained in terms of excitation of plasmon surface modes on the aperture ridge, the origin of the maximum that occurs at a radius-to-wavelength ratio smaller than 1/4 was not clear. Using a rigorous electromagnetic theory of light diffraction in cylindrical geometry, we show that it is linked to the appearance of the fundamental mode propagating inside the aperture. We obtain good agreement between the theoretical and the experimental results.

Differential theory of diffraction by finite cylindrical objects.

We present a differential theory for solving Maxwell equations in cylindrical coordinates, projecting them onto a Fourier-Bessel basis. Numerical calculations require the truncation of that basis, so that correct rules of factorization have to be used. The convergence of the method is studied for different cases of dielectric and metallic cylinders of finite length. Applications of such a method are presented, with a special emphasis on the near-field map inside a hole pierced in a plane metallic film.

Light diffraction by a three-dimensional object: differential theory.

The differential theory of diffraction of light by an arbitrary object described in spherical coordinates is developed. Expanding the fields on the basis of vector spherical harmonics, we reduce the Maxwell equations to an infinite first-order differential set. In view of the truncation required for numerical integration, correct factorization rules are derived to express the components of D in terms of the components of E, a process that extends the fast Fourier factorization to the basis of vector spherical harmonics. Numerical overflows and instabilities are avoided through the use of the S-matrix propagation algorithm for carrying out the numerical integration. The method can analyze any shape and/or material, dielectric or conducting. It is particularly simple when applied to rotationally symmetric objects.

Enhanced transmission of light through a circularly structured aperture.

Using the differential theory of light diffraction by finite cylindrical objects, we study light transmission through a small circular aperture in a metallic screen with concentric corrugation around the nanohole. Poynting vector maps in the region below the screen show that the field enhancement compared with an unstructured aperture is obtained with corrugation lying on the entrance face of the screen. Corrugation on the exit face leads to a more directional radiation close to the normal to the screen. The spectral dependence of the transmission shows a sharp maximum linked with surface plasmon excitation.

Optimization of plasmon excitation at structured apertures.

Surface plasmon excitation that is due to a single or a structured circular aperture in a flat metallic screen is investigated theoretically and numerically with a view to enhancing the electric field close to the metallic surface. A systematic study of the homogeneous solution of the electromagnetic scattering problem is made with cylindrical coordinates, expanding Maxwell equations on a Fourier-Bessel basis. A perturbation analysis devoted to simple physical analyses of different types of cylindrical nanostructure is developed for the optimization of plasmon excitation by a normally incident linearly polarized monochromatic plane wave. The conclusions drawn from this analysis agree well with the results of rigorous electromagnetic calculations obtained with the differential theory of diffraction in cylindrical coordinates.

Surface plasmon excitation on a single subwavelength hole in a metallic sheet.

The diffraction of light by a single subwavelength hole in a highly conductive metallic sheet is analyzed with a recently developed differential theory that is able to plot the nearly electromagnetic field. Using rigorous electromagnetic and phenomenological analysis, we show that a single subwavelength hole can excite surface-plasmon resonance that contributes greatly to extraordinary transmission.

Factorization of products of discontinuous functions applied to Fourier-Bessel basis.

The factorization rules of Li [J. Opt. Soc. Am. A 13, 1870 (1996)] are generalized to a cylindrical geometry requiring the use of a Bessel function basis. A theoretical study confirms the validity of the Laurent rule when a product of two continuous functions or of one continuous and one discontinuous function is factorized. The necessity of applying the so-called inverse rule in factorizing a continuous product of two discontinuous functions in a truncated basis is demonstrated theoretically and numerically.

Differential theory of gratings made of anisotropic materials.

Arbitrary profiled gratings made with anisotropic materials are discussed; the anisotropic character concerns electric and/or magnetic properties. Our aim is to avoid the use of the staircase approximation of the profile, whose convergence is questionable. A coupled first-order differential-equation set is derived by taking into account Li's remarks about Fourier factorization [J. Opt. Soc. Am. A 13, 1870 (1996)], but the present formulation shows that, in return for a convenient form of the differential system, it is possible to use only the intuitive Laurent rule. Our method, when applied to the simpler case of isotropic gratings, is shown to be consistent with that of previous studies. Moreover, from the numerical point of view, the convergence of our formulation for an anisotropic grating is faster than that of the conventional differential method.

Diffraction theory in TM polarization: application of the fast Fourier factorization method to cylindrical devices with arbitrary cross section.

The diffraction of an electromagnetic wave by a cylindrical object with arbitrary cross section is studied by taking advantage of recent progress in grating theories. The fast Fourier factorization method previously developed in Cartesian coordinates is extended to cylindrical coordinates thanks to the periodicity of both the diffracting object and the incident wave with respect to the polar angle theta. Thus Maxwell equations in a truncated Fourier space are derived and separated in TE and TM polarization cases. The new set of equations for TM polarization is resolved numerically with the S-matrix propagation algorithm. Examples of elliptic cross sections and cross sections including couples of nonconcentric circles show fast convergence of the results, for both dielectric and metallic materials, as well as good agreement with previous published results. Thus the method is suitable for an extension to conical (out-of-plane) diffraction, which will allow studying mode propagation along microstructured fibers.

Differential theory: application to highly conducting gratings.

The recently developed fast Fourier factorization method, which has greatly improved the application range of the differential theory of gratings, suffers from numerical instability when applied to metallic gratings with very low losses. This occurs when the real part of the refractive index is small, in particular, smaller than 0.1-0.2, for example, when silver and gold gratings are analyzed in the infrared region. This failure can be attributed to Li's "inverse rule" [L. Li, J. Opt. Soc. Am. A 13, 1870 (1996)] as shown by studying the condition number of matrices that have to be inverted. Two ways of overcoming the difficulty are explored: first, an additional truncation of the matrices containing the coefficients of the differential system, which reduces the numerical problems in some cases, and second, an introduction of lossier material inside the bulk, thus leaving only a thin layer of the highly conducting metal. If the layer is sufficiently thick, this does not change the optical properties of the system but significantly improves the convergence of the differential theory, including the rigorous coupled-wave method, for various types of grating profiles.