A Onelab model for the parametric study of mono-dimensional diffraction gratings

This document aims at presenting both theoretical and practical aspects of the grating_2D Onelab model (available at http://onelab.info/wiki/Diffraction_grating). This model applies to so-called mono-dimensional grating, i.e. structures having one direction of invariance. Various geometries and materials can be handled or easily added. The two classical polarization cases, denoted here E// and H//, are addressed. The output consists in a full energy balance of the problem computed from the field maps. This model is based on free the GNU softwares Gmsh, GetDP and their interface Onelab.Comment: arXiv admin note: text overlap with arXiv:1302.103

Calculation and analysis of complex band structure in dispersive and dissipative two-dimensional photonic crystals

Numerical calculation of modes in dispersive and absorptive systems is performed using the finite element method. The dispersion is tackled in the frame of an extension of Maxwell's equations where auxiliary fields are added to the electromagnetic field. This method is applied to multi-domain cavities and photonic crystals including Drude and Drude-Lorentz metals. Numerical results are compared to analytical solutions for simple cavities and to previous results of the literature for photonic crystals, showing excellent agreement. The advantages of the developed method lie on the versatility of the finite element method regarding geometries, and in sparing the use of tedious complex poles research algorithm. Hence the complex spectrum of resonances of non-hermitian operators and dissipative systems, like two-dimensional photonic crystal made of absorbing Drude metal, can be investigated in detail. The method is used to reveal unexpected features of their complex band structures.Comment: to be submitted for publicatio

Discontinuities in open photonic waveguides: Rigorous 3D modeling with the finite element method

In this paper, a general methodology to study rigorously discontinuities in open waveguides is presented. It relies on a full vector description given by Maxwell's equations in the framework of the finite element method. The discontinuities are not necessarily small perturbations of the initial waveguide and can be very general, such as plasmonic inclusions of arbitrary shapes. The leaky modes of the invariant structure are first computed and then injected as incident fields in the full structure with obstacles using a scattered field approach. The resulting scattered field is finally projected on the modes of the invariant structure making use of their bi-orthogonality. The energy balance is discussed. Finally, the modes of open waveguides periodically structured along the propagation direction are computed. The relevant complex propagation constants are compared to the transmission obtained for a finite number of identical cells. The relevance and complementarity of the two approaches are highlighted on a numerical example encountered in infrared sensing. Open source models allowing to retrieve most of the results of this paper are provided.Comment: The GetDP/Gmsh scripts allowing to retrieve the results are attache

Photonics in highly dispersive media: The exact modal expansion

We present exact modal expansions for photonic systems including highly dispersive media. The formulas, based on a simple version of the Keldysh theorem, are very general since both permeability and permittivity can be dispersive, anisotropic, and even possibly non reciprocal. A simple dispersive test case where both plasmonic and geometrical resonances strongly interact exemplifies the numerical efficiency of our approach

Surface plasmon hurdles leading to a strongly localized giant field enhancement on two-dimensional (2D) metallic diffraction gratings

International audienceAn extensive numerical study of diffraction of a plane monochromatic wave by a single gold cone on a plane gold substrate and by a periodical array of such cones shows formation of curls in the map of the Poynting vector. They result from the interference between the incident wave, the wave reflected by the substrate, and the field scattered by the cone(s). In case of a single cone, when going away from its base along the surface, the main contribution in the scattered field is given by the plasmon surface wave (PSW) excited on the surface. As expected, it has a predominant direction of propagation, determined by the incident wave polarization. Two particular cones with height approximately 1/6 and 1/3 of the wavelength are studied in detail, as they present the strongest absorption and field enhancement when arranged in a periodic array. While the PSW excited by the smaller single cone shows an energy flux globally directed along the substrate surface, we show that curls of the Poynting vector generated with the larger cone touch the diopter surface. At this point, their direction is opposite to the energy flow of the PSW, which is then forced to jump over the vortex regions. Arranging the cones in a two-dimensional subwavelength periodic array (diffraction grating), supporting a specular reflected order only, resonantly strengthens the field intensity at the tip of cones and leads to a field intensity enhancement of the order of 10 000 with respect to the incident wave intensity. The enhanced field is strongly localized on the rounded top of the cones. It is accompanied by a total absorption of the incident light exhibiting large angular tolerances. This strongly localized giant field enhancement can be of much interest in many applications, including fluorescence spectroscopy, label-free biosensing, surface-enhanced Raman scattering (SERS), nonlinear optical effects and photovoltaic

Finite Element Method

International audienceIn this chapter, we demonstrate a general formulation of the Finite Element Method allowing to calculate the diffraction efficiencies from the electromagnetic field diffracted by arbitrarily shaped gratings embedded in a multilayered stack lightened by a plane wave of arbitrary incidence and polarization angle. It relies on a rigorous treatment of the plane wave sources problem through an equivalent radiation problem with localized sources. Bloch conditions and a new Adaptative Perfectly Matched Layer have been implemented in order to truncate the computational domain. We derive this formulation for both mono-dimensional gratings in TE/TM polarization cases (2D or scalar case) and for the most general bidimensional or crossed gratings (3D or vector case). The main advantage of this formulation is its complete generality with respect to the studied geometries and the material properties. Its principle remains independent of both the number of diffractive elements by period and number of stack layers. The flexibility of our approach makes it a handy and powerful tool for the study of metamaterials, finite size photonic crystals, periodic plasmonic structures..

Transmission enhancement through square coaxial apertures arrays in metallic film: when leaky modes filter infrared light

We consider arrays of square coaxial apertures in a gold layer and study their diffractive behavior in the far infrared region. These structures exhibit a resonant transmission enhancement that is used to design tunable bandpass filters. We provide a study of their spectral features and show by a modal analysis that the resonance peak is due to the excitation of leaky modes of the open photonic structure. Fourier transform infrared (FTIR) spectrophotometry transmission measurements of samples deposited on Si substrate show good agreement with numerical results and demonstrate angular tolerance up to 30 degrees of the fabricated filters.Comment: 4 pages, 3 figure