Jean-Pierre Plumey

Rigorous and efficient grating-analysis method made easy for optical engineers

The coordinate-transformation-based differential method of Chandezon et al. [J. Opt. (Paris) 11, 235 (1980); J. Opt. Soc. Am. 72, 839 (1982)] (the C method) is one of the simplest and most versatile methods for modeling surface-relief gratings. However, to date it has been used by only a small number of people, probably because, traditionally, elementary tensor theory is used to formulate the method. We reformulate the C method without using any knowledge of tensor, thus, we hope, making the C method more accessible to optical engineers.

Polarization independence of a one-dimensional grating in conical mounting

We demonstrate theoretically a polarization-independent guided-mode resonant filter with only a one dimensional grating. A rigorous method, the modal method by Fourier expansion, is used to compute the diffracted efficiencies of the grating. Wave-vector analysis fails to correctly design a polarization-independent structure. We show that a rigorous analysis of the resonances must be employed to obtain such a device; using a pole approach, we study the effects of grating parameters on the resonances of both polarizations.

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.

Differential covariant formalism for solving Maxwell's equations in curvilinear coordinates: oblique scattering from lossy periodic surfaces

A rigorous differential method describing the diffraction properties of lossy periodic surfaces is presented. A nonorthogonal coordinate system and a covariant formalism of Maxwells equation are used simplifying boundary conditions expression. Only one eigenvalue system, unique for the TE and TM polarizations even for an oblique incidence, needs to be solved. Thus the numerical treatment is very efficient and CPU requirements significantly reduced. Numerical results are successfully compared with those obtained by an integral method using the boundary element method (BEM) as a numerical procedure. >

Generalization of the coordinate transformation method with application to surface-relief gratings

The coordinate-transformation-based differential method, initially used by Chandezon et al. for modeling surface-relief gratings, is now known as a powerful rigorous formalism for solving diffraction problems. We explain a coordinate transformation that generalizes the original one, and we extend the formulation to a wide class of monodimensional surface shapes. The boundary-value problem turns on the same eigenvalue problem for the TE and TM polarizations.

Application of Heisenberg's uncertainty principle and C-method to the study of Fraunhofer diffraction by a metallic ribbon

Until the early of nineteenth century the corpuscular theory of light of Newton was largely dominant and the wave theory of Huygens practically abandoned. This is to Thomas Young and Augustin Fresnel that we owe its return in the early nineteenth century to explain the phenomena of diffraction and interference in particular the Youngs double-slit experiment. To decide between the wave theory and corpuscular theory, the Paris Sciences Academy had organized a competition in 1819, on the subject of the problem of diffraction. Fresnel won the prize by performing the first calculations of diffraction from the wave theory of light showing that in the middle of the shadow of an opaque circular disc, against all expectations, there is a bright spot called the Poisson spot.

Rigorous electromagnetic analysis of 2D resonant subwavelength metallic gratings by parametric Fourier-modal method

The parametric Fourier Modal Method is extended to the case of lamellar gratings that are periodic in two directions. We provide numerical evidence that improved convergence rates can be obtained. As an example, we calculate the optical transmission of a gold grating and rather good agreement with Ebbessens experimental data is observed.

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.

Unified Numerical Formalism of Modal Methods in Computational Electromagnetics and the Latest Advances: Applications in Plasmonics

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.

A scattering matrix interpolation from perturbation method: application to scatterometry for profile control

The scatterometric and electromagnetic signatures of a pattern are computing with the perturbation method combined with the Fourier Modal Method (FMM) in order to reduce computational time. In electromagnetic point of view, the grating is characterized by its scattering matrix which allows the computation of the reflection and transmission coefficient. A slight variation of profile parameters or electrical ones provides a small fluctuation of the scattering matrix, consequently, an analytical expression of the local behavior of its eigenvectors and eigenvalues can be obtained by using a perturbation method.