Kofi Edee

Enhanced transmission of slit arrays in an extremely thin metallic film

Horizontal resonances of slit arrays are studied. They can lead to an enhanced transmission that cannot be explained using the single-mode approximation. A new type of cavity resonance is found when the slits are narrow for a wavelength very close to the period. It can be excited for very low thicknesses. Optimization shows these structures could constitute interesting monochromatic filters.

Modal method based on subsectional Gegenbauer polynomial expansion for lamellar gratings

A first approach of a modal method by Gegenbauer polynomial expansion (MMGE1) is presented for a plane wave diffraction by a lamellar grating. Modal methods are among the most popular methods that are used to solve the problem of lamellar gratings. They consist in describing the electromagnetic field in terms of eigenfunctions and eigenvalues of an operator. In the particular case of the Fourier modal method (FMM), the eigenfunctions are approximated by a finite Fourier sum, and this approximation can lead to a poor convergence of the FMM. The Wilbraham-Gibbs phenomenon may be one of the reasons for this poor convergence. Thus, it is interesting to investigate other basis functions that may represent the fields more accurately. The approach proposed in this paper consists in subdividing the pattern in homogeneous layers, according to the periodicity axis. The field is expanded, in each layer, on the basis of Gegenbauers polynomials. Boundary conditions are rigorously written between adjacent layers; thus, an eigenvalue equation is obtained. The approach presented in this paper proves to describe the fields accurately. Finally, it is demonstrated that the results obtained with the MMGE1 are more accurate than several existing modal methods, such as the classical and the parametric FMM.

Modal analysis of lamellar gratings using the moment method with subsectional basis and adaptive spatial resolution

We formulate the problem of diffraction by a one-dimensional lamellar grating as an eigenvalue problem in which adaptive spatial resolution is introduced thanks to a new coordinate system that takes into account the permittivity profile function. We use the moment method with triangle functions as expansion functions and pulses as test functions. Our method is successfully compared with the Fourier modal method and the frequency domain finite difference method.

Analysis of Defect in Extreme UV Lithography Mask Using a Modal Method Based on Nodal B-Spline Expansion

This paper details to an electromagnetic modeling of an extreme ultraviolet (EUV) lithography mask. For that purpose, a modal method based on a spline nodal expansion (MMSNE) is presented. The results obtained using first, and second-order splines as basis functions are compared with those obtained using other modal methods, such as modal method by Fourier expansion (MMFE). The agreement between the results obtained using different methods is very good, and a convergence test is also performed. The spline nodal basis function implemented in this paper is the first step toward the realization of a multiresolution scheme that is expected to perform much more efficiently than conventional schemes.

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.

Beam implementation in a nonorthogonal coordinate system: Application to the scattering from random rough surfaces

The C method is known to be one of the most efficient and versatile tools established for modeling diffraction gratings. Its main advantage is the use of a coordinate system in which the boundary conditions apply naturally and are, ipso facto, greatly simplified. In the context of scattering from random rough surfaces, we propose an extension of this method in order to treat the problem of diffraction of an arbitrary incident beam from a perfectly conducting (PEC) rough surface. For that, we were led to revisit some numerical aspects that simplify the implementation and improve the resulting codes.

Perturbation method for the Rigorous Coupled Wave Analysis of grating diffraction

The perturbation method is combined with the Rigorous CoupledWave Analysis (RCWA) to enhance its computational speed. In the original RCWA, a grating is approximated by a stack of lamellar gratings and the number of eigenvalue systems to be solved is equal to the number of subgratings. The perturbation method allows to derive the eigensolutions in many layers from the computed eigensolutions of a reference layer provided that the optical and geometrical parameters of these layers differ only slightly. A trapezoidal grating is considered to evaluate the performance of the method.

Complex coordinate implementation in the curvilinear coordinate method: application to plane-wave diffraction by nonperiodic rough surfaces.

We investigate the electromagnetic modeling of plane-wave diffraction by nonperiodic surfaces by using the curvilinear coordinate method (CCM). This method is often used with a Fourier basis expansion, which results in the periodization of both the geometry and the electromagnetic field. We write the CCM in a complex coordinate system in order to introduce the perfectly matched layer concept in a simple and efficient way. The results, presented for a perfectly conducting surface, show the efficiency of the model.

A Hybrid Method for the Study of Plane Waves Scattering by Rough Surfaces

We present a modified version of the curvilinear coordinate method (C.C.M.) for simulating electromagnetic waves scattering by rough surfaces. Numerically the field is obtained from the solution of an eigenvalue problem in Fourier Space. Unfortunately, it appears that the field suffers from parasitic oscillations related to finite spectral resolution. These oscillations are successfully removed by coupling the C.C.M. with the Stratton-Chu formulas.

Numerical scheme for the modal method based on subsectional Gegenbauer polynomial expansion: application to biperiodic binary grating

The modal method based on Gegenbauer polynomials (MMGE) is extended to the case of bidimensional binary gratings. A new concept of modified polynomials is introduced in order to take into account boundary conditions and also to make the method more flexible in use. In the previous versions of MMGE, an undersized matrix relation is obtained by solving Maxwells equations, and the boundary conditions complement this undersized system. In the current work, contrary to this previous version of the MMGE, boundary conditions are incorporated into the definition of a new basis of polynomial functions, which are adapted to the boundary value problem of interest. Results are successfully compared for both metallic and dielectric structures to those obtained from the modal method based on Fourier expansion (MMFE) and MMFE with adaptative spatial resolution.