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

Abstract

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 Maxwell's 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.

Physicomathematical models of seeds and errors in calculating the volume of an electro terminator filled with seeds

“…Many researchers have considered methods of calculating three-dimensional bodies, convex bodies. In these works, mathematical formulas and various research methods are given in detail [5][6][7][8][9][10][11][12][13][14][15].…”

Polynomial modal method for analysis of the coupling between a gap plasmon waveguide and a square ring resonator

“…For the numerical evaluation through the subsectional polynomial basis approach MMGE, [5][6][7][8] the slot waveguide is subdivided into four homogeneous domains (intervals) (I ð1Þ…”

“…This boundary value problem is efficiently solved throughout a polynomial modal method based on Gegenbauer expansion (MMGE). [5][6][7][8] I first show that this numerical scheme allows avoidance of any uncertainties in the numerical model. A new physical analysis and interpretation of the transmission spectrum anomaly is then suggested.…”

Coupling between subwavelength nano-slit lattice modes and metal-insulator-graphene cavity modes: a semi-analytical model

“…In order to explain the origin of this particular behaviour, we first split the hybrid system into a couple of sub-systems. Second, thanks to a modal analysis through the polynomial modal method (PMM: one of the most efficient methods for modeling the electromagnetic properties of periodic structures) [26][27][28][29], we demonstrate that the scattering parameters of each sub-system can be computed through a concept of weak and strong couplings. Finally we provide analytical expressions of the reflection and transmission coefficients of the structure and describe the mechanisms leading to Lorentz and Fano resonances occurring in it.…”