MODAL METHOD BASED ON SPLINE EXPANSION FOR THE ELECTROMAGNETIC ANALYSIS OF THE LAMELLAR GRATING

This paper reports an exact and explicit representation of the differential operators from Maxwellʹs equations. In order to solve these equations, the spline basis functions with compact support are used. We describe the electromagnetic analysis of the lamellar grating as an eigenvalues problem. We choose the second degree spline as basis functions. The basis functions are projected onto a set of test functions. We use and compare several test functions namely: Dirac, Pulse and Spline. We show that the choice of the basis and test functions has a great influence on the convergence speed. The outcomes are compared with those obtained by implementing the Finite-Difference Modal Method which is used as a reference. In order to improve the numerical results an adaptive spatial resolution is used. Compared to the reference method, we show a significantly improved convergence when using the spline expansion projected onto spline test functions.