Second‐kind Fredholm integral‐equation analysis of scattering by layered dielectric gratings

Abstract

Abstract Scattering of the E‐polarised plane electromagnetic wave from two different but of the same‐period all‐dielectric rectangular bar gratings on substrates is analysed using a volume‐integral‐equation (VIE) method. Here, VIE is a Fredholm integral equation of the second kind with unknown function being the electric field in the gratings regions. Discretisation of the VIE is performed by applying an entire‐domain Galerkin technique. The developed algorithm possesses guaranteed convergence, provides accuracy, and is easily controlled by the order of discretisation. Numerical results for frequency‐selective reflection, manipulation of light to propagate in prescribed directions, and the ultrahigh‐Q lattice‐modes resonances are presented and discussed.

Keywords

• convergence of numerical methods
• diffraction gratings
• electromagnetic wave polarisation
• electromagnetic wave scattering
• Fredholm integral equations
• Galerkin method