The element level time domain (ELTD) method for the analysis of nano-optical systems: II. Dispersive media

We study a 3-dimensional, dual-field, fully explicit method for the solution of dispersive Maxwell's equations in the time domain on unstructured, tetrahedral grids. In a previous paper, we investigated the element level time domain (ELTD) algorithm for solving electromagnetic problems with parameters independent of the excitation frequency content, i.e. nondispersive materials. The suitability of the ELTD method for the numerical analysis of nanometer structured systems in the optical frequencies was thoroughly studied. This paper introduces the generalization of the method and its implementation as a computer code for problems with dispersive material properties. We profit from the ELTD formulation in conjunction with the auxiliary differential equation (ADE) approach for modeling dispersion. Examples with analytical solutions are solved and verified in order to benchmark the method. Eventually, to demonstrate the potential of the method, we consider the structure of a single field emitter and solve for the electromagnetic fields when illuminated by a plane wave. We have obtained a flexible and versatile method of 2nd order accuracy that is applicable to both dispersive and nondispersive problems with a wide range of nano-optical configurations.

► The perviously developed ELTD method is generalized for dispersive problems.
► Its suitability for the numerical analysis of nano-optical devices is investigated.
► The theoretical details and its implementation as a computer code are introduced.
► The convergence behavior and stability conditions are examined.
► Through the analysis of analytically solvable problems the method is benchmarked.