Propagation of electromagnetic waves in media with relaxation: Numerical modeling using Laguerre transform

We model propagation of electromagnetic waves in frequency-dependent media applying the Laguerre transform in time domain. The new algorithm is fourth-order accurate in space and computationally efficient. Maxwell's equations are reduced to a harmonic series of linear algebraic equations in which only the right side depends on the harmonic number and the inverse matrix is the same for all harmonics. The efficiency of computation for the algebraic equations is improved by fitting the free parameter of the Laguerre transform. The value of this parameter is easy to find and is likewise the same for all harmonics. The Laguerre scheme provides a better accuracy than the second-order accurate finite-difference solution at large path lengths. The method is stable both in the region of the wavefield where conductivity approaches zero and the spectral Fourier method is unstable, and in the high-conductivity region where the explicit FDTD code requires a too small time step.