Abstract
An algorithm for the numerical solution of the inhomogeneous Maxwell's equations is presented. The algorithm solves the inhomogeneous vector wave equation of the electric field by writing the solution as a convergent Born series. Compared to two dimensional finite difference time domain calculations, solutions showing the same accuracy can be calculated more than three orders of magnitude faster.
Highlights
Today there are numerous applications where solutions of Maxwell’s equations in inhomogeneous media are required
Very small cell sizes have to be used. This restriction can partly be overcome by using the pseudo spectral time domain (PSTD) method [11, 12] where the spatial derivatives are calculated using a Fourier transformation
A further method is the discrete dipole approximation (DDA), [13, 14] where the system is discretized by small polarizable grains
Summary
Today there are numerous applications where solutions of Maxwell’s equations in inhomogeneous media are required. For this purpose several numerical methods have been developed These methods include the finite difference time domain (FDTD) method [9, 10] where the time integration of Maxwell’s equations is performed on a discrete grid using finite differences to calculate the spatial derivatives. For this method, very small cell sizes have to be used. In the second part we describe the new algorithm with special attention to its comparison to the work of Osnabrugge et al In the third and fourth part we present numerical results using the described algorithm These results are compared with an analytical theory for scattering by multiple cylinders [7, 18,19,20].
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