Application of Cauchy Integral Equation on Clifford Algebra for Forward-Backward Wave Decomposition

Abstract

A novel decomposition technique of the forward and backward propagating waves is presented. This technique exploits the Cauchy integral equation based on Clifford algebra application which the integral operators satisfying with Maxwell's equations provide all components of electromagnetic fields along the boundary of the problem. It is able to solve the boundary value problem in the case of partial transmission and reflection. The presented technique is implemented with the boundary element method to verify the performance by decomposing the summation of forward and backward propagating waves of a sample boundary whose shape is a cube. These recovered fields on continuous (flat) and discontinuous (edge and corner) surfaces are more accurate when increase the number of elements. The measured error is about 0.02%-0.3% at wavenumber k = 1.0Rad/m.