A hybrid technique combining the mode-matching method and the geometrical theory of diffraction for edge discontinuities

The mode-matching method based on the least squares approach and Rayleigh theorem has been put forward as the simple and effective method for the numerical solution of scattering problems. Although this method has a rigorous proof of convergence, it does not always give us a desirable solution for edge discontinuities due to the inevitable limitation of computer memory. The poor convergence prevents more precise computation at higher frequencies. The proposed hybrid technique combining the mode-matching method and the geometrical theory of diffraction (GTD) is presented to accelerate the convergence of numerical solution for the scattering problem associated with edge discontinuities. To combine GTD with the mode-matching method, the singular integral equation technique which provides a quasi-static approximation is introduced in the procedure of formulation. As an example to illustrate the proposed technique, we applied it to the well-known scattering problem of an infinite plane grating. The numerical results show that the power errors are improved and are much better than those of the mode-matching method itself.