Rigorous and fast convergent analysis of a coupler slotted in common wall between two dissimilar rectangular waveguides is described by a mode-matching method combined with Fourier transform technique and consideration of the singularity of electromagnetic field around edges. Comparing with a conventional mode-matching method, the present method has two advantages. One is that it can avoid the usage of the dyadic Green's function, the other is that it can overcome the relative convergence problem. The consideration of the field singularity has greatly improved the convergence and the calculated accuracy of a solution. This analysis is rigorous and the computer cost is very low.
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