In this paper a new method based on the complex images technique has been presented to efficiently compute the Green's functions required in a Mixed Potential Integral Equation (MPIE) analysis of a periodic structure located in a layered medium. This method leads to a closed-form representation for these slowly convergent series valid for sub-wavelength as well as super-wavelength cell sizes for all source point to field point distances. Comparison between the results obtained by the proposed method with ones obtained from other numerical approaches verifies its accuracy. Fast convergence, simple final form and versatility of the proposed method are its main advantages which make it suitable for the analysis of the periodic structures using the integral equation techniques.
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