In this paper, an efficient mode reduction technique for eigenmode expansion method is developed to analyze 2-D waveguide grating structures which are a special class of piecewise uniform waveguides. To take advantage of the periodicity property of the structure, the eigenmode expansion method (EEM) is used with the scattering matrix method and a recursive-doubling procedure. In this situation, our proposed mode reduction technique achieves a significant speedup for gratings with large number of periods. Comprehensive numerical examples on the waveguide gratings are studied to validate the efficiency of our proposed mode reduction technique.
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