Periodic dielectric grating structures are utilized to obtain frequency selective surfaces and are important in dichroic subreflectors for large reflecting antennas, resonant filters, distributed feedback amplifiers, multiplexers, and demultiplexers. The scattering phenomena by dielectric grating waveguides have already been analyzed by differential equation methods such as the rigorous coupled-wave analysis [1] and the modal method [2]. Their disadvantages consist in the facts that they are computationally intensive, require time-consuming root searches, large numerical matrices, and multiple time-intensive steps to determine the resonance's width [3].
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