The calculation of local absorption is very important in the context of lithography and in photo-detector design. We present a rigorous method for calculating the local absorption in periodic structures. The computation depends primarily on the calculation of the electric field inside the structure. Since the standard definitions produce unsatisfactory results, we use a modified version of a method published by Lalanne [J. Modern Opt. 45, 1357 (1998)]. The results for these field definitions agree very accurately with results obtained by the law of conservation of energy. We present some examples which are typical for the application scenarios of lithography and detectors.
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