Exact analytical and approximate analyses of Bragg reflectors with nonrectangular index profiles
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Exact reflectivity spectra for sawtooth gratings are obtained by an analytical transfer matrix and are compared with approximate spectra obtained from the first-order coupled-wave method and from transfer matrix calculations based on representations of the sawtooth by piecewise constant segments. We find that the discrepancy between the exact spectra and the spectra obtained from approximate calculations is most evident for long or short gratings and increases with the depth of the index modulation in the grating.
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