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Abstract
We present here a differential method to calculate the fields diffracted by corrugated gratings characterized by a dielectric constant. We consider the general case in which the wave-vector of the incident plane wave is not contained in the main section of the grating. To simplify the boundary conditions the regions above and below the grating surface are transformed into half planes by means of conformal and non-conformal mappings. Numerical examples validating the effectiveness of the developed algorithm are provided for the case of cycloidal and triangular profile gratings.