A rigorous solution is presented for plane-wave scattering by an asymmetric diffraction grating, which consists of a corrugated structure with three different groove depths per period. After establishing that asymmetry effects in the scattered amplitudes may be observed only if at least three spectral orders are present, we find that maximum asymmetry occurs when the angle of incidence closely satisfies a Bragg condition. For normal incidence, the peak asymmetry coincides with blazing, the degree of which may be quite significant. By employing simple phasing considerations, we derive a scheme for optimizing the grating design, and present examples illustrating that very high blazing efficiencies are easily attainable.
R. J. Ikola, A. Hessel, and T. Tamir, "Asymmetry and blazing effects in corrugated structures," J. Opt. Soc. Am. 63, 408-415 (1973)