Higher‐order bragg diffraction by dielectric gratings

Abstract

AbstractThis paper analyzes the diffraction of a TE‐polarized plane wave incidence from a dielectric grating based on the modal expansion in which the orthogonalities of the Mathieu functions are used as almost periodic functions. This method provides good convergence particularly when the incident angle of the incident plane wave is close to the Bragg angle. As numerical examples, the incidence of a plane wave with a particular wave number for a given diffraction grating is shown for the incident angle near the first‐, second‐, and third‐order Bragg angles. The diffraction efficiency versus the grating thickness has been studied for the incidence at the first, second and third Bragg angles. The angular selectivity has also been investigated in the case where the incident angle is deviated from the Bragg angle of each order for the grating thickness for which the perfect extinction condition is satisfied for a straight‐through wave. On the anomalous diffraction due to the slab mode excited in a grating with its average dielectric constant larger than that of surroundings, the case of near second‐order Bragg angle incidence has been studied in detail. In the Appendix, new expansion coefficients of the Mathieu functions found by the Whittaker's method are provided for use in the analysis for near even‐order Bragg angle incidence.