Normal vector method for convergence improvement using the RCWA for crossed gratings.

The rigorous coupled wave analysis (RCWA) is a widely used method for simulating diffraction from periodic structures. Since its recognized formulation by Moharam [J. Opt. Soc. Am. A12, 1068 and 1077 (1995)], there still has been a discussion about convergence problems. Those problems are more or less solved for the diffraction from line gratings, but there remain different concurrent proposals about the convergence improvement for crossed gratings. We propose to combine Popov and Nevière's formulation of the differential method [Light Propagation in Periodic Media (Dekker, 2003) and J. Opt. Soc. Am. A18, 2886 (2001)] with the classical RCWA. With a suitable choice of a normal vector field we obtain a better convergence than for the formulations that are known from the literature.

Rigorous analysis of shadowing effects in blazed transmission gratings.

Blazed transmission gratings have become crucial components in many hybrid optical systems. Shadowing effects are known to occur at their passive blaze facets, which may impair the system's efficiency performance. For optical designs, it is desirable to have a simple but accurate description of this phenomenon. We show that the efficiency reduction in low diffraction orders is dominated by a linear dependence on the ratio of wavelength to grating period rather than a quadratic dependence as proposed in extended scalar theory. The strength of the electromagnetic shadowing will be determined using rigorous diffraction methods and discussed with respect to imaging optical components. Results are compared to existing ray-optical models.

Area-coded effective medium structures, a new type of grating design.

We propose a new way to design gratings with desired diffraction properties by using subwavelength feature sizes perpendicular to the ordinary superwavelength grating period. This is different from well-known one-dimensional binary-blazed gratings that use a structuring along the grating period and thus opens new flexibility in generating arbitrary effective-index distributions in the direction of the grating period. Since the subwavelength features form contiguous areas, they are called area-coded effective medium structures (ACES). Compared with well-known binary subwavelength structures in two-dimensional arrangements consisting of pillars, ACES are more stable and have comparable efficiency properties. As an example we show how to design in principle a four-level area-coded effective medium grating, compare the efficiency of ACES with binary-blazed and échelette gratings, and optimize the subwavelength period of ACES.