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.

Several design-concepts are presented for so-called efficiency achromatized diffractive optical elements (EA-DOEs) possessing a diffraction efficiency larger than 97% over a broad spectral range. We start with tracing two different methods for surface relief profiles well known from the literature: common depth and multilayer EA-DOEs. Successively we present the following new approaches together with design parameters and performance properties: 1) gradient-index EA-DOEs, 2) sub-wavelength EA-DOEs, and 3) a so-called cut-and-paste strategy. All designs are based on scalar assumptions and certain necessary dispersion relations of two different materials. The scalar assumption is no real limitation as the minimum zone width of our main application, the correction of chromatic aberrations, is 50. .. 100 times the wavelength. From aforementioned relations, design parameters as profile heights are derived and the resulting diffraction efficiency can be deduced. Moreover, for the multilayer and for the GRIN EA-DOEs we are able to show that if the dispersion relations of the materials can be accurately described by second order Cauchy series, the efficiency becomes generic and will be the same regardless of which materials are chosen.

We give a general introduction into polarized imaging and report on a Jones-pupil approach for a complete evaluation of the resulting optical performance. The Jones pupil assigns a Jones matrix to each point of the exit pupil describing the impact of both the global phase and the polarization on imaging. While we can learn already a lot about the optical system by taking a close look at the Jones pupil -and starting imaging simulations from it -a quantitative assessment is necessary for a complete evaluation of imaging. To do this, we generalize the concept of scalar Zernike aberrations to Jones-Zernike aberrations by expansion of the Jones pupil into vector polynomials. The resulting method is nonparaxial, i.e. the effect of the polarization dependent contrast loss for high numerical apertures is included. The aberrations of the Jones-matrix pupil are a suitable tool to identify the main drivers determining the polarization performance. Furthermore, they enable us to compare the polarized and the unpolarized performance of the such characterized lithographic system.

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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.

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.

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