We present an effective modeling approach for a fast calculation of the Talbot carpet from an initially 2-dimensional mask pattern. The introduced numerical algorithm is based on a modified angular-spectrum method, in which it is possible to consider the border effects of the Talbot region from a mask with a finite aperture. The Bluestein’s fast Fourier transform (FFT) algorithm is applied to speed up the calculation. This approach allows as well to decouple the sampling points in the real space and the spatial frequency domain so that both parameters can be chosen independently. As a result an extended three-dimensional Talbot-carpet can be calculated with a minimized number of numerical steps and computation time, but still with high accuracy. The algorithm was applied to various 2-dimensional mask patterns and illumination setups. The influence of specific mask patterns to the resulting field intensity distribution is discussed.

The diffraction efficiencies of modified sinusoidal and blazed gratings are investigated in the high spatial frequency regime by rigorous numerical methods and are compared to experimentally manufactured gratings. The introduced modifications take actual technological induced variations of the profile geometries, such as specific corner rounding, into account. The high spatial frequency regime (resonance regime) is characterized by a local grating period, g, to wavelength, λ , ratio of 0.7 ≤ g/ λ ≤ 4 and shows an important relevance for applications in spectroscopy and diffractive imaging. The investigations are carried out for both reflection on metallic surfaces and transmission of dielectric structures over a broad range of grating periods and incidence angles. It was found that near the grating resonance, the more simply producible sine gratings can compete in diffraction efficiency with sawtooth structures. Additionally, for certain application conditions, holographically modified sine structures achieve higher efficiencies than the ideal sine profile. It is also shown that holographic sinusoidal-like profiles measured by AFM can be fitted to a super-Gaussian shape, which is then used to inversely reconstruct the structure profiles from efficiency data.

In this contribution we are focusing on two challenges concerning the development of new spectrometer concepts. First, we present different concepts to adjust or even to increase the detection efficiency of spectrometer modules over a broad spectral range. The discussion involves a spectral recycling loop, a reflective multilayer approach for efficiency achromatization and a concept based on spectral pre-selection. The second focus of this contribution concerns the miniaturization of spectrometer setups. We present a highly compact imaging miniature spectrometer module for applications that allow a very limited installation volume. The miniature spectrometer has an optical volume of just 11 x 6 x 5 mm(3). The implementation of the spectroscopic "multi-order principle", which exploits successive diffraction orders, means that the central stress field between high spectral resolution and a large bandwidth can be dissolved. The manufacturing process of the spectrometer includes the mastering of the concave grating by interference lithography, the tooling and the replication process by injection molding.

A solid immersion lens based on diffraction (dSIL) is proposed as an alternative to the conventional design based on refraction. A design analogous to a Fresnel zone plate is derived in accordance with the Huygens-Fresnel principle. Fabrication of a binary dSIL is achieved by electron-beam lithography and reactive-ion etching on LaSF35, with index n = 2.014. Measurement of the point-spread function is performed with near-field optical microscopy. The results are in accord with the expected resolution enhancement of a factor n with respect to the diffraction limit.

Rigorous modelling by electromagnetic diffraction theory is used to design the diffractive polarizing beam splitters (DPBS) and to reach the best compromise between fabrication, feasibility and optical quality of the optical device. We use two types of integration methods: the rigorous coupled-wave analysis (RCWA) and a finite element method (FEM), where the latter comprises an optimization algorithm to solve the inverse diffraction problem by applying the method of gradient descend to minimize an integral functional over the visible spectral range involving the desired diffraction efficiencies.