In this contribution we simulate theoretically the resulting 3D Talbot-carpets of different initial close-packed 2D
mask structures. Especially, we investigate the transition from regular periodic to quasi-periodic tessellations. For
the pure periodic mask structure a hexagonally tessellation was selected. The calculated field distribution adjacent to
the mask still shows a lateral six-fold symmetry but also a rather complex characteristics in the propagation
direction. In particular, the appearance and the repetition of self-imaging planes deviate significantly from the
classical Talbot-effect.
For the quasi-periodic tessellation a Penrose tapestry based on rhombus pairs was chosen. A pronounced lateral fivefold
symmetry becomes visible in the field distribution. In the propagation direction dominant planes with increased
intensity are observed clearly, but, instead of a simple periodicity, a complex behavior becomes obvious. The
numerical algorithm used in our simulations is based on a modified angular spectrum method, in which Bluestein's
fast Fourier (FFT) algorithm is applied. This approach allows to decouple the sampling points in the real space and
in the spatial frequency domain so that both parameter can be chosen independently. The introduced fast and flexible
algorithm requires a minimized number of numerical steps and a minimal computation time, but still offers high
accuracy.
Imaging diffractive optical elements (DOEs), randomly distributed microlenses and sub-λ-structures allow
the improvement of the performance of Excimer-based imaging and illumination systems. Here we present
the concept study of a hybrid imaging system for Excimer laser high power application at a working
wavelength of 308 nm. In this hybrid approach a focus has to be put onto the impact of the non-desired
diffraction orders to the optical performance and also to the amount of light remaining in the system and
causing lens heating. Hereby the diffraction efficiency of the DOE is of enormous importance. Especially
the influence of the passive facet of blazed transmission gratings has to be considered. For illumination
systems we discuss the transfer of the uneven raw profile of an Excimer-laser into a Gaussian far-field
distribution by introducing a microlens array with a 2-dimensional Voronoi-pattern. The holographic
record of the microlens array allows additionally to influence the coherence parameters.
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 mm3. 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.
The performance predictions and optimization of blazed diffraction gratings are key issues for their application in hybrid
optical systems, both in the case of imaging and analyzing systems. Scalar and vectorial theories are often used for a first
performance estimation whenever applicable. However, in the intermediate structure regime, characterized by a grating
period within the transition from the validity of the scalar to the fully electromagnetic theory, rigorous numerical
simulations are inevitable for accurate modeling of blaze structures with sawtooth-shaped profiles. A variety of
electromagnetic algorithms exists to determine the diffraction efficiency, such as integral equation methods, finite
element methods or rigorous coupled-wave analyses. An effect known as shadowing occurs and has a significant
influence on the diffraction efficiency of the blazed grating. A simple but accurate model describing the shadowing
phenomena would be of enormous practical importance for the optical design of hybrid systems. Commonly, dielectric
transmission gratings are regarded, when the efficiency behavior due to shadowing is discussed. We succeeded in filling
the modeling gap in the intermediate structure regime and have derived a rigorous-based semi-analytical model for
dielectric gratings. We are able to extend this model to the case of metallic reflection gratings. For both types of gratings,
we find that the blaze efficiency obeys a linear dependence on the ratio of blaze wavelength to grating period, which
dominates the performance in the first diffraction order. We define the linear coefficient of shadowing strength and
discuss its dependence on the material properties.
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