Oliver Sandfuchs

Diffraction-based solid immersion lens

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 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 systems 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.

Flexible mask illumination setup for serial multipatterning in Talbot lithography

A flexible illumination system for Talbot lithography is presented, in which the Talbot mask is illuminated by discrete but variable incidence angles. Changing the illumination angle stepwise in combination with different exposure doses for different angles offers the possibility to generate periodic continuous surface relief structures. To demonstrate the capability of this approach, two exemplary micro-optical structures were manufactured. The first example is a blazed grating with a stepsize of 1.5 μm. The second element is a specific beam splitter with parabolic-shaped grating grooves. The quality of the manufacturing process is evaluated on the basis of the optical performance of the resulting micro-optical elements.

Analysis of the influence of the passive facet of blazed transmission gratings in the intermediate diffraction regime.

Blazed diffraction gratings are of enormous practical importance for imaging and analyzing hybrid optical systems. The intermediate diffraction regime is characterized by the transition from the scalar to the rigorous electromagnetic theory. An effect known as shadowing occurs and reduces the diffraction efficiency. Based on rigorous calculations for optimized sawtooth-shaped and binary-multilevel blaze profiles, we deduce a semianalytical model describing the shadowing phenomenon for the general case of oblique incidence. We discuss illumination both from air and from the substrate. Though a multilevel blaze possesses a discrete substructure, our shadowing model remains valid, if substructural effects are neglected. We find that electromagnetic effects due to the passive blaze facet lead to the efficiency reduction, and the blazing efficiency shows a linear dependence on the ratio of blaze wavelength to grating period. Our shadowing model is applied to predict the performance of a Littrow-like blazing condition in transmission geometry as, e.g., for a diffractive solid immersion lens.

Rigorous modeling of dielectric and metallic blaze gratings in the intermediate structure regime

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.

Talbot-carpets of periodic and quasi-periodic close-packed 2D mask structures calculated by a modified chirp-z-algorithm

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 Bluesteins 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.

Optimization of holograms for application in automotive headlamps with LED illumination

To prepare holograms for application in automotive headlamps, LED characteristics are considered during design and simulation. First experimental results to verify algorithms are presented and necessary steps for further improvements are discussed.

Influence of oblique illumination on perfect Talbot imaging and nearly perfect self-imaging for gratings beyond five diffraction orders

The Talbot self-imaging effect of amplitude gratings is afflicted with aberrations that distort the self-image. This occurs especially if the grating period p is only a few times larger than the illumination wavelength λ. For example, for lithographic applications of the Talbot effect these aberrations lower the lateral writing resolution and should be minimized. Noponen found, however, some discrete ratios of p/λ in the interval of 2.0<p/λ<3 that are aberration-free. We generalize the definition of the Talbot distance to include oblique illumination and show how Noponens discrete ratios can be shifted by it. In the second part, we look at ratios of p/λ larger than 3, so that there are more than five diffraction orders behind the grating. For this region we present a method to find ratios of p/λ with at least minimal aberrations and present some self-image examples that are of interest for lithographic purposes up to the range of p/λ≈12.

Microstructured optics for excimer-based systems: applications for imaging, beam shaping, and coherence management

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.

Design and rigorous modelling of structured multilayer gratings for broadband applications in the visible spectrum

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.