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Sobolev mappings and Luzin condition N
Matějka, Milan ; Hencl, Stanislav (advisor) ; Malý, Jan (referee)
A mapping f from R^{n} to R^{n} is said to satisfy the Luzin condition N if f maps sets of measure zero to sets of measure zero. It is known to be valid for mappings in the Sobolev space W^{1,p} for p > n and for p <= n there are counterexamples. The aim of this thesis is to summarize known results and study the validity of Luzin condition N for mappings in the Sobolev space W^{2,p}.
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Blaze Gratings with a Ribbed Back Slope
Krátký, Stanislav ; Meluzín, Petr ; Horáček, Miroslav ; Kolařík, Vladimír ; Matějka, Milan ; Chlumská, Jana ; Král, Stanislav
Binary relief phase-modulated gratings provide symmetrical diffraction of the incoming light beam. Asymmetrical gratings, e.g. asymmetrical triangular blazed gratings, are characteristic by an asymmetrical diffraction behavior, where one of the first diffraction orders is more important than the other one. Electron beam lithography is a suitable and flexible tool for patterning of such kind of gratings. High quality results can be readily obtained when the period of the grating is relatively large and the relief depth is relatively low, this is the case of gratings with a small blaze angle. As the blaze angle increases, the quality of result suffers from several patterning-related issues. One of the problems is a reflection of the incoming light beam from the back slope (anti-blaze facet) of the blaze grating. We propose a novel configuration, with a ribbed modulation of the back slope. This modulation is perpendicular to the direction of the grating grooves. This paper presents an analysis of the proposed blazed grating configuration. E-beam pattern generators were used to prepare a few\nsamples of blaze gratings with a ribbed back slope. One part of the experiment was performed with a Gaussianshaped beam and another one with the variable-shaped beam. Results of the experiment are presented.\nFinally, we discuss the optical performance of two blaze gratings with similar parameters, one of them is with the flat back slope and another one is with the ribbed back slope.
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Parameter Optimization of Multi-Level Diffraction Gratings
Matějka, Milan ; Kolařík, Vladimír ; Horáček, Miroslav ; Král, Stanislav
Originally, the e-beam lithography (EBL) is a technique for creating high-resolution black and white masks for the optical lithography. Multi-level relief structures can be also prepared using EBL patterning. Their preparation is based on the image patterning with a gradient of exposure doses. Large-area multi-level structures can be effectively prepared using the electron beam pattern generator with a variable shaped beam. We present several writing strategies. Basically, the main writing strategy uses one stamp (i.e. one elementary exposure of the shaped electron beam) per one elementary area with the same exposure dose. This simple approach is fast and flexible, however it does not guarantee optimal results. The main problem is an imperfection of the stamps (size, shape, and homogeneity). Advanced algorithms are based on multiple\nexposure of the same elementary area, the total local exposure dose is a sum of several different elementary exposures (stamps). Using these algorithms, a smoother surface of the structure can be achieved. On the other hand, the writing speed is considerably decreased. Tradeoff between the achieved parameters and the writing speed is discussed for selected set of writing strategy algorithms.
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Nanopatterning of Silicon Nitride Membranes
Matějka, Milan ; Krátký, Stanislav ; Řiháček, Tomáš ; Kolařík, Vladimír ; Chlumská, Jana ; Urbánek, Michal
Membranes are typically created by a thin silicon nitride (SIN) layer deposited on a silicon wafer. Both, top and bottom side of the wafer is covered by a thin layer of the silicon nitride. The principle of silicon nitride membranes preparation is based on the wet anisotropic etching of the bottom side of the silicon wafer with crystallographic orientation (100). While the basic procedure for the preparation of such membranes is well known, the nano patterning of thin membranes presents quite important challenges. This is partially due to the mechanical stress which is typically presented within such membranes. The resolution requirements of the membrane patterning have gradually increased. Advanced lithographic techniques and etching procedures had to be developed. This paper summarizes theoretical aspects, technological issues and achieved results. The application potential of silicon nitride membranes as a base for multifunctional micro system (MMS) is also\ndiscussed.
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SMV-2016-03: Precise relief structures
Matějka, Milan ; Horáček, Miroslav ; Meluzín, Petr ; Chlumská, Jana ; Král, Stanislav ; Kolařík, Vladimír ; Krátký, Stanislav ; Fořt, Tomáš ; Oulehla, Jindřich ; Šerý, Mojmír
Research and development in the field of precise relief structures using electron beam lithography and other ultra-precise micro manufacturing techniques.
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Laser and Phyllotaxy
Kolařík, Vladimír ; Horáček, Miroslav ; Krátký, Stanislav ; Meluzín, Petr ; Chlumská, Jana ; Matějka, Milan ; Král, Stanislav
The paper presents planar diffractive structures with optical elements arranged in positions according to a phyllotactic model. Further, we discuss the creation of a diffractive phyllotactic pattern and its properties. One of the particular arrangements, a nesting of two different phyllotactic models possessing a different level of fineness, is described in details. The discussed arrangement of elements within a circle can be used also in the laser beam splitting application.
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Submicron Structures with Deep Relief — Technology of Preparation
Matějka, Milan ; Kuřitka,, Ivo (referee) ; Mgr. Petr Klapetek Ph.D (referee) ; Kolařík, Vladimír (advisor)
The dissertation thesis is focused on research and development in the field of microfabrication by the technology of electron beam lithography. In the first part of this work, the extensive study is conducted in the field of technology of electron beam lithography in terms of physical principles, writing strategies and resist materials. This is followed with description of physical principles of etching for the transfer of relief structures into substrates. The thesis describes innovative techniques in modelling, simulation, data preparation and optimization of manufacturing technology. It brings new possibilities to record deep binary or multilevel microstructures using electron beam lithography, plasma and reactive ion etching technology. Experience and knowledge in the large area of microlithography, plasma and anisotropic wet-etching of silicon have been capitalized to the design process of manufacturing of nano-patterned membranes. It was followed with practical verification and optimization of the microfabrication process.
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