In this paper, we describe the development of a novel instrument, tentatively called tomographic Mueller-matrix scatterometer (TMS), which enables illuminating sequentially a sample by a plane wave with varying illumination directions and recording, for each illumination, the polarized scattered field along various directions of observation in the form of scattering Mueller matrices. The incidence angle is varied from 0° to 65.6° with the rotation of a flat mirror that changes the position of the focal point of a light beam on the back focal plane of a high numerical aperture objective lens. The scattering Mueller matrices are collected over a wide range of scattering angles (0°-67°) and azimuthal angles (0°-360°). The developed instrument was then applied for the measurement of nanostructures in combination with an inverse scattering problem solving technique. The experiment performed on a periodic nanostructure preliminarily demonstrates the performance of TMS as well as its potential in nanostructure metrology. It is expected that the TMS would be a powerful tool for characterizing the polarized scattered-field distributions and measuring nanostructures in nanomanufacturing.
In this work, we combine conventional boundary element method (BEM) with the reduced-basis method (RBM) and propose a reduced-basis boundary element method (RB-BEM) to realize efficient modeling for parameterized electromagnetic scattering problems of dielectric scatterers. The RB-BEM allows for splitting the modeling process into a parameter-independent offline part and parameter-dependent online part, and replacing the high-dimensional original model obtained by conventional BEM with a low-dimensional reduced-basis model to improve computational efficiency of the online part. We also propose an improved greedy algorithm based on multi-grid to improve the computational efficiency of the offline part. The numerical experiments indicate that the efficiency of the improved greedy algorithm is several times higher than that of the standard one, and the solving efficiency of the reduced-basis model is several times to dozens of times higher than that of the original model with a prescribed approximation accuracy.
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