Mirza Karamehmedovic

Comparison of numerical methods in near-field computation for metallic nanoparticles

Four widely used electromagnetic field solvers are applied to the problem of scattering by a spherical or spheroidal silver nanoparticle in glass. The solvers are tested in a frequency range where the imaginary part of the scatterer refractive index is relatively large. The scattering efficiencies and near-field results obtained by the different methods are compared to each other, as well as to recent experiments on laser-induced shape transformation of silver nanoparticles in glass.

Tikhonov regularization in Lp applied to inverse medium scattering

This paper presents Tikhonov- and iterated soft-shrinkage regularization methods for nonlinear inverse medium scattering problems. Motivated by recent sparsity-promoting reconstruction schemes for inverse problems, we assume that the contrast of the medium is supported within a small subdomain of a known search domain and minimize Tikhonov functionals with sparsity-promoting penalty terms based on Lp-norms. Analytically, this is based on scattering theory for the Helmholtz equation with the refractive index in Lp, 1 < p < ∞, and on crucial continuity and compactness properties of the contrast-to-measurement operator. Algorithmically, we use an iterated soft-shrinkage scheme combined with the differentiability of the forward operator in Lp to approximate the minimizer of the Tikhonov functional. The feasibility of this approach together with the quality of the obtained reconstructions is demonstrated via numerical examples.

Profile estimation for Pt submicron wire on rough Si substrate from experimental data

An efficient forward scattering model is constructed for penetrable 2D submicron particles on rough substrates. The scattering and the particle-surface interaction are modeled using discrete sources with complex images. The substrate micro-roughness is described by a heuristic surface transfer function. The forward model is applied in the numerical estimation of the profile of a platinum (Pt) submicron wire on rough silicon (Si) substrate, based on experimental Bidirectional Reflectance Distribution Function (BRDF) data.

Numerical simulation of Electron Energy Loss Spectroscopy using a Generalized Multipole Technique

We numerically simulate low-loss Electron Energy Loss Spectroscopy (EELS) of isolated spheroidal nanoparticles, using an electromagnetic model based on a Generalized Multipole Technique (GMT). The GMT is fast and accurate, and, in principle, flexible regarding nanoparticle shape and the incident electron beam. The implemented method is validated against reference analytical and numerical methods for plane-wave scattering by spherical and spheroidal nanoparticles. Also, simulated electron energy loss (EEL) spectra of spherical and spheroidal nanoparticles are compared to available analytical and numerical solutions. An EEL spectrum is predicted numerically for a prolate spheroidal aluminum nanoparticle. The presented method is the basis for a powerful tool for the computation, analysis and interpretation of EEL spectra of general geometric configurations.

Inclusion estimation from a single electrostatic boundary measurement

We present a numerical method for the detection and estimation of perfectly conducting inclusions in conducting homogeneous host media in . The estimation is based on the evaluation of an indicator function that depends on a single pair of Cauchy data (electric potential and current) given at the boundary of the medium. The indicator function is derived using Green’s third identity with the fundamental solution for the Dirichlet Laplacian on the unit disc. Using a truncated Taylor expansion, the indicator function is expressed in terms of an integral over a perturbed inclusion boundary, resulting in a natural physical interpretation. The method is implemented numerically, tested on different example problems and compared to a decomposition approach based on the method of fundamental solutions. The method shows promising results and seems robust to noisy, low sampling-frequency data.

Stable source reconstruction from a finite number of measurements in the multi-frequency inverse source problem

We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the source. We study the problem in a certain finite dimensional setting: from measurements made at a finite set of frequencies we uniquely determine and reconstruct sources in a subspace spanned by finitely many Fourier–Bessel functions. Further, we obtain a constructive criterion for identifying a minimal set of measurement frequencies sufficient for reconstruction, and under an additional, mild assumption, the reconstruction method is shown to be stable. Our analysis is based on a singular value decomposition of the source-to-measurement forward operators and the distribution of positive zeros of the Bessel functions of the first kind. The reconstruction method is implemented numerically and our theoretical findings are supported by numerical experiments.