Related papers: Upper bounds on absorption and scattering
Polymers have appealing optical, biochemical, and mechanical qualities, including broadband transparency, ease of functionalization, and biocompatibility. However, their low refractive indices have precluded wavelength-scale optical…
The positive effects of various perturbations introduced in a bidimensional photonic-crystal patterned membrane on its integrated absorption are investigated numerically and theoretically. Two phenomena responsible for the enhanced…
Multiple scattering of waves in disordered media is a nightmare whether it be for detection or imaging purposes. The best approach so far to get rid of multiple scattering is optical coherence tomography. It basically combines confocal…
Wavefront shaping enables control of classical light through scattering media. Extending these techniques to spatially entangled photons promises new quantum applications, but their fundamental limits, especially when both photons scatter,…
The matrix spectral and nuclear norms appear in enormous applications. The generalizations of these norms to higher-order tensors is becoming increasingly important but unfortunately they are NP-hard to compute or even approximate. Although…
We prove upper bounds on the graph diameters of polytopes in two settings. The first is a worst-case bound for polytopes defined by integer constraints in terms of the height of the integers and certain subdeterminants of the constraint…
We present a generalized formalism to describe the optical energy flow and spatially resolved absorption in arbitrarily anisotropic layered structures. The algorithm is capable of treating any number of layers of arbitrarily anisotropic,…
The problem of plane-wave diffraction on semi-infinite orthorhombic electromagnetic (photonic) crystals of general kind is considered. Boundary conditions are obtained in the form of infinite system of equations relating amplitudes of…
We introduce a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$ - $\Omega$ a…
The dielectric microsphere can be directly embedded into the traditional microscope, which can significantly improve the resolution of the microscope and provide a simple and feasible way to break through the diffraction limit of optical…
The scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this…
Employing plasmonic antennas for subdiffraction focusing of light on recording media requires to take into account the complete structure of the medium, including dielectric cover layers. We find, with finite difference time domain…
Nanoscale manufacturing requires high-precision surface inspection to guarantee the quality of the produced nanostructures. For production environments, angle-resolved scatterometry offers a non- invasive and in-line compatible alternative…
Global stability of the spherically symmetric nonisentropic compressible Euler equations with positive density around global-in-time background affine solutions is shown in the presence of free vacuum boundaries. Vacuum is achieved despite…
We analyze scattering in a system of two (distinguishable) particles moving on the half-line $\overline{\rz}_+$ under the influence of singular two-particle interactions. Most importantly, due to the spatial localization of the interactions…
We consider diffraction at random point scatterers on general discrete point sets in $\R^\nu$, restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence…
Existence and uniqueness of the scattering solutions is proved for a class of bounded rough obstacles which is much larger than the class of Lipschitz obstacles. Integral equations method is not used. The approach is based on the…
In this paper we consider the inverse scattering problem for high-contrast targets. We mathematically analyze the experimentally-observed phenomenon of super-resolution in imaging the target shape. This is the first time that a mathematical…
Numerical optimization for the inverse design of photonic structures is a tool which is providing increasingly convincing results -- even though the wave nature of problems in photonics makes them particularly complex. In the meantime, the…
The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…