Related papers: Refractive index profiles for a $\mathcal{PT}$-sym…
In the present paper we describe a method for solving inverse problems for the Helmholtz equation in radially-symmetric domains given multi-frequency data. Our approach is based on the construction of suitable trace formulas which relate…
The aims of the reported work are to provide new insights into the quantum dot optical properties confined in an inverse of a quadratic Hellmann potential. The Schr\"odinger equation is solved using the Nikiforov-Uvarov (NU) method, in…
For the first time exact analytical solutions to the eikonal equations in (1+1) dimensions with a refractive index being a saturated function of intensity are constructed. It is demonstrated that the solutions exhibit collapse; an explicit…
We derive spectral width estimates for traces of tempered solutions of a large class of multiplier equations in $\mathbf{R}^n$. The estimates are uniform for solutions up to a given order. In the process, we find a rather explicit…
We consider reflectionless wave propagation in networks modeled in terms of the nonlocal nonlinear Schr\"odinger (NNLS) equation on metric graphs, for which transparent boundary conditions are imposed at the vertices. By employing the…
Ehrenborg and Jung recently related the order complex for the lattice of d-divisible partitions with the simplicial complex of pointed ordered set partitions via a homotopy equivalence. The latter has top homology naturally identified as a…
There are two main physical properties needed to fabricate 1D photonic structures and form perfect photonic bandgaps: the quality of the thickness periodicity and the refractive index of their components. Porous silicon (PS) is a…
We study one-dimensional optical wave turbulence described by the 1D Schr{\"o}dinger-Helmholtz model for nonlinear light propagation in spatially nonlocal nonlinear optical media such as nematic liquid crystals. By exploiting the specific…
Quantitative tissue information, like the light scattering properties, is considered as a key player in the detection of cancerous cells in medical diagnosis. A promising method to obtain these data is optical coherence tomography (OCT). In…
In this paper we construct a parametrix for the fractional Helmholtz equation $((-\Delta)^s - \tau^{2s} r(x)^{2s} + q(x))u=0$ making use of geometrical optics solutions. We show that the associated eikonal equation is the same as in the…
The broken and unbroken phases of PT and supersymmetry in optical systems are explored for a complex refractive index profile in the form of a Scarf potential, under the framework of supersymmetric quantum mechanics. The transition from…
This work introduces a novel reinterpretation of structured illumination (SI) microscopy for coherent imaging that allows three-dimensional imaging of complex refractive index (RI). To do so, we show that coherent SI is mathematically…
An isolated hypersurface singularity comes equipped with many different pairings on different spaces, the intersection form and the Seifert form on the Milnor lattice, a polarizing form for a mixed Hodge structure on a dual space, and a…
We discuss a time-harmonic inverse scattering problem for a nonlinear Helmholtz equation with compactly supported inhomogeneous scattering objects that are described by a nonlinear refractive index in unbounded free space. Assuming the…
We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly…
We consider a type of hypothetical compound materials in which its refractive index in spatial distribution meet $n(-x)=-n^{*}(x)$, belonging to anti-parity-time (APT) symmetric structures. Additionally, we demand balanced real positive-…
In this paper, we consider the inverse spectral problem of determining the spherically symmetric refractive index in a bounded spherical region of radius $b$. Instead of the usual case of the refractive index $\rho\in W^2_2$, by using…
The identification of the refractive index and wave vector for general (possibly active) linear, isotropic, homogeneous, and non-spatially dispersive media is discussed. Correct conditions for negative refraction necessarily include the…
Negative refractive index materials have attracted significant research attention due to their unique electromagnetic response characteristics. In this paper, we employ the complementing boundary condition to establish rigorous a priori…
The construction of exactly solvable refractive indices allowing guided TE modes in optical waveguides is investigated within the formalism of Darboux-Crum transformations. We apply the finite-difference algorithm for higher-order…