Related papers: Generalized Finite Differences Method Applied to F…
We present a systematic numerical approach to compute the eigenmodes and the related eigenfrequencies of a disordered photonic crystal, characterized by small fluctuations of the otherwise periodic dielectric profile. The field eigenmodes…
In this paper we introduce a new approach and obtain new results for the problem of studying polynomial images of affine subspaces of finite fields. We improve and generalise several previous known results, and also extend the range of such…
In this paper we give a unified approach in categorical setting to the problem of finding the Galois closure of a finite cover, which includes as special cases the familiar finite separable field extensions, finite unramified covers of a…
Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to the complex nature, direct numerical simulations on the fine grid are prohibitively expensive. It is therefore important to develop…
The phenomenon of photonic band gaps in one-dimensional optical lattices is reviewed using a microscopic approach. Formally equivalent to the transfer matrix approach in the thermodynamic limit, a microscopic model is required to study…
We present a generalization of the RBF-FD method that computes RBF-FD weights in finite-sized neighborhoods around the centers of RBF-FD stencils by introducing an overlap parameter $\delta \in [0,1]$ such that $\delta=1$ recovers the…
This article investigates a space-time differential model related to the degradation of stone artifacts caused by exposure to air and atmospheric agents, which specifically lead to the accumulation of salt crystals in the material. A…
Let a graph be observed through a finite random sampling mechanism. Spectral methods are routinely applied to such graphs, yet their outputs are treated as deterministic objects. This paper develops finite-sample inference for spectral…
Due to strong absorption of the incident light, the media with high refractive index are considered restrictive for applications in photonic crystals (PhCs). The possibility to resolve this problem by optical saturation effectively…
It is shown in this paper that the light field distribution in a band gap within periodic structures for one-dimensional photonic crystal fibers is described by a decaying factor multiplied by a periodical function that has the same period…
The "flexible boundary condition" method, introduced by Sinclair and coworkers in the 1970s, remains among the most popular methods for simulating isolated two-dimensional crystalline defects, embedded in an effectively infinite atomistic…
A new approach is presented for the solution of spectral problems on infinite domains with regular ends, which avoids the need to solve boundary value problems for many trial values of the spectral parameter. We present numerical results…
A new $z$-stretching finite difference method is established for simulating the paraxial light beam propagation through a lens in a cylindrically symmetric domain. By introducing proper domain transformations, we solve corresponding…
Heterogeneously integrated hybrid photonic crystal cavities enable strong light-matter interactions with solid-state, optically addressable quantum memories. A key challenge to realizing high quality factor (Q) hybrid photonic crystals is…
Photon Green function (GF) is the vital and most decisive factor in the field of quantum light-matter interaction. It is divergent with two equal space arguments in arbitrary-shaped lossy structure and should be regularized. We introduce a…
We study the kinetic mean-field limits of the discrete systems of interacting particles used for halftoning of images in the sense of continuous-domain quantization. Under mild assumptions on the regularity of the interacting kernels we…
We consider conditions under which photonic crystals (PCs) can be homogenized in the higher photonic bands and, in particular, near the $\Gamma$-point. By homogenization we mean introducing some effective local parameters $\epsilon_{\rm…
We show that the finite-difference frequency-domain method is well-suited to study subwavelength lensing effects in left-handed materials (LHM's) and related problems. The method is efficient and works in the frequency domain, eliminating…
Two-dimensional ternary locally resonant phononic crystals used to consist of cylindrical scatterers with uniform coatings in their exterior. An alternative coating scheme with a comblike profile is proposed and investigated in this letter.…
We present a new method for the decomposition of multi-loop Euclidean Feynman integrals into quasi-finite Feynman integrals. These are defined in shifted dimensions with higher powers of the propagators, make explicit both infrared and…