相关论文: Aperiodic photonics of elliptic curves

Isogenies, the mappings of elliptic curves, have become a useful tool in cryptology. These mathematical objects have been proposed for use in computing pairings, constructing hash functions and random number generators, and analyzing the…

Exotic forms of wave control have been emerging by engineering matter in space and time. In this framework, temporal photonic interfaces, i.e., abrupt changes in the electromagnetic properties of a material, have been shown to induce…

We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…

We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…

Light curves of astrophysical objects frequently contain strictly periodic signals. In those cases we can use that property to aid the detrending algorithm to fully disentangle an unknown periodic signal and an unknown baseline signal with…

Hybrid inverse problems are mathematical descriptions of coupled-physics (also called multi-waves) imaging modalities that aim to combine high resolution with high contrast. The solution of a high-resolution inverse problem, a first step…

We obtain explicit formulas for the number of non-isomorphic elliptic curves with a given group structure (considered as an abstract abelian group). Moreover, we give explicit formulas for the number of distinct group structures of all…

Light scattering in random media is usually considered within the framework of the three-dimensional Anderson universality class, with modifications for the vector nature of electromagnetic waves. We propose that the linear dispersiveness…

This monograph introduces key concepts and problems in the new research area of Periodic Geometry and Topology for materials applications.Periodic structures such as solid crystalline materials or textiles were previously classified in…

Predicting the optical response of macroscopic arrangements of individual scatterers is a computational challenge, as the problem involves length scales across multiple orders of magnitude. We present a full-wave optical method to highly…

Rapidly growing demands for high-performance computing, powerful data processing systems, and big data necessitate the advent of novel optical devices to perform demanding computing processes effectively. Due to its unprecedented growth in…

Scattering media, being ubiquitous in nature and critically important for assessments (e.g., biological tissues), are often considered as nuisance in optics. Here we show that it is not always the case and scattering media could be…

We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring…

We create hybrid topological-photonic localisation of light by introducing concepts from the field of topological matter to that of photonic crystal fiber arrays. S-polarized obliquely propagating electromagnetic waves are guided by…

The concept of local symmetry is a powerful tool in predicting complex transport phenomena in aperiodic media. A nonlocal continuity formalism reveals how local symmetries are encoded into the dynamics of light propagation in discrete…

Recent studies on fully dielectric multilayered metamaterials have shown that the negligibly small nonlocal effects (spatial dispersion) typically observed in the limit of deeply subwavelength layers may be significantly enhanced by…

This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…

The need to increase data transfer rates constitutes a key challenge in modern information-driven societies. Taking advantage of the transverse spatial modes of light to encode more information is a promising avenue for both classical and…

A well-known and difficult problem in computational number theory and algebraic geometry is to write down equations for branched covers of algebraic curves with specified monodromy type. In this article, we present a technique for computing…

A boundary integral equation method for the 3-D Helmholtz equation in multilayered media with many quasi-periodic layers is presented. Compared with conventional quasi-periodic Green's function method, the new method is robust at all…