Related papers: Band Gap Optimization of Two-Dimensional Photonic …
We present designs of 2D isotropic, disordered photonic materials of arbitrary size with complete band gaps blocking all directions and polarizations. The designs with the largest gaps are obtained by a constrained optimization method that…
We study time-varying semidefinite programs (TV-SDPs), which are semidefinite programs whose data (and solutions) are functions of time. Our focus is on the setting where the data varies polynomially with time. We show that under a strict…
We describe a factor-revealing convex optimization problem for the integrality gap of the maximum-cut semidefinite programming relaxation: for each $n \geq 2$ we present a convex optimization problem whose optimal value is the largest…
We propose a Generalized Finite-Differences in the Frequency Domain method for the computation of photonic band structures of finite photonic crystals. Our approach is to discretize some fundamental domain instead of a single unit cell,…
We investigate the effect of small spatiotemporal modulations in subwavelength-dimensioned phononic crystals with large band gaps, on the frequency spectrum for elastic waves polarized in the plane of periodicity. When the radius of…
It is often the case that the computed optimal solution of an optimization problem cannot be implemented directly, irrespective of data accuracy, due to either (i) technological limitations (such as physical tolerances of machines or…
In this paper, a non-Hermitian two-dimensional photonic crystal flat lens is proposed. The negative refraction of the second band of photonic crystal is utilized to realize super-resolution imaging of the point source. Based on the…
Photonic crystals (PhCs) have emerged as a popular platform for realizing various topological phases due to their flexibility and potential for device applications. In this article, we present a comprehensive classification of topological…
We study two-dimensional photonic crystals composed of elliptical dielectric rods arranged according to stealthy hyperuniform point patterns. These patterns are characterized by the structure factor, which vanishes for 0 < |k| <= K, where k…
We suggest an inverse dispersion method for calculating photonic band diagram for materials with arbitrary frequency-dependent dielectric functions. The method is able to calculate the complex wave vector for a given frequency by solving…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
In 1998, Carl Bender challenged the perceived wisdom of quantum mechanics that the Hamiltonian operator describing any quantum mechanical system has to be Hermitian. He showed that Hamiltonians that are invariant under combined parity-time…
A two dimensional eigenvalue problem (2DEVP) of a Hermitian matrix pair $(A, C)$ is introduced in this paper. The 2DEVP can be viewed as a linear algebraic formulation of the well-known eigenvalue optimization problem of the parameter…
This paper develops a new storage-optimal algorithm that provably solves generic semidefinite programs (SDPs) in standard form. This method is particularly effective for weakly constrained SDPs. The key idea is to formulate an approximate…
In photonics, band degeneracies at high-symmetry points in wavevector space have been shown to exhibit rich physical phenomena. However, obtaining degenerate bands away from such points is highly nontrivial. In this work, we achieve complex…
In this paper, we study the non-convex problem of continuous frequency optimal spectrum management in multiuser frequency selective interference channels. Firstly, a simple pairwise channel condition for FDMA schemes to achieve all Pareto…
The spectrum of excitations a two-dimensional, planar honeycomb lattice of two-level atoms coupled by the in-plane electromagnetic field may exhibit band gaps that can be opened either by applying an external magnetic field or by breaking…
This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang,…
Exceptional points (EPs) are special spectral degeneracies of non-Hermitian operators: at the EP, the complex eigenvalues coalesce, i.e., they become degenerate in both their real and imaginary parts. In two-dimensional (2D) photonic…
A three-dimensional (3D) photonic band gap crystal is an ideal tool to completely inhibit the local density of optical states (LDOS) at every position in the crystal throughout the band gap. This notion, however, pertains to ideal infinite…