Related papers: Computational Bounds For Photonic Design
In the photonic design problem, a scientist or engineer chooses the physical parameters of a device to best match some desired device behavior. Many instances of the photonic design problem can be naturally stated as a mathematical…
Topology optimization has matured to become a powerful engineering design tool that is capable of designing extraordinary structures and materials taking into account various physical phenomena. Despite the method's great advancements in…
In a physical design problem, the designer chooses values of some physical parameters, within limits, to optimize the resulting field. We focus on the specific case in which each physical design parameter is the ratio of two field…
Our ability to structure materials at the nanoscale has, and continues to, enable key advances in optical control. In pursuit of optimal photonic designs, substantial progress has been made on two complementary fronts: bottom-up structural…
We show that global lower bounds to the mode volume of a dielectric resonator can be computed via Lagrangian duality. State-of-the-art designs rely on sharp tips, but such structures appear to be highly sub-optimal at nanometer-scale…
We develop a unified framework for identifying bounds to maximum resonant nonlinear optical susceptibilities, and for "inverse designing" quantum-well structures that can approach such bounds. In special cases (e.g. second-harmonic…
Optical devices lie at the heart of most of the technology we see around us. When one actually wants to make such an optical device, one can predict its optical behavior using computational simulations of Maxwell's equations. If one then…
A computer model can be used for predicting an output only after specifying the values of some unknown physical constants known as calibration parameters. The unknown calibration parameters can be estimated from real data by conducting…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
We consider an experiment with two qualitative factors at 2 levels each and a binary response, that follows a generalized linear model. In Mandal, Yang and Majumdar (2010) we obtained basic results and characterizations of locally D-optimal…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
We consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation…
In this paper, we are concerned about optimal two-dimensional optical orthogonal codes with $\lambda$ = 2. Some combinatorial constructions are presented and many infinite families of optimal two-dimensional optical orthogonal codes with…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
We extend the theoretical framework of non-local optimized Schwarz methods as introduced in [Claeys,2021], considering an Helmholtz equation posed in a bounded cavity supplemented with a variety of conditions modeling material boundaries.…
Photonic inverse design typically seeks designs parameterized by binary arrays, where the values of each element correspond to the presence or absence of material at a particular point in space. Gradient-based approaches to photonic inverse…
The Lagrange mesh method is a very simple procedure to accurately solve eigenvalue problems starting from a given nonrelativistic or semirelativistic two-body Hamiltonian with local or nonlocal potential. We show in this work that it can be…
We study the boundary control of solutions of the Helmholtz and Maxwell equations to enforce local non-zero constraints. These constraints may represent the local absence of nodal or critical points, or that certain functionals depending on…
Bayesian optimization has been successfully applied to optimize black-box functions where the number of evaluations is severely limited. However, in many real-world applications, it is hard or impossible to know in advance which designs are…