Related papers: Study of singular radius and surface boundary cons…
The mathematical notion of a spectral singularity admits a physical interpretation as a zero-width resonance. It finds an optical realization as a certain type of lasing effect that occurs at the threshold gain. We explore spectral…
Range profiling refers to the measurement of target response along the radar slant range. It plays an important role in automatic target recognition. In this paper, we consider the design of transmit waveform to improve the range profiling…
We provide an explicit geometric algorithm involving only ruler and compass constructions in order to specify the specular reflection point on the surface of a reflecting sphere of radius $r$ given two focal points $A$ and $B$ lying outside…
We propose a method for designing refractive optical elements for collimated beam shaping. In this method, the problem of finding a ray mapping is formulated as a linear assignment problem, which is a discrete version of the corresponding…
In recent years, there has been a mounting interest in better methods of measuring nanoscale objects, especially in fields such as nanotechnology, biomedicine, cleantech, and microelectronics. Conventional methods have proved insufficient,…
Radiality constraints are involved in both distribution system restoration and reconfiguration problems. However, a set of widely used radiality constraints, i.e., the spanning tree (ST) constraints, has its limitations which have not been…
To effectively apply passive speckle reduction methods, it is essential to use an illumination system that maximally exploits the non-ideal temporal coherence and angular diversity (spatial coherence reduction) of laser light. This study…
We study of the shape of a compact singular minimal surface in terms of the geometry of its boundary, asking what type of {\it a priori} information can be obtained on the surface from the knowledge of its boundary. We derive estimates of…
A lens limited by diffraction and having two parabolic surfaces is presented. The knowledge of the following parameters: object distance, relative refractive index, lens thickness, and image distance, enables to analytically calculate the…
In this work we consider the problem of optimizing a stellarator subject to hard constraints on the design variables and physics properties of the equilibrium. We survey current numerical methods for handling these constraints, and…
The radial limits of a nonparametric prescribed mean curvature surface uniquely determine the surface.
We give an explicit formula for singular surfaces of revolution with prescribed unbounded mean curvature. Using it, we give conditions for singularities of that surfaces. Periodicity of that surface is also discussed.
The Shape From Shading is one of a computer vision field. It studies the 3D reconstruction of an object from a single grayscale image. The difficulty of this field can be expressed in the local ambiguity (convex / concave). J.Shi and Q.Zhu…
Band topology has been studied as a design principle of realizing robust boundary modes. Here, by exploring non-Hermitian topology, we propose a three-dimensional topological laser that amplifies surface modes. The topological surface laser…
We present a technique to optimize the reflectivity of a surface while preserving its overall shape. The naive optimization of the mesh vertices using the gradients of reflectivity simulations results in undesirable distortion. In contrast,…
Algebraic surfaces in the complex projective space with a high number of A-type singularities have been presented in a recent paper. We extend the construction in order to obtain lower bounds for the maximal number of A singularities for…
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 present an abstract method in the setting of compact metric spaces which is applied to solve a number of problems in geometric optics. In particular, we solve the one source near field refraction problem. That is, we construct surfaces…
Rapid developments in the emerging field of stretchable and conformable photonics necessitate analytical expressions for boundary conditions at metasurfaces of arbitrary geometries. Here, we introduce the concept of conformal boundary…
In stellarator optimization studies, the boundary of the plasma is usually described by Fourier series that are not unique: several sets of Fourier coefficients describe approximately the same boundary shape. A simple method for eliminating…