Related papers: Study of singular radius and surface boundary cons…

Numerous applications require the simultaneous redistribution of the irradiance and phase of a laser beam. The beam shape is thereby determined by the respective application. An elegant way to control the irradiance and phase at the same…

Electromagnetic metasurfaces have attracted significant interest recently due to their low profile and advantageous applications. Practically, many metasurface designs start with a set of constraints for the radiated far-field, such as…

Refraction is a common physical phenomenon and has long been researched in computer vision. Objects imaged through a refractive object appear distorted in the image as a function of the shape of the interface between the media. This hinders…

Suitable shaping (in particular, flattening and broadening) of the laser beam has recently been proposed as an effective device to reduce internal (mirror) thermal noise in advanced gravitational wave interferometric detectors. Based on…

This survey is devoted to discussing the problems of the unique determination of surfaces that are the boundaries of (generally speaking) nonconvex domains. First (in Sec. 2) we examine some results on the problem of the unique…

We present a general framework for inverse design of nanopatterned surfaces that maximize spatially averaged surface-enhanced Raman (SERS) spectra from molecules distributed randomly throughout a material or fluid, building upon a recently…

For generic maps from compact surfaces with boundary into the plane we develop an explicit algorithm for minimizing both the number of cusps and the number of components of the singular locus. More precisely, we minimize among maps with…

Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the investigation of an optimal control problem for surface shape…

We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.

We motivate then formulate a novel variant of the near-field reflector problem and call it the near-field reflector problem with spatial restrictions. Let $O$ be an anisotropic point source of light and assume that we are given a bounded…

The conditions for a cuspidal edge, swallowtail and other fundamental singularities are given in the context of Lie sphere geometry. We then use these conditions to study the Lie sphere transformations of a surface.

Surface-enhanced Raman spectroscopy (SERS) allows single-molecule detection due to the strong field localization occurring at sharp bends or kinks of the metal-vacuum interface. An important question concerns the limits of the signal…

The principles behind the sharp, singular structures in a crumpled sheet are well understood. Here we discuss more general ways of exploiting such sharp structures to control the shape of a sheet by deforming or forcing it elsewhere. Often,…

This lecture provides an overview of the principles and methodologies involved in linear optics design. It aims to introduce key concepts such as the matrix formalism, the symplecticity, the quantities that are preserved in the single…

In continuing the study of harmonic mapping from 2-dimensional Riemannian simplicial complexes in order to construct minimal surfaces with singularity, we obtain an a-priori regularity result concerning the real analyticity of the free…

Recently it has been proposed that a planar slab of material, for which both the permittivity and permeability have the values of -1, could bring not only the propagating fields associated with a source to a focus, but could also refocus…

We investigate the problem of shaping radially symmetric annular beams into desired intensity patterns along the optical axis. Within the Fresnel approximation, we show that this problem can be expressed in a variational form equivalent to…

This paper deals with a kind of design of a ruled surface. It combines concepts from the fields of computer aided geometric design and kinematics. A dual unit spherical B\'ezier-like curve on the dual unit sphere (DUS) is obtained with…

Light reflection plays a crucial role in a number of modern technologies. In this paper, analytical expressions for maximal reflected power in any direction and for any polarization are given for generic planar structures made of a single…

We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…