Related papers: Hyperbolic reflections as fundamental building blo…
Using concepts and techniques of bilinear algebra, we construct hyperbolic planes over a euclidean ordered field that satisfy all the Hilbert axioms of incidence, order and congruence for a basic plane geometry, but for which the hyperbolic…
We study relations between reflections in (positive or negative) points in the complex hyperbolic plane. It is easy to see that the reflections in the points q_1,q_2 obtained from p_1,p_2 by moving p_1,p_2 along the geodesic generated by…
Advances in graphene plasmonics offer numerous opportunities for enabling the design and manufacture of a variety of nanoelectronics and other exciting optical devices. However, due to the limitation of material properties, its operating…
We investigate the optical properties of an ultrathin film of a topological insulator in the presence of an in-plane magnetic field. We show that due to the combination of the overlap between the surface states of the two layers and the…
We use properties of the hyperbolic metric and properties of the modular function to show that the Bohr's radius for covering maps onto hyperbolic domains is greater or equal to exponential minus pi. This includes almost all known classes…
Nonlocal (spatial-dispersion) effects in multilayered metamaterials composed of periodic stacks of alternating, deeply subwavelength dielectric layers are known to be negligibly weak. Counterintuitively, under certain critical conditions,…
We study nonlinear reactive transport in a layered porous medium separated by an $\varepsilon$-thin, highly heterogeneous fracture whose aperture and obstacle pattern vary periodically. Species transport in the bulk is governed by parabolic…
The goal of this paper is to study two basic problems of hyperbolic geometry. The first problem is to compare the hyperbolic and Euclidean distances. The second problem is to find hyperbolic counterparts of some basic geometric…
We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal…
We show that word-hyperbolic groups satisfy linear isoperimetric functions for all homotopy types of surface diagrams. This generalises the linear isoperimetric functions for disc and annular diagrams.
Using the transfer-matrix approach and solving time-domain differential equations, we analyze the loss compensation mechanism in multilayer systems composed of an absorbing transparent conductive oxide and dielectric doped with an active…
In this paper we consider ultra-parallel complex hyperbolic triangle groups of type $[m_1,m_2,0]$, i.e. groups of isometries of the complex hyperbolic plane, generated by complex reflections in three ultra-parallel complex geodesics two of…
Nonlinear optics underpins a broad range of photonic technologies, from classical and quantum light sources to emerging nonlinear photonic neural networks. Yet, conventional nonlinear optical devices exhibit static functionality: their…
Stimulated emission depletion microscopy inspired direct laser writing (STED-DLW) processes can offer diffraction-unlimited fabrication of 3D-structures, not possible with traditional electron-beam or optical lithography. We propose a…
We consider ``hyperideal'' circle patterns, i.e. patterns of disks appearing in the definition of the Delaunay decomposition associated to a set of disjoint disks, possibly with cone singularities at the center of those disks. Hyperideal…
Based on transformation optics, we introduce another set of generalized laws of reflection and refraction (differs from that of [Science 334, 333 (2011)]), through which a transformation media slab is derived as a meta-surface, producing…
Upon using fundamental electromagnetic properties of metasurfaces we build a platform to classify reciprocal bianisotropic metasurfaces from typical experimental measurements and determine isotropic, anisotropic, bi-isotropic (chiral), and…
We propose methods that use specular, multibounce lidar returns to detect and map specular surfaces that might be invisible to conventional lidar systems that rely on direct, single-scatter returns. We derive expressions that relate the…
Reducing a set of diverse bulk-optic-based optical components to a single ultrathin and compact element that enables the same complex functionality has become an emerging research area, propelling further integration and miniaturization in…
Hyperbolic topological transitions refer to the transformation of is isofrequency contours in hyperbolic materials from one topology (e.g., hyperbolic) to another (e.g., elliptical or a different hyperbolic topology). However, current…