Related papers: Hyperbolic Transverse Patterns in Nonlinear Optica…
An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems.…
Guided waves modes in a slab waveguide formed from the isotropic dielectric layer embedded by hyperbolic materials are investigated. Optical axis is normal to the slab plane. The dispersion relations for TE and TM waves are found. The…
Magnetic-free nonreciprocal optical devices that can prevent backscattering of signals are essential for integrated optical information processing. The achieved nonreciprocal behaviors mostly rely on various dispersive effects in optical…
This paper is devoted to superlensing using hyperbolic metamaterials: the possibility to image an arbitrary object using hyperbolic metamaterials without imposing any conditions on size of the object and the wave length. To this end, two…
In this paper, we investigate the problem of electromagnetic wave propagation in hyperbolic nonlinear media. To address this problem, we consider the scalar hyperbolic nonlinear Schr\"odinger system and its coupled version, namely…
This paper employs layer potential techniques to investigate wave scattering in two-dimensional elastic media exhibiting high contrasts in both Lam\'{e} parameters and density. Our contributions are fourfold. First, we construct an…
We develop an approach to use nanostructured plasmonic materials as a non-magnetic negative-refractive index system at optical and near-infrared frequencies. In contrast to conventional negative refraction materials, our design does not…
Properties of solutions of generic hyperbolic systems with multiple characteristics with diagonalizable principal part are investigated. Solutions are represented as a Picard series with terms in the form of iterated Fourier integral…
Photonic hyper-crystals combine the most interesting features of hyperbolic metamaterials and photonic crystals. Since the dispersion law of extraordinary photons in hyperbolic metamaterials does not exhibit the usual diffraction limit,…
In this paper I discuss nonlinear parabolic systems that are generalizations of scalar diffusion equations. I show that when potential is a convex function that depends only on the norm of the solution, then bounded weak solutions of these…
This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws. The basic idea is that the "meaningful objects" are the fluxes, evaluated across domain…
The spectral fluctuations of a quantum Hamiltonian system with time-reversal symmetry are studied in the semiclassical limit by using periodic-orbit theory. It is found that, if long periodic orbits are hyperbolic and uniformly distributed…
We study radiative energy transfer between a donor-acceptor pair across a hyperbolic metamaterial slab. We show that similar to a perfect lens a hyperbolic lens allows for giant energy transfer rates. For a realistic realization of a…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
This work models the propagation of an optical pulse in a 4-level atomic system in the electromagnetic induced transparency regime. By demonstrating that linear and nonlinear optical properties can be externally controlled and tailored by a…
The study of transverse optical pattern formation has been studied extensively in nonlinear optics, with a recent experimental interest in studying the phenomenon using cold atoms, which can undergo real-space self-organization. Here, we…
Propagation, transmission and reflection properties of linearly polarized plane waves and arbitrarily short electromagnetic pulses in one-dimensional dispersionless dielectric media possessing an arbitrary space-time dependence of the…
The paper is devoted to hyperbolic (generally speaking, non-Lagrangian and nonlinear) partial differential systems possessing a full set of differential operators that map any function of one independent variable into a symmetry of the…
We examine the optical properties of two different configurations of a cylindrical device made from a hyperbolic metamaterial with optical axis defined by circular and radial director fields. The hyperbolic metamaterial is an uniaxial…
The development of plasmonics and related applications in the terahertz range faces limitations due to the intrinsic high electron density of standard metals. All-dielectric systems are profitable alternatives, which allows for customized…