Related papers: Numerical analysis of eikonal equation
Nowadays the geometric approach in optics is often used to find out media parameters based on propagation paths of the rays because in this case it is a direct problem. However inverse problem in the framework of geometrical optics is…
In this paper we introduce an optical approximation into the theory of impedance calculation, one valid in the limit of high frequencies. This approximation neglects diffraction effects in the radiation process, and is conceptually…
For research in the field of transformation optics and for the calculation of optically inhomogeneous lenses the method of geometrization of the Maxwell equations seems to be perspective. The basic idea is to transform the coefficients of…
It is shown that the geometrical optics limit of the Maxwell equations for certain nonlinear media with slow variation along one axis and particular dependence of dielectric constant on the frequency and fields gives rise to the…
The approximate cloaking is investigated for time-harmonic Maxwell's equations via the approach of transformation optics. The problem is reduced to certain boundary effect estimates due to an inhomogeneous electromagnetic inclusion with an…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
The WKB approximation of geometrical optics is widely used in plasma physics, quantum mechanics and reduced wave modeling in general. However, it is well-known that the approximation breaks down at focal and turning points. In this work we…
In this paper we construct a parametrix for the fractional Helmholtz equation $((-\Delta)^s - \tau^{2s} r(x)^{2s} + q(x))u=0$ making use of geometrical optics solutions. We show that the associated eikonal equation is the same as in the…
We present some new derivations of the effect of a plane gravitational wave on a light ray. A simple interpretation of the results is that a gravitational wave causes a phase modulation of electromagnetic waves. We arrive at this picture…
We construct a regular isotropic approximate cloak for the Maxwell system of equations. The method of transformation optics has enabled the design of electromagnetic parameters that cloak a region from external observation. However, these…
We present a study of geometric phases in classical wave and polarisation optics using the basic mathematical framework of quantum mechanics. Important physical situations taken from scalar wave optics, pure polarisation optics, and the…
We present algorithms for solving high-frequency acoustic scattering problems in complex domains. The eikonal and transport partial differential equations from the WKB/geometric optic approximation of the Helmholtz equation are solved…
Computational methods for electromagnetic and light scattering can be used for the calculation of optical forces and torques. Since typical particles that are optically trapped or manipulated are on the order of the wavelength in size,…
We present a method to obtain explicit solutions of the complex eikonal equation in the plane. This equation arises in the approximation of Helmholtz equation by the WKBJ or EWT methods. We obtain the complex-valued solutions (called…
We present a formalism for light optics starting with the Maxwell equations and casting them into an exact matrix form taking into account the spatial and temporal variations of the permittivity and permeability. This $8 \times 8$ matrix…
The analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system of equations describing in terms of ray trajectories a very wide family of wave-like phenomena (including diffraction and interference) going much beyond…
The geometrical approximation of the extended Maxwell equation in curved spacetime incorporating interactions induced by the vacuum polarization effects is considered. Taking into account these QED interactions and employing the analogy…
The robustness of XRD methods for the determination of the lattice parameters of crystals is well established. These methods have been extended to helical atomic structures using twisted x-rays \cite{friesecke_twisted_2016}. Building on an…
The relationship between two different asymptotic techniques developed in order to describe the propagation of waves beyond the standard geometrical optics approximation, namely, the Wigner-Weyl kinetic formalism and the complex geometrical…
Optical forces in dielectric structures are typically analyzed by utilizing either the Maxwell stress tensor or energy-based methods from which they can be derived by means of the eigenfrequencies and the effective refractive indices…