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Matrix representations of the Maxwell equations are well-known. However, all these representations lack an exactness or/and are given in terms of a {\em pair} of matrix equations. We present a matrix representation of the Maxwell equation…

Optics · Physics 2010-02-23 Sameen Ahmed Khan

Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…

Optics · Physics 2012-08-20 Ulrich Brosa

Lobachewsky geometry simulates a medium with special constitutive relations. The situation is specified in quasi-cartesian coordinates (x,y,z). Exact solutions of the Maxwell equations in complex 3-vector form, extended to curved space…

Mathematical Physics · Physics 2011-09-02 E. M. Ovsiyuk , V. M. Red'kov

Interfaces between media with negative relative refractive index generically support propagating electromagnetic surface polariton modes with large wavenumber. The relation of these modes to a recent prediction by Pendry of ``perfect (real)…

Condensed Matter · Physics 2007-05-23 F. D. M. Haldane

It is shown that perfect absorption and giant amplification can be realized when a wave impinges on a special metamaterial layer with zero real parts of the permittivity and permeability. The imaginary parts of the permittivity and…

Optics · Physics 2011-05-26 Y. Jin , S. S. Xiao , N. A. Mortensen , S. L. He

The possibility of an incompletness of the equations of electromagnetism is analyzed using a thought experiment that shows a non-physical behavior according to classical electromagnetism. Basically, from Maxwell equations it is shown that a…

General Physics · Physics 2010-05-03 Fernando O. Minotti

The mean force exerted upon a perfect mirror moving in vacuum in a two dimensional spacetime has the same expression as the radiation reaction force computed in classical electron theory. It follows that unacceptable runaway solutions are…

Quantum Physics · Physics 2009-11-07 Marc-Thierry Jaekel , Serge Reynaud

The Maxwell's fisheye (MFE) lens, due to its focusing properties, is an interesting candidate for implementing the crossing of multiple waveguides. The MFE lens is implemented by two different structures: concentric cylindrical multilayer…

Concave mirrors are fundamental optical elements, yet some easily observed behaviors are rarely addressed in standard textbooks, such as the formation of multiple reflected images. Here we investigate self-imaging -- where the observer is…

Optics · Physics 2025-12-30 Thach A. Nguyen , Kaitlyn S. Yasumura , Duy V. Tran , Trung V. Phan

In this letter, we show that a perfect lens can be employed to make multiple objects appear like only one in the far field, leading to a new concept of illusion optics. Numerical simulations are performed to verify the functionalities for…

Optics · Physics 2011-05-10 Yadong Xu , Shengwang Du , Lei Gao , Huanyang Chen

An invisibility device should guide light around an object as if nothing were there, regardless where the light comes from. Ideal invisibility devices are impossible due to the wave nature of light. This paper develops a general recipe for…

Optics · Physics 2007-05-23 Ulf Leonhardt

We investigate the quantum optical properties of Maxwell's two-dimensional fish eye lens at the single-photon and single-atom level. We show that such a system mediates effectively infinite-range dipole-dipole interactions between atomic…

Quantum Physics · Physics 2018-09-12 Janos Perczel , Péter Kómar , Mikhail D. Lukin

We consider the time-harmonic Maxwell equations in a complex geometry. We are interested in geometries that model polarization filters or Faraday cages. We study the situation that the underlying domain contains perfectly conducting…

Analysis of PDEs · Mathematics 2025-01-30 Ben Schweizer , David Wiedemann

In this paper, we present the proof of superlensing an arbitrary object using complementary media and we study reflecting complementary media for electromagnetic waves. The analysis is based on the reflecting technique and new results on…

Mathematical Physics · Physics 2016-03-29 Hoai-Minh Nguyen

We give a set of local geometric conditions on a spacetime metric which are necessary and sufficient for it to be a null electrovacuum, that is, the metric is part of a solution to the Einstein-Maxwell equations with a null electromagnetic…

General Relativity and Quantum Cosmology · Physics 2015-06-16 C. G. Torre

Very little previous literature has considered the *exact* solution to Maxwell's equations for an infinite ideal cylindrical solenoid with an arbitrary time-dependent azimuthal surface current $K(t) \hat{\bf \phi}$. Most of the previous…

Classical Physics · Physics 2024-04-04 Edward Parker

The aim of this paper is to examine some obtained exact solutions of the Einstein-Maxwell equations, especially their properties from a chronological point of view. Each our spacetime is stationary cylindrically symmetric and it is filled…

General Relativity and Quantum Cosmology · Physics 2009-10-31 P. Klepac , J. Horsky

A perfect Euler cuboid is a rectangular parallelepiped with integer edges and integer face diagonals whose space diagonal is also integer. The problem of finding such parallelepipeds or proving their non-existence is an old unsolved…

Number Theory · Mathematics 2012-06-19 Ruslan Sharipov

Optical chirality has been recently suggested to complement the physically relevant conserved quantities of the well-known Maxwell's equations. This time-even pseudoscalar is expected to provide further insight in polarization phenomena of…

We describe the most general homogenous, planar, light-ray-direction-changing sheet that performs one-to-one imaging between object space and image space. This is a non-trivial special case (of the sheet being homogenous) of an earlier…

Optics · Physics 2015-06-17 Stephen Oxburgh , Johannes Courtial