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 in presence of sources in a medium with varying permittivity and permeability. It is shown that such a representation necessarily requires $8 \times 8$ matrices and an explicit representation for them is presented.
Radiation from a charged particle moving in a medium with Maxwell fish eye refraction index profile is considered. It is shown that the radiation spectrum has a discrete character. The main emitted wavelength is proportional to the refractive profiles radius and has a dipole character in a regular medium. Cherenkov like threshold velocity is established. A cardinal rearrangement of angular distribution in a lossless medium is predicted. This behavior is caused by the total internal reflection in a lossless medium as opposed to photons attenuated total reflection in the regular medium. Lossless…
Spatial Kerr solitons, typically associated with the standard paraxial nonlinear Schroedinger equation, are shown to exist to all nonparaxial orders, as exact solutions of Maxwell's equations in the presence of vectorial Kerr effect. More precisely, we prove the existence of azimuthally polarized, spatial, dark soliton solutions of Maxwell's equations, while exact linearly polarized (2+1)-D solitons do not exist. Our ab initio approach predicts the existence of dark solitons up to an upper value of the maximum field amplitude, corresponding to a minimum soliton width of about one fourth of the…
\noindent This manuscript proposes a new imaging medium via isotropic refractive index of heterogeneous medium. We exploit conformal-map to transfers the full Maxwell fisheye into a mapped profile within a unit circle. The imaging resolution of this new profile can be maintained as good as the mirrored Maxwell fisheye profile or its conformally-mapped counterpart in previous literature.
As quantum optical phenomena are based on Maxwell's equations, and it is becoming important to understand quantum optical phenomena at short distances, so it is important to analyze quantum optics using short distance corrected Maxwell's equation. Maxwell's action can be obtained from quantum electrodynamics using the framework of effective field theory, and so the leading order short distance corrections to Maxwell's action can also be obtained from the derivative expansion of the same effective field theory. Such short distance corrections will be universal for all quantum optical systems, a…
We consider the propagation of polarized light in the medium with Maxwell fish eye refraction index profile. We show that polarization violates the additional symmetries of medium, so that ray trajectories no longer remain closed. Then we suggest a modified, polarization-dependent Maxwell fish eye refraction index which restores all symmetries of initial profile and yields closed trajectories of polarized light. Explicit expressions for the polarization dependent integrals of motion and the solutions of corresponding ray trajectories are presented.
Comment on 'Perfect drain for the Maxwell fish eye lens'
已经提出了非磁损耗材料（2011 New J.Phys.13 023038）来模拟麦克斯韦鱼接目镜（MFL）中的无源完美漏极。在这篇评论中，我们认为，这种被动介质只能被视为一个完美的吸收体，可以完全吸收所有入射辐射，而不被它散射，但它不能模仿一个完美的焦点。因此，这种被动介质不能帮助实现MFL的完美聚焦。
Topological spin transport of photons: "magnetic monopole" gauge field in Maxwell equations and polarization splitting of rays in periodically inhomogeneous media
A transparent linear magneto-dielectric material in free space that is illuminated by a finite quasimonochromatic field is a thermodynamically closed system, definitively, regardless of what field and material subsystems that one defines. The energy--momentum tensor that is formally derived from the Maxwell--Minkowski field equations is inconsistent with both angular and linear momentum conservation in this closed system; this very solid fact is the foundational and continuing issue of the Abraham--Minkowski controversy. The extant resolution of the Abraham--Minkowski dilemma is to treat Maxwe…
An exact calculation of the local electric field ${\bf E}({\bf r})$ is described for the case of a time dependent point electric dipole ${\bf p}e^{-iωt}$ in the top layer of an $ε_2$, $ε_1$, $ε_2$ three parallel slabs composite structure, where the $ε_1$ layer has a finite thickness $2d$ but the $ε_2$ layers are infinitely thick. For this purpose we first calculate all the eigenstates of the full Maxwell equations for the case where $μ=1$ everywhere in the system. The eigenvalues appear as special, non-physical values of $ε_1$ when $ε_2$ is given. These eigenstates are then used to develop an …
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 qubits, which can be used to entangle multiple pairs of distant qubits. We find that the rate of the photon exchange between two atoms, which are detuned from the cavity resonances, is well described by a model, where the photon is focused to a diffraction-limited area during absorption. We consider the effect of losses on the system and study the fidelity of …
We present the theoretical foundations and the implementation details of a density-functional approach for coupled photons, electrons, and effective nuclei in non-relativistic quantum electrodynamics. Starting point of the formalism is a generalization of the Pauli-Fierz field theory for which we establish a one-to-one correspondence between external fields and internal variables. Based on this correspondence, we introduce a Kohn-Sham construction which provides a computationally feasible approach for ab-initio light-matter interactions. In the mean-field limit for the effective nuclei the for…
We derived the Berry connection of vector vortex states (VVSs) from the "true" Hamiltonian obtained through the Maxwell--Schrödinger equation for an inhomogeneous anisotropic (IA) medium, and we experimentally demonstrated measurement of the corresponding Pancharatnam--Berry (PB) geometrical phase of VVSs. The PB phase (PBP) of VVSs can be divided into two phases: homogeneous and inhomogeneous PBPs. Homogeneous and inhomogeneous PBPs are related to the conventional PBP and the spatially-dependent geometric phase given by an IA medium such as a polarization converter, respectively. We theoretic…
At a boundary between two transparent, linear, isotropic, homogeneous materials, derivations of the electromagnetic boundary conditions and the Fresnel relations typically proceed from the Minkowski {E,B,D,H} representation of the macroscopic Maxwell equations. However, equations of motion for macroscopic fields in a transparent linear medium can be written using Ampere {E,B}, Chu {E,H}, Lorentz, Minkowski, Peierls, Einstein-Laub, and other formulations of continuum electrodynamics. We present a representation-independent derivation of electromagnetic boundary conditions and Fresnel relations …
Multimode waveguide crossings are crucial components for novel mode-division-multiplexing systems. One of the challenges of multimode waveguide routing in MDM systems is decreasing the inter-mode crosstalk and mode leakage of waveguide crossings. In this work, we present the intersections of three and four waveguides based on polygonal Maxwell's fisheye lens via transformation optics. The designed lenses are implemented by mapping their refractive index to the thickness of guiding Si layer. The three-dimensional finite-difference time-domain simulations are used to evaluate the performance of …
In this paper, the Maxwell's equations for the tensorial magneto-electric (ME) medium have been solved which in fact is the extension of anisotropic nonmagnetic medium. All of the dielectric permittivity, magnetic permeability and the ME tensors are considered. The transverse polarization is shown explicitly and the propagation of electromagnetic wave in the ME medium is found to have the Double Jones Birefringence. We also find the condition of D'yakonov surface wave for magneto-isotropic but with ME anisotropic medium. Especially when the incident angle is $\fracπ{4}$, it may be measurable i…
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 usually not given attention. The aim of this work is to demonstrate the work of the proposed the algorithm in the framework of geometrical approach to optics for solving the problem of finding the propagation path of the electromagnetic radiation depending on environmental parameters. The methods of differential geometry are used for effective metrics constructio…
The Hamiltonian formalism is extremely elegant and convenient to mechanics problems. However, its application to the classical field theories is a difficult task. In fact, you can set one to one correspondence between the Lagrangian and Hamiltonian in the case of hyperregular Lagrangian. It is impossible to do the same in gauge-invariant field theories. In the case of irregular Lagrangian the Dirac Hamiltonian formalism with constraints is usually used, and this leads to a number of certain difficulties. The paper proposes a reformulation of the problem to the case of a field without sources. …
Recently suggested transformation optics-based magnifying Maxwell fisheye lenses, which are made of two half-lenses of different radii, has been fabricated and characterized. The lens action is based on control of polarization-dependent effective refractive index in a lithographically formed tapered waveguide. We have studied wavelength and polarization dependent performance of the lenses.
The inverse design of optical metasurfaces is a rapidly emerging field that has already shown great promise in miniaturizing conventional optics as well as developing completely new optical functionalities. Such a design process relies on many forward simulations of a device's optical response in order to optimize its performance. We present a data-driven forward simulation framework for the inverse design of metasurfaces that is more accurate than methods based on the local phase approximation, a factor of $10^4$ times faster and requires $15$ times less memory than mesh based solvers, and is…
A Dyson map explicitly determines the appropriate basis of electromagnetic fields which yields a unitary representation of the Maxwell equations in an inhomogeneous medium. A qubit lattice algorithm (QLA) is then developed perturbatively to solve this representation of Maxwell equations. QLA consists of an interleaved unitary sequence of collision operators (that entangle on lattice-site qubits) and streaming operators (that move this entanglement throughout the lattice). External potential operators are introduced to handle gradients in the refractive indices, and these operators are typicall…
