Maxwell's Equations In Free Space Research Articles

Nonparaxial accelerating waves as a superposition of nondiffracting Bessel-lattice optical fields.

In the first part of this work, we introduce a monochromatic solution to the scalar wave equation in free space, defined by a superposition of monochromatic nondiffracting half Bessel-lattice optical fields, which is determined by two scalar functions; one is defined on frequency space, and the other is a complete integral to the eikonal equation in free space. We obtain expressions for the geometrical wavefronts, the caustic region, and the Poynting vector. We highlight that this solution is stable under small perturbations because it is characterized by a caustic of the hyperbolic umbilical type. In the second part, we introduce the corresponding solution to the Maxwell equations in free space.

Polarization of electromagnetic pulses

We show the impossibility, for localized and exact solutions of the Maxwell equations, of perfect circular polarization in a fixed plane, or perfect linear polarization along a fixed direction. A measure of polarization of electromagnetic pulses is obtained by analogy with that useful in monochromatic radiation, and its limitations discussed. Using oscillatory solutions of the free-space Maxwell equations, for which all components of the electric and magnetic fields satisfy the wave equation, we construct explicit examples of TE pulses which are linearly polarized with an azimuthal electric field, TE+iTM pulses approximately linearly polarized along the propagation direction, and also approximately circularly polarized pulses. The latter have perfect circular polarization on the propagation axis.

Null Poynting vector electromagnetic torus

Maxwell equations in free space are solved for a standing wave torus configuration under axisymmetry, which provides a mathematical support to the microwave cavity hypothesis of ball lightning. With a null Poynting vector with the outgoing part canceling the incoming part, this torus configuration satisfies the E→//B→ gauge of the Maxwell equations.

An adaptive local discrete convolution method for the numerical solution of Maxwell’s equations

We present a numerical method for solving the free-space Maxwell's equations in three dimensions using compact convolution kernels on a rectangular grid. We first rewrite Maxwell's Equations as a system of wave equations with auxiliary variables and discretize its solution from the method of spherical means. The algorithm has been extended to be used on a locally-refined nested hierarchy of rectangular grids.

A real-space Green’s function method for the numerical solution of Maxwell’s equations

Author(s): Lo, B; Minden, V; Colella, P | Abstract: A new method for solving the transverse part of the free-space Maxwell equations in three dimensions is presented. By taking the Helmholtz decomposition of the electric field and current sources and considering only the divergence-free parts, we obtain an explicit real-space representation for the transverse propagator that explicitly respects finite speed of propagation. Because the propagator involves convolution against a singular distribution, we regularize via convolution with smoothing kernels (B-splines) prior to sampling based on a method due to Beyer and LeVeque (1992). We show that the ultimate discrete convolutional propagator can be constructed to attain an arbitrarily high order of accuracy by using higher-order regularizing kernels and finite difference stencils and that it satisfies von Neumann's stability condition. Furthermore, the propagator is compactly supported and can be applied using Hockney's method (1970) and parallelized using the same observation as made by Vay, Haber, and Godfrey (2013), leading to a method that is computationally efficient.

Orbital angular momentum and highly efficient holographic generation of nondiffractive TE and TM vector beams

This paper discusses the angular momentum to energy ratio for a class of nondiffractive vector beams. Using the Humblet decomposition, we introduce closed form equations for the orbital, the spin, and the surface angular momenta in both paraxial and nonparaxial regimes. The considered monochromatic beams are exact solution to the Maxwell equations in free space and can be either transverse electric (TE) or transverse magnetic (TM). In this context, we analytically show that the total angular momentum is purely orbital. Additionally, we address both numerically and experimentally the generation of nondiffractive vector beams. In the generation of the vector beams, we propose a general approach to encode the corresponding scalar beams into the Kinoform, which possesses the upper bound diffraction efficiency. Our approach is general in the sense that we can encode arbitrary nondiffractive TE and TM vector beams. The experimental setup consists of two stages; a 4-f system and a common path interferometer. To highlight the proposed approach, we experimentally generate high efficiency Bessel, Mathieu, and Weber vector beams.

Dynamics of Light in Teleparallel Bianchi-Type I Universe

In the present study, using the Fourier analysis method and considering the Bianchi-type I spacetime, we investigate the dynamics of photon in the torsion gravity, and show that the free-space Maxwell equations give the same results. Furthermore, we also discuss the harmonic oscillator behavior of the solutions.

Dual electromagnetism: helicity, spin, momentum and angular momentum

The dual symmetry between electric and magnetic fields is an important intrinsic property of Maxwell equations in free space. This symmetry underlies the conservation of optical helicity and, as we show here, is closely related to the separation of spin and orbital degrees of freedom of light (the helicity flux coincides with the spin angular momentum). However, in the standard field-theory formulation of electromagnetism, the field Lagrangian is not dual symmetric. This leads to problematic dual-asymmetric forms of the canonical energy–momentum, spin and orbital angular-momentum tensors. Moreover, we show that the components of these tensors conflict with the helicity and energy conservation laws. To resolve this discrepancy between the symmetries of the Lagrangian and Maxwell equations, we put forward a dual-symmetric Lagrangian formulation of classical electromagnetism. This dual electromagnetism preserves the form of Maxwell equations, yields meaningful canonical energy–momentum and angular-momentum tensors, and ensures a self-consistent separation of the spin and orbital degrees of freedom. This provides a rigorous derivation of the results suggested in other recent approaches. We make the Noether analysis of the dual symmetry and all the Poincaré symmetries, examine both local and integral conserved quantities and show that only the dual electromagnetism naturally produces a complete self-consistent set of conservation laws. We also discuss the observability of physical quantities distinguishing the standard and dual theories, as well as relations to quantum weak measurements and various optical experiments.

An experimental adaptation of Higdon-type non-reflecting boundary conditions to linear first-order systems

Experiments in adapting the Higdon non-reflecting boundary condition (NRBC) method to linear 2-D first-order systems are presented. Finite difference implementations are developed for the free-space Maxwell equations, the linearized shallow-water equations with Coriolis, and the linearized Euler equations with uniform advection. This NRBC technique removes up to 99% of the reflection error generated by the Sommerfeld radiation condition with only a modest increase in computational overhead.

Maxwell equations for the generalised Lagrangian

The author deals with the problem of the construction of the Lagrange functional for an electromagnetic field. The generalised Maxwell equations for an electromagnetic field in free space are introduced. The main idea relies on the change of Lagrange function under the action integral. Usually, the Lagrange functional which describes the electromagnetic field is built with the quadrate of the electromagnetic field tensor Fik. Such a quadrate term is the reason, from a mathematical point of view, for the linear form of the Maxwell equations in free space. The author does not make this assumption and nonlinear Maxwell equations are obtained. New material parameters of free space are established. The Maxwell equations obtained are quite similar to the well-known Maxwell equations.

Optimized Small-Bore, High-Pass Resonator Designs

The radiofrequency field homogeneity and quality factor ( Q) of a number of high-pass resonator designs are compared theoretically and experimentally for small-bore coils. It was found that for high-pass resonators with the number of distributed capacitors greater than eight, a significant and unacceptable decrease in Q resulted. A number of schemes are proposed and investigated to improve the homogeneity of eight-capacitor high-pass resonators, thus balancing Q and homogeneity. These designs include variation in rung width, interrung feeding, a new hybrid coil design, and the use of internal guard rings. Eleven high-pass resonators were modeled and built to test the designs. The current density in each conductor was calculated using a novel numerical technique based on the inverse finite Hilbert transform which implicitly includes the effects of RF eddy currents. It was found that the effect of such eddy currents is important in coils of small geometry. RF fields were calculated from the current densities by using a retarded-potential solution to the free-space Maxwell equations. The interrung-fed hybrid coil design with guard rings was found to be superior to conventional designs.

Spreading of electromagnetic pulses

It is shown that for any finite-energy solution of the free-space Maxwell equations without sources, the energy contained in an infinite slab of finite thickness approaches zero as time tends to infinity.