The following inverse problem is discussed. A static electromagnetic field generated by a limited system of charges and currents is supposed to be known with its first derivatives at a point somewhere far from the system. This allows to reconstruct the position of the system, its net charge, and the electric and magnetic moments of the system.
The expression for the intensity of the electromagnetic field radiation is derived in the approximation next to the dipole one. The presented approach is based on fundamental equations from the introductory course on classical electrodynamics and straightforward mathematical transformations.
The Lorentz force law of classical electrodynamics states that the force F exerted by the magnetic induction B on a particle of charge q moving with velocity V is given by F=qVxB. Since this force is orthogonal to the direction of motion, the magnetic field is said to be incapable of performing mechanical work. Yet there is no denying that a permanent magnet can readily perform mechanical work by pushing/pulling on another permanent magnet -- or by attracting pieces of magnetizable material such as scrap iron or iron filings. We explain this apparent contradiction by examining the magnetic Lor…
The inverse electromagnetic source scattering problem from multi-frequency sparse electric far field patterns is considered. The underlying source is a combination of electric dipoles and magnetic dipoles. We show that the locations and the polarization strengths of the dipoles can be uniquely determined by the multi-frequency electric far field patterns at sparse observation directions. The unique arguments rely on some geometrical discussions and ingenious integrals of the electric far field patterns with properly chosen functions. Motivated by the uniqueness proof, we introduce two indicato…
Infinitesimal electric and magnetic dipoles are widely used as an equivalent radiating source model. In this paper, an improved method for dipole extraction from magnitude-only electromagnetic-field data based on genetic algorithm and back-and-forth iteration algorithm [1] is proposed. Compared with conventional back-and-forth iteration algorithm, this method offers an automatic flow to extract the equivalent dipoles without prior decision of the type, position, orientation and number of dipoles. It can be easily applied to electromagnetic-field data on arbitrarily shaped surfaces and minimize…
We theoretically show that an externally driven dipole placed inside a cylindrical hollow waveguide can generate a train of ultrashort and ultrafocused electromagnetic pulses. The waveguide encloses vacuum with perfect electric conducting walls. A dipole driven by a single short pulse, which is properly engineered to exploit the linear spectral filtering of the cylindrical hollow waveguide, excites longitudinal waveguide modes that are coherently re-focused at some particular instances of time. A dipole driven by a pulse with a lower-bounded temporal width can thus generate, in principle, a fi…
Transverse Kerker effect is known by the directional scattering of an electromagnetic plane wave perpendicular to the propagation direction with nearly suppression of both forward and backward scattering. Compared with plane waves, localized electromagnetic emitters are more general sources in modern nanophotonics. As a typical example, manipulating the emission direction of a quantum dot is of virtue importance for the investigation of on-chip quantum optics and quantum information processing. Herein, we introduce the concept of transverse Kerker effect of localized electromagnetic sources ut…
In this work by using the assumptions that wavelength is much smaller than charge separation distance of an electric dipole, which in turn is much smaller than a distance up to the point of observation, the new results for radiation of an electric dipole were obtained. These results generalize and extend the standard classical solution, and they indicate that under the above assumptions the electric dipole emits both long-range longitudinal electric and transverse electromagnetic waves. For a specific values of the dipole system parameters the longitudinal and transverse electric fields are di…
A uniformly-charged spherical shell of radius $R$, mass $m$, and total electrical charge $q$, having an oscillatory angular velocity $Ω(t)$ around a fixed axis, is a model for a magnetic dipole that radiates an electromagnetic field into its surrounding free space at a fixed oscillation frequency $ω$. An exact solution of the Maxwell-Lorentz equations of classical electrodynamics yields the self-torque of radiation resistance acting on the spherical shell as a function of $R$, $q$, and $ω$. Invoking the Newtonian equation of motion for the shell, we relate its angular velocity $Ω(t)$ to an ext…
For an oscillating electric dipole in the shape of a small, solid, uniformly-polarized, spherical particle, we compute the self-field as well as the radiated electromagnetic field in the surrounding free space. The assumed geometry enables us to obtain the exact solution of Maxwell's equations as a function of the dipole moment, the sphere radius, and the oscillation frequency. The self field, which is responsible for the radiation resistance, does not introduce acausal or otherwise anomalous behavior into the dynamics of the bound electrical charges that comprise the dipole. Departure from ca…
Wave optical imaging of an oscillating electric dipole orbiting a black hole
Niels Bohr Institute（尼尔斯·玻尔研究所）；CENTRA, Departamento de Física, Instituto Superior Técnico – IST, Universidade de Lisboa – UL（里斯本大学高等理工学院物理中心）；CAMGSD, Departamento de Matemática, Instituto Superior Técnico – IST, Universidade de Lisboa – UL（里斯本大学高等理工学院数学应用与计算科学中心）
In view of the observed flat rotation curves of spiral galaxies and motivated by the simple fact that within newtonian gravity a stationary axisymmetric mass distribution or dark matter vortex of finite extent readily displays a somewhat flattened out velocity rotation curve up to distances comparable to the extent of such a vortex transverse to the galaxy's disk, the possibility that such a flattening out of rotation curves may rather be a manifestation of some stationary axisymmetric space-time curvature of purely gravitational character, without the need of some dark matter particles, is co…
Despite being studied for over a century, the use of quadrupoles have been limited to Cartesian coordinates in flat spacetime due to the incorrect transformation rules used to define them. Here the correct transformation rules are derived, which are particularly unusual as they involve second derivatives of the coordinate transformation and an integral. Transformations involving integrals have not been seen before. This is significantly different from the familiar transformation rules for a dipole, where the components transform as tensors. It enables quadrupoles to be correctly defined in gen…
