Electromagnetic Formalism Research Articles

Electrodynamic interaction between two atoms in near-field contact.

A theoretical study of elements of the quantum electrodynamic interaction between two single-electron atoms in near-field contact is presented. The framework of the study is an electromagnetic propagator formalism that allows one to describe the near-field space-time interaction in such a manner that the Einstein causality and lack of photon localizability are manifest. First we set up the atom-field Hamiltonian in the so-called G-gauge, starting from the Coulomb Hamiltonian, and thereafter we show that this leads to a correct propagator description for the retarded part of the transverse electromagnetic field (operator). In the G-gauge approach, renormalization of the two-particle energy level structure stemming from the transverse self-field occurs. The intraparticle renormalization is calculated for a three-level atom (it is trivial for a two-level atom), and the interparticle renormalization, which depends on the atomic separation, is determined for two two-level atoms. The magnitude of the energy renormalization is always finite in our theory because we do not consider the atoms to be point-like objects from an electromagnetic point of view. Throughout, we relate our G-gauge formalism to the multipole theory often used in studies of interatomic electrodynamics.

NONLINEAR OPTICS IN THE NEAR-FIELD ZONE OF ATOMS

Elements of a new quantum electrodynamic theory which might enable one to obtain a better understanding of the linear and nonlinear interaction between atomic systems in near-field contact is presented. To follow the space-time dynamics in the atomic near-field zone an electromagnetic propagator formalism with polychromatic photons is constructed. A first-quantized description based on the photon energy wave function for free polychromatic photons is extended in such a manner that the birth process of the photon, which takes place in the near-field zone of the source, can be followed. In order to be able to describe harmonic generation processes in near-field optics polychromatic photons of the simple wave-train type are used. The wave mechanical (first-quantized) description based on wave-train photons is upgraded to a field-theoretic (second-quantized) formalism using a new so-called propagator gauge which is closely related to the Poincaré gauge underlying the multipole description of quantum electrodynamics.

Electromagnetic degrees of freedom of an optical system

We present a rigorous electromagnetic formalism for defining, evaluating, and optimizing the degrees of freedom of an optical system. The analysis is valid for the delivery of information with electromagnetic waves under arbitrary boundary conditions communicating between domains in three-dimensional space. We show that, although in principle there is an infinity of degrees of freedom, the effective number is finite owing to the presence of noise. This is in agreement with the restricted classical theories that showed this property for specific optical systems and within the scalar and paraxial approximations. We further show that the best transmitting and receiving functions are the solutions of well-defined eigenvalue equations. The present approach is useful for understanding and designing modern optical systems for which the previous approaches are not applicable, as well as for application in inverse and synthesis problems.

Photon Drag in Coupled Double Quantum Wells: Electronic Coupling Effects

An electromagnetic propagator formalism is used to calculate the local field in a quantum-well structure consisting of two electronically coupled identical wells each containing only one bound state. Therefore, the photon-drag current, arising as a result of the nonlinear response to the prevailing field, is determined as function of the photon energy and the angle of incidence of the driving field. It is shown that the photon-drag current can be modified significantly by changing the electronic coupling between wells.

Linear gravitational waves and electrodynamic formalism in cosmology

The propagation of linear gravitational waves is studied in open and multiply connected Robertson-Walker cosmologies. In order for the group velocity of the gravitational wave packets to coincide with the speed of light, the linear wave equation must be conformally coupled. This opens the possibility of using the electromagnetic formalism. The gravitational analogue to the electromagnetic field tensor is introduced, and a tensorial counterpart to Maxwell's equations on the spacelike 3-slices is derived. The energy-momentum tensor for linear gravitational waves is constructed without averaging procedures, a strictly positive energy density is obtained, and it is shown that the overall energy of a gravitational pulse scales with the inverse of the expansion factor.

A Tai's Result Revisited

Introducing a pseudotime variable, Tai has given recently a simple solution to the problem of the transient radiation in a uniformly moving isotropic medium. Using suitably dilated space variables and the 3D-complex formalism of electromagnetism we give an alternative solution to the same problem with the aid of the Green's function of the scalar wave equation.

Radiation forces on a micrometer-sized sphere in an evanescent field

Electromagnetic wave theory is used to predict the radiation forces exerted upon a micrometer-sized spherical particle illuminated by evanescent waves penetrating across a dielectric interface. These forces are quantified for two incident beam polarizations (p and s polarization) and for different refractive-index media. The electromagnetic formalism that we use is based on theoretical studies of Barton et al. [ J. Appl. Phys.64, 1632 ( 1988);J. Appl. Phys.66, 4594 ( 1989)]. The novelty of the present research is to apply this general formalism to the calculation of forces when the evanescent field is identified with the incident field. Our theoretical results for the horizontal and vertical force components are shown graphically in nondimensional form as functions of the size parameter of the sphere. Moreover, our results are found to be in reasonable agreement with recent experimental findings of Kawata and Sugiura [ Opt. Lett.17, 772 ( 1992)].

Phase images of grooves in a perfectly conducting surface

Scattering of an arbitrary two-dimensional electromagnetic field by an isolated rectangular groove in a perfectly conducting substrate is modeled using a rigorous electromagnetic diffraction formalism. By calculating the phase of that part of the scattered field, which propagates in directions that fall within the numerical aperture of a microscope objective, we examine the resolution limits of a Linnik-type interference microscope with focused coherent illumination. It is shown that accurate groove width and depth determination by phase measurement should be possible, even when the groove width is somewhat smaller than the optical wavelength, if use is made of reference data obtained by rigorous computations. However, our results do not support some recent experimental results that suggest the possibility of achieving superresolution by interference microscopy.

Harmonic plane waves in a chiral slab.

We illustrate the three-dimensional complex formalism of electromagnetism previously developed [P. Hillion, Phys. Rev. E 47, 1365 (1993)] for time-harmonic plane waves propagating in an isotropic homogeneous chiral slab.

On an initial boundary value problem involving Beltrami-Moses fields in electromagnetic theory

The so-called Harmuth ansatz consists of including autonomous magnetic sources in the time-dependent Maxwell postulates. The Beltrami fields are eigenfunctions of the curl operator, and have been used by Moses for propagation in infinite media. These developments are of relatively recent provenances in electromagnetic theory. We discuss an initial-boundary value problem (IBVP) within the framework of a manifestly covariant electromagnetic formalism by using the Harmuth ansatz. We also show how a covariant formulation of the Beltrami-Moses fields may be used for solving electromagnetic IBVPS.

Electromagnetism in anisotropic chiral media.

We present here for homogeneous anisotropic chiral media an electromagnetic formalism manifestly covariant under the complex rotation group O(3,C). The constitutive relations, the electromagnetic field equations, and the boundary conditions are discussed. To display the main features of this formalism, we discuss the propagation of plane waves in a medium that is anisotropic and chiral but simple enough to make calculations tractable

Rigorous formulation of scattering at a randomly varying impedance plane: general case of oblique incidence

The problem of scattering of electromagnetic plane waves at one-dimensional surfaces (random gratings) is solved in the general case in which the incident wave vector does not lie on the main section of the cylindrical surface (oblique incidence). The scatterer is simulated by a plane boundary characterized by a coordinate-dependent impedance that varies along one of the two coordinates on the surface. This representation could be regarded as a canonical model of one-dimensional surfaces with height corrugations. A rigorous electromagnetic formalism for calculating the fields scattered at the impedance plane is presented. The fields above the scatterer are represented by spectral domain expansions. It is shown that the wave vectors of the scattered waves lie on the surface of a cone containing the direction of specular reflection and whose axis coincides with the direction of the grooves of the random grating. The theory is exemplified by calculating the angular distribution of the mean intensity scattered from an ensemble of surfaces with similar statistical parameters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Goursat problem for Maxwell’s equations

Using the spinor formalism of electromagnetism, the Goursat problem for Maxell’s equations is defined and some examples of solutions are given.

The surface impedance of metallic objects: rigorous calculations for imperfectly conducting diffraction gratings

An accurate computation of the surface impedance of highly conducting metallic gratings is presented. A rigorous electromagnetic formalism is used for solving for the fields at the grating boundary. The influence of the local curvature of the grating profile, the refractive index of the metal, and the angle of incidence are studied. Particular attention is given to the comparison between the efficiencies obtained using the rigorous method and those obtained assuming that the surface impedance is a constant. >

Diffraction pattern of circular and rectangular apertures in the spinor formalism of electromagnetism

The spinor formalism is applied to the diffraction of electromagnetic energy of plane apertures in the following way. It is first assumed that the diffraction pattern DFP is known in some particular plane P. Then using DFP as boundary condition, the diffraction patterns are obtained outside P because of the existence (under mild restrictions) of a unique solution to the spinor equations for a plane wave. Using this method the diffraction patterns of circular and rectangular apertures are discussed with as boundary condition the Fraunhofer diffraction in the focal plane of a lens. The approximations needed to obtain the results supplied by the Kirchhoff theory are described. A particular feature of the spinor formalism is to give the polarization changes of the electromagnetic field by diffraction.

Generalization of the electromagnetic spinor formalism to anisotropic media

We generalize to magnetically isotropic but electrically anisotropic media the spinor formalism previously developed for isotropic media.

Phenomenological quantum electrodynamics when εμ = 1: theory and some applications including the Casimir effect

The canonical quantum theory for an electromagnetic field within an isotropic nondispersive medium, whose permittivity ε and permeability μ satisfy the condition εμ = 1, is developed. This condition is found to simplify the electromagnetic formalism considerably and is of interest not only to quantum electrodynamics (QED) but also to quantum chromodynamics (QCD) in view of the formal analogy existing between these two theories to the zero-order in the gauge coupling constant. After giving a survey of the general formalism, this paper discusses appropriate modifications of known experiments in optics: the Ashkin–Dziedzic pressure experiment (1973), the Barlow torque experiment (1912), and the levitation experiment of Ashkin (1970) and others. Finally, a calculation is given of Casimir (i.e., zero-point) surface force acting on one of two spherical interfaces separating three media from each other, under certain simplifying conditions.

ASPECTS OF ELECTRODYNAMICS OF ELECTROCHEMICAL SYSTEMS

Fundamentals of electromagnetic response formalism and the role of collective modes in interfacial electrochemistry are discussed. These concepts are used to derive a point of view on the optico-electrochemical problems of bulk and interfacial collective and single-particle modes and to collect some ideas on the possible physical effects.

Determination of the coupling coefficient of a holographic thin film coupler

In two previous papers, we proposed a rigorous electromagnetic formalism to study the coupling resonances which occur when a plane wave illuminates a grating coupler waveguide system under a convenient angle of incidence. We deal here with the case when a limited incident beam impinges on the system, and we try to optimize the parameters of the beam in order to get the best coupling coefficient. Numerical results are given for both lossless and lossy photo-resists.

About the theory of optical grating coupler-waveguide systems

It is well known that photoresist gratings can be used for coupling light into and out of optical waveguides. To understand the coupling phenomena, and as a first step of a theoretical study, we deal here with the diffraction of a plane electromagnetic wave by a photoresist grating lying on a dielectric optical guide. Using a rigorous electromagnetic formalism, we find the sharp resonances already described by Hope and relate them with the existence of modes in the optical guide.