Vector Electromagnetic Waves Research Articles

Double scatter of vector electromagnetic waves from rough metal and dielectric surfaces using the Kirchhoff approximation

This paper presents calculations of a formulation of the 3D Kirchhoff approximation which allows calculation of the scattering of vector waves from 2D rough surfaces containing infinite slopes. Results are presented for scattering from surfaces with rectangular surface structures. This type of surface has applications, for example, in remote sensing and in testing or imaging of printed circuits. Some preliminary calculations for rectangular-shaped grooves in a plane are presented for the 2D surface method.

On the concept of “tractor beams”

We demonstrate the existence of a class of optical beams where the nonconservative forces can be locally oriented in a direction opposite to the propagation wave vector. Objects placed in the vicinity of these locations will move toward the source of light. The behavior of these negative forces is discussed for the particular case of nondiffracting rotating scale-invariant vector electromagnetic waves.

Numerical calculation of a converging vector electromagnetic wave diffracted by an aperture using Borgnis potentials II Application to the study of focal shift

Focal shift of the converging spherical wavefront light diffracted by a circular aperture is numerically studied with the method of calculating the vector diffractive field by using Borgnis potentials given in Part I [J. Opt. Soc. Am. A23, 872 (2006)]. The quantitative dependence of the focal shift on the geometric parameters is discussed. The focal shift is mainly determined by the Fresnel number (N(f)) on the geometric focusing plane of the converging light, and an empirical formula between the fractional focal shift and the Fresnel number is deduced for N(f)<2. The focal shift of the same geometry is also studied on the basis of the scalar Rayleigh theory of diffraction, and its comparison with and difference from the result of our method are presented.

Numerical calculation of a converging vector electromagnetic wave diffracted by an aperture by using Borgnis potentials I General theory

A method is proposed, on the basis of the vector electromagnetic theory, for the numerical calculation of the diffraction of a converging electromagnetic wave by a circular aperture by using Borgnis potentials as auxiliary functions. The diffraction problem of vector electromagnetic fields is simplified greatly by solving the scalar Borgnis potentials. The diffractive field is calculated on the basis of the boundary integral equation, taking into consideration the contribution of the field variables on the diffraction screen surface, which is ignored in the Kirchhoff assumption. An example is given to show the effectiveness and suitability of this method and the distinctiveness of the diffractive fields caused by the vector characteristics of the electromagnetic fields.

Vector Wave Beams. Changing Polarization of Electromagnetic Wave Beams on Reflection from a Dielectric Plate

We consider electromagnetic vector wave beams and a change in their polarization upon passage through a plane-parallel dielectric plate. A study is based on rigorous solutions of equations for an electromagnetic field.We find the structures of the transmitted and reflected fields. In the case of comparatively narrow beams (with a width of about one wavelength), we determine the reflection coefficients for both normal incidence and incidence at the Brewster angle.

Scattering theorems for dyadic chiral fields

A time-harmonic plane dyadic electromagnetic field is scattered by a chiral body in a chiral environment. The body is either a perfect conductor or a dielectric. The incident field is a linear combination of left-circularly polarized and right-circularly polarized dyadic electromagnetic fields, each of which has a different wave number. We prove reciprocity and scattering theorems in dyadic form, which incorporate as special cases the corresponding known theorems for vector electromagnetic waves. Specializing to the same direction of incidence and observation in the general scattering theorems we obtain forward scattering theorems.

Conversion between two bases of rotationally symmetric spheroidal vector wavefunctions

A conversion between two eigenfunction bases of spheroidal vector wavefunctions is described, both bases comprising two independent sets of solutions for the electro-magnetic vector wave equation with azimuthal symmetry. A set of definite integrals over the angular variable, arising in the conversion is evaluated in closed form, each integral containing a product of two angular spheroidal wavefunctions with m = 0 or 1, weighted by algebraic functions.

Exact description of free electromagnetic wave fields in terms of rays

A set of representations are proposed for vector electromagnetic waves in free space (or homogeneous media) of any state of coherence. These representations take the form of a radiance, i.e., the weight of a ray. The intensity, energy density or Poynting vector at any point correspond simply to the sum of the weights of all the rays through that point. This formalism is valid even for fields with components traveling in all directions, but without evanescent components.

Performing Interpolation and Anterpolation Entirely by Fast Fourier Transform in the 3-D Multilevel Fast Multipole Algorithm

The fast multipole methods are used for solving a scalar acoustic or vector electromagnetic wave equation by integral equation methods with a large number of unknowns. In this paper a new method is presented for performing interpolation and anterpolation in both spherical coordinates $\theta$ and $\phi$ by FFT in the three-dimensional (3-D) multilevel fast multipole algorithm (MLFMA). The key idea is to approximate functions on the unit sphere by truncated Fourier series in two variables rather than by the usual spherical harmonics. The proposed method is exact in interpolating and anterpolating and has the high numerical efficiency of FFT. The method is numerically compared to the method of performing interpolation and anterpolation using Lagrangian interpolation, which presently is probably the fastest method for those operations, and the results suggest that the proposed new method is equally or more efficient, depending on the desired accuracy.

Numerical studies of (partial-) waveguide FELs

We investigate two different approaches to analyze the excitation of 3D-time dependent fields by short electron bunches in parallel-plate waveguide FELs. In the first approach the Lienard–Wiechert solution of the four vector electromagnetic wave equation is adopted to the waveguide-FEL problem by means of image currents method. The second approach is based on the commonly used method of solving paraxial wave equation for the amplitudes of the excited waveguide modes in time and axial dimension. The loss mechanism in a partially waveguided cavity with toroidal mirrors is incorporated into the latter formalism accounting for the outcoupling of the radiation fields through a hole, mode conversion and clipping-off due to the waveguide apertures.

Finite element‐based model order reduction of electromagnetic devices

AbstractIn this paper an efficient algorithm is presented for the development of compact and passive macro‐models of electromagnetic devices through the systematic reduction of the order of discrete models for these devices obtained through the use of finite elements. The proposed methodology is founded on a new finite element formulation that casts Maxwell's curl equations in a state‐space form. Such state‐space representations are very compatible with a class of robust model order reduction techniques based on Krylov subspaces. However, the advantage of this compatibility appears to be hindered by the fact that the state matrix of the discretized Maxwellian system is of dimension almost twice that obtained from the finite element approximation of the electromagnetic vector wave equation. It is shown in this paper that the apparent penalty in both memory and computation efficiency can be avoided by a proper selection of the finite element expansion functions used for the discretization of the electromagnetic fields. More specifically, it is shown that the proper selection of expansion functions renders the state‐space form of the Maxwellian system equivalent to the discrete problem obtained from the approximation of the vector wave equation using tangentially continuous vector finite elements. This equivalence is then used to effect Krylov‐based model order reduction directly from the finite element approximation of the vector wave equation. In particular, a passive model order reduction algorithm is used for this purpose. The proposed reduced order macro‐modelling algorithm is demonstrated through its application to a variety of microwave passive components. Copyright © 2002 John Wiley &amp; Sons, Ltd.

Solution of capacitance systems using incomplete Cholesky fixed point iteration

Application of the Galerkin finite element method to the electromagnetic vector wave equation yields an implicit system of equations that must be evolved in time. The left-hand matrix has units of capacitance and is analogous to the mass matrix in continuum mechanics. In this letter we point out the interesting fact that for a Cartesian grid the Cholesky decomposition of the capacitance matrix has the same sparsity as the original matrix, i.e. there is no zero-fill during the course of the Cholesky decomposition. Therefore an iterative method using the incomplete Cholesky decomposition as a preconditioner is quite efficient for nearly orthogonal quadrilateral or hexahedral grids. Copyright © 1999 John Wiley & Sons, Ltd.

Solution of capacitance systems using incomplete Cholesky fixed point iteration

Application of the Galerkin finite element method to the electromagnetic vector wave equation yields an implicit system of equations that must be evolved in time. The left-hand matrix has units of capacitance and is analogous to the mass matrix in continuum mechanics. In this letter we point out the interesting fact that for a Cartesian grid the Cholesky decomposition of the capacitance matrix has the same sparsity as the original matrix, i.e. there is no zero-fill during the course of the Cholesky decomposition. Therefore an iterative method using the incomplete Cholesky decomposition as a preconditioner is quite efficient for nearly orthogonal quadrilateral or hexahedral grids. Copyright © 1999 John Wiley & Sons, Ltd.

New types of surface waves in antiferromagnetics with magnetoelectrical effect

The new types of surface electromagnetic waves (polaritons) in tetragonal antiferromagnetics (AFM) with magnetoelectrical (ME) effect are investigated theoretically. The main attention is paid to two cases: when the AFM vector L is parallel and normal both to surface of specimen and electromagnetic wave vector. In the first case polaritons exist only in the frequency range of optical phonons oscillations. ME effect results in the effect of inambiguity. In the second case at large magnitude ME effect the surface waves can exist both near to frequencies of a magnetic subsystem oscillations, and in the region of frequencies of optical phonons oscillations. At small ME effect surface waves exist only near to frequencies range of optical phonons oscillations. In this geometry the polaritons oscillate deep into sample with period which is proportional to ME interaction succeptibility magnitude.

Radiative transfer theory with time delay for the effect of pulse entrapping in a resonant random medium: General transfer equation and point-like scatterer model

A pulse propagation of a vector electromagnetic wave field in a discrete random medium under the condition of Mie resonant scattering is considered on the basis of the Bethe–Salpeter equation in the two-frequency domain in the form of an exact kinetic equation which takes into account the energy accumulation inside scatterers. The kinetic equation is simplified using the transverse field and far wave zone approximations which give a new general tensor radiative transfer equation with strong time delay by resonant scattering. This new general radiative transfer equation, being specified in terms of the low-density limit and the resonant point-like scatterer model, takes the form of a new tensor radiative transfer equation with three Lorentzian time-delay kernels by resonant scattering. In contrast to the known phenomenological scalar Sobolev equation with one Lorentzian time-delay kernel, the derived radiative transfer equation does take into account effects of (i) the radiation polarization, (ii) the energy accumulation inside scatterers, (iii) the time delay in three terms, namely in terms with the Rayleigh phase tensor, the extinction coefficient and a coefficient of the energy accumulation inside scatterers, respectively (i.e. not only in a term with the Rayleigh phase tensor). It is worth noting that the derived radiative transfer equation is coordinated with Poynting's theorem for non-stationary radiation, unlike the Sobolev equation. The derived radiative transfer equation is applied to study the Compton–Milne effect of a pulse entrapping by its diffuse reflection from the semi-infinite random medium when the pulse, while propagating in the medium, spends most of its time inside scatterers. This specific albedo problem for the derived radiative transfer equation is resolved in scalar approximation using a version of the time-dependent invariance principle. In fact, the scattering function of the diffusely reflected pulse is expressed in terms of a generalized time-dependent Chandrasekhar H-function which satisfies a governing nonlinear integral equation. Simple analytic asymptotics are obtained for the scattering function of the front and the back parts of the diffusely reflected Dirac delta function incident pulse, depending on time, the angle of reflection, the mean free time, the microscopic time delay and a parameter of the energy accumulation inside scatterers. These asymptotics show quantitatively how the rate of increase of the front part and the rate of decrease of the rear part of the diffusely reflected pulse become slower with transition from the regime of conventional radiative transfer to that of pulse entrapping in the resonant random medium.

Diffusion asymptotics of the Bethe-Salpeter equation for electromagnetic waves in discrete random media

We present an exact expression for the diffusion constant of vector electromagnetic waves in a random medium of dielectric scatterers in the form of the Green-Kubo relation. The derivation is based on a proper version of the Ward-Takahashi identity for classical waves. The relation between the density of states of the electromagnetic field and the absorption length in the model of weakly absorbing scatterers is discussed.

Poynting's theorem and electromagnetic wave multiple scattering in dense media near resonance: modified radiative transfer equation

A new version of nonstationary radiative transfer theory for vector electromagnetic wave multiple scattering in a discrete random medium is presented in which the electromagnetic energy within dielectric scatterers may be large. The starting point is the general two frequency Bethe-Salpeter equation for the coherence tensor-function of the wave electric field. In the two frequency domain it is proved that the Poynting's theorem can be decomposed into (1) a theorem for the spectral component of the electric energy density multiplied by two and (2) a theorem for the difference between the spectral components of the electric and the magnetic energy densities. The Poynting's theorem is closely connected with a generalized two-frequency Ward-Takahashi identity according to which the extinction of a nonsteady radiation is conditioned by the incoherent scattering, the real absorption and changing of the energy accumulation inside scatterers. As result a new radiative transfer equation is obtained for the radiance tensor of a pulse radiation in unbounded random medium. This equation differs from the traditional one by a term with the time derivative where the inverse value of the group velocity is replaced by a tensor-operator which determines the average rate of the electromagnetic energy change within scatterers.

Efficient computation of three-dimensional scattering of vector electromagnetic waves

A review of different methods of solving for the solution of scattering by three-dimensional objects is presented. There are two main classes of methods: one is for solving the differential equation directly, and the other is for solving the integral equation derived from the differential equation. The differential equation method has the advantage of generating a sparse matrix but could potentially suffer from grid-dispersion error. The radiation condition in the differential equation approach is sometimes approximated. The alternative approach, which is the integral equation approach, provides a solution that satisfies the radiation condition immediately and possibly with less grid-dispersion error. However, it gives rise to a dense matrix that is more computationally intensive to solve and to invert. Recent methods developed for inverting and solving the integral equation efficiently are discussed. They involve the recursive method, the nesting method, and the iterative method. The recursive method seeks the solution of (n + 1) subscatterers from the solution of n subscatterers. The nesting method nests a smaller problem within a larger problem. The iterative method uses the conjugate gradient method but exploits recursion and nesting to expedite the matrix-vector multiply in the conjugate gradient method. Some results for solving three-dimensional scattering of electromagnetic fields are presented.

Photonic band structures of two- and three-dimensional periodic metal or semiconductor arrays.

The photonic band structures of a square lattice array of metal or semiconductor cylinders, and of an fcc array of metal or semiconductor spheres, are computed numerically. The frequency-dependent dielectric function of the metal or semiconductor is assumed to have the free-electron form e(ω)=1-(ω p 2 /ω 2 ), where ω p is the plasma frequency of the charge carriers. A plane-wave expansion is used to transform the vector electromagnetic wave equation into a matrix equation. The frequencies of the electromagnetic modes are found as the zeros of the determinant of the matrix. In general, the plane-wave method is found to be most effective for structures with filling fractions f≤0.1% but provides a semiquantitative description of the band structures of these systems for f>0.1%

Electromagnetic scattering from turbulent plasmas.

A self-consistent multiple-scattering theory of vector electromagnetic waves scattered from a turbulent plasma is presented. This approach provides a general and systematic treatment to all orders in turbulence of the scattering of electromagnetic waves in terms of the properties of the turbulent structure of the scattering system and is applicable in the full regime from underdense to overdense plasmas. To illustrate the theory, a plasma consisting of a finite number density of discrete scatterers with a simple geometry and statistical properties is chosen. In this approach the exact solution for a single scatterer is obtained first. From it the configuration-dependent solution for N scatterers is constructed. Rather than solving explicitly for this solution and then averaging, the averaging operation will be taken first in order to find an approximate equation obeyed by the mean or coherent field. The coherent and incoherent scattering are then determined in terms of the coherent field and the backscatter is evaluated. The coherent and incoherent scattering, our principal results, are expressed in a plane-wave basis in a form suitable for numerical computation. A number of interesting phenomena which may readily be incorporated into the theory are indicated.