Expansion Of Fields In Terms Research Articles

Analytical averaging of cross-sections for randomly oriented layered particles in the modified [formula omitted]-matrix method

Two modifications of the T-matrix method developed earlier for layered scatterers are extended by a procedure of analytical averaging of cross-sections for randomly oriented particles. One of the approaches uses spheroidal coordinates and field expansions in terms of the spheroidal wave functions and is practically equivalent to the separation of variables method formulated for spheroids. The applicability of the suggested approaches is discussed, and some numerical results are presented.

Theory of fluorescence in photonic crystals

We present a formalism for the description of fluorescence from optically active materials embedded in a photonic crystal structure possessing a photonic band gap or pseudogap. An electromagnetic field expansion in terms of Bloch modes of the crystal is used to develop the equations for fluorescence in terms of the local density of photon modes available to the emitting atoms in either the high or low dielectric regions of the crystal. We then obtain expressions for fluorescence spectra and emission dynamics for luminescent materials in photonic crystals. The validity of our formalism is demonstrated through the calculation of relevant quantities for model photon densities of states. The connection of our calculations to the description of realistic systems is discussed. We also describe the consequences of these analyses on the accurate description of the interaction between radiative systems and the electromagnetic reservoir within photonic crystals.

Multiresolution time-domain algorithm using CDF biorthogonal wavelets

A new approach to the multiresolution time-domain (MRTD) algorithm is presented in this paper by introducing a field expansion in terms of biorthogonal scaling and wavelet functions. Particular focus is placed on the Cohen-Daubechies-Feauveau (CDF) biorthogonal-wavelet class, although the methodology is appropriate for general biorthogonal wavelets. The computational efficiency and numerical dispersion of the MRTD algorithm are addressed, considering several CDF biorthogonal wavelets, as well as other wavelet families. The advantages of the biorthogonal MRTD method are presented, with emphasis on numerical issues.

Space-time duality and average number of terms in mode decomposition of pulse fields

Consequences of the spatio-temporal symmetry in the deterministic expansion of complex light fields in terms of factorized components are considered. Relationships between the characteristics of the transverse and temporal wave coherences are derived and the mean number of coherent modes is estimated for a Gaussian ensemble of their small-scale structure. The results obtained are compared with alternative statistical variants of mode formalism.

Field distribution in He-Ne waveguide lasers

In a waveguide laser, the laser light is guided in a hollow dielectric waveguide which also serves to confine the discharge. In this paper we study the radial distribution of the resonant field progressive components for such a laser, both theoretically and experimentally. To compute the resonant field distribution, we use a numerical method based on a field expansion in terms of a set of Bessel functions.

Novel differential formulation of electromagnetic scattering by dielectric cylinders of arbitrary cross-section

A new differential method of electromagnetic scattering from dielectric cylinders is presented. The formulation is based on a harmonic expansion of fields in terms of cylindrical wave functions and their matching at appropriate boundaries. An infinite dimensional differential system results in for the unknown expansion coefficients. This system is projected into a finite dimensional one whose numerical solution is the essential step. The method is seen to produce highly reliable results in the resonance region for TM, TE and line-source excitations.

Low-loss optical branching waveguides consisting of anisotropic materials

Low-loss branching waveguides of the mode-conversion type consisting of anisotropic materials are proposed, and their basic wave-guiding characteristics are studied by means of coupled-mode theory. Two mode-conversion sections are introduced on both input and output sides of a conventional symmetric branching waveguide. Each arm of the branching waveguides is assumed to be a single-mode slab waveguide except for the tapered section. A coupled-mode system of equations describing mode-conversion phenomena with respect to the transverse magnetic (TM) mode in the branching waveguides is derived from the field expansion in terms of local normal modes. A Runge-Kutta-Gill method is used to numerically solve the coupled-mode equations. It is found that the proposed branching waveguides suffer mode-conversion losses to a much lesser extent than conventional branching waveguides. >

Analysis of waveguides with metal inserts

A systematic analysis of waveguides with metal inserts is presented. The method is based on a field expansion in terms of the normal modes of the corresponding hollow waveguide without metal inserts. The analysis leads to two formulations: a matrix formulation and a moment-method formulation. The matrix formulation is suitable for structures with smooth metal inserts which are free from sharp edges, while the moment method is more suitable for metal sheets (e.g. strips and fins) or metal inserts with sharp edges (e.g. ridges). The validity of the method is tested by investigating some special cases in which the surface of the metal insert coincides with one of the coordinate surfaces, e.g. a bifurcation in circular or rectangular waveguides. The method is then applied to the analysis of striplines and ridge waveguides. It leads to a generalization of the widely used spectral-domain technique in that ridges, fins, and strips with finite thickness can now be analyzed likewise. Any existing routine for the analysis of planar structures which is based on the spectral-domain technique can then be slightly modified in order to take the metallization thickness into account.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fundamental mode distribution in a diaphragmed cavity

It is well known that if a circular aperture is placed inside a laser cavity, the resonant field spatial distribution is different from the Gaussian distribution. In this paper, the authors study the radial distribution of the resonant field progressive components, and show that the latter are characterised by distinct widths. The values of these widths depend on the diaphragm opening. To compute the resonant field distribution, they use a numerical method based on a field expansion in terms of a set of Gauss-Laguerre functions.

Wave optical theory for fast self-focusing of laser beams in plasmas

A theory based on the field and non-linearity expansions interms of Laguerre-Gauss functions is presented. The theoryi useful when very fast self focusing occurs, as in the case of relativistic self focusing. Results for self trapping with a saturable non-linearity are closer to the numerical results than those obtained by any other theory.

Scalar waves in the mixmaster universe. II. Particle creation

Solutions to the complete time-dependent scalar wave equation in the mixmaster universe are presented. Differential equations for the mode amplitudes are given corresponding to field expansions in terms of the asymmetric- and the symmetric-top wave functions and for both minimal and conformal couplings of the scalar field to gravity. The theory of quantized fields in the mixmaster space is summarized. Creation and annihilation operators in the Heisenberg picture develop in time under a general Bogolubov transformation which expresses mathematically the physical processes of particle creation and mode mixing. The problem of particle creation is discussed here in the light of the classical theory of wave propagation. In the adiabatic limit when the expansion for the universe is slow, little production takes place. Higher-order expressions for the production amount are derived by the method of successive WKB approximations. Finally, numerical solutions of the wave equation for the uncoupled modes are presented. The effects of geometric shape, level energy, and particle mass on production are studied for the characteristic "small oscillation" and "bounce" solutions of the mixmaster universe. The anisotropic dynamics of the background gives rise to strong directional effects in particle creation. Production of particles of higher mass or energy is less abundant and less sensitive to the shape or level. The process of mode mixing, which is a distinct feature of the mixmaster universe, will be studied in a later paper.

On the Incompleteness of E and H Modes in Wave Guides

It is shown that a field expansion in terms of E and H modes for an arbitrary current source in a wave guide is complete for points outside the source region but does not give the complete field within the source region in general. It is also shown how the expansion may be completed by the addition of an extra term of simple form.

Eigenfunctions of the Curl Operator, Rotationally Invariant Helmholtz Theorem, and Applications to Electromagnetic Theory and Fluid Mechanics

In the present paper we introduce eigenfunctions of the curl operator. The expansion of vector fields in terms of these eigenfunctions leads to a decomposition of such fields into three modes, one of which corresponds to an irrotational vector field and two of which correspond to rotational circularly polarized vector fields of opposite signs of polarization. Under a rotation of coordinates, the three modes which are introduced in this fashion remain invariant. Hence we have introduced the Helmholtz decomposition of vector fields in an irreducible, rotationally invariant form.These expansions enable one to handle the curl and divergence operators simply. As illustrations of the use of the curl eigenfunctions, we solve four problems. The first problem that is solved is the initial value problem of electromagnetic theory with given time- and space-dependent sources and currents and we show that the radiation and longitudinal modes uncouple in a very simple way. In the second problem we show how fluid motion...