Arbitrary Complex Permittivity Research Articles

Comment on “Revisiting the Balazs thought experiment in the presence of loss: electromagnetic-pulse-induced displacement of a positive-index slab having arbitrary complex permittivity and permeability”

The article Appl. Phys. A 105, 267-281 (2011) by Chau and Lezec contains a serious error in the citation of prior art. The force density which was shown to be incorrect cannot be attributed to the work of Kemp et al., and the cor- rect time-domain force equation was previously published in one of the misrepresented works. Furthermore, we show that unreferenced prior art weakens the overall contribution of the work.

Revisiting the Balazs thought experiment in the presence of loss: electromagnetic-pulse-induced displacement of a positive-index slab having arbitrary complex permittivity and permeability

Over a half-century ago, Balazs proposed a thought experiment to deduce the form of electromagnetic momentum in a lossless and non-dispersive slab by imposing conservation of global momentum and system center-of-mass velocity after a pulse has traveled through the slab. Here, we revisit the Balazs thought experiment by explicit calculations of momentum transfer and center-of-mass displacement of a non-dispersive, positive-index slab of arbitrary complex permittivity and permeability using a set of postulates consisting only of Maxwell’s equations, a generalized Lorentz force law, the Abraham form of the electromagnetic momentum density, and conservation of both pulse and slab mass. In the case where the slab is lossless, we show that a pulse of arbitrary shape incident onto the slab conserves both global momentum and system center-of-mass velocity, consistent with the starting postulates of the Balazs thought experiment. In the case where the slab is lossy, we show, within the context of the above postulates, that global momentum is always conserved and that system center-of-mass velocity is conserved only when mass transfer from the pulse to the slab is described by an incremental pulse-mass-transfer model, proposed here, in which the pulse deposits mass in the slab with a distribution corresponding to the instantaneous mass density profile of the pulse.

Scattering by a lossy dielectric cylinder in a waveguide cross-junction

A complete analysis of a lossy composite dielectric cylinder in an H-plane waveguide cross-junction is developed. The sample is centred in the square connecting cavity which is filled with a material as well. The metallic post with a sleeve is a particular case of the insert. A series solution utilises the symmetry of the structure and is based on the domain-product technique. The analysis leads to infinite sets of linear algebraic equations, which are solved numerically after appropriate truncation. A direct use of the information concerned with the edge effect increases the accuracy and efficiency of the computations. A rapidly converging algorithm is applied to the scattering characteristics of the junction. The data are effectively obtained for arbitrary complex permittivity and any possible radius of the cylinder.

Electrical and optical properties of dense composites

Effective cluster models have been developed that treat disordered suspensions of monodisperse metal spheres as mixtures of isolated spheres and compact clusters of spheres using the Clausius–Mossotti equation [Phys. Rev. B 42, 9319 (1990); J. Appl. Phys. 71, 3926 (1992)] and the Bruggeman equation [J. Appl. Phys. 78, 6165 (1995)]. These effective cluster models are adapted to suspensions of dielectric particles with arbitrary complex permittivity. The models are compared with the coated sphere model of Sheng [Phys. Rev. Lett. 45, 60 (1980); J. Opt. Soc. Am. B 15, 1022 (1998)]. Model calculations are compared with the measurements of the optical transmission spectra and low frequency electrical conductivity of Au–SiO2 films by Cohen, Cody, Coutts, and Abeles [Phys. Rev. B 8, 3689 (1973)], and with the low frequency permittivity measurements on suspensions of Ag spheres in KCl of Grannan, Garland, and Tanner [Phys. Rev. Lett. 46, 375 (1981)]. The models accurately predict the percolation thresholds seen in the electrical measurements and are in good agreement with all of the experiments over the entire range of volume loading.

Optical response of arrays of spheres from the theory of hypercomplex variables

Transformation from the three-dimensional hypercomplex X(x,y,z) frame to another which has infinite dimensions but has the symmetry properties of an array built in allows the Laplace equation to be solved in structures for which it is nonseparable. The power and practicality of this technique is demonstrated on pairs and chains of spheres of arbitrary complex permittivity in a quasiconstant electric field. New results include strong absorption enhancement at long wavelengths in high density chains due to structurally induced resonances.

Shift of the complex resonance frequency of a dielectric-loaded cavity produced by small sample insertion holes

The presence of small sample insertion holes in a cylindrical cavity produces a shift in the complex resonance frequency of the cavity. A mathematical model is proposed to compute the shift when the cavity oscillates in an axially symmetric TM/sub 0mp/ mode The treatment applies to samples with arbitrary complex permittivity. The model is compared to other treatments and checked against measured results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Boundary‐element analysis of plane‐wave diffraction from metallic gratings with arbitrary complex permittivity

AbstractFor the problem of plane‐wave diffraction from metallic gratings with arbitrary complex permittivity, a new analysis method based on the boundary‐element method is proposed. First, this diffraction problem is analyzed by the boundary‐element method as a two‐media boundary value problem taking into consideration the metallic loss. Further, a simple method is proposed in which an approximate boundary condition using the surface impedance is incorporated into the discretized equation by the boundary‐element method. Especially, in the method using the surface impedance approximation, the region to be analyzed is reduced to only the incident side so that efficiency of both the formulation and the numerical calculation can be improved significantly. The diffraction characteristics of the sinusoidal grating and the Fourier grating were actually computed. The results were compared with those by other methods and by experiments so that the validity and usefulness of the present method are confirmed.

Analysis of electromagnetic scattering from dielectrically coated conducting cylinders using a multifilament current model

A method of moments solution is presented for the problem of transverse magnetic scattering from dielectrically coated conducting cylinders. The solution uses fictitious filamentary electric sources of yet unknown currents to simulate both the field scattered by the cylinder and the field inside the dielectric coating. The simulated fields obey the boundary conditions, namely, the continuity of the tangential components of the electric and magnetic fields across the air-dielectric interface and the vanishing of the tangential component of the electric field at the perfect conductor, at selected sets of points on these respective surfaces. The result is a matrix equation that is readily solved for the unknown current. The currents can be used to determine approximate values for the fields and field-related parameters of interest. The procedure is simple to implement and is general in that cylinders of smooth but otherwise arbitrary shape and coating of arbitrary complex permittivity can be handled. Illustrative examples are considered and compared with available data, demonstrating the efficiency of the solution.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Finite‐element analysis of plane wave diffraction from metallic gratings with arbitrary complex permittivity

AbstractA method of analysis based on the finite‐element method is presented for the problem of plane wave diffraction from metallic gratings with arbitrary complex permittivity. First, the problem of diffraction of a plane wave from the metallic reflected‐type grating is analyzed rigorously as a two‐media boundary value problem by the finite‐element method. Next, a new method is proposed in which an approximate boundary condition using the surface impedance is incorporated into the discretized equations by the finite‐element method. Especially, in the method of using the surface impedance approximation, the region to be analyzed is reduced substantially from the one for the two‐media boundary value problem, and the computational effort is expected to be reduced significantly. The diffraction characteristics of grooved gratings with sinusoidal, triangular and rectangular profiles are actually calculated and the results are compared with those by other methods and experiments. In the case of the TE wave incidence, it is found that the results by the two‐media boundary value problem and those by the surface impedance approximation agree well. On the other hand, in the case of the TM wave incidence, the results are substantially different depending on the grating profile. By comparison of the results with those based on the assumption of a perfect conductor, it is found that the loss in the metal must be considered at a longer wavelength in the case of the TM wave incidence than in the case of the TE wave incidence.

Self-consistent modal field analysis of injection-laser devices

The paper reports a new method of modal field analysis specifically designed to allow simulation of certain types of multiple coupled waveguides. The analysis, based on a transverse resonance method, allows direct determination of a required optical mode (or supermode) in waveguides of arbitrary complex permittivity profiles. The method solves Maxwell's equations and includes a stability analysis to improve accuracy. The feasibility of using this numerical method in a self-consistent laser simulation has been investigated by modelling the operation of inverted-rib-waveguide structures. Good agreement has been obtained with experimental observation.

Rigorous coupled-wave analysis of metallic surface-relief gratings

A rigorous coupled-wave analysis for metallic surface-relief gratings is presented. This approach allows an arbitrary complex permittivity to be used for the material and thus avoids the infinite conductivity (perfect-conductor) approximation. Both TE and TM polarizations and arbitrary angles of incidence are treated. Diffraction characteristics for rectangular-groove gold gratings with equal groove and ridge widths are presented for free-space wavelengths of 0.5, 1.0 and 10.0 μm for all diffracted orders as a function of period, groove depth, polarization, and angle of incidence. Results include the following: (1) TM-polarization diffraction characteristics vary more rapidly than do those for TE polarization, (2) 95% first-order diffraction efficiency occurs for TM polarization at 10.0 μm, (3) &lt;0.1% zero-order specular reflectivity occurs for both TE and TM polarizations, (4) &gt;50% absorption of incident power occurs at 0.5 μm, and (5) the perfect-conductor approximation is not valid for TM polarization at any of the wavelengths and is not valid for TE polarization at 0.5 μm.

Scattering by a Cylindrical Post of Complex Permittivity in a Waveguide

An exact solution of the discontinuity problem of a circular cylindrical post of arbitrary complex permittivity centered in a rectangular waveguide with the axis parallel to the electric field vector of the dominant mode has been set up and numerical results based directly on this solution have been found rising an electronic computer. The method used divides the waveguide up into three different regions by introducing two imaginary plane walls perpendicular to the waveguide walls. In the center region, which contains the cylindrical rod, the electromagnetic field is expanded in cylindrical waves and in the outer regions the field is expanded in waveguide modes. By setting up the boundary conditions at all discontinuity surfaces and performing numerical matching of the fields at the two imaginary walls, a system of linear equatious determining the coefficients of reflection, transmission, and absorption of the field due to the cylindrical rod is found. The structure which is of most interest in the case of a plasma column is a coaxial structure consisting of an inner dielectric cylinder with complex permittivity (the plasma) surrounded by a dielectric sleeve with real, positive permittivity (the glass tube). The theory is therefore developed to apply generally for such structures. From the numerical results, curves have been obtained showing the relationship between the coefficients of reflection and transmission and the (complex) permittivity of the rod material. Such curves maybe used for deducing the microwave properties of a cylindrical rod from measurements of the reflection and transmission coefficient of the rod.