Inhomogeneous Dielectrics Research Articles

Calculation of the intensity of electromagnetic fields of thermal microwave detectors at high temperatures. II

The second moments are found for the spectral amplitudes of the thermal electromagnetic field of a dielectric inhomogeneity of complicated geometry heated to a temperature T.

Propagation of Cladded Inhomogeneous Dielectric Waveguides

An approximate theory on the propagation of modes in an arbitrarily inhomogeneous optical waveguide embedded in a homogeneous medium is presented. Simple formulas are given, whereby the propagation constants can be determined assuming that the analytic solution is known in the absence of cladding. The results obtained applying the theory to a truncated parabolic-index profile are shown to be in good agreement with those obtained by the rigorous analysis. The theory is also applied to the propagation of TE and TM waves in truncated near-parabolic-index media.

Quantum electrodynamics in the presence of dielectrics and conductors. V. The extinction and moment theorems for correlation functions and relativistic aspects of blackbody fluctuations

Dynamical laws describing the space-time development of the response functions and second-order correlation functions of the electromagnetic fields in a linear dielectric medium are presented in the form of a number of differential and integral equations. The boundary conditions on the response functions are expressed as extinction theorems, which are particularly useful for systems involving rough surfaces and metallic gratings. Higher-order correlation functions are shown to be related to the linear-response functions in a manner analogous to the moment theorem for Gaussian random processes. A modified form of the fluctuation-dissipation theorem is obtained and is used to calculate free-space blackbody fluctuations in a moving frame. Fluctuations in a moving dielectric are obtained from the transformation of fields under Lorentz transformation. Contact with the earlier works of Mehta and Wolf, Eberly and Kujawski, and the recent work of Baltes and co-workers on blackbody radiation is made wherever possible. Finally, the correlation functions in a moving frame are used to discuss the relaxation of a moving atom. The discussion in the last section is for the case of free space. In part I of this series of papers, ' we showed how the linear-response theory can be used with ease to compute various types of electromagnetic-field correlation functions in the presence of dielectric bodies. In subsequent papers, ' we used such correlation functions to discuss a number of surfacedependent eff ects. However, some fundamental aspects of the present theory, such as equations of motion, boundary conditions etc. , were not elaborated upon in detail. In this paper, we consider such questions, discuss the relation of the higher-order correlation functions (which are needed, e.g. , in the treatment of the decay of metastable states') to response functions, and present a generalized fluctuation-dissipation theorem appropriate to relativistic ensembles. '4 In Sec. II, we obtain a number of differential and integral equations satisfied by the response functions g;»» g;&«, g;;8» g;~«. Both first-order and second-order differential equations are given. These equations in turn lead to a set of equations for the correlation functions 8;;, 9;~, 8;~, K;z. The response functions satisfy much simpler equations than correlation functions. However, for the free-space case, the equations for correlation functions are simple. In Sec. III, the boundary conditions are presented in the form of an extinction theorem. ' ' A simple example is given to illustrate the use of this theorem. In Sec. IV we prove that the thermal fluctuations in a linear dielectric (occupying arbitrary domain) are Gaussian. This, in general, is not true for a nonlinear medium. In Sec. V, we obtain a modified form of the fluctuation-dissipation theorem that is applicable to relativistic ensembles. A number of the symmetry properties of the correlation functions in a moving frame are discussed. The correlation functions in a moving frame are used to discuss the relaxation of a moving atom in Sec. VI. In part VI of this series we will present the theoryof Lippmannfringes. In part VII, we will deal with the general problem of scattering from rough surfaces as well as scattering from the dielectric inhomogeneities. Use will be made of the integral

Depolarization of light back scattered from rough dielectrics*

The depolarization of light from a laser, back scattered from inhomogeneous dielectrics, was investigated both experimentally and theoretically. A theoretical model that includes back scattering from both the surface and subsurface was developed by use of the Kirchhoff approach. The subsurface polarized and depolarized back-scattered components are independent of surface roughness. The model predicts results in agreement with experimental measurements performed with a dual-polarized laser back-scattering system. The measurements indicate that a significant contribution to the total back-scattered power results from subsurface contributions; in some cases, this contribution completely masks the effects due to the surface.

Analysis of Lossy Inhomogeneous Waveguides Using Shooting Methods (Short Papers)

Shooting methods are used to analyze rectangular waveguides containing inhomogeneous lossy dielectrics. The technique obtains the electromagnetic fields inside the waveguide by solving Maxwell's equations using trial and error procedures to match the boundary conditions at the conducting waveguide surface. Dispersion and attenuation curves are obtained which show how continuous dielectric inhomogeneities and losses affect the transmission characteristics of these waveguides.

Gaussian Light Beams in Inhomogeneous Media

Vector wave solutions are obtained for the propagation of beams of light in media having slow spatial variations of the gain, loss, or index of refraction. The formalism developed here is applicable to a wide range of problems, and an exa mple considered in detail is the propagation of off-axis beams in lenslike laser materials and optical waveguides. A procedure is also described for the diagnosis of localized dielectric inhomogeneities such as plasmas by means of Gaussian laser beams.

Propagation Modes, Equivalent Circuits, and Characteristic Terminations for Multiconductor Transmission Lines with Inhomogeneous Dielectrics

The theory of wave propagation on Iossless multiconductor transmission lines with inhomogeneous dielectrics is developed using matrix analysis. The treatment is concise and complete and has the advantage of identifying propagation modes in a way that permits straightforward physical interpretation. The equivalent circuit for the general line is derived and its application to the solution of wave problems with reflections is demonstrated. Special consideration is given to the problem of characteristically terminating a multiconductor line, i.e., terminating without reflections. The realizability of such a characteristic termination network is discussed, and proofs of realizability are given for the important cases of all lines with homogeneous dielectrics and all three-conductor lines, regardless of dielectric inhomogeneities. Symmetric three-conductor lines are discussed to exemplify the general theory, and an application to the problem of mode conversion on symmetric and asymmetric shielded strip lines is given.

Probability distribution of the breakdown electric fields of polymer dielectrics

The probability distribution is derived for the breakdown electric field of polymers, treated as inhomogeneous dielectrics. The extremal distribution and the Weibull distribution are shown to be particular cases of the result found. The experimental results found with low-pressure polyethylene and polyethylene, Styroflex, and polyethylene terephthalate films are consistent with the theoretical probability distribution found for the breakdown electric field.

The Effect of the Subsurface on the Depolarization of Rough‐Surface Backscatter

Most theoretical treatments of single‐surface scatter indicate negligible depolarized scatter into the plane of incidence. However, experimental measurements show that this scatter component is present. Several investigators have attempted to develop an explanation for the contradiction by attributing the depolarization to multiple scatter on the surface, but there is also evidence that the depolarization arises from volume scatter beneath the surface. In the Reneau et al. [1967, p. 463] measurements of laser scatter from inhomogeneous dielectrics they found, “… strong evidence that the depolarization process occurs primarily within the volume.” In similar studies Leader [1970, p. 11] also found, “The depolarized component is many orders of magnitude less than the polarized component when there is little contribution from the volume of the sample.” This paper presents a development for backscatter from rough surfaces, based on the single‐surface Kirchhoff method as employed by Fung [1967], which incorporates components due to volume scatter from the subsurface. The resulting expression contains a depolarized backscatter component due exclusively to the volume scatter. Calculation of polarized and depolarized backscatter and depolarization ratios are shown for several values of dielectric constants and volume reflection coefficients.

Self-focusing of laser beams in inhomogeneous dielectrics

This paper presents a theoretical investigation of the propagation and focusing of an electromagnetic wave in an inhomogeneous dielectric whose dielectric constant is given byɛ=ɛ0(z)+Φ(r, z), whereZ-axis is the direction of propagation of the beam. The quantity Φ(r, z) may either be due to non-linear effects or due to inhomogeneity in the actual fabrication of the guide.

High‐Frequency Backscattering From a Perfectly Conducting Sphere Coated With a Radially Inhomogeneous Dielectric

In this paper, the backscattered electric field is derived when a plane electromagnetic wave is incident upon a perfectly conducting sphere coated with a radially inhomogeneous dielectric. The Mie series is obtained and then subjected to an asymptotic analysis that is valid for very short wave‐lengths. In particular, the first two terms for the reflected portion of the electric field are derived and the formulation for the creeping wave contribution is presented. Also, a numerical computation of the monostatic cross section is performed for various thicknesses of the coating by considering the reflected portion of the backscattered electric field. It is shown that this particular type of inhomogeneous sheath reduces considerably the monostatic cross section of the perfectly conducting sphere as its thickness increases.

Method for the Solution of Electromagnetic Scattering Problems for Inhomogeneous Dielectrics as a Power Series in the Ratio (Dimension of Scatterer) /Wavelength

In this paper the definitive work of Stevenson for the Rayleigh series expansion of electromagnetic scattering from homogeneous scatterers is extended to inhomogeneous scatterers. Furthermore, it is shown that a determination of the strength of the multipoles induced by the incident radiation is sufficient to determine the far field and therefore the scattering cross section, without relying on an awkward expansion and subsequent matching of far and near fields. The calculations are thus enormously simplified.

The analogy of the elastic and dielectric spherical inhomogeneity for cubic and isotropic media

AbstractThe elastic spherical inhomogeneity in an infinite medium is treated in analogy to the dielectric inhomogeneity. In the isotropic and cubic cases the formulas for the homogeneous internal field and the induced dipole are analogous to those for the electric case except for the sign of the polarization. In the isotropic elastic case octopoles are induced in addition to the dipoles, whereas in the cubic case an infinite series of multipoles appears. The electric and elastic Clausius‐Mossotti formulas for polarizable and for reorienting dipoles are very similar. However in the cubic medium the elastic dipoles in the Lorentz sphere contribute always to the strain in the centre.

Waves and Evanescent Fields in Rectangular Waveguides Filled with a Transversely Inhomogeneous Dielectric

A numerical-calculation method for rectangular waveguides containing a transversely inhomogeneous dielectric is presented. The method is not restricted to the cutoff case or to special inhomogeneities. The relative permittivity of the dielectric can be an arbitrary function of the cross-sectional coordinates. The electric-and magnetic-field strengths, the dispersion characteristics of the propagating modes, and the attenuation constants of the evanescent modes result from the solution of a matrix eigenvalue problem with typically 8000 matrix elements. Propagating and evanescent modes in a waveguide containing a longitudinal semicircular dielectric rod are calculated as examples. The accuracy of the calculation method is confirmed by measurements and by calculating a special example with an exactly known solution. The error of the field intensities is typically 5 percent; the error of the dispersion characteristics and of the attenuation constants is typically 0.5 percent.

Numerical Determination of Potential in Inhomogeneous Dielectrics by Earnshaw's Theorem

Earnshaw's theorem, a characterization of potential functions equivalent to Poisson's equation, expresses a relation between the value of the potential at a point and an average of the function over a spherical surface centered at the point. The theorem therefore lends itself to use in numerical computation of the potential. A formulation of the theorem is presented with particular reference to determination of the potential in a region which is inhomogeneously occupied by dielectric media. This provides a rigorous basis for the formulas used to determine the potential at points on a dielectric interface, in that it avoids the ambiguity which arises in the evaluation of the finite-difference approximation to the Laplacian at such points. The use of the formulation is illustrated by examples of computer-generated graphs giving the potential in the presence of irregular dielectric objects.

Parameters of microstrip

The program computes the capacitance, effective permittivity, characteristic impedance and phase velocity of single strips, and of the normal modes of coupled pairs of strips, in an approximation in which the longitudinal components of the fields and the thickness of the conducting strips are neglected. Within this model, the inhomogeneous dielectric is treated in a rigorous manner.

Coupled Transmission Line Networks in an Inhomogeneous Dielectric Medium

In this paper, two-port networks composed of two identical, coupled transmission lines embedded in an inhomogeneous dielectric (e.g., suspended substrate, microstrip) are investigated. The ABCD parameters of circuit configurations, considered by Jones and Bolljahn, are obtained for the case of inhomogeneous dielectilc. Equivalent circuits of these networks are also given. It is shown that the characteristics of such circuits differ markedly from those embedded in a homogeneous medium. In addition, experimental results are presented for three types of circuits which have been constructed and tested. There is excellent agreement between the experimental results and those predicted theoretically on the basis of the equivalent circuits.

Radar cross section of perfectly conducting spheres coated with a certain class of radially inhomogeneous dielectrics

The geometrical optics technique is applied to obtain the reflected electric field from a perfectly conducting sphere coated with a special class of spherically inhomogeneous dielectrics. The result is compared to the second-order approximation which is obtained by asymptotic theory. Numerical computations of the percent error involved in computing the monostatic cross section using the geometrical optics solution instead of the higher order solution have been performed for 50 \leq ka \leq 1000 . Also, the effect of coating a perfectly conducting sphere with a radially inhomogeneous dielectric of the diverging or converging kind is discussed.

Guided Waves in Inhomogeneous Focusing Media Part III: Wall Effects, Losses, and the Transition from Fast to Slow Waves

This paper is concerned with the determination of field patterns, propagation constants, and losses for axially propagating modes guided by an enclosed circular cylindrical, radially inhomogeneous dielectric of the type discussed in Parts I and II. The homogeneous outer medium (/spl gamma/ /spl ges/ /a) is assumed to have a large relative permittivity /spl epsiv//sub 2/, and the analysis includes the perfect conductor case /spl epsiv//sub 2/ /spl rarr/ /spl infin/. The transition to trapped waves as the binding effect increases is demonstrated. Propagation constants in the case with loss are determined using a perturbation technique.

Propagation in Rectangular Waveguide Partially Filled with an Inhomogeneous Dielectric (Correspondence)

Propagation in Rectangular Waveguide Partially Filled with an Inhomogeneous Dielectric (Correspondence)