On the eigenfunction expansion of electromagnetic dyadic Green's functions

A relatively simple approach is described for developing the complete eigenfunction expansion of time-harmonic electric (bar{E}) and magnetic (bar{H}) fields within exterior or interior regions containing an arbitrarily oriented electric current point source. In particular, these results yield directly the complete eigenfunction expansion of the electric and magnetic dyadic Green's functionsbarbar{G}_{e}andbarbar{G}_{m}that are associated withbar{E}andbar{H}, respectively. This expansion ofbarbar{G}_{e}andbarbar{G}_{m}contains only the solenoidal type eigenfunctions. In addition, the expansion ofbarbar{G}_{e}also contains an explicit dyadic delta function term which is required for making that expansion complete at the source point. The explicit dyadic delta function term inbarbar{G}_{e}is found readily from a simple condition governing the behavior of the eigenfunction expansion at the source point, provided one views that condition in the light of distribution theory. These general expressions for the eigenfunction expansion ofbarbar{G}_{e}andbarbar{G}_{m}reduce properly to those obtained previously for special geometries by Tai.     

The mean Green's dyadic for a half-space random medium: A nonlinear approximation

The vector problem of a source embedded in a halfspace random medium is considered, and a zeroth-order solution for the mean Green's dyadic in the nonlinear approximation is derived. This is done by applying a two-variable expansion method to obtain a perturbation solution of the Dyson equation for the mean Green's dyadic. The final results of the dyadic are given in closed form as a corrected effective propagation constant, including terms of the orderk_{a}^{2}sigma^{2}l^{2}wherek_{a}is the wavenumber in the average medium,lis the correlation length, andsigma^{2}is the variance of the permittivity fluctuations. These results show a significant difference from those of the one-dimensional problem considered by Tsang and Kong [4]. Whereas the scalar solution gives different effective propagation constants for the component waves in the Green's function, the vector solution derived contains only a single propagation constant for all of the components in the Green's dyadic.     

Dyadic Green's functions for a coaxial line

The eigenfunction expansions of the dyadic Green's functions for a coaxial line have been derived based on the method ofbarbar{G}_{m}, whereby the irrotational vector wave functionbar{L}is not needed. A dyadic boundary condition for the discontinuity of the tangential component ofbarbar{G}_{m}has been used to facilitate the derivation of the expression for the electric dyadic Green's function.     

Electric dyadic Green's functions in the source region

A straightforward approach that does not involve delta-function techniques is used to rigorously derive a generalized electric dyadic Green's function which defines uniquely the electric field inside as well as outside the source region. The electric dyadic Green's function, unlike the magnetic Green's function and the impulse functions of linear circuit theory, requires the specification of two dyadics: the conventional dyadic G^-eoutside its singularity and a source dyadic L^-which is determined solely from the geometry of the "principal volume" chosen to exclude the singularity of G^-e. The source dyadic L^-is characterized mathematically, interpreted physically as a generalized depolarizing dyadic, and evaluated for a number of principal volumes (self-cells) which are commonly used in numerical integration or solution schemes. Discrepancies at the source point among electric dyadic Green's functions derived by a number of authors are shown to be explainable and reconcilable merely through the proper choice of the principal volume. Moreover, the ordinary delta-function method, which by itself is shown to be inadequate to extract uniquely the proper electric dyadic Green's function in the source region, can be supplemented by a simple procedure to yield unambiguously the correct Green's function representation and associated fields.     

Microstrip disk antennas, Part I: Efficiency of space wave launching

A theoretical study on the problem of surface wave excitation of microstrip disk antennas is presented. The cavity model with magnetic sidewalls and dyadic Green's functions in stratified media is used to obtain the radiated fields in an integral form. Lossless media are assumed such that there is no cross coupling between the powers in the space (P_{SP}) and surface (P_{SU}) waves. The separate contributions of these two powers is examined. With the assumption thatP_{SU}does not contribute to the main radiation patterns of the antenna an efficiency of space wave launching and a corresponding antenna directivity are defined. Values of efficiency and directivity as functions of the dimensions of the antenna and for two values of dielectric constants of the substrate are shown. Agreement of these results with some of the available data is observed. It is worth noting thatP_{SU}may correspond to an appreciable portion of the total radiated power.     

A useful transformation of the free-space Green's function with applications to analyses of wire structures

The free-space Green's function of electromagnetics is transformed to a form which simplifies analyses of wire structures. The useful property of the new form is that it enables one to compute the electric field componentE_{s}by applying only [(partial^{2}/partial s^{2}) + k^{2}] to a potential integral (with new Green's function) even though such an integral is, in general, to be taken over currents that are nots-directed. It can be shown that the transformation effectively yieldsE_{s}in terms of a TM representation.     

On the dyadic Green's function for a planar multilayereddielectric/magnetic media

A complete plane wave spectral eigenfunction expansion of the electric dyadic Green's function for a planar multilayered dielectric/magnetic media is given in terms of a pair of the (zˆ)-propagating solenoidal eigenfunctions, where (z ˆ) is normal to the interface, and it is developed via a utilization of the Lorentz reciprocity theorem. This expansion also contains an explicit dyadic delta function term which is required for completeness at the source point. Some useful concepts such as the effective plane wave reflection and transmission coefficients are employed in the present spectral domain eigenfunction expansion. The salient features of this Green's function are also described along with a physical interpretation     

Short-channel MOSFET VT-VDScharacteristics model based on a point charge and its mirror images

Short-channel MOS transistordV_{T}/dV_{DS}characteristics are expressed by an analytic function of fundamental device parameters. The expression is derived from a simple model of short-channel MOS transistors in threshold condition, which is based on a point charge and its mirror images. With this expression,dV_{T}/dV_{DS}is found to be proportional to1/L^{2}-1/L^{4}, whereLis channel length. Following factors are also found, wherein the source and drain junction depth effect is only logarithmic ondV_{T}/dV_{DS}characteristics,dV_{T}/dV_{SUB}anddV_{T}/dV_{DS}are closely related in short-channel MOS transistors, and short-channel effects are expected to be smaller in MOS transistors on SOS than on bulk silicon, due to a large number of Si/sapphire interface states. This model is simple, and it can be applied to short-channel MOS transistor designing and circuit simulations.     

Analysis of a Post Discontinuity in an Oversized Circular Waveguide

This paper presents the analysis of scattering characteristics of a radially directed thin post in a circular waveguide using the method of moments. Electric type dyadic Green's function has been used to compute the scattered field in a circular waveguide considering variation of current only in the axial direction of the post. Simulated data on return loss and power coupling in the dominant mode and higher order modes have been compared with the data computed using Ansoft's High Frequency Structure Simulator. The data on return loss and coupling for the incident ${rm TE}_{11}$ mode have been compared with experimental data.      

Effect of gap length on the input admittance of center fed coaxial waveguides and infinite dipoles

The input admittance of a coaxial waveguide fed by a gap of length2din the center conductor is evaluated using the dyadic Green's function of the guide and a band of equivalent magnetic surface current proportional to the gap's axial electric field via the equivalence principle. The axial electric field is expressed in terms of a rapidly convergent series of ultraspherical polynomials whose weighting function satisfies the edge conditions at each end of the gap. If the inner and outer radii of the coaxial guide areaandb, respectively, then the limiting case ofb rightarrow inftyis an infinite dipole in free space. Numerical results for the admittance are given as a function ofka (0.01 leq ka leq 0.50)with parameterb/a = 2, 5,10and 50 for the coaxial guide. For the infinite dipole the admittance is presented as a function ofd/a (10^{-3} leq d/a leq 10)withkaas a parameter (0.001 leq ka leq 0.1).     

Accurate asymptotic solution for the surface field due to apertures in a conducting cylinder

Asymptotic solutions for the surface field due to a magnetic point source on a cylinder can simplify the computational task in the analysis of mutual coupling-e.g. in conformal arrays. Although several asymptotic solutions are at present available, their accuracy is limited. The aim here is to obtain a new approximate solution with improved accuracy. An asymptotic solution of the exact modal solution for the field on a cylinder which contains terms up to(k_{0}t)^{-2}, wheretis the distance from the source, is derived. Approximate terms up to(k_{0}t)^{-3}are included from the solution for a source on a plane conductor and an earlier asymptotic solution. The new approximate solution consists of the exact solution for a plane conductor, modulated by a Fock function, plus a contribution associated with the cylinder which vanishes in the limit of infinite radius. Typically for cylinders of radius greater than one and half wavelengths it agrees to within 0.5 dB in magnitude and1degin phase of the modal solution. Results for dominant mode mutual and self-admittances of rectangular apertures on a cylinder obtained from this solution are presented. A formula is also given for calculating self-admittances from an asymptotic solution. There is excellent agreement between admittances computed from the asymptotic solution and the modal solution. One exception is the self-susceptance of an axial slot where the error is larger than expected, although the error is low enough to be acceptable in most practical cases.     

7B4--Absorption and emission properties of optically pumped ruby

Several experiments on optically excited ruby are described. First, absorption transitions initiated from the metastable states,tmin{2}max{3}²Eandtmin{2}max{3}²T1, are investigated in the photon energy range from 5500 to 45 000 cm^-1. The absorption spectrum of these excited states is determined in bothpi-and σ-polarizations and assignments for the observed absorption bands are achieved. Obtained results are compared with other experiments reported in the literature. Next, emission properties of pink ruby are studied in the region near theRlines. The emission spectrum is determined point by point by means of intense flash excitation. The observed weak bands are ascribed to theR'and phonon assistedRtransitions. Laser actions in these bands are discussed and experimental results on phonon terminated laser amplification are presented. An experiment using a giant pulse as an excitation source reveals that the transition time fromtmin{2}max{3}²Etotmin{2}max{3}²T1is shorter than a fraction of 1μs at room temperature.     

构造平面分层均匀媒质并矢Green函数的本征谱方法

本文从自由空间中的并矢Green函数出发,引入一种构造平面分层均匀媒质中并矢Green函数的新方法。根据平面分层均匀媒质中不同取向的点源辐射在场点处的响应得到并矢Green函数的谱矢量,进而得出平面分层均匀媒质中并矢Green函数的积分表达式。     

Electrical and physical characteristics of thin nitrided oxides prepared by rapid thermal nitridation

Ultrathin oxides (5-12 nm) were nitrided by lamp-heated rapid thermal annealing in ammonia at temperatures of 900-1150°C for 5-300 s. Elemental depth profiles were measured by Auger electron spectroscopy (AES) and secondary ion mass spectroscopy (SIMS). Both the nitrogen concentration measured by AES and the hydrogen one measured by SIMS for a nitrided oxide are found to increase monotonically as nitridation proceeds. The AES depth profiles of oxygen show that the Si-SiO2interface does not move during nitridation. Dependences of midgap interface state density (D_{it}_{m}) and fixed charge density (Nf) on nitridation temperature and on oxide thickness were studied. For a given temperature, bothD_{it}_{m}and (Nf) are found to show turnarounds as nitridation time increases in a similar manner: at first both increase, reach respective maxima at a certain nitridation timet_{max}, and then decrease gradually. The (D_{it}_{m}) and (Nf) increase more rapidly and thet_{max}is shorter as the nitridation temperature is raised or the oxide film is thinner. The maximum ofD_{it}_{m}increases as the oxide film is thinner. A two-step model is newly proposed to explain the turn-around behaviors ofD_{it}_{m}and Nf: the first step is defect formation as a result of nitrogen incorporation and the second step is reduction of the defects by an annealing-type process. The simulation reproduces the turnaround behaviors very well.     

Integrating the dyadic Green's function near sources

Formulas are derived which allow the dyadic Green's function to be integrated for well-behaved currents in the source region. The result is that the electric field due to a current distribution local to an observer can be expressed as a function of the current and its spatial derivatives at the point of observation plus a nonsingular integral over a surface containing the local currents. Although a spherical principal volume is used to derive the theory, the field due to this principal volume is exactly canceled by other terms. The exact form for pulse currents is derived. The theory is extended to nonpulse currents in an appendix     

A Relationship Between Phase Delay and Attenuation Due to Rain and Its Applications to Satellite and Deep-Space Tracking

We present and discuss two main results concerning the relationship between phase delay due to rain and rain attenuation, useful in calculations concerning high precision tracking of satellites and deep-space spacecrafts using interferometry techniques. We have found these two results with the Synthetic Storm Technique [SST] applied to a large data bank of rain rate time series collected at three sites in Italy. The first result concerns a formula that provides the extra signal phase delay $tau$ (picoseconds) due to rain as a function of rain attenuation $A$ (dB), frequency $f$ (GHz) and slant path elevation angle $theta$ (degrees), given by $tau = (860.4 - 4.82 theta)f^{- 1.71}A^{0.73}$, for $20^{circ} leq theta ≪ 44^{circ}$, and by $tau = 648.3f^{- 1.71}A^{0.73}$, for $44^{circ} leq theta leq 90^{circ}$ . The formula allows estimating the phase delay due to rain attenuation, with overall average (normalized) error ${-}3hbox{%}$, standard deviation 11.1%, root-mean square 11.5% for 20$^{circ}$ slant paths. The second result concerns a method to predict phase delay from the probability distribution of rain rate (SST probability model), very useful when only the probability distribution of rain rate is known.      

Planar, buried, ion-exchanged glass waveguides: Diffusion characteristics

A detailed theoretical and experimental study of Ag+-Na+ exchange in soda-lime silicate glasses in a molten bath containing a mixture of NaNO3and Ag+ is presented. With no applied field, concentration profilesC(x, t)(and therefore, the index profiles for low concentrations) are given by complementary error function. The estimated value for the self-diffusion coefficientDof Ag+ is 0.133 μm²/min for low concentrations and it monotonically increases with the surface concentration C0until it saturates at about 0.3 μm²/min forC_{0} geq 10^{-3}MF. However, square root dependence of diffusion depth with time seems to be independent of the C0. Presence of an external fieldEcauses the effective depth of diffusion to increase. In fact, for largeEfields, the profile can accurately be described byC/C_{0} = frac{1}{2} erfc(x' - r)wherer = mu Et/sqrt{2Dt}where μ is the ionic mobility of Ag⁺in glass. We define a new diffusion depthWas the distance from the surface to the1/econcentration point, and for large fields,Wvaries linearly withEandt. Experimental results yielded a value of 15.55 μm²/Vmin forμ. As before, square root dependence ofWwithtand the linear variation ofWversus C0forC_{0} leq 10^{-3}MF, withWsaturating forC_{0} > 10^{-3}MF, were observed in the case of field assisted diffusion. A two-step process, where a surface waveguide formed in the first step with eitherEequal to zero or some finite value, is modified by performing a second diffusion in pure sodium nitrate to produce a buried, symmetrical fiber-like profile. This process is also studied in detail.     

An observation on the Sommerfeld-integral representation of theelectric dyadic Green's function for layered media

The authors discuss the electric dyadic Green's function for layered dielectrics. It is known that for the free-space electric dyadic Green's function, evaluation of the electric field at observation points within the source region requires specification of a principal volume along with the corresponding depolarizing dyad. Special considerations are invoked for layered background media which are appropriate for the electromagnetics of integrated electronics. It is shown that use of the Sommerfeld-integral representation of the electric dyadic Green's function leads to an innate choice for the depolarizing dyad. A corresponding principal volume is subsequently identified; it is demonstrated that there exists an alternative choice for this excluding region which leads to the same depolarizing dyad