On the electromagnetic dyadic Green's functions for planar multi-layered anistropic uniaxial material media

A complete, plane-wave spectral, vector-wave function expansion of the electromagnetic, electric, and magnetic, dyadic Green's function for electric, as well as magnetic, point currents for a planar, anisotropic uniaxial multi-layered medium is presented. It is given in terms ofz-propagating, source-free vector-wave functions, where ? is normal to the interfaces, and it is developed via a utilization of the Lorentz reciprocity theorem. The electromagnetic dyadic Green's function for periodic electric as well as magnetic point current sources is also presented. Some salient features of the Green's dyadics, along with a physical interpretation are also described.     

Spectral dyadic Green's function formulation for planar integratedstructures

The problem of the complete determination of the dyadic spectral Green's function for an integrated planar structure with a grounded dielectric slab has been considered and solved in a rigorous way by using the spectral theory of the electromagnetic field. The reciprocity theorem and the geometrical symmetry of the structure have demonstrated the different roles played by the independent terms of the spectral Green's function in the evaluation of the electromagnetic characteristics of the grounded slab excited with a general source. Furthermore, an equivalent circuit representation of the structure, allowing a noteworthy simplification in the determination of the total power, has been obtained. These equivalent circuits and the derived spectral Green's function presented here can be used to analyze and design microstrip antennas of arbitrary shape with a general type of loading, such as matched or unmatched loads, parasitic, and shorting pins     

Dyadic Green's function for a multilayered planar medium-a dyadic eigenfunction approach

A new formulation of the dyadic Green's function for a planarly layered medium is presented, based on dyadic eigenfunctions of the Green's function operator. The general development of the dyadic Green's function is shown, resulting in a three-dimensional purely spectral representation. The spectral form is converted to a Hankel-function form using standard techniques, analogous to the sum-of-residues plus branch-cut representation often obtained from the Sommerfeld Green's function. Advantages and disadvantages of both the eigenfunction and Hankel function forms are outlined, and compared to other Green's function representations. Examples of the Green's dyadic for free space and for a grounded dielectric slab environment are provided, and the role of the continuous and discrete spectrum is discussed.     

Electromagnetic dyadic Green's function in cylindricallymultilayered media

A spectral-domain dyadic Green's function for electromagnetic fields in cylindrically multilayered media with circular cross section is derived in terms of matrices of the cylindrical vector wave functions. Some useful concepts, such as the effective plane wave reflection and transmission coefficients, are extended in the present spectral domain eigenfunction expansion. The coupling coefficient matrices of the scattering dyadic Green's functions are given by applying the principle of scattering superposition. The general solution has been applied to the case of axial symmetry (n=0, n is eigenvalue parameter in φ direction) where the scattering coefficients are decoupled between TM and TE waves. Two specific geometries, i.e., two- and three-layered media that are frequently employed to model the practical problems are considered in detail, and the coupling coefficient matrices of their dyadic Green's functions are given, respectively     

On the longitudinal component of the Green's function dyadic

Discussion of the divergenceless property of the right-hand side of the dyadic-wave equation for the Green's dyad has centered on the inconsistency of expanding the Green's dyad only in terms of transverse-wave functions. By including the longitudinal functions in the Ohm-Rayleigh expansion of the dyad, a simple closed form expression for the longitudinal component is derived which yields the expected singular quasi-static field. The result is verified in a coordinate independent manner with the aid of the Helmholtz theorem.     

Efficient calculation of the electromagnetic dyadic Green's function in spherical layered media

A numerical methodology is proposed for the evaluation of the electromagnetic fields of an electric or magnetic dipole of arbitrary orientation in spherical stratified media. The proposed methodology is based on the numerical solution of the differential equation in the radial coordinate that is satisfied by each coefficient in the spherical harmonics expansion of the governing Helmholtz equation. More specifically, the finite-difference solution of this equation may be cast in a pole-residue form that allows the analytic evaluation of the spherical harmonics series by means of the Watson transformation. Thus, a closed-form expression is obtained for the electromagnetic fields in terms of a short series of associated Legendre functions P/sup m//sub /spl nu//(cos(/spl theta/)) of integer order m and complex degree /spl nu/. The number of terms in the series is strongly dependent on the angle /spl theta/, and decreases very fast when the point of observation moves away from the source. The method allows for arbitrary variation in the permittivity and permeability profiles in the radial directions.     

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     

Novel closed-form Green's function in shielded planar layered media

A new method is proposed for the construction of closed-form Green's function in planar, stratified media between two conducting planes. The new approach does not require the a priori extraction of the guided-wave poles and the quasi-static part from the Green function spectrum. The proposed methodology can be easily applied to arbitrary planar media without any restriction on the number of layers and their thickness. Based on the discrete solution of one-dimensional ordinary differential equations for the spectral-domain expressions of the appropriate vector potential components, the proposed method leads to the simultaneous extraction of all Green's function values associated with a given set of source and observation points. Krylov subspace model order reduction is used to express the generated closed-form Green's function representation in terms of a finite sum involving a small number of Hankel functions. The validity of the proposed methodology and the accuracy of the generated closed-form Green's functions are demonstrated through a series of numerical experiments involving both vertical and horizontal dipoles     

Ray-optical solution for the dyadic Green's function in a rectangular cavity

The ray-optical method, which has been successfully employed for the analysis of diffraction and scattering problems, is used to derive the Green's function in a rectangular cavity. Despite the asymptotic approximations inherent in the method, it is shown that it gives a physical or geometrical insight into the mechanisms of propagation in guiding structures leading to exact or rigorous solutions not always provided by other methods.     

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     

The dyadic Green's function for the cylindrical chirostrip antenna

Using the eigenfunction expansion of dyadic Green's function in unbounded chiral medium, and the method of scattering superposition, the expressions of dyadic Green's function for the one and two—layer cylindrical chirostrip antennas are derived, when the field sources are placed in any layer of cylindrical chirostrip antenna. Also, using the method of saddle point integration, the asymptotic expression of dyadic Green's function for the wraparound chirostrip antenna is obtained. The results can be directly used to analyse the radiation characteristics of cylindrical chirostrip dipolc antenna, et al.     

On the dyadic Green's functions for Beltrami fields

A simple derivation of the Green's functions for Beltrami fields is presented for use with time-harmonic electromagnetism in homogeneous biisotropic media.     

A simplified expression of the dyadic Green's function for a conducting half-sheet

Simple analytical expressions of the dyadic Green's function for a conducting half-sheet have been derived. These expressions involve some finite integrals which can be easily calculated by a digital computer and are much simpler than those involving the vector mode function expansion. Input impedances of monopole antennas on and near an edge of a conducting half-sheet and the impedance of a notch antenna have been obtained, and the usefulness of these simplified expressions has been proved. The present results can be applied to check the limits of the applicability of the asymptotic theories, e.g., the geometrical theory of diffraction (GTD) and the uniform asymptotic theory of diffraction (UAT).     

Properties of the dyadic Green's function for an unboundedanisotropic medium

Radiation in an unbounded anisotropic medium is treated analytically by studying the dyadic Green's function of the problem, initially expressed as a triple Fourier integral which is next reduced to a double one. Under certain conditions, the existence of incoming waves is verified. It is also found that exponentially decaying waves are possible in such media. Finally, the existence of branch points in the remaining integrand function is investigated, and appropriate branch cuts are proposed     

Fast convergent dyadic Green's function in a rectangular waveguide

Alternative formulas for the dyadic Green's function in a rectangular waveguide are presented. These new functions are deduced by modifying part of Rahmat-Samii's derivation procedures by employing the Poisson summation technique. The Green's function obtained owns fast convergence property and is proved to be more suitable for numerical applications.     

One- and two-dimensional dyadic Green's functions in chiral media

The one-dimensional and two-dimensional dyadic Green's functions are calculated for 1D and 2D electric sources in an unbounded, lossless, reciprocal chiral medium which is electromagnetically described by a set of symmetric constitutive relations. It is shown that in two- and one-dimensional cases, similar to the three-dimensional case, the medium supports two eigenmodes of propagation with two different wavenumbers. One of them corresponds to the right-circularly polarized wave and the other one to the left-circularly polarized wave. The eigenmode amplitudes a and b are similar to those of the three-dimensional case     

New formulation of dyadic Green's function applied to a microstripline

We have modified the conventional two-layer dyadic Green's function analysis to include finite metal conductivity. The modified Green's function allows us to calculate the current distributions and conductor losses in microstrip circuits. A sample calculation has been applied to a microstrip line     

On the eigenfunction expansion of dyadic Green's functions

As a result of an error, the singular behavior of the eigenfunction expansion of the dyadic Green's function is not correctly formulated in my book (C. T. Tai, Dyadic Green's Functions in Electromagnetic Theory, Scranton, Pa.: International Textbook, 1971). The correct expressions are given here and an improved method for deriving the residue series is presented.     

Spectral dyadic Green's function formulation for uniaxial bianisotropic superstrate-substrate structure

In this paper, spectral-domain dyadic Green's functions for the time harmonic electric current source embedded in a two-layer grounded uniaxial bianisotropic media are obtained using Fourier tranform. It is shown that in the uniaxial bianisotropic medium, total spectral electromagnetic field can also be separated into the superposition of transverse electric (TE) and transverse magnetic (TM) wave. Because of the generality of constitutive relations our results include the special cases of achiral, uniaxial, reciprocal and nonreciprocal biisotropic media.