No abstract

No abstract

A review is presented of the extrapolation methods for accelerating the convergence of Sommerfeld-type integrals (i.e., semi-infinite range integrals with Bessel function kernels), which arise in problems involving antennas or scatterers embedded in planar multilayered media. Attention is limited to partition-extrapolation procedures in which the Sommerfeld integral is evaluated as a sum of a series of partial integrals over finite subintervals and is accelerated by an extrapolation method applied over the real-axis tail segment (a a a, 1 1 1) of the integration path, where a a a > > > 0 is selected to ensure that the integrand is well behaved. An analytical form of the asymptotic truncation error (or the remainder), which characterizes the convergence properties of the sequence of partial sums and serves as a basis for some of the most efficient extrapolation methods, is derived. Several extrapolation algorithms deemed to be the most suitable for the Sommerfeld integrals are described and their performance is compared. It is demonstrated that the performance of these methods is strongly affected by the horizontal displacement of the source and field points and by the choice of the subinterval break points. Furthermore, it is found that some well-known extrapolation techniques may fail for a number of values of and ways to remedy this are suggested. Finally, the most effective extrapolation methods for accelerating Sommerfeld integral tails are recommended.

No abstract

No abstract

No abstract

The classical Sommerfeld half-space problem is revisited, with generalizations to multilayer and plasmonic media and focus on the surface field computation. A new ab initio solution is presented for an arbitrarily oriented Hertzian dipole radiating in the presence of a material half-space with arbitrary horizontal stratification. The solution method combines the vector potential approach and the spectral domain transmission line analog of the medium, which results in the most compact formulation and facilitates the inclusion of any number of layers in the analysis. Following Sommerfeld, the solution is first expressed in terms of the Fourier-Bessel transforms, also known as Sommerfeld integrals. Analytical properties of the integrands in the complex plane are then investigated, including the location of the Sommerfeld pole, which gives rise to the Zenneck wave (ZW) or surface plasmon polariton (SPP), and alternative field representations are developed by a deformation of the integration path and analytic continuation of the integrand functions, using hyperbolic and vertical branch cuts. Closed-form expressions for the asymptotic surface fields are also derived and the rôle of the ZW and SPP is elucidated. Numerical examples are included to illustrate the theory, from radio frequencies to visible light.

No abstract