The efficient computation of periodic Green's functions is discussed here for an arbitrarily directed array of point sources in layered media. These Green's functions are necessary to formulate boundary integral equations for arrays of scatterers inside a general layered medium, solved with the method of moments in the spatial domain. For this reason, mixed-potential Green's functions-having a mild spatial singularity-are selected. The case of horizontally oriented dipoles is rather simple and has been previously solved. On the other hand, the case of vertically oriented dipoles (i.e., aligned perpendicular to the layers) is more intricate, since the extracted terms cannot be transformed into well-known Green's functions. Previous works dealt with arrays of line and point sources, but did not address the critical task of computing the curl of the dyadic potentials, required to treat slot arrays and dielectric inclusions, whose available Floquet series expressions do not converge if the source and observation points lie in the same transverse plane.

The development of computationally efficient Green's functions in layered-media environments is important when applying the method of moments (MoM) using the mixed-potential integral equation (MPIE) formulation (K. A. Michalski and D. Zheng, IEEE Trans. Antennas Propag., vol. 38, pp. 335–344, Mar. 1990). However, their computation poses difficulties in terms of accuracy and computation time due to the presence of slowly converging integrals and/or series. Extensive work has been carried out to accelerate the Green's function computation for the case of a single dipole source in a layered media. Considerably less effort has been devoted to accelerate the Green's functions due to a one-dimensional (1-D) periodic arrangement of dipole sources. These are required to study 1-D periodic structures in layered media, including scattering structures and guiding structures such as leaky-wave antennas (LWAs) made from layered media.

An efficient mixed-potential integral equation formulation is proposed for the analysis of one-dimensional (1-D) periodic leaky-wave antennas (LWAs) based on planar stratified configurations with inclusions of arbitrarily oriented metallic or dielectric perturbations. Both the transverse and vertical components of the mixed-potential Green's functions due to a 1-D phased array of dipoles in a layered medium are accelerated using suitable homogeneous-medium asymptotic extractions from the standard spectral series of Floquet harmonics. A novel acceleration procedure is applied for the computation of the vertical potentials whose extracted terms can be expressed as potentials from a 1-D phased array of half-line sources in a homogeneous medium. Their numerical calculation requires a suitable modification of the Ewald method, thus resulting in new modified spectral and spatial series, having Gaussian convergence even in the case of complex modes and improper harmonics. Numerical comparisons for the 1-D periodic potentials, both in the case of bounded and unbounded (e.g., leaky) harmonics, validate the efficiency and accuracy of the proposed acceleration technique. The method is illustrated and verified by determining the dispersion behavior of both bound and leaky modes for several LWA test cases.

A new type of printed periodic leaky-wave antenna is proposed, which is able to continuously scan a beam from backward to forward endfire. The unit cell consists of a microstrip line loaded with long lengths of transmission line folded as a U-stub and an interdigital capacitor. This U-stub geometry, which is characterized by a compact longitudinal size, permits operation at frequencies lower than other conventional periodic leaky-wave antennas. At the same time, the presence of the interdigital capacitor makes the radiating U-stub discontinuity self-matching, thus allowing for an elimination of open-stopband effects and for an achievement of an almost constant gain while the beam is scanned through broadside. A noteworthy aspect of the present design is that it represents the first periodic leaky-wave antenna that scans through broadside by radiating from the fundamental harmonic, without being a quasi-homogeneous metamaterial structure.

The research activity jointly developed during the last decade between the groups coordinated by P. Lampariello in Europe and by D. R. Jackson in the U.S.A. is reviewed, on the basis of the fruitful scientific interaction had with Prof. Oliner since the Eighties. The main focus here is on advances in leaky waves and leaky-wave antennas based on periodic structures. This involves topics of different nature, such as issues of numerical modeling in periodic Green's functions, leakage features in metamaterials and other innovative media, and one-dimensional and two-dimensional configurations of printed and planar leaky-wave radiators.

Original acceleration procedures are proposed for the efficient calculation of the vertical components of the dyadic and scalar mixed-potential layered-media periodic Green's functions for various types of periodic structures. The extraction of suitable asymptotic terms, i.e., quasi-static images, is performed in order to speed up the convergence of the relevant spectral series. The extracted terms can be expressed as potentials for array of half-plane and half-line sources, depending on the type of the considered periodic Green's function. The relevant numerical results show the remarkable improvements in the efficiency of the approach.

We discuss and verify experimentally the design of a 1-D planar periodic combline leaky-wave antenna that avoids the open-stopband effects as the beam is scanned through broadside.

In this paper the problem of obtaining efficient broadside radiation in one-dimensional (1-D) periodic printed leaky-wave antennas (LWAs) is addressed. In particular, a technique for the elimination of the open stopband (OSB) is presented, which is based on a π network that matches the Bloch-wave impedance of the structure to a desired (non-zero) value at broadside. Three different matching conditions are investigated. Their advantages and drawbacks are briefly discussed and the effectiveness of the technique is demonstrated on a real structure.

Design techniques for leaky-wave antennas usually require complex analysis methods for the rigorous characterization of the radiating structures as a function of the various geometrical and physical parameters involved. An increasing number of such antenna topologies are based on planar stratified configurations with suitable inclusions of periodic metallic or dielectric perturbations. The prediction of the leaky-wave parameters (i.e., phase and leakage constants, etc.) is a difficult task to achieve in an accurate and efficient fashion. In this connection, the present contribution is focused on the computational aspects related to an integral-equation approach to the problem based on a mixed-potential formulation. By means of specific asymptotic extractions, powerful acceleration techniques for the relevant scalar and dyadic Green's functions are proposed and tested for different types and dimensions of periodicity. Numerical results are provided and discussed for various significant types of periodic structures.

Four different methods are examined to evaluate the potential due to a half-line source in a homogeneous space. The derivatives of the potential, which are needed to calculate the fields, are also treated. All four methods are compared in terms of accuracy and computational cost in order to determine the most efficient among them for each region of space. The gradient of the potential is also examined.

Compact, wide-bandstop electromagnetic-band-gap (EBG)-based microstrip filters are studied for harmonic-tuned integrated power amplifiers to be used in high-efficiency transmitters operating in Ku band. An accurate characterisation of EBG filters is performed by means of a full-wave modal analysis based on a periodic method of moments in the spatial domain. The synthesis of optimal values for the antenna input impedance at the fundamental, second and third harmonic frequencies is achieved through suitable perturbations of the unit-cell geometries, which lead to appropriate tapered filter configurations. Numerical simulations of the input impedance and of the radiation properties are provided for a circular patch antenna by means of different independent commercial software in order to validate the proposed approach.

A common approach to perform dispersive analyses of waveguides periodic along one direction is based on the electromagnetic simulation of a single spatial period of the structure. However, the resulting equivalent two-port network representation of the single cell may lead to inaccurate modal results, since mutual coupling between cells has been neglected. When a finite number of adjacent cells are simulated, with the aim of improving the accuracy of the analysis, spurious solutions are introduced; they are shown here to be related to the nonuniqueness of root-extraction operations in the complex plane. A simple automatic method is proposed to recover the correct solution and to test the convergence of the analysis as the number of simulated cells is increased.

The dyadic Green's functions arising from the Method of Moments (MoM) discretization for problems involving layered media require the computation of costly Sommerfeld integrals. Here we propose a scheme to efficiently interpolate the regularized Green's functions by means of a first-order extraction of the singularities. The interpolation scheme is performed in a barycentric coordinate system, which further improves its efficiency. Numerical experiments are presented in order to show the effectiveness of the approach in reducing the matrix filling time.

We present a comprehensive analysis of natural modes of a planar metamaterial layer (metalayer) formed by arrayed pairs of metallic dogbone-shaped conductors separated by a thin dielectric layer. The in-plane modes are classified based on the symmetric and anti-symmetric current distributions in the pairs. Of particular interest are the anti-symmetric modes, since the anti-symmetric current is associated with the magnetic resonance in metamaterial particles made of tightly coupled pairs. It is shown that the modal spectrum includes both TE and TM bound (proper real) and leaky (proper complex and improper complex) modes. An interesting observation is that a peculiar dominant TM improper leaky wave with a low attenuation constant, for the anti-symmetric current distribution, occurs at low frequencies, with a potential application in periodic leaky-wave antennas.