BUSCADOR RECOLECTA

A 2-D periodic array of annular apertures (or ring slots) is studied using an accurate circuit model. The model accounts for distributed and dynamic effects associated with the excitation of high-order modes operating above or below cutoff but not far from their cutoff frequencies. This paper allows to ascertain the substantial differences of the underlying physics when this structure operates as a classical frequency selective surface or in the extraordinary-transmission (ET) regime. A discussion of two different designs working at each regime is provided by means of the equivalent circuit approach (ECA), full wave simulation results, and experimental characterization. The agreement between the equivalent circuit calculation applied here and the simulation and experimental results is very good in all the considered cases. This validates the ECA as an efficient minimal-order model and a low computational-cost design tool for frequency selective surfaces and ET-based devices. Additional scenarios such as oblique incidence and parametric studies of the structural geometry are also considered., This work was supported in part by the Spanish Ministerio
de Economía y Competitividad with the European Union FEDER funds
under Project TEC2013-41913-P and Project TEC2014-51902-C2-2-R and in
part by the Spanish Junta de Andalucía under Project P12-TIC-1435. The
work of P. Rodríguez-Ulibarri was supported by the Universidad Pública
de Navarra under a Pre-Doctoral Scholarship. The work of M. Navarro Cía
was supported by the University of Birmingham under the Birmingham
Fellowship

Metallic plates with a two-dimensional (2D) periodic distribution of sub-wavelength apertures are known to exhibit extraordinary transmission of electromagnetic waves. Stacking two or more of such plates gives place to the so-called fishnet structures, which constitute a popular way of achieving an effective negative index medium at frequencies ranging from microwaves to optics. Unfortunately, a general wideband equivalent circuit has not yet been proposed to facilitate its understanding and design. This
work presents this circuit model with closed-form expressions for the circuit elements, thus making it possible to obtain the electrical response for this class of structures in a very efficient way. This
procedure is much faster than alternative numerical methods at the same time that it retains a high level of accuracy when compared with some other oversimplified models. The circuit model also provides a simple rationale as well as a good physical insight in order to explain the qualitative behavior of such structures, independently of the number of stacked layers., This work was supported by the Spanish Ministry of Economy and Competitiveness with European Union Feder Funds (under grants TEC2011-28664-C02-01, TEC2014-51902-C2-2-R, TEC2013-41913-P, and Consolider EMET CSD2008-00066, and by the Spanish Junta de Andalucía under Project P12-TIC-1435). The work of M. Beruete was supported by the Spanish Government via RYC-2011-08221.

Common-mode rejection filters operating at microwave frequencies have been the subject of intensive research activity over the last decade. These filters are of interest for the suppression of common-mode noise in high-speed digital circuits, where differential signals are widely employed due to the high immunity to noise, electromagnetic (EM) interference, and crosstalk of differential-mode interconnects. These filters can also be used to improve common-mode rejection in microwave filters and circuits dealing with differential signals. Ideally, common-mode stopband filters should be transparent for the differential mode from dc up to very high frequencies (all pass), preserve the signal integrity for such mode, and exhibit the widest and deepest possible rejection band for the common mode in the region of interest. Moreover, these characteristics should be achieved by means of structures with the smallest possible size.

In this paper, an analytical method to estimate the complex dielectric constant of liquids is presented. The method is based on the measurement of the transmission coefficient in an embedded microstrip line loaded with a complementary split ring resonator (CSRR), which is etched in the ground plane. From this response, the dielectric constant and loss tangent of the liquid under test (LUT) can be extracted, provided that the CSRR is surrounded by such LUT, and the liquid level extends beyond the region where the electromagnetic fields generated by the CSRR are present. For that purpose, a liquid container acting as a pool is added to the structure. The main advantage of this method, which is validated from the measurement of the complex dielectric constant of olive and castor oil, is that reference samples for calibration are not required.

When reflectarray antennas are designed under the local periodicity assumption, the problem of the scattering of plane waves by multilayered pe- riodic structures has to be solved many times. The Method of oments (MoM) in the spectral domain is the numerical technique usually employed for the analysis of these multilayered structures. Unfortu- nately, it is not computationally efficient since it requires the determination of slowly convergent dou- ble infinite summations. In this paper the Mixed Potential Integral Equation (MPIE) formulation of the MoM in the spatial domain is invoked to transform the slowly convergent summations into singular finite double integrals that can be efficiently computed. The novel MoM approach in the spatial do- main has been found to be between one and two orders of magnitude faster than the traditional spectral domain MoM both in the analysis of multilay- ered periodic structures, and in the design of reflecflectarray antennas with cell characterization based on the local periodicity assumption.

When reflectarray antennas made of cells with stacked rectangular patches are designed under the local periodicity assumption, one needs to solve many times the problem of the scattering of plane waves by periodic arrays of stacked rectangular patches in multilayered substrates. Although this problem has been usually tackled by means of the Method of Moments (MoM) in the spectral domain, this is not an efficient computational approach since it requires the determination of slowly convergent double infinite summations. In this paper, the slowly convergent summations are transformed into singular finite double integrals by invoking the Mixed Potential Integral Equation (MPIE) formulation of the MoM in the spatial domain. The multilayered periodic Green?s functions involved in these double integrals are judiciously interpolated in terms of 2-D Chebyshev polynomials. Also, Ma-Rokhlin-Wandzura quadrature rules are used to handle the logarithmic singularities of the double integrals. Thanks to these two strategies that help to save CPU time, the novel MoM approach in the spatial domain turns out to be between one and two orders of magnitude faster than the standard MoM approach in the spectral domain for the analysis of periodic structures made of cells with stacked rectangular patches (and therefore, for the design of the reflectarray antennas containing these cells) when an accuracy of two significant figures is required.

A hybrid version of the Method of Moments (MoM) is applied to the analysis of the scattering of plane waves by periodic multilayered structures containing dipoles at two metallization levels. The MoM matrix entries involving basis functions (BFs) at different metallization levels are computed in the spectral domain as double infinite summations with fast exponential convergence. The MoM matrix entries involving BFs at the same metallization level are computed in the spatial domain as double integrals, which require low-order quadrature rules. The integrands are cross correlations between BFs times multilayered periodic Green?s functions (MPGFs). The cross correlations between BFs are obtained in terms of elliptic integrals of first and second kind. Also, the MPGFs are accurately interpolated in 4-D in terms of both the spatial variables and the angles of incidence. The hybrid MoM proposed is used in the design of dual polarization reflectarray antennas under the local periodicity assumption. Thanks to the 4-D interpolation of the MPGFs, which minimizes the total number of MPGFs that have to be computed per reflectarray element, the proposed hybrid MoM is shown to be around 15 times faster than the standard spectral domain MoM in the design of the antennas.

The spectral domain Method of Moments (MoM) is customarily used in the analysis of multilayered periodic structures. In this paper a hybrid MoM is introduced for the analysis of multilayered periodic structures containing sets of dipoles at two metallization levels. In the hybrid MoM the matrix entries involving basis functions of dipoles at different metallization levels are computed in the spectral domain. However, the matrix entries involving basis functions at the same metallization level are computed in the spatial domain. The implemented hybrid MoM is applied to the design of multilayered reflectarray antennas made of dipoles under the local periodicity assumption. Thanks to the use of interpolated expressions for the periodic spatial Green's functions in terms of both coordinates and incidence angles, the CPU time required by the hybrid MoM in the design of the antennas is around twenty times faster than that required by the spectral domain MoM.

A novel hybrid spectral-spatial method of moments (MoM) approach is introduced for the analysis of multilayered periodic structures containing either patches or dipoles in the unit cell. The novel hybrid MoM approach and the pure spectral MoM approach are both applied to the analysis and design of reflectarray antennas made of patches or dipoles under the local periodicity assumption. The results indicate that the hybrid approach is always at least one order of magnitud faster than the spectral approach in the analysis and design of the antennas.