Efficient Spectral Domain MoM for the Design of Circularly Polarized Reflectarray Antennas Made of Split Rings

The method of moments (MoM) in the spectral domain is used for the analysis of the scattering of a plane wave by a multilayered periodic structure containing conducting concentric split rings in the unit cell. Basis functions accounting for edge singularities are used in the approximation of the current density on the split rings, which makes it possible a fast convergence of MoM with respect to the number of basis functions. Since the 2-D Fourier transforms of the basis functions cannot be obtained in closed-form, judicious tricks (controlled truncation of infinite summations, interpolations, etc.) are used for the efficient numerical determination of these Fourier transforms. The implemented spectral domain MoM software has been used in the design of a circularly polarized reflectarray antenna based on split rings under the local periodicity condition. The antenna has been analyzed with our spectral domain MoM software, with CST and with HFSS, and good agreement has been found among all sets of results. Our software has proven to be around 27 times faster than CST and HFSS

The contribution of Julien Perruisseau-Carrier to reconfigurable reflectarray antennas

An invited talk on the Contribution of Julien Perruisseau-Carrier to Reconfigurable Reflectarray Antennas

Enhanced integral equation analysis of multilayered periodic structures useful for the design of reflectarray antennas

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

Computationally efficient analysis of extraordinary optical transmission through infinite and truncated subwavelength hole arrays

The authors present a computationally efficient technique for the analysis of extraordinary transmission through both infinite and truncated periodic arrays of slots in perfect conductor screens of negligible thickness. An integral equation is obtained for the tangential electric field in the slots both in the infinite case and in the truncated case. The unknown functions are expressed as linear combinations of known basis functions, and the unknown weight coefficients are determined by means of Galerkin's method. The coefficients of Galerkin's matrix are obtained in the spatial domain in terms of double finite integrals containing the Green's functions (which, in the infinite case, is efficiently computed by means of Ewald's method) times cross-correlations between both the basis functions and their divergences. The computation in the spatial domain is an efficient alternative to the direct computation in the spectral domain since this latter approach involves the determination of either slowly convergent double infinite summations (infinite case) or slowly convergent double infinite integrals (truncated case). The results obtained are validated by means of commercial software, and it is found that the integral equation technique presented in this paper is at least two orders of magnitude faster than commercial software for a similar accuracy. It is also shown that the phenomena related to periodicity such as extraordinary transmission and Wood's anomaly start to appear in the truncated case for arrays with more than 100 (10×10) slots

Radar cross section of stacked circular microstrip patches on anisotropic and chiral substrates

Galerkin's method in the Hankel transform domain (HTD) is applied to the determination of the radar cross section (RCS) of stacked circular microstrip patches fabricated on a two-layered substrate which may be made of a uniaxial anisotropic dielectric, a magnetized ferrite or a chiral material. Concerning the case of stacked patches printed on magnetized ferrites, the results show that substantial RCS reduction can be achieved inside the tunable frequency band where magnetostatic mode propagation is allowed. It is also shown that both the frequency and the level of the RCS peaks obtained for circular patches fabricated on anisotropic dielectrics or chiral materials may be substantially different from those obtained when substrate anisotropy or substrate chirality are ignored.Centro de Investigación Científicas y Tecnológicas TIC98-063

Full-wave analysis of nonplanar transmission lines on layered medium by means of mpie and complex image theory

In this paper, a multiconductor transmission line consisting of arbitrary cross-sectional perfect conductors printed on a layered isotropic or uniaxial anisotropic dielectric medium is analyzed by solving the mixed-potential integral equation for the free-surface currents. Closed-form expressions of the two-dimensional space-domain Green's functions for the electrodynamic potentials are used. These expressions are obtained by applying the complex image technique to the spectral functions remaining after removing the asymptotic and pole contributions from the original Green's functions. A single set of complex images is obtained for any guess value of the unknown propagation constant and for any pair of source/field points. In addition, the reaction integrals involved in the application of the method of moments are worked out in a quasi-analytical way. The final result is an accurate and highly efficient computation code for analyzing multiconductor structures printed on a layered medium

Evaluation of the radar cross section of circular microstrip patches on anisotropic and chiral substrates

Galerkin's method in the Hankel transform domain (HTD) is applied to the determination of the radar cross section (RCS) of a circular microstrip patch printed on a substrate which may be an uniaxial anisotropic dielectric, a magnetized ferrite, or a chiral material. The results obtained for circular patches on magnetized ferrites show that the RCS of these patches can be substantially reduced in a tunable frequency band when a bias magnetic field is applied. It is also shown that the results obtained for the RCS of circular patches printed on chiral materials can be substantially different from those obtained when substrate chirality is ignored

Full-wave analysis of tunable microstrip filters fabricated on magnetized ferrites

The method of moments in the spectral domain was employed in the rigorous full-wave numerical determination of the scattering parameters of two-port microstrip circuits fabricated on magnetized ferrite substrates. The numerical algorithm developed was applied to the analysis of microstrip bandpass filters fabricated on ferrites. Results show that the center frequency of the filters can be tuned over a wide range as a magnitude and/or the orientation of the bias magnetic field are varied. However, tunability was achieved at the expense of bandwidth reduction

Full-wave analysis of a wide class of microstrip resonators fabricated on magnetized ferrites with arbitrarily oriented bias magnetic field

A numerical code has been developed for the full-wave determination of the resonant frequencies and quality factors of microstrip patches with right-angle corners of arbitrary shape in the case in which the substrate of the patches is a magnetized ferrite with arbitrarily oriented bias magnetic field. The code is based on the solution of an electric-field integral equation by means of Galerkin's method in the spectral domain. The evaluation of the infinite integrals arising from the application of the numerical method is efficiently carried out by means of a technique based on the interpolation of the spectral dyadic Green's function. The numerical results obtained indicate that microstrip patches fabricated on ferrite substrates present cutoff frequency regions in which resonances cannot occur owing to the excitation of magnetostatic modes. The limits of these cutoff regions are shown to be dependent on the orientation and the magnitude of the bias magnetic field, on the shape of the patches, and even on the nature of every particular resonant mode. The numerical results also show that the resonant frequencies of microstrip patches on magnetized ferrites can always be tuned over a wide frequency range provided the orientation of the bias magnetic field is suitably chosen

Determination of the radar cross section of stacked circular microstrip patches

Galerkin's method in the Hankel transform domain (HTD) was used to determine the radar cross section (RCS) of stacked circular microstrip patches. Numerical results show that the RCS values of a pair of stacked circular patches may be very different from those obtained for one patch in the absence of the other patch