Raul Rodriguez-Berral

Analytical Wideband Model for Strip/Slit Gratings Loaded With Dielectric Slabs

This paper presents a fully analytical model to determine the transmission and reflection properties of planar 1-D distributions of metal strips or slits made in thin metal screens. In contrast with other analytical or quasi-analytical approaches, the formulation incorporates the presence of dielectric slabs and is valid over a wide frequency band, from the long wavelength limit to the grating lobes operation. The model has been adapted to the case where two 1-D planar grids are stacked or a single grid is printed on a grounded substrate. In these cases, the model rigorously takes into account higher order mode interaction between the two stacked arrays of strips/slits or with the ground plane. Oblique incidence and both TE and TM polarizations have been considered. The analytical results show a good agreement with those computed by high-performance numerical methods, accounting for very fine details of extremely complicated transmission/reflection spectra. These results are of straightforward application to a variety of practical situations from microwaves to the terahertz regime. The present methodology can still be useful at higher frequencies provided that adequate models of the planar conductors are incorporated. In general, the model provides physical insight on the nature of the expected spectra and facilitates the design of devices based on planar metallic gratings.

Quasi-Analytical Modeling of Transmission/Reflection in Strip/Slit Gratings Loaded With Dielectric Slabs

This paper presents a quasi-analytical approach to study the classic topic of transmission/reflection of electromagnetic waves through 1-D periodic arrays of strips/slits in metal screens. The approach is based on standard waveguide discontinuity theory. Starting from field equations, it is inferred a circuit-like reduced-order model with just one parameter to be determined. The value of this parameter can be obtained from the transmission/reflection coefficient provided by any full-wave method at just one single frequency. In this way, the computation effort to obtain very wide-band responses of periodically distributed slits or strips under oblique TE/TM illumination in the presence of loading dielectric slabs is reduced to the full-wave analysis of the structure at a single frequency value. For relatively narrow strip/slit gratings, this procedure gives very accurate results even for very complicated transmission/reflection spectra. An additional advantage of the present approach is that it allows for an easy understanding of the underlying physics of the phenomena involved.

Circuit model for a periodic array of slits sandwiched between two dielectric slabs

This paper proposes an equivalent circuit model that uses lumped elements and transmission lines to explain the transmission of electromagnetic waves through a conducting screen periodically perforated with slits and sandwiched between two different dielectric slabs. The present model relies on the impedance-matching point of view, previously introduced by some of the authors, rather than on the surface plasmon polariton concept. Thus, the model constitutes a simple and insightful framework that easily leads to accurate qualitative and quantitative predictions about the nature of the transmission spectrum of such structures.

Analytical Multimodal Network Approach for 2-D Arrays of Planar Patches/Apertures Embedded in a Layered Medium

A fully analytical multimodal equivalent circuit is presented for the modeling of the scattering of an obliquely incident plane wave by a two-dimensional (2-D) periodic array of metallic patches (or apertures in a metallic screen) embedded in a layered medium. The topology of the equivalent network is rigorously derived in the analysis and all the network parameters are given in closed form. In contrast with the previously reported explicit circuit models, the proposed approach accounts for dynamical effects over a very wide frequency range, which enables the application of the model to a great variety of situations. The key advantages of the reported multimodal network representation are its analytical nature, its extremely low-computational cost and that the physical phenomena involved in the scattering can be easily understood in terms of transmission line and lumped circuital reasonings.

Analytical model for the transmission of electromagnetic waves through arrays of slits in perfect conductors and lossy metal screens

This paper presents a very simple analytical model for the analysis of the resonant transmission of microwaves or millimeter waves through periodically distributed slits in a thick metal screen. The model is based on equivalent circuits consisting of transmission line elements of known characteristic admittances and propagation constants loaded by capacitors. Closed-form analytical expressions are provided for all the circuit parameters. Alternatively, the circuit parameters can be quickly computed from numerical simulations carried out at a few frequency points. The proposed analytical model accounts for all the details of the observed transmission spectrum, including conventional Fabry-Perot (FP) resonances, which are controlled by the thickness of the screen, as well as extraordinary transmission peaks, which are related to the periodicity. The range of validity of the model as a function of dimensional parameters is discussed. The experimentally observed and numerically predicted redshift of the Fabry...

Simplified Circuit Model for Arrays of Metallic Dipoles Sandwiched Between Dielectric Slabs Under Arbitrary Incidence

This work presents an equivalent circuit to model the transmission/reflection of a plane wave that impinges obliquely on a periodic arrangement of metallic rectangular dipoles embedded between two dielectric slabs. The equivalent circuit takes advantage of the periodicity of the structure to reformulate the original problem as a certain equivalent waveguide scattering problem. Equivalent transmission lines are used to simulate the wave propagation whereas equivalent lumped circuit elements account for presence of the metallic patches. The obtaining of the circuit parameters is carried out via a systematic procedure, which provides a robust strategy that gives rise to surprisingly accurate results even for rather complex situations. The proposed equivalent circuit model simplifies considerably the original complex electromagnetic problem and provides a valuable physical insight into the parameters that are relevant in the phenomenon as well as an in-depth understanding of the operation principles of the periodic surface. Thus, the reported reduced-order model of the corresponding scattering problem can be a very convenient and helpful tool for the analysis and/or design of many practical devices.

Appropriate formulation of the Characteristic equation for open nonreciprocal Layered waveguides with different upper and lower half-spaces

This paper will study the most convenient way of formulating the characteristic equation for shielded, parallel-plate, grounded, and open reciprocal/nonreciprocal planar layered waveguides, including the possibility of different upper and lower half-spaces. A detailed study of the suitable mapping for each kind of waveguide will lead to the formulation of analytic characteristic equations for shielded/parallel-plate/grounded reciprocal/nonreciprocal waveguides and also for open reciprocal ones. Although no mapping has been found to remove all the branch points of the characteristic equation for open nonreciprocal waveguides with different half-spaces, a robust approach will be proposed to overcome the main drawbacks caused by the multivalued nature of this problem. The combination of the suitable formulation of the characteristic equation with a systematic integral-nature root-searching strategy bears a reliable and efficient method. Some novel numerical results will be presented for open anisotropic reciprocal waveguides and for open magnetized ferrite slabs to illustrate the performance of the present proposal.

Enhanced implementation of the complex images method to study bound and leaky regimes in layered planar printed lines

The discrete complex image technique, originally developed to deal with three-dimensional planar structures, has been recently applied to two-dimensional planar and nonplanar transmission lines embedded in layered substrates. In spite of successive refinements, some important practical issues concerning the sampling path, treatment of spectral Greens functions poles, and extension to the leaky regime are still open and deserve deeper examination. It is shown that a suitable choice of the sampling path is key to reducing the number of images and to avoid the necessity of extracting spectral poles when the bound regime is considered. The situation arising from the analysis of the leaky regime becomes more complex and the adequate choice of the sampling path, as well as an appropriate pole extraction, turn out to be essential. In particular, a new pole-extraction strategy able to deal with poles associated with both proper and improper modes of the background waveguide is proposed. The advantages of using the theory in this paper are illustrated by diverse numerical results for the bound/leaky regime of various planar lines. Finally, the suitability of the method for covered planar lines is demonstrated.

Excitation of a Periodic Microstrip Line b>y an Aperiodic Delta-Gap Source

The current excited by a delta-gap source on a periodically loaded microstrip line is studied by means of the array scanning method. The method requires the efficient solution of a large number of auxiliary Floquet-periodic subproblems, cast here in the form of an electric-field integral equation (EFIE) that has been discretized with the method of moments (MoM) in the unit cell. Numerical results are provided for a specific structure in both bound and radiative frequency ranges and are validated through independent codes.

Gap Discontinuity in Microstrip Lines: An Accurate Semianalytical Formulation

A semianalytical full-wave formulation is used to analyze a narrow gap in a microstrip line. The analysis assumes that the length of the gap is small compared to the strip width, but allows for an arbitrarily high frequency. The formulation accounts for radiation from the gap into space and into surface waves. Based on this formulation, the scattering parameters of the gap are obtained along with the complete equivalent circuit of the gap. The percentage of power lost due to gap radiation from an incident mode on the microstrip line is found, and the physics of the gap radiation are examined.