Carlos Molero

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.

Dynamical Equivalent Circuit for 1-D Periodic Compound Gratings

Metallic compound gratings are studied in this work by means of an analytical equivalent circuit approach in order to obtain its transmission and reflection properties when illuminated by a TM-polarized plane wave. A compound grating consists of the periodic repetition of a finite number of slits carved out of a thick metal slab (reflection grating) or connecting two separated open regions through groups of slits in the metal slab (transmission grating). The equivalent circuit is rigorously obtained starting from a simplified version of the integral equation for the electric field at the slits apertures. That equivalent circuit involves transmission-line sections that account for the fundamental and lowest order diffracted modes (which does give the “dynamical” nature to the present equivalent circuit), and lumped components to model the effect of all the higher order diffracted modes. All the relevant and complex features of the spectra can be satisfactorily explained in terms of the topology and characteristics of the equivalent circuit. In contrast with some previously reported circuit models, all the dynamical and quasi-static circuit elements are analytically and explicitly obtained in terms of the geometric and electrical parameters of the grating. The accuracy of the approximate circuit model is very good over a very wide band, as it is demonstrated by comparison with full-wave data computed with commercial electromagnetic solvers.

Wideband analytical equivalent circuit for one-dimensional periodic stacked arrays.

A wideband equivalent circuit is proposed for the accurate analysis of scattering from a set of stacked slit gratings illuminated by a plane wave with transverse magnetic or electric polarization that impinges normally or obliquely along one of the principal planes of the structure. The slit gratings are printed on dielectric slabs of arbitrary thickness, including the case of closely spaced gratings that interact by higher-order modes. A Π-circuit topology is obtained for a pair of coupled arrays, with fully analytical expressions for all the circuit elements. This equivalent Π circuit is employed as the basis to derive the equivalent circuit of finite stacks with any given number of gratings. Analytical expressions for the Brillouin diagram and the Bloch impedance are also obtained for infinite periodic stacks.

Analytical Circuit Model for 1-D Periodic T-Shaped Corrugated Surfaces

An analytical circuit model is obtained to study the reflection of TM polarized electromagnetic waves that impinge obliquely on a 1-D periodic corrugated surface consisting of dielectric-loaded T-shaped planar corrugations backed by an infinite ground plane. The model is based on transmission line theory and equivalent lumped-element circuits. For the case of perfect conductors, the topology of the circuit is directly inferred from a rigorous full-wave formulation of the periodic problem without using any heuristic argument. This procedure leads to fully analytical expressions for all the circuit parameters. Ohmic losses are further incorporated in the model under the assumption of strong skin effect. The results thus obtained are compared with those given by an accurate Method of Moments numerical code and HFSS software showing a very good agreement. The strong numerical efficiency as well as the good physical insight provided by the present equivalent circuit model can be advantageously employed for the analysis and/or design of a variety of devices. As examples of the latter, the circuit model is used for the first-stage design of an electrically thin hard impedance surface, a corrugated surface that prevents specular reflection, and an absorber.

Analytical circuit model for stacked slit gratings

This work presents a rigorous circuit model to compute the transmission/reflection properties of a finite number of stacked slit gratings printed on dielectric slabs of arbitrary thickness. A key aspect of the present approach is that the circuit model itself leads us to find fully analytical expressions for the finite stacked-grating structure. An analytical model to obtain the Brillouin diagram for the fully periodic structure (infinite number of identical unit cells) is also provided.

Wideband analytical equivalent circuit for coupled asymmetrical nonaligned slit arrays

Microstructured metallic devices have been extensively studied because of their interesting properties for controlling the transmission, reflection, and absorption of electromagnetic waves. A very simple implementation is an array of infinitely long parallel metal strips printed on a dielectric substrate. In the past few years, several analytical models have been reported based on the use of equivalent circuits with distributed and lumped components to account for the electrical performance of these structures. However, the proposed models are restricted to highly symmetrical configurations of the basic unit cell of the periodic structure. The purpose of this paper is to present the nontrivial extension of such circuit models to deal with nonsymmetrical structures. More specifically, a wideband equivalent-circuit model will be developed to describe the scattering properties of a pair of coupled different nonaligned slit gratings printed on a dielectric slab of arbitrary thickness. The relevant consequences of the lack of symmetry of the structures under study will be thoroughly discussed. The obtained equivalent network can be straightforwardly used to model stacked structures with an arbitrary number of nonsymmetrical striplike arrays.

Making metals transparent: a circuit model approach.

Solid metal films are well known to be opaque to electromagnetic waves over a wide frequency range, from low frequency to optics. High values of the conductivity at relatively low frequencies or negative values of the permittivity at the optical regime provide the macroscopic explanation for such opacity. In the microwave range, even extremely thin metal layers (much smaller than the skin depth at the operation frequency) reflect most of the impinging electromagnetic energy, thus precluding significant transmission. However, a drastic resonant narrow-band enhancement of the transparency has recently been reported. The quasi-transparent window is opened by placing the metal film between two symmetrically arranged and closely spaced copper strip gratings. This letter proposes an analytical circuit model that yields a simple explanation to this unexpected phenomenon. The proposed approach avoids the use of lengthy numerical calculations and suggests how the transmissivity can be controlled and enhanced by manipulating the values of the electrical parameters of the associated circuit model.

Transmission control in compound-grating structures using equivalent circuits

This paper describes an accurate analytical model that accounts for the reflection and transmission of electromagnetic waves from 1-D periodic compound gratings comprising combinations of several grooves and slits in each period. The model makes use of interconnections between transmission lines and lumped circuit elements to drastically speed up the computation of the characteristics of the structure, thus allowing for a fast design of filtering devices. All the circuit components involved in the model are computed using fully-analytical expressions. A good agreement with results obtained with well-known commercial full-wave simulators has been found.

Equivalent Circuit Approach for Practical Applications of Meander-Line Gratings

This letter reports an analytical circuit model to characterize periodic arrangements of printed meander lines. The methodology employed for the derivation of the model is presented together with two typical examples of its possible application: a polarizer and an absorber. Comparisons with results provided by a commercial software evidence the good accuracy provided by the equivalent circuit.

Accurate circuit models for the analysis of stacked metal gratings

Stacked periodic planar structures have been a continuous subject of research interest due to their ability to control the polarization, transmission, reflection, and absorption of electromagnetic waves. The scattering of plane waves by one-dimensional (1-D) and two-dimensional (2-D) arrays of metal patches (or apertures) can be accurately modeled using suitable equivalent circuits. The structures obtained by stacking periodic systems of this type can easily be modeled using transmission line sections to account for the dielectric region between the periodic surfaces. However, this task is not straightforward if the separation between the periodically structure surfaces is electrically small. This contribution will describe a methodology to obtain valid and accurate circuit models for tightly spaced periodic arrays of apertures. The proposed theory allows for the modeling of devices that have attracted a lot of attention in recent years, such as the fishnet structures employed to obtain an effective negative index of refraction.