Francisco Mesa

Comparative analysis of edge- and broadside- coupled split ring resonators for metamaterial design - theory and experiments

This paper develops a quasi-analytical and self-consistent model to compute the polarizabilities of split ring resonators (SRRs). An experimental setup is also proposed for measuring the magnetic polarizability of these structures. Experimental data are provided and compared with theoretical results computed following the proposed model. By using a local field approach, the model is applied to the obtaining of the dispersion characteristics of discrete negative magnetic permeability and left-handed metamaterials. Two types of SRRs, namely, the so-called edge coupled- and broadside coupled- SRRs, have been considered. A comparative analysis of these two structures has been carried out in connection with their suitability for the design of metamaterials. Advantages and disadvantages of both structures are discussed.

Extraordinary Transmission Through Arrays of Electrically Small Holes From a Circuit Theory Perspective

Extraordinary optical transmission of light or electromagnetic waves through metal plates periodically perforated with subwavelength holes has been exhaustively analyzed in the last ten years. The study of this phenomenon has attracted the attention of many scientists working in the fields of optics and condensed matter physics. This confluence of scientists has given rise to different theories, some of them controversial. The first theoretical explanation was based on the excitation of surface plasmons along the metal-air interfaces. However, since periodically perforated dielectric (and perfect conductor) slabs also exhibit extraordinary transmission, diffraction by a periodic array of scatterers was later considered as the underlying physical phenomenon. From a microwave engineering point of view, periodic structures exhibiting extraordinary optical transmission are very closely related to frequency-selective surfaces. In this paper, we use simple concepts from the theory of frequency-selective surfaces, waveguides, and transmission lines to explain extraordinary transmission for both thin and thick periodically perforated perfect conductor screens. It will be shown that a simple transmission-line equivalent circuit satisfactorily accounts for extraordinary transmission, explaining all of the details of the observed transmission spectra, and easily gives predictions on many features of the phenomenon. Although the equivalent circuit is developed for perfect conductor screens, its extension to dielectric perforated slabs and/or penetrable conductors at optical frequencies is almost straightforward. Our circuit model also predicts extraordinary transmission in nonperiodic systems for which this phenomenon has not yet been reported.

Common-Mode Suppression in Microstrip Differential Lines by Means of Complementary Split Ring Resonators: Theory and Applications

This paper is focused on the application of complementary split-ring resonators (CSRRs) to the suppression of the common (even) mode in microstrip differential transmission lines. By periodically and symmetrically etching CSRRs in the ground plane of microstrip differential lines, the common mode can be efficiently suppressed over a wide band whereas the differential signals are not affected. Throughout the paper, we present and discuss the principle for the selective common-mode suppression, the circuit model of the structure (including the models under even- and odd-mode excitation), the strategies for bandwidth enhancement of the rejected common mode, and a methodology for common-mode filter design. On the basis of the dispersion relation for the common mode, it is shown that the maximum achievable rejection bandwidth can be estimated. Finally, theory is validated by designing and measuring a differential line and a balanced bandpass filter with common-mode suppression, where double-slit CSRRs (DS-CSRRs) are used in order to enhance the common-mode rejection bandwidth. Due to the presence of DS-CSRRs, the balanced filter exhibits more than 40 dB of common-mode rejection within a 34% bandwidth around the filter pass band.

A general algorithm for computing the bidimensional spectral Green's dyad in multilayered complex bianisotropic media: the equivalent boundary method

A systematic method to obtain the bidimensional spectral dyadic Greens function of stratified planar structures with arbitrary complex bianisotropic layers is developed. The method is based on the uniqueness and equivalence electromagnetic theorems. A first-order partial differential formulation for the electromagnetic field inside each layer is used. An explicit algorithm makes it possible to go from the single-layer formulas to the general multilayer matrix formulation. The perturbative nature of the method provides good numerical efficiency and straightforward determination of asymptotic behavior. >

The theory of surface-wave and space-wave leaky-mode excitation on microstrip lines

This paper discusses the excitation and physical validity of both surface-wave and space-wave leaky modes on microstrip lines. This is done by analyzing the discrete modal spectrum excited by a realistic source on or near an infinite microstrip line. A semi-analytical three-dimensional (3-D) Greens function is used for this purpose, which provides the current excited on the conducting strip due to the source. The 3-D Greens function is in the form of a spectral integration (inverse Fourier transform) in the longitudinal wavenumber plane. The poles of the integrand directly determine the excitation amplitudes of the modes on the structure that are launched by the source. The integrand also has different types of branch points, and the location of the poles on the various Riemann sheets is used to determine the physical significance of the leaky modes. Although the theory presented here is illustrated for a microstrip line, the conclusions apply in general to open printed-circuit structures.

Three-dimensional superresolution in metamaterial slab lenses: Experiment and theory

This paper presents a theoretical and experimental study on the viability of obtaining two- and threedimensional superresolution i.e., resolution overcoming the diffraction limit for all directions in space by means of metamaterial slab lenses. Although the source field cannot be actually reproduced at the back side of the lens with superresolution in all space directions, the matching capabilities of metamaterial slabs does make possible the detection of images with three-dimensional superresolution. This imaging takes place because of the coupling between the evanescent space harmonic components of the field generated at both the source and the detector.

Extraordinary Transmission Through Arrays of Slits: A Circuit Theory Model

Extraordinary transmission and other interesting related phenomena for 1-D periodic arrays of slits (compound diffraction gratings) have recently been the object of intense research in the optics and solid state physics communities. This case should be differentiated from the extraordinary transmission through arrays of small apertures on metal screens since small holes only support below-cutoff modes, whereas slits can also support transverse electromagnetic modes without cutoff frequency. In this paper, an equivalent-circuit approach is proposed to account for the most relevant details of the behavior of slit-based periodic structures: extraordinary transmission peaks, Fabry-Perot resonances, and transmission dips observed in compound structures. The proposed equivalent-circuit model, based on well-established concepts of waveguide and circuit theory, provides a simple and accurate description of the phenomenon that is appropriate for educational purposes, as well as for the design of potential devices based on the behavior of the structures under study.

An excitation theory for bound modes, leaky modes, and residual‐wave currents on stripline structures

The nature of the current on a general multilayered printed-circuit stripline structure excited by a delta-gap source is investigated. The current is obtained through the construction of a semianalytical three-dimensional (3-D) Greens function, which accounts for the presence of the infinite conducting strip and the layered background structure. The 3-D Greens function is obtained by Fourier transforming the delta-gap source in the longitudinal (z) direction, which effectively resolves the 3-D problem of a delta-gap source into a superposition of 2-D problems, each of which is infinite in the z direction. The analysis allows for a convenient decomposition of the strip current into a sum of constituent parts. In particular, the strip current is first resolved into a set of bound-mode current waves and a continuous-spectrum current. The continuous-spectrum current is then represented as a set of physical leaky-mode currents in addition to a set of “residual-wave” currents, which arise from the steepest-descent integration paths. An asymptotic analysis reveals that the residual-wave currents decay algebraically as z−3/2. Far away from the source, the residual-wave currents dominate the continuous-spectrum strip current. Results are shown for a specific type of stripline structure, but the analysis and conclusions are valid for arbitrary multilayer stripline structures.

Quasi-TEM analysis of multilayered, multiconductor coplanar structures with dielectric and magnetic anisotropy including substrate losses

A quasi-TEM (transverse electromagnetic) analysis of multiconductor planar lines embedded in a layered structure involving lossy iso/anisotropic electric and/or magnetic materials is achieved. Conditions under which a quasi-TEM assumption is valid are theoretically determined. An efficient spectral-domain analysis is used to determine the complex capacitance and inductance matrices characterizing the transmission system. computation of the inductance matrix is reduced to the computation of an equivalent capacitance matrix when media characterized for a fully general permeability tensor are present. It is also shown that most actual monolithic microwave integrated circuit (MMIC) microstrip-type structures (where semiconductor substrates are present) and possible future applications including lossy magnetic materials can be analyzed by using the simple quasi-TEM model. The validity of the results has been verified by comparison with full-wave theoretical and experimental data on microstrip lines on magnetic substrates and slow-wave structures. >

Application of Total Least Squares to the Derivation of Closed-Form Green's Functions for Planar Layered Media

A new technique is presented for the numerical derivation of closed-form expressions of spatial-domain Greens functions for multilayered media. In the new technique, the spectral-domain Greens functions are approximated by an asymptotic term plus a ratio of two polynomials, the coefficients of these two polynomials being determined via the method of total least squares. The approximation makes it possible to obtain closed-form expressions of the spatial-domain Greens functions consisting of a term containing the near-field singularities plus a finite sum of Hankel functions. A judicious choice of the coefficients of the spectral-domain polynomials prevents the Hankel functions from introducing nonphysical singularities as the horizontal separation between source and field points goes to zero. The new numerical technique requires very few computational resources, and it has the merit of providing single closed-form approximations for the Greens functions that are accurate both in the near and far fields. A very good agreement has been found when comparing the results obtained with the new technique with those obtained via a numerically intensive computation of Sommerfeld integrals