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This article proposes a ray-tracing and physical-optics (RT-PO) model that allows for an accurate and time-efficient evaluation of planar Mikaelian lens antennas implemented by parallel plate waveguides. With an intrinsic flat shape and axis-symmetry of refractive-index distribution characteristic, the planar Mikaelian lens antennas are easy to fabricate and integrate to standard planar feeds. A numerical computation of the ray paths based on the Snell’s law gives a description of the phase of the electric field in the lens aperture, while the ray-tube power conservation theory is employed to evaluate the amplitude. The field equivalence principle is then used to calculate the far field of the lens antenna. The information of far-field directivity, gain, and dielectric efficiency is further obtained, considering a small loss in the dielectric materials. Our approach is validated by comparing the results of a particular Mikaelian lens antenna with those computed using a commercial full-wave simulator, demonstrating high accuracy and significant reduction in computation resources and times.

This article investigates the dispersion properties of metasurfaces with hexagonal lattices, including potential higher symmetric configurations. We explore the relationships between the periodicity of hexagonal lattices and their dispersion properties, paying special attention to how hexagonal periodic structures can be analyzed with either a hexagonal primitive unit cell or a rectangular supercell. We also study the possibility of introducing higher symmetries into hexagonal periodic structures, including glide symmetry and mirrored half-turn symmetry. To complement and validate the analysis, we designed a graded-index Luneburg lens antenna with a dielectric-filled hexagonal holey structure working in the Ka-band. The antenna generates steerable highly directive beams from 26 GHz to 30 GHz, which corroborates our analysis. Our findings provide valuable insight into the dispersion properties of hexagonal-lattice metasurfaces and demonstrate the feasibility of using such structures in practical applications.

This article describes a detailed procedure that allows for a time-efficient design of fully metallic geodesic H -plane horn antennas using an in-house ray-tracing method together with an optimization algorithm. With all the propagation in the air, geodesic H -plane horn antennas are low-loss and highly efficient. The proposed geodesic H -plane horn antennas provide a new degree of freedom, the height profile, to alleviate phase errors, realizing high gains and aperture efficiencies. Optimizations are implemented to design the height profile for a given target, enabled by the highly accurate and time-efficient in-house ray-tracing model. To demonstrate the correctness and versatility of the proposed design procedure, two prototypes are manufactured with computerized numerical control (CNC) machining and compared to their planar counterparts, with the aim of a high increased gain and aperture efficiency, respectively. The prototypes maintain good frequency stability from 26 to 33 GHz, with side lobe levels lower than -15 dB and return loss better than 15 dB. The first prototype improves the realized gain by over 5 dB compared to the reference horn, while the second prototype achieves an aperture efficiency of around 65% within the operating frequency band.

The Physical Optics (PO) method is used to derive simplified expressions to compute the radiation electric fields of planar graded-index and geodesic lenses based on a parallel-plate waveguide (PPW) implementation. If the PO method is combined with ray-tracing (RT) techniques, the resulting RT-PO procedure is capable of computing radiation patterns and gain of the PPW-based lens antennas when their apertures have a general shape and the electric field is vertically polarized. The RT-PO method is validated by comparing it with the full-wave simulation results of the commercial software ANSYS HFSS for three application cases. The results show that the RT-PO approach is not only very efficient from a computational point of view but also accurate, thus being a very convenient analysis/design tool for this kind of antenna.

We propose and implement a geodesic half-Maxwell fish-eye (MFE)-lens antenna. The lens was optimized using an in-house physical optics (PO) code adapted for generalized geodesic lenses. The final antenna design was validated with commercial electromagnetic simulation software. The antenna combines a modulated geodesic half-MFE lens and a transition to a linear flare, which is needed to preserve the linear polarization in the aperture. The antenna prototype, designed to operate in the Ka -band, was manufactured with computer numerical control (CNC) milling and measured in an anechoic chamber. The design provides continuous beam scanning because of a mechanically actuated feed. Promising beam scanning properties are demonstrated in an angular range of ±45° with a scan loss below 3 dB, as well as good frequency stability from 26 to 32 GHz. Since the antenna is fully metallic, its radiation efficiency is high (approximately 90%).

The equivalent circuit approach (ECA) is used in this work to analyze and design a previously proposed one-dimensional planar blazed grating of the resonant type. The analysis covers both the classical Littrow configuration, when the direction of the relevant diffracted order coincides with that of the incident wave (Bragg blazing), and when these directions are different (off-Bragg blazing). Once the scattering problem of the grating structure is posed as a discontinuity problem inside an equivalent generalized waveguide (corresponding to the unit cell of the original structure) and studied in terms of its equivalent circuit network, the possibility of transferring all the power of the incident plane wave into one single-diffraction order is seen as a simple impedance matching problem. An associated resonance phenomenon is also found to be implicitly associated with this matching condition. This simplifying and fruitful standpoint makes it possible to set up a systematic design procedure to find the specifications of the planar grating for either Bragg or non-Bragg blazing operation. Dielectric and strong skin-effect ohmic losses are easily implemented in the ECA and its effects in the practical design of structures are discussed.

In this paper, we explore the excitation of magnetic current surface waves in truncated periodic arrays of slots in a conducting screen. A specialized Method of Moments (MoM) implementation is presented, which makes it possible to efficiently solve the scattering problem involving truncated arrays of several thousands of slots. By making use of the dispersion diagrams of surface waves propagating along infinite periodic arrays of slots, we are able to explain the absence of magnetic current surface waves in the arrays at frequencies in the neighborhood of the transmission peak associated to the slots natural resonances (length roughly equal to half the wavelength), while they are present when the arrays are excited under extraordinary transmission (EOT) conditions. In order to experimentally check this different behavior, an aluminium plate periodically perforated with slots has been fabricated and fed by means of a pyramidal horn, and the electric field behind the plate has been measured with a planar near-field system at a few centimeters from the plate. Our experimental results and MoM simulations agree, demonstrating the presence of a standing wave pattern of magnetic current surface waves at the EOT frequency, and the absence of surface waves at the slots natural resonant frequency.

This paper presents an eigenproblem for computing the resonances of multiresonant irislike discontinuities in waveguides. The formulation of the eigenproblem is based on integral equation methods, and its solution provides the resonance frequencies (eigenvalues) and the associated resonant aperture field's patterns (eigenvectors). These eigenvectors can be used as a basis for the expansion of the aperture fields at any frequency within the band of interest, thus leading to a significant reduction of the size of the method-of-moments admittance matrix. Moreover, under certain approximations, the orthogonality of the eigenvectors allows for the derivation of a Foster-like canonical equivalent circuit with capacitances and inductances that present a smooth frequency dependence. In order to obtain an equivalent Foster circuit with frequency-independent inductors and capacitors, a straightforward and simple iterative refinement is proposed. The circuit thus obtained accurately reproduces the response of the multiresonant irislike discontinuity over a wide frequency band.

A symmetrical pair of differential microstrip lines implemented in hybrid microstrip/coplanar waveguide (CPW) technology is proposed. Transmission-line models are used to analyze differential-and common-mode responses, allowing efficient design with minimal optimization effort. The structure behaves as a conventional transmission line pair under differential-mode excitation, whereas asymmetrical coupled transmission line theory has to be applied to characterize common-mode operation. The common mode is strongly suppressed thanks to the introduction of a controllable transmission zero. A two-stage version of the structure is used to increase the common-mode rejection bandwidth. All the electrical parameters of the transmission lines have been obtained using an in-house fast quasi-TEM code. The good agreement between transmission-line models, full-wave simulations and measurements confirms the benefits of the structure and the design procedure.

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.

Subwavelength imaging of the near field of a magnetic line-source excitation is studied for several wire-medium (WM) lens topologies using complex-plane analysis of the radiation integral. Nonlocal homogenization is used for the wire medium, resulting in an analytical expression for the transfer function of the lens. It is shown that by evaluating the Sommerfeld integral of the transmitted field in terms of the discrete and continuous spectra provides a general framework for better understanding of electromagnetic phenomena involved with subwavelength imaging. Results are obtained for a WM slab, and for a wire medium loaded with graphene monolayers and periodic arrays of graphene patches, demonstrating the interplay of the discrete and continuous spectral components in different operating regimes of the lenses. The imaging with a stack of silver slabs is also considered for comparison purposes.

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.

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 communication extends a previously reported analytical circuit that models the plane wave scattering by 2-D arrays of planar patches/apertures embedded in a layered media. In this extension, it is assumed that the current/electric field spatial profile in the patch/aperture region can directly be taken from the eigenfields of a waveguide whose cross section matches the scatterer boundaries. This methodology exploits all the advantages of the circuit modeling and gives place to a very efficient computational tool for many practical frequency-selective surfaces (FSSs). The circuit model is expected to work up to frequencies where the isolated scatterers have their third resonance. Thus, it allows us to provide unified equivalent circuits to deal with conical incidence and with certain symmetric cases involving two or three patches/apertures in the unit cell.

A novel balanced bandpass filter (BPF) based on folded stepped impedance resonators (FSIR's) with modified ground plane is presented in this work. By symmetrically introducing a series-LC resonant structure below the FSIR's, common-mode (CM) propagation can be rejected without affecting differential-mode (DM) performance. The filter presents two main advantages with respect to the conventional solid-ground-plane FSIR filter: i) an important improvement of the CM rejection level within the differential passband and ii) an enhanced filter selectivity due to the inclusion of an extra transmission zero in the differential passband. Both the conventional and the novel filters have been modeled as lumped-element circuits that fully account for DM and CM operation. Simulation and measurement results confirm the benefits of the proposed balanced BPF.

Novel methods are presented for the independent resonance tuning in rectangular waveguide epsilon-near-zero (ENZ) structures. This kind of tuning is achieved using short longitudinal and inclined slots placed in the middle of the ENZ channel. It is demonstrated that the tunneling frequency and Fabry-Pérot resonance (FPR) can be shifted by as much as 8% and 9.7%, respectively. Equivalent circuits for the tuning slots are given, and their equivalent parameters are extracted and validated. Analytical expressions for the equivalent slot reactances are also provided, and they show very good agreement with the extracted parameters. Experimental verification of both presented tuning methods is provided, and the agreement between simulated and experimental results is excellent (error less than 1%).

A novel non-uniform sinusoidally modulated half-mode microstrip structure with application to near-field focused leaky-wave radiation in the backward Fresnel zone is proposed. First, it is presented a dispersion analysis of the constituent backward leaky wave in the sinusoidally modulated unit cell in half-width microstrip technology. This information is then used to design a finite non-uniform line that focuses the radiated fields at the desired point. Finally, eight similar line sources are arranged in a radial array to generate a three-dimensional focused spot located at the desired focal length over the simple central coaxial feeding. Simulated and experimental results are presented to validate the proposed simple approach.

A simple strategy is proposed to design differential-mode bandpass filters with good common-mode (CM) rejection using simple resonators. Specifically, the CM rejection is enhanced by using conventional open-loop resonators as well as folded stepped-impedance resonators without the addition of printed or lumped elements along the symmetry plane of the filter or the use of defected ground solutions. The novelty of the present proposal is that a good CM rejection is achieved by the use of magnetic coupling instead of the more commonly employed electrical coupling. Magnetic coupling inherently yields poorer CM transmission as requested by good differential filters. The resonators, due to their geometrical simplicity, can easily be cascaded to implement high-order filters. The use of simple geometries also simplifies the design methodology and makes final tuning based on electromagnetic simulation simpler or unnecessary.

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.

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.

An enhanced equivalent circuit approach for the magnetic/electric interaction of single split-ring resonators (SRRs) with printed lines is presented in this paper. A very simple and efficient lumped-element network is proposed to model the behavior of metamaterial-based printed lines over a wide frequency band. The same circuit topology can be used for the single- and two-mirrored SRRs loaded microstrip line. The corresponding circuit parameters are obtained from the multiconductor transmission line theory as well as from closed-form expressions that make use of just the resonance frequency and minimum of the reflection coefficient (which should be previously extracted from experiments or full-wave simulations). The comparison of our equivalent circuit results with measurements and full-wave simulations has shown a very good agreement in a considerably wider frequency band than other previously proposed simple equivalent circuits.

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.

A self-complementary metasurface is studied in this paper. The metasurface is a 2-D periodical arrangement of unit cells formed by a metallic printed split ring resonator and its complementary counterpart. It is demonstrated that this structure behaves like a very selective band-pass filter for a certain linear polarization while band-stop filtering is achieved for the orthogonal polarization over the same frequency range. This idea opens the door to a new class of frequency selective surfaces made of connected and unconnected elements, whose filtering properties are mechanically tunable from band-pass to band-stop by rotating the surface or the polarization.

This contribution provides a fully analytical transmission-line circuit model for the transmission/reflection of an obliquely incident plane wave by a periodic array of printed dipoles. The topology of the equivalent circuit is rigorously derived in the analysis. In contrast with previously reported circuit models, the proposed approach accounts for dynamical effects that enable the application of the model in a very wide frequency range.

We report on the dual nature (capacitive and inductive) of the surface impedance of periodic graphene patches at low-terahertz frequencies. The transmission spectra of a graphene-dielectric stack shows that patterned graphene exhibits both the low-frequency (capacitive) passband of metal patch arrays and the higher-frequency (inductive) passband of metal aperture arrays in a single tunable configuration. The analysis is carried out using a transfer matrix approach with two-sided impedance boundary conditions, and the results are verified using full-wave numerical simulations.

Two frequency selective surfaces (FSSs) made of an infinite set of parallel 1-D chains of interconnected split ring resonators (I-SRRs) and interconnected complementary split ring resonators (I-CSRRs) are studied. The main result was that the central frequencies of the stopband and passband can be strongly tuned by controlling the angle of incidence.

An analytical model is presented for the analysis of multilayer wire media loaded with 2-D arrays of thin material terminations, characterized in general by a complex surface conductivity. This includes the cases of resistive, thin metal, or graphene patches and impedance ground planes. The model is based on the nonlocal homogenization of the wire media with additional boundary conditions (ABCs) at the connection of thin (resistive) material. Based on charge conservation, new ABCs are derived for the interface of two uniaxial wire mediums with thin imperfect conductors at the junction. To illustrate the application of the analytical model and to validate the new ABCs, we characterize the reflection properties of multilayer absorbing structures. It is shown that in such configurations the presence of vias results in the enhancement of the absorption bandwidth and an improvement in the absorptivity performance for increasing angles of an obliquely incident TM-polarized plane wave. The results obtained using the analytical model are validated against full-wave numerical simulations.

We present an analytical model to study the reflection properties of a multilayered wire media loaded with 2-D arrays of thin imperfect conductors. Based on charge conservation, generalized additional boundary conditions (ABCs) for the interface of two uniaxial wire mediums loaded with thin arbitrary imperfect conductors at the junction are derived. It is observed that by proper selection of the structural parameters, the mushroom structure acts as a wideband absorber for an obliquely incident TM-polarized plane wave. The presented model along with the new ABCs are validated using the full-wave numerical simulations.

In this paper, we report on the analysis of transmissivity of electromagnetic waves through a stack of dielectric slabs loaded with atomically thin graphene sheets at low-terahertz frequencies. It is observed that the structure supports a series of bandpass regions separated by bandgap regions, similar to the case of stacked metallic meshes separated by dielectric slabs at microwave/THz frequencies or metal-dielectric stack at optical frequencies. The transmission resonances in the bandpass region are identified as coupled Fabry-Pérot resonances associated with the individual dielectric slabs loaded with graphene sheets. The study is carried out using a simple circuit theory model, with the results verified against the numerical simulations.

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.

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.

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.

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.

A fully analytical solution for the scattering of a uniform TE polarized plane wave by an infinite periodic printed array of narrow slits is provided in this contribution. The model is based on some simplifications made on the formulas arising from a rigorous full-wave formulation. The present approach gives the topology of the transverse equivalent network as well as closed-form expressions for all its components, and overall very accurate results.

A novel microstrip differential transmission line with common-mode noise suppression is proposed and experimentally validated. It is implemented by periodically etching complementary split ring resonators (CSRRs) in the ground plane. For the differential signals, the symmetry of the structure efficiently cancels the electric field components axial to the CSRRs, and these particles have no effect on signal transmission. However, the CSRRs are activated under common mode excitation, with the result of a stop-band behavior. For the designed and fabricated prototype device, over 20 dB suppression of common-mode noise is achieved over a frequency range from 1.18 GHz to 1.74 GHz.

The transmission and reflection of electromagnetic waves impinging on metallic surfaces with periodically distributed slits (diffraction gratings) have been the subject of thorough studies using numerical and experimental approaches. Of special interest are the properties of the so-called compound gratings, which are periodic arrays of slits whose unit cell contains several of them. The transmission properties of such diffraction gratings have been studied along the last few years both theoretically (D.C. Skigin and R.A. Depine, Phys. Rev. Lett., 95, 217402, 2005) and experimentally (A.P. Hibbins et al., Phys. Rev. Lett., 96, 257402, 2006; M. Navarro-Ca et al., App. Phys. Lett., 94, 091107, 2009). However, analytical models are very useful for design purposes and, moreover, they provide physical insight that is not obvious from numerical approaches. For compound transmission gratings, the authors of this contribution recently developed a circuit-model-based analytical approach (F. Medina, F. Mesa and D.C. Skigin, IEEE Trans. on Mic. Theory Tech., 58, 105-115, 2010) that captures the essential physics of these optical systems. Thus, compound transmission gratings are now well understood, and numerical or analytical design tools are available.

We present a simple and efficient circuit model for the analysis of multi-band absorption characteristics of a stack of sub-wavelength grids (fishnets or patch arrays) in a layered environment with a single resistive sheet placed on top. It is shown that at low frequencies the resonances of total absorption occur, which are explained in terms of Fabry-Pèrot resonances associated with the individual reactively loaded dielectric slabs (that are strongly coupled through the sub-wavelength grids). It is observed that the number of absorption peaks in the absorption band corresponds to the number of reactively loaded dielectric slabs. The results of the proposed analytical model are validated with the full-wave simulations, showing good agreement.

This presents an equivalent transmission-line circuit that accounts for the scattering of a TE polarized plane wave that impinges obliquely on a periodic array of metallic patches sandwiched in a dielectric slab. The proposed approach gives a very efficient reduced-order model of the electromagnetic phenomenon able to reproduce all the fine quantitative details of the reflection/ transmission spectrum. Also, our model provides an easy theoretical frame to predict and/or understand all the qualitative behavior of the scattering when both oblique incidence and dielectric slabs are considered.

Extraordinary transmission through periodic distributions of sub-wavelength holes made in opaque screens has been demonstrated and exhaustively studied along the last decade. More recently, extraordinary transmission has also been predicted and experimentally observed through electrically small diaphragms located inside hollow pipe waveguides. This last phenomenon cannot be explained in terms of surface waves excited along the periodic system (the so-called surface plasmon polaritons). Transverse resonances can be invoked, however, as a sound explanation for extraordinary transmission in this kind of systems. In this paper, a simple waveguide system, exhibiting exactly the same behavior previously observed in periodic 2-D arrays of holes, is analyzed in depth. Analogies and differences with the periodic case are discussed. The theoretical and experimental results reported in this paper provide strong evidence in favor of the point of view emphasizing the concept of impedance matching versus surface wave excitation. The role of material losses is discussed as an important practical issue limiting the maximum achievable subwavelength transmission level. Most of our conclusions can be applied to both periodic arrays of holes and diaphragms in closed waveguides.

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, FabryProt 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.

A folded stepped impedance resonator (SIR) modified by adding an inner quasi-lumped SIR stub is used as the basic block of a new configuration of dual band-pass filter. The main advantage of the proposed filter is to allow independent control of the features of the first and the second pass bands. Additional design flexibility can be achieved by allowing the stub to be located at an arbitrary position along the high impedance line section of the main SIR. The positions of the tapped lines have been optimized in order to match the filter at the central frequencies of both pass bands. Some designs are reported to illustrate the possibilities of the structure.

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 metalair 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.

This work proposes a circuit model based explanation for the extraordinary transmission (ET) of light phenomenon studied in recent scientific literature [1], [2]. ET mainly stands for unexpected transmission of light through periodic arrays of subwavelength holes in a metal screen. The study of this phenomenon has attracted the attention of many scientists working in the fields of Optics and Condensed Matter Physics, giving place to some controversial explanations. The existence of surface plasmons supported by the metal/air interface at optical frequencies has been considered the underlying reason behind ET. Our contribution tries to offer a relatively simple explanation of ET based on conventional waveguide/transmission-line theory. It will be shown how this simplified microwave-engineering standpoint offers satisfactory explanation for most ET findings. Indeed, ET should be expected not only at optical frequencies but also at lower frequencies, when surface plasmons are not possible.

This paper presents an algorithm for the acceleration of the series involved in the computation of 2-D homogeneous Green's functions with 1-D and 2-D periodicities. The algorithm is based on an original implementation of the spectral Kummer-Poisson's method, and it can be applied to the efficient computation of a wide class of infinite series. In the algorithm the number of asymptotic terms retained in Kummer's transformation is externally controlled so that any of the series that has to be accelerated is split into one series with exponential convergence and another series with algebraic convergence of arbitrarily large order. Numerical simulations have shown that there is an "optimum" number of asymptotic terms retained in Kummer's transformation for which the CPU time needed in the summation of the series is minimized. The CPU times required by Ewald's method for the evaluation of 2-D Green's functions with 1-D and 2-D periodicities have been compared with those required by the present algorithm, and the algorithm has been found to be between 1.2 and 3 times faster than Ewald's method when working in "optimum" operation conditions.

The rational function fitting method has been found useful in the derivation of closed-form expressions of spatial-domain Green's functions for multilayered media. However, former implementations of the rational function fitting method lead to Green's functions expressions that are not accurate in the far field when this far field is dominated by the continuous spectrum instead of being dominated by surface waves (as it happens, for instance, in the case of lossy multilayered media). In this paper, the authors introduce a novel implementation of the rational function fitting method, which leads to Green's functions expressions that are accurate in the far field when this is dominated either by the continuous spectrum or by surface waves. In the new approach, the far-field contribution of the continuous spectrum to the Green's functions is numerically fitted in terms of functions with closed-form Hankel transforms, and this far-field contribution is explicitly added to the total least squares approximations of the Green's functions. The numerical results obtained for the Green's functions with the new approach have been compared with numerical results obtained via direct numerical integration of Sommerfeld integrals, and excellent agreement has been found despite the contribution - continuous spectrum or surface waves - dominating the far field.

A new technique is presented for the numerical derivation of closed-form expressions of spatial-domain Green's functions for multilayered media. In the new technique, the spectral-domain Green's 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 Green's 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 Green's 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.

This paper presents a quasi-TM approach for the fundamental mode of transmission lines with semiconductor substrates and nonperfect metallic conductors. The approach has allowed us to develop a transmission-line model by properly defining frequency-dependent parameters in terms of the quasi-static electric potential and the electric current density along the propagation direction in the line. The previous quasi-TM analysis avoids the involved numerical root finding process typical in full-wave analysis, and overcomes the limitations of the conventional quasi-TEM approach to account for the effects of the longitudinal currents present both in the lossy substrates and in the nonperfect conductors. The transmission-line parameters have been computed by a hybrid technique that combines the method of lines with the method of the moments (MoM). The total CPU effort has been considerably reduced thanks to the possibility of finding closed-form expressions for the reaction integrals appearing in the MoM. Comparisons with previous computed and measured results show the validity of the present model

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 Green's functions poles, and extension to the leaky regime are still open and deserve deeper examination. It will be 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 will be illustrated by diverse numerical results for the bound/leaky regime of various planar lines. Finally, the suitability of the method for covered planar lines will be demonstrated.

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.

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.