Asymptotic Corrugation Boundary Conditions Research Articles

Analysis of Leaky-Wave Radiation From Corrugated Parallel-Plate Waveguides With Steerable Beams by Rotatable Corrugations

This article presents a modal analysis entailing classical vector potentials and asymptotic corrugations boundary conditions for treating a leaky-wave antenna (LWA) composed of a corrugated parallel-plate waveguide with mutually rotatable grated surfaces and whose upper grille is penetrable to the exterior space. Beam steering at fixed frequencies is achieved by rotating both or either of the base and top gratings, thus finding roles that conventional frequency-steered LWAs are unable to serve. Within millimeter-wave (mm-wave) and THz regimes where components become strongly miniaturized, the advantages of electronic beam-scanning at lower microwave frequencies begin to get offset by the benefits of mechanical steering. Not only does the rotational form of steering enjoy the benefits of simplicity and low cost, it also circumvents the need for complex networks at mm-wave/THz regimes required by electronic-steering that annuls the strengths of LWA in the first place. The rotation in the horizontal plane also offers high weight-handling capability, making it all the more able to manage miniaturized structures at mm-wave/THz regimes. Numerical results computed by the modal approach are validated with those simulated by commercial software. Measurements on a manufactured prototype demonstrate the efficacy of the steerable LWA just as the numerical designs have predicted.

Analysis of Doubly-Stacked Rotated Gratings Using Asymptotic Corrugations Boundary Conditions

In this paper, we present a highly efficient analysis of double-layered stacked gratings that are rotated from each other by any arbitrary angle using the asymptotic corrugations boundary conditions (ACBC) along with classical vector potentials. By casting the resultant system of linear equations into a homogeneous matrix equation, the eigenvalue problem can then be solved, after which the surface-wave dispersion diagram may be generated. In addition to the solutions for modal resonances under sourceless conditions, reflection and transmission analyses of plane-wave incidences constituting source-driven problems are also presented for both normal and oblique incidences. The properties of copolarization and cross-polarization levels in those scenarios are also discussed. The results computed by the code written based on this proposed modal method are compared and validated with those simulated using a commercial full-wave solver. A prototype of the structure was also manufactured and measured.

Modal Analysis of Corrugated Plasmonic Rods for the Study of Field Localization, Conductor Attenuation, and Dielectric Losses

By virtue of the strong confinement of surface-wave fields that it provides, the transverse corrugated conducting rod is an important structure in the fields of plasmonics and metasurfaces, finding applications in focusing, sensing, imaging, spectroscopy, and subwavelength optics, among others. This paper presents an analytical modal method for treating such grated rods with generally dielectric-filled grooves, one which offers rapid yet accurate surface-wave modal solutions. Based on the asymptotic corrugation boundary conditions, the formulation is simple and elegant, providing not only the dispersion relationship between the frequency and wavenumber but also the explicit functional forms of the fields. Dispersion and modal field results obtained by the proposed method are validated with an independent full-wave solver. Because of its candidacy for microwave applications at high powers and high frequencies, as well as transmissions over long distances, studies of dielectric and conductor losses are also carried out, for both the grooved rod and its likewise corrugated circular waveguide counterpart. Parametric studies are conducted on three aspects, namely, the degree of field localization on the surface of the rod, as well as attenuation due to dielectric and metal losses. Measurements of dispersion and field decay properties conducted on a manufactured rod that concur with theory are also reported.

Generalised asymptotic boundary conditions and their application to composite right/left‐handed rectangular waveguide with double‐ridge corrugations

A generalised form of the asymptotic corrugation boundary conditions (ACBCs) is presented and employed to analyse a composite right/left-handed rectangular waveguide loaded with double-ridge stubs. Enforcing the ACBCs yields the dispersion relation as well as the field distribution in the main waveguide without the need for any sophisticated modal analysis. The asymptotic solution proves to provide accurate results within a wide frequency band. The effect of the various geometrical parameters and the aspect ratios is investigated to determine the range of validity of the ACBCs. The results compared with the full-wave simulations exhibit very good agreement.

Corrugated Surfaces With Tailorable Dark Sectors Within Prescribed Frequency Bands

Electromagnetic bandgap (EBG) surfaces have customarily been defined as being prohibitive of surface-waves within frequency ranges called bandgaps, for all directions along the surface, this latter specification being an understood presumed condition. However, not all practical applications require such an entire bandgap in terms of surface directions. Rather, there could be situations where surface-wave suppression is needed along directions only within an angular sector but are instead desirable towards others outside, over a frequency band, termed herein as a sectoral dark band (SDB). This work investigates this aspect using planar corrugated surfaces as the vehicle for study, in virtue of its ease of surface-wave modal analysis of dispersion by asymptotic corrugations boundary conditions (ACBC). A systematic design procedure for tailoring surfaces to any specified dark sector of weak signals prevailing over any prescribed band is presented.

Modal Analysis of All-Walls Longitudinally Corrugated Rectangular Waveguides Using Asymptotic Corrugations Boundary Conditions

The asymptotic corrugations boundary conditions (ACBCs) are used together with classical theory of vector potentials and an innovative combination of matrix systems to analyze rectangular waveguides having all four walls being longitudinally (axially) corrugated. One matrix system is composed of the ACBCs of two opposite walls, while the other comprises those of the other pair of corrugated walls. A transcendental characteristic equation is derived, from which the modal dispersion diagram can be obtained, for all three modal wave-tyoes: fast space, slow surface, and evanescent waves. From the formulation, analytical modal field functions in closed form are also acquired. Results of dispersion graphs and modal field distributions generated by this method are compared favorably with those obtained by a commercial full-wave solver.

Rapid Surface-Wave Dispersion and Plane-Wave Reflection Analyses of Planar Corrugated Surfaces by Asymptotic Corrugations Boundary Conditions Even for Oblique Azimuth Planes

The asymptotic corrugations boundary condition (ACBC) is used together with classical theory of vector potentials to analyze planar corrugations. A transcendental characteristic equation is derived, from which the dispersion diagram can be obtained, thereby conveying surface wave passband and stopband properties, even for propagation within oblique azimuth planes as well as both principal TE and TM polarizations. From the formulation, field distributions for the regions within the grooves and above the corrugations can also be generated. When compared with the dispersion graphs obtained from characteristic equations derived by the classical transverse resonance technique (TRT), the newly presented ACBC method provides superior accuracy. Explicit formulas for the complex reflection coefficient (amplitude and phase) for both TE and TM polarized plane-wave incidences are also derived as closed-form analytic functions of all parameters (especially the azimuth phi angle of incidence) using a novel concept of unusual transversely phased plane-waves. These proposed approaches are massively more efficient than full-wave solvers, providing unparalleled speedup of computation by thousands of times. The surface-wave and reflection properties of planar corrugations are thus herein analyzed in a unified, complete, and elegant manner that is also highly efficient but yet accurate. This thorough work is thus a great boost to the continued use of corrugated surfaces as artificial magnetic conductors (AMC), electromagnetic bandgap (EBG) structures, and soft/hard surfaces in all walks of antenna design, especially in terms of speed and accuracy.

Analysis of left-handed rectangular waveguides with dielectric-filled corrugations using the asymptotic corrugation boundary conditions

The asymptotic corrugation boundary conditions are employed to analyse left-handed rectangular waveguides with dielectric-filled transverse corrugations. The dispersion relations as well as the field expressions in the waveguide and the corrugation are derived. An equivalent multiport network model for the case of the two-walled corrugated waveguide is presented, and can easily be reduced to the one-walled case. Compared to the rather sophisticated full-wave solution, the asymptotic solution proves to provide accurate results within a wide frequency band. The limitations of the asymptotic boundary conditions are investigated to determine the range of validity of the presented solution.

Oblique plane‐wave scattering from circular cylinders of periodic circular discs using asymptotic corrugated boundary conditions

AbstractAn infinite circular cylinder, made of periodic circular conducting discs separated by circular dielectric discs, is considered. The cylinder is excited by an oblique plane‐wave incident. A simple asymptotic solution is presented for the problem by considering that the periodicity period approaches zero. The asymptotic corrugation boundary conditions are enforced on the cylinder's surface. The series solution is verified with the numerical solution when the ratio between the separation distances between the conducting discs to the period is finite and ≤1. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 33–35, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11278