The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

Theory of waveguides

A wideband switched beam antenna array system operating from 2 to 5 GHz is presented. It is comprised of a $4\times 1$ Vivaldi antenna elements and a $4\times 4$ Butler matrix beamformer driven by a digitally controlled double-pole four-throw RF switch. The Butler matrix is implemented on a multilayer structure, using 90° hybrid couplers and 45° phase shifters. For the design of the coupler and phase shifter, we propose a unified methodology applied, but not limited, to elliptically shaped geometries. The multilayer realization enables us to avoid microstrip crossing and supports wideband operation of the beamforming network. To realize the Butler matrix, we introduce a step-by-step and stage-by-stage design methodology that enables accurate balance of the output weights at the antenna ports to achieve a stable beamforming performance. In this paper, we use a Vivaldi antenna element in a linear four-element array, since such element supports wideband and wide-scan angle operation. A soft condition in the form of corrugations is implemented around the periphery of the array, in order to reduce the edge effects. This technique improved the gain, the sidelobes, and helped to obtain back radiation suppression. Finally, impedance loading was also utilized in the two edge elements of the array to improve the active impedance. The proposed system of the Butler matrix in conjunction with the constructed array can be utilized as a common RF front end in a wideband air interface for a small cell 5G application and beyond as it is capable to simultaneously cover all the commercial bands from 2 to 5 GHz.

/pdf/a-cost-effective-wideband-switched-beam-antenna-system-for-a-4qf4pc1oqq.pdf

A Cost-Effective Wideband Switched Beam Antenna System for a Small Cell Base Station

The flnite-difierence frequency-domain (FDFD) method is a very simple and powerful approach for rigorous analysis of electromagnetic structures. It may be the simplest of all methods to implement and is excellent for fleld visualization and for developing new ways to model devices. This paper describes a simple method for incorporating anisotropic materials with arbitrary tensors for both permittivity and permeability into the FDFD method. The algorithm is bench marked by comparing transmission and re∞ection results for an anisotropic guided-mode resonant fllter simulated in HFSS and FDFD. The anisotropic FDFD method is then applied to a lens and cloak designed by transformation optics.

/pdf/finite-difference-frequency-domain-algorithm-for-modeling-26x9xhipap.pdf

Finite-difference frequency-domain algorithm for modeling electromagnetic scattering from general anisotropic objects

The propagation characteristics of twisted hollow waveguides are considered, and various analysis methods are proposed. It is shown that a twisted hollow waveguide can support waves that travel at a speed slower than the speed of light c. These modes are of particular interest, as slow wave structures have many potential applications in accelerators and electron traveling wave tubes. Since there is no exact closed form solution for the electromagnetic fields within a twisted waveguide or cavity, several previously proposed approximate methods are examined. It is found that the existing perturbation theory methods yield adequate results for slowly twisted structures; however, our efforts here are geared toward analyzing rapidly twisted structures using newly developed finite-difference methods. To validate the results of the theory and simulations, rapidly twisted cavity prototypes have been designed, fabricated, and measured. These measurement results are compared to simulated results, and very good agreement has been demonstrated.

Analysis of Rapidly Twisted Hollow Waveguides

An eigenvalue analysis numerical technique for curved closed waveguiding structures loaded with inhomogeneous and/or anisotropic materials is presented. For this purpose, a frequency-domain finite-difference method is developed for a general orthogonal curvilinear coordinate system. The main strength of the technique is the accurate modeling of curved transverse boundaries, as well as curved geometries along the propagation direction, under certain limitations for the latter. This feature avoids the necessity of a fine mesh, while it retains a high accuracy and it is free of any staircase effects. In general, the proposed method shares the finite-element technique capabilities in modeling complex boundaries, while it preserves the finite-difference convenience in handling inhomogeneous and anisotropic material loadings. The resulting eigenvalue-based problem is solved using the Arnoldi algorithm, which exploits the system matrix sparcity and the overall technique is robust, unconditionally stable with minimal computational and memory requirements. Numerical results are validated against analytical results and results from 3-D commercial electromagnetic simulators. Finally, novel results are also given.

Eigenvalue Analysis of Curved Waveguides Employing an Orthogonal Curvilinear Frequency-Domain Finite-Difference Method

A two-dimensional finite difference frequency domain eigenvalue method employing orthogonal curvilinear co-ordinates is established. Its main strength is the accurate modelling of curved interfaces enabling the accurate evaluation of the complex propagation constants of curved waveguides. Numerical results for multilayer-multiconductor microstrip lines printed on curved substrates prove the validity of the method.

Eigenvalue analysis of curved waveguides employing FDFD method in orthogonal curvilinear co-ordinates

The current work elaborates on the study of periodic structures loaded either with anisotropic or isotropic media. An eigenanalysis methodology is adopted using Finite Difference in Frequency Domain (FDFD) in order to evaluate the Floquet wavenumbers. An eigenvalue problem is addressed and solved with Arnoldi iterative Algorithm. The periodicity of the structure is accounted in two alternative approaches. Initially Periodic Boundary Conditions (PBCs) are imposed on the periodic surfaces whose results found to be in a very good agreement with analytical ones. However, there is a deviation when the phase difference between periodic surfaces rise above 150 degrees. In order to get more accurate results, a Floquet Field Expansion is incorporated into the FDFD formulation. Also, adaptive meshing is employed for the accurate study of very fine discontinuities. In turn certain periodic structures loaded with anisotropic media are simulated in order to reveal the so-called Frozen Modes.

Periodic structures eigenanalysis incorporating the Floquet Field Expansion

An eigenanalysis of an array of periodically located wires covered with axially magnetized ferrites is presented. The interest in this structure stems from our previous analytical study which revealed that such a wire may support backward surface and possibly backward leaky waves. It is thus expected that a periodic array of these ferrite loaded wires may behave as a backward wave media offering an equivalent negative index of refraction as well as electromagnetic band gaps. These possibilities are examined herein by extending our previous two - dimensional curvilinear frequency domain finite difference method (FDFD) toward the eigenanalysis of periodic structures. Initially, the periodicity is accounted through periodic boundary conditions, while latter the related Floquet expansion will be introduced within the FDFD formulation.

Backward wave eigenanalysis of a tuneable two-dimensional array of wires covered with magnetized ferrite

The aim of this paper is the investigation of nonreciprocal phenomena in anisotropically loaded 2-D periodic structures For this purpose, our well-established 2-D curvilinear finite difference frequency domain method is combined with periodic boundary conditions and extended toward the eigenanalysis of periodic structures loaded with both isotropic and general anisotropic materials The periodic structures are simulated in a 2-D domain, while uniformity is considered along the third axis The propagation constant along the third axis can either be zero (in-plane-propagation) or nonzero (out-of-plane propagation) Particular effort was devoted to the identification of the appropriate irreducible Brillouin zone to be scanned during the eigenanalysis It was herein realized that similar to geometrically artificial crystal anisotropy, the wave propagation directional asymmetries modify the irreducible Brillouin zone in the microwave regime as well Both gyrotropic and particularly magnetized ferrite as well as full tensor anisotropic (arbitrarily biased ferrite) material loadings are investigated through the eigenanalysis of different periodic structures, including strip grating Interesting nonreciprocal backward wave and unidirectional phenomena are justified as expected

C. S. Lavranos

Papers

Eigenvalue Analysis of Curved Waveguides Employing an Orthogonal Curvilinear Frequency-Domain Finite-Difference Method

Eigenvalue analysis of curved waveguides employing FDFD method in orthogonal curvilinear co-ordinates

Periodic structures eigenanalysis incorporating the Floquet Field Expansion

Backward wave eigenanalysis of a tuneable two-dimensional array of wires covered with magnetized ferrite

Investigation of Nonreciprocal Dispersion Phenomena in Anisotropic Periodic Structures Based on a Curvilinear FDFD Method