Presented herein is a coupled-mode formulation for coupled microstrip lines on a magnetized ferrite substrate. The formulation discussed here is an extension of the coupled-mode theory for microstrip lines on an isotropic substrate. Since the magnetized ferrite exhibits a biaxial anisotropy in its permeability, the guidedwave fields in the magnetized ferrite are not subject to the conventional reciprocity relation for fields in an isotropic medium. Thus, a generalized reciprocity relation is first derived from two sets of guidedwave fields, which propagate in ferrite magnetized transversely along the strip surface. The reciprocity relation is then used to derive coupled-mode equations for coupled microstrip lines on a ferrite substrate. As a basic numerical example, the new formulation is applied to two coupled microstrip lines on a ferrite substrate.

This paper describes the steepest-descent evaluation of the radiation field for both TE and TM modes of an asymmetric planar open waveguide. The cover, film and substrate field will be formulated in the spectral domain. The steepest-descent path in the complex axial transform plane (ζ-plane) is identified as a direct method and that in the complex φ-plane (φ = σ +jη: complex polar coordinate) is also identified as an indirect method in order to validate the steepestdescent path in the complex axial transform plane (ζ-plane). The branch cut integration will be rigorously analyzed through complexphasor diagrams. An alternative integration path will be also identified since it is an effective method to validate the steepest-descent and branch cut integrations. Then, the steepest-descent evaluation of cover and substrate fields and numerical results for TE modes will be presented and numerical implementation for TM modes will be accommodated in the future research.

This paper presents an eigenfunction expansion of the electric-type dyadic Green's functions for both a unbounded gyroelectric chiral medium and a cylindrically-multilayered gyroelectric chiral medium in terms of the cylindrical vector wave functions. The unbounded and scattering Green dyadics are formulated based on the principle of scattering superposition for the electromagnetic waves, namely, the direct wave and scattered waves. First, the unbounded dyadic Green's functions are correctly derived and some mistakes occurring in the literature are pointed out. Secondly, the scattering dyadic Green's functions are formulated and their coefficients are obtained from the boundary conditions at each interface. These coefficients are expressed in a compact form of recurrence matrices; coupling between TE and TM modes are considered and various wave modes are decomposed one from another. Finally, three cases, where the impressed current source are located in the first, the intermediate, and the last regions respectively, are taken into account in the mathematical manipulation of the coefficient recurrence matrices for the dyadic Green's functions.

Complex permittivity of a number of liquids and binary mixtures has been studied by measurement using the waveguide techniques at the X and Ku band. Particular pieces of WR90 and WR62 waveguides were designed for the measurement of liquid materials. The custom designed TRL calibration kits are applied for calibration of the waveguide system. The measured results of complex permittivity of liquid dielectrics, such as methanol, propyl alcohol, ethyl alcohol, chlorobenzene, dioxane, cyclohexane and binary mixtures, are presented. Particular pieces of open-ended waveguides for the X and Ku bands were also designed for holding liquids and the measured data using the open-ended waveguide technique were compared with those measured using the waveguide technique. Some of the measured results are also compared with calculated data using the Debye equation and published data measured by the Fourier transform spectroscopy.

In this paper, we present numerical analysis for the following scattering problems: the radar cross-section, the backscattering enhancement, and the angular correlation function for waves scattered from practical targets embedded in random media. We assume perfect conducting targets with various cross-sections to study the effect of target configuration on the scattering problems. Also, we consider different random media with taking account of incident wave polarization. The scattering waves from conducting targets in random media can be estimated by a numerical method that solves the scattering problem as a boundary value problem. In this method, we use current generator and Green's function to obtain an expression for the scattering waves.

The electromagnetic scattering from a conducting cylinder coated with metamaterials, which have both negative permittivity and permeability, is derived rigorously by using the classic separation of variables technique. It is found that a conducting cylinder coated with metamaterials has anomalous scattering cross section compared to that coated with conventional dielectric materials. Numerical results are presented and discussed for the scattering cross section of a conducting cylinder coated with metamaterials.

In this paper new stability theorems for Yee's Finite- Difference Time-Domain (FDTD) formulation are derived based on the energy method. A numerical energy expression is proposed. This numerical energy is dependent on the FDTD model's E and H field components. It is shown that if the numerical energy is bounded, then all the field components will also be bounded as the simulation proceeds. The theorems in this paper are inspired by similar results in nonlinear dynamical system. The new theorems are used to prove the stability of a FDTD model containing non-homogeneous dielectrics, perfect electric conductor (PEC) boundary, nonlinear dielectric and also linear/nonlinear lumped elements. The theorems are intended to complement the well-known Courant-Friedrich-Lewy (CFL) Criterion. Finally it is shown how the theorems can be used as a test, to determine if the formulation of new lumped element in FDTD is proper or not. A proper formulation will preserve the dynamical stability of the FDTD model. The finding reported in this paper will have implications in the manner stability analysis of FDTD algorithm is carried out in the future.

Abstract-In this work, we study the reflection properties of coplanar waveguides (CPW) periodically loaded with shunt connected capacitances and periodically perturbed by varying the slot width. These structures are of interest because the low pass frequency response with spurious frequency bands, inherent to the presence of capacitors, can be improved. This is achieved through the attenuation of frequency parasitics that is obtained by the introduction of slot width modulation. Both sinusoidal and square wave patterns are considered and the effects of the relative position of reactive elements with regard to the perturbation geometry is analysed. According to coupled mode theory, the central frequencies of the rejected bands in periodic transmission media are given by the spectrum of the perturbation function. However, it is demonstrated that, due to the presence of capacitors, multiple spurious bands can be simultaneously suppressed even in the case of a singly tuned (sinusoidal) perturbation geometry. This result points out that the frequency selective behaviour associated to the presence of slot width modulation can not be interpreted in the framework of coupled mode theory, since the rejection of spurious bands in periodic loaded CPWs is not merely given by the spectrum of the perturbation geometry.

The homogenization of cubically arranged, homogeneous spherical inclusions in a background material is addressed. This is accomplished by the solution of a local problem in the unit cell. An exact series representation of the effective relative permittivity of the heterogeneous material is derived, and the functional behavior for small radii of the spheres is given. The solution is utilizing the translation properties of the solutions to the Laplace equation in spherical coordinates. A comparison with the classical mixture formulas, e.g., the Maxwell Garnett formula, the Bruggeman formula, and the Rayleigh formula, shows that all classical mixture formulas are correct to the first (dipole) order, and, moreover, that the Maxwell Garnett formula predicts several higher order terms correctly. The solution is in agreement with the Hashin-Shtrikman limits.

3-dimensional photonic bandgap structures working in the visible have been given increasing attention in recent years encouraged by the possibility to control, modify or confine electromagnetic waves in all three dimensions, since this could have considerable impact on novel passive and active optical devices and systems. Although substantial progress has been made in the fabrication of 3D Photonic crystals by means of nano-lithography and nanotechnology, it still remains a challenge to fabricate these crystals with feature sizes of the half of the wavelength in the visible. Self-assembling of colloidal particles is an alternative method to prepare 3-dimensional photonic crystals. The aim of this article is to show how to use colloidal crystals as templates for photonic crystals and how to monitor the changes of their optical properties due course of the modification.

In this work, we study a novel type of optical waveguide, whose properties derive from a periodic arrangement of fibers (not necessarily circular), and from a central structural defect along which the light is guided. We first look for propagating modes in photonic crystal fibers of high indexcore region which can be single mode at any wavelength [1-4]. Unlike the first type of photonic crystal fibers, whose properties derive from a high effective index, there exists some fundamentally different type of novel optical waveguides which consist in localizing the guided modes in air regions [4-5]. These propagating modes are localized in a low-indexstructural defect thanks to a photonic bandgap guidance for the resonant frequencies (coming from the photonic crystal cladding). We achieve numerical computations with the help of a new finite element formulation for spectral problems arising in the determination of propagating modes in dielectric waveguides and particularly in optical fibers [7]. The originality of the paper lies in the fact that we take into account both the boundness of the crystal (no Bloch wave expansion or periodicity boundary conditions) and the unboundness of the problem (no artificial boundary conditions at finite distance). We are thus led to an unbounded operator (open guide operator) and we must pay a special attention to its theoretical study before its numerical treatment. For this, we choose the magnetic field as the variable. It involves both a transverse field in the section of the guide and a longitudinal field along its axis. The section of the guide is meshed with triangles and Whitney finite elements are used, i.e., edge elements for the transverse field and node elements for the longitudinal field. To deal with the open problem, a judicious choice of coordinate transformation allows the finite element modeling of the infinite exterior domain. It is to be noticed that the discretization of the open guide operator leads to a generalized eigenvalue problem, solved thanks to the Lanczos algorithm. The code is validated by a numerical study of the classical cylindrical fiber for which the eigenmodes are known in closed form. We then apply the code to Low IndexPhotonic Crystal Fibers (LPCF) and to High IndexPhotonic Crystal Fibers (HPCF).

This paper deals with the use of Photonic Crystal (PC) structures as substrates in patch antenna configurations in order to mitigate the effect of the surface wave mode propagation. The case of a single antenna has been studied. A comparison between a conventional substrate based patch and a patch with a PC as substrate has been performed. The antennas were fabricated and measured. Improvements in all the main parameters of the antenna were obtained when usinga PC. The frequency dependence of the radiation patterns is significantly reduced when using a PC as substrate.

Photonic Band-Gapmaterials (PBG) are periodic structures composed of dielectric materials or metal. They exhibit frequency bands for which no propagation mode can propagate. Unfortunately, they are bulky and their period has to be at least a quarter wavelength. One extension of the PBG structures is called High impedance ground planes (High Z). Their period is much smaller and they exhibit frequency bands in which no surface wave can propagate. Their electromagnetic characteristics make them particularly interesting for antenna applications. On the one hand, they reduce the interaction between an antenna and its backward surroundings, with smaller size than usual ground planes. On the other hand, they can be used for planar antenna solutions, as the radiating element can be placed right on the top of the ground plane. After a presentation of the steps which lead to High Impedance ground planes, the electromagnetic characteristics of such ground planes are presented. Then, some antenna applications illustrate the interest of such structures.

This paper reviews recent advancements in the research and development of Uniplanar Compact Photonic Bandgap (UCPBG) structures for microwave and millimeter-wave applications. These planar periodic structures are particularly attractive and have been intensively investigated due to their easy fabrication, low cost, and compatibility with standard planar circuit technology. In this paper, basic properties of UC-PBG will be studied such as the slowwave effect, distinct stopband and passband, leakage suppression of surface waves, and realization of a magnetic surface. Owing to the different features of UC-PBG, these structures have been applied to microwave circuits to improve microstrip filters and patch antennas, to perform harmonic tuning in power amplifiers, to suppress leakage in conductor-backed coplanar waveguide, to realize TEM waveguides, and to implement low-profile cavity-backed slot antennas.

We have demonstrated guiding and bending of electromagnetic (EM) waves in planar and coupled-cavity waveguides built around three-dimensional layer-by-layer photonic crystals. We observed full transmission of the EM waves through these waveguide structures. The dispersion relations obtained from the experiments were in good agreement with the predictions of our waveguide models. We also reported a resonant cavity enhanced (RCE) effect by placing microwave detectors in defect structures. A power enhancement factor of 3450 was measured for planar cavity structures. Similar defects were used to achieve highly directional patterns from monopole antennas.

Metallo-dielectric electromagnetic bandgap (EBG) structures are studied in the millimeter regime with a finite difference time domain (FDTD) simulator. Several EBG waveguiding structures are considered for millimeter-wave power splitting, switching and filtering operations. It is demonstrated that triangular EBG structures lend themselves naturally to the design of Y-power splitters. Square EBG structures with circular and square rods are shown to lead naturally to straight in-line waveguide filter applications. Comparisons between EBG millimeter-wave waveguide filters formed with dielectric and metallic rods are given. It is shown that high quality broad bandwidth, millimeter-wave bandstop filters can be realized with square EBG structures with circular metallic rods. It is demonstrated that multiple bandstop performance in a single device can be obtained by cascading together multiple EBG millimeter-wave waveguide filters. It is also demonstrated that one can control the electromagnetic power flow in these millimeter-wave EBG waveguide devices by introducing additional local defects. It is shown that the Y-power splitter can be made reconfigurable by using imposed current distributions to achieve these local defects and, consequently, that a millimeter-wave EBG switch can be realized.

Abstract-Photonic Bandgap (PBG) materials have been investigated for their versatility in controlling the propagation of electromagnetic waves [1, 2]. In order to determine PBG structures responses, several analytical or numerical methods are used, such as:

• The plane wave method applied to solve Maxwell's equations [3].
• The transfer matrix method, based on the wire grating impedance developed by N. Marcuvitz [4].
• The Finite Element Method (FEM) exhibits, e.g., the frequency response of reflection and transmission coefficients of the PBG materials when they have infinite surfaces and are excited by plane wave. The FEM method can be also used in the case of finite structure fed by a dipole.
• solves the discretized Maxwell's equations in the time domain and evaluates the electromagnetic field components. These EM fields are then obtained in the frequency domain thanks to a Fourier Transform.

First of all, we present a parametrical study using a 3D Finite Element method software. This study allows to estimate the role of any parameters on the reflection and transmission coefficients and then to design a PBG structure in the X-band (8-12 GHz). Continuous and discontinuous structures are presented. Then, we present a numerical analysis of PBG structures, using the FDTD method in order to understand the propagation phenomena in these periodic materials.

Since the first demonstration of a complete photonic band gap by E. Yablonovitch in 1987 [1], photonic band gap materials have attracted a very significant interest in Electromagnetism but also in Solid State Physics. Doped photonic crystals that have a point defect (a local disturbance) have been extensively studied with the emergence of this new area of Physics. They present localized modes in the band gap and triggered many potential applications. Fewer papers have been devoted to strongly disordered photonic crystals that are periodic on the average. These structures are disturbed on the overall feature and the defect corresponding is referred to as extended. Analogue at a first glance to amorphous semiconductors, these materials could present interesting properties. Moreover, manufacture of photonic crystals is still a real challenge for the optical domain and undesirable extended defects can appear leading to a compulsory study of the tolerances of periodicity for such new materials.

Based on the eigenvalue equations of vector fields ⃗E and ⃗H by extending Bloch theorem to the vector field Maxwell equations, the characteristics of 2-D dielectric rod array with square cross-section elements arranged in square lattice is analyzed in detail. From the numerical results, empirical expressions for both the relative bandwidth of frequency band gap and the midgap frequency with respect to the average permittivity, under the optimal filling fraction of dielectric/air in cross-section for wider bandwidth, are formulated by means of data fit.

We present an original study which makes use of a convenient representation of the dispersion diagrams of Bloch modes for the design of angular selective sources. These diagrams provide us all the pertinent information about the radiative properties of the photonic crystal, and a guideline to optimize the structure in order to obtain the suitable properties. We apply these tools in two cases: when the radiated field propagates normally to the device, and also for an off-axis radiating device. Several numerical examples obtained from a rigorous numerical method show the relevance of this approach.