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.

Multipole methods have evolved to be an important class of theoretical and computational techniques in the study of photonic crystals and related problems. In this chapter, we present a systematic and unified development of the theory, and apply it to a range of scattering problems including finite sets of cylinders, two-dimensional stacks of grating and the calculation of band diagrams from the scattering matrices of grating layers. We also demonstrate its utility in studies of finite systems that involve the computation of the local density of states.

In this paper, a new computational technique is presented for the first time. In this method, physical differential equations are incorporatedin to interpolations of basic element in finite element methods. This is named physical spline finite element method (PSFEM). Theoretically, the physical spline interpolation introduces many new features. First, physical equations can be usedin the interpolations to make the interpolations problem-associated. The algorithm converges much faster than any general interpolation while keeping the simplicity of the first order Lagrange interpolation. Second, the concept of basis functions may need to be re-examined. Thirdly, basis functions could be complex without simple geometric explanations. The applications to typical one-dimensional electromagnetic problems show the great improvements of the newly developed PSFEM on accuracy, convergence andstabilit y. It can be extendedto other applications. Extension to two- andthree-d imensional problems is briefly discussed in the final section.

The usual aim with any waveguide is to operate it with only the fundamental mode propagating. With fully closed waveguides, finding the band over which this is possible turns on no more than knowledge of the cutoff frequencies of the fundamental and first higher order modes. With open waveguides, the question is not so simply answered. Such waveguides propagate at most a finite set of bound modes together with a continuous modal spectrum that has no counterpart with closed guides. In this paper, for several particular two-conductor transmission lines, we investigate the circumstances under which leaky wave modes, though not themselves members of any orthonormal set of basis functions, can be used to set bounds on the band over which it is to be expected that the transmitted field is substantially contained in the fundamental TEM mode. The method used relies on transverse resonance.

Abstract-The paper deals with the modeling, based on the Finite Difference Time Domain method, of active one- and twodimensional photonic crystals. The onset of laser oscillation is observed by simulating the active substance as having a negative frequency-dependent Lorentzian-shaped conductivity so including into Maxwell's equations an electric current density. Particular attention is devoted to the implementation of uniaxial perfectly matched layer absorbing boundary conditions for the simulation of infinitely extending structures having gain features. Laser behaviour is simulated as a function of various parameters; the threshold wavelengthand conductivity are evaluated as the wavelengthand conductivity where the transmittance diverges. Moreover, the properties of the active two-dimensional photonic band gap structures are given in terms of a Q quality factor which increases by increasing the crystal size and strongly depends on the lattice shape. For the square lattice, when the crystal size increases from N = 2 to N = 8 the Q-factor increases by about an order of magnitude (from 0.027 to 0.110) for TE polarization while for TM polarization it decreases from 0.025 to 0.022. At last the Q-factor pertaining to the chess-board lattice, to parity of other parameters, assumes greater values and already for N = 4, it reaches the values obtained for the 16×8 square lattice, for bothTE and TM polarizations.

It is shown that in hyperbolic spaces, an electromagnetic radiation experiences shifts in spectrum as a function of curvature and distance. The equation relating distance in hyperbolic space, its curvature, and spectral shift is derived by method of horospheres. The active nature of the Lobachevskian vacuum is discussed with applications to physics.

Propagation of waves in circular waveguide withth e boundary condition of hard surface is considered. The waveguide is filled with uniaxial chiral material. This study is a generalization of previously studied cases withisotropic chiral or anisotropic material filling. The eigenvalue equation is formed and the corresponding eigenmodes are presented. It is seen that the hard surface boundary condition simplifies the field analysis remarkable. While the eigenwaves in anisotropic waveguide were TE and TM fields in this more general case the eigenwaves are elliptically polarized hybrid fields. Since the eigenwaves are certain combinations of TE and TM fields and propagate withdifferen t propagation factors, uniaxial chiral medium can be used for polarization transformation. Reflection and transmission from a uniaxial chiral section of a waveguide is analyzed withn umerical examples.

An analytical model of a grid composed of small S-shaped conducting particles located on the surface of a dielectric slab is presented. This approach replaces the original one-layer structure with metallic particles printed on the interface by a multilayered structure with homogenized permittivities for each layers. This way one can homogenize the arrays of small resonant particles. The analytical model is verified by numerical simulations for the case of normal incidence of the plane wave. The homogenization is possible due to the small sizes of S-particles compared to the resonant wavelength in the substrate and due to the small thickness of the whole structure.

We consider oscillations in cylindrical slotted resonators formed by combinations of rectangular domains with several slots cut in the walls using the methods of approximate semi-inversion of integral operator-valued functions with a logarithmic singularity of the kernel. The initial boundary value problems for the Helmholtz equation are reduced to Fredholm integral equations and systems of integral equations of the first kind with a logarithmic singularity. In the case of narrow slots, the dispersion equations are obtained and evaluated using perturbations and the small-parameter method. Eigenfrequencies and eigenfields are calculated explicitly. The values of geometrical and material parameters are determined that lead to the interaction of oscillations. The results obtained are used for improving the design of filters and switches on the basis of simple model prototype structures.

A Combined Genetic Algorithm and Method of Moments design methods is presented for the design of unusual near-field antennas for use in Magnetic Resonance Imaging systems. The method is successfully applied to the design of an asymmetric coil structure for use at 190 MHz and demonstrates excellent radiofrequency field homogeneity.

This paper presents an improved variant of timedomain method for predicting crosstalk on parallel-coupled matched terminated microstrip lines. This method derives simple near-end and far-end time-domain crosstalk expressions which are applicable to lossless case with significant harmonic frequency < 1 GHz. The expressions are in polynomial form with geometrical dimensions of the structure and stimulus information as the only required entry parameters. They are simpler as compared to other methods because the difficult-to-determine distributed RLCG electrical parameters of the coupled lines are not needed. A look-up table for the polynomial coefficients is generated for easy application of this technique. The expressions are applicable for board thickness of 4-63 mils, 30-70Ω line characteristic impedance, 0.5W-4.0W (where W is the line width) inner edge to edge separation, and 3-5 dielectric constant. For significant harmonic frequency > 1 GHz, the effect of both losses and dispersion on the crosstalk levels is accounted for by investigating the gradient of the distorted driving signal. The peak crosstalk levels are then predicted by modifying the time derivative term in the lossless expressions. In addition, the far-end crosstalk is proved to saturate at half of the magnitude of the driving signal entering the active line. The saturation phenomenon is studied from the viewpoint of difference in odd-mode and even-mode propagation velocities.

The paper deals with proposition and evaluation of new and specific methods to represent vector radar data acquired by means a side-looking measurement in order to use compression process of Lind, Buzo, Gray (LBG), and Kohonen's self organizing feature maps of topology. The aim is to enable after coding, transmission, and decoding a high-resolution reconstruction image using the Synthetic Aperture Radar (SAR) methods. The approach proposed for compression uses the statistical properties of the signals to be compressed in order to perform the vector quantification in an optimal way.

A new synthesis algorithm for shaped, double-reflector antennas with complex array feed is presented. The approach presented here aims to improve the efficiency of synthesis techniques without missing the required accuracy. The algorithm is based on a convenient splitting of the original problem into two phases, each one involving a sub-problem significantly simpler than the original one. A double reflector synthesis problem involving only Fourier Transform (FT) operators is of concern during the first phase. The subre- flector surface and a first estimate of the main reflector geometry are obtained in this step. A single reflector synthesis problem is considered during the second phase wherein the final main reflector surface and the excitation coefficients of the primary feed array are obtained. While in the first phase only approximate relationships between the unknowns and the secondary radiated field are exploited, in the second phase accurate radiation operators are involved. Despite this accuracy, the second phase is still numerically effective since it involves a single reflector synthesis problem and exploits, as "good" starting point, the main reflector estimate obtained during the first phase. The effectiveness of the approach is due to the fact that the necessity of dealing simultaneously with two reflector surfaces, the key of the synthesis difficulties, is afforded only during the first phase where efficient computational tools are allowed. A numerical example shows the effectiveness of the proposed approach.

Dyadic Green's functions for inhomogeneous parallel-plate waveguides are considered. The usual residue series form of the Green's function is examined in the case of modal degeneracies, where secondorder poles are encountered. The corresponding second-order residue contributions are properly interpreted as representing "associated functions" of the structure by constructing a new dyadic root function representation of the Hertzian potential Green's dyadic. The dyadic root functions include both eigenfunctions (corresponding to first-order residues) and associated functions, analogous to the idea of Jordan chains in finite-dimensional spaces. Numerical results are presented for the case of a two-layer parallel-plate waveguide.