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Vol. 41

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PIER Vol. 41, 307-335, 2003. doi:10.2528/PIER02010894

Three Dimensional Photonic Crystals in the Visible Regime

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.

PIER Vol. 41, 271-305, 2003. doi:10.2528/PIER02010893

Numerical and Theoretical Study of Photonic Crystal Fibers

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).

PIER Vol. 41, 257-269, 2003. doi:10.2528/PIER02010891

Simulated and Measured Performance of a Patch Antenna on a 2-Dimensional Photonic Crystals Substrate

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.

PIER Vol. 41, 237-255, 2003. doi:10.2528/PIER02010892

Antennas on High Impedance Ground Planes: on the Importance of the Antenna Isolation

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.

PIER Vol. 41, 211-235, 2003. doi:10.2528/PIER02010890

Analysis and Applications of Uniplanar Compact Photonic Bandgap 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.

PIER Vol. 41, 185-209, 2003. doi:10.2528/PIER02010808

Microwave Applications of Photonic Crystals

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.

PIER Vol. 41, 159-183, 2003. doi:10.2528/PIER02010807

FDTD Simulations of Reconfigurable Electromagnetic Band Gap Structures for Millimeter Wave Applications

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.

PIER Vol. 41, 133-157, 2003. doi:10.2528/PIER02010806

Numerical Studies of Metallic PBG Structures

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.

PIER Vol. 41, 107-131, 2003. doi:10.2528/PIER02010805

Numerical Studies of Disordered Photonic Crystals

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.

PIER Vol. 41, 83-106, 2003. doi:10.2528/PIER02010804

Study on Bandwidth of 2-D Dielectric PBG Material

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.

PIER Vol. 41, 61-81, 2003. doi:10.2528/PIER02010803

Dispersion Diagrams of Bloch Modes Applied to the Design of Directive Sources

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.

PIER Vol. 41, 21-60, 2003. doi:10.2528/PIER02010802

Rayleigh Multipole Methods for Photonic Crystal Calculations

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.

PIER Vol. 41, 1-20, 2003. doi:10.2528/PIER02010801

An Introduction to Photonic Band Gap (PBG) Materials

Geraldine Guida, Andre De Lustrac, and Alain C. Priou

This paper introduces photonic band gap (PBG) materials that are periodic dielectric or metallo-dielectric materials conceived to control the propagation of electromagnetic waves. Firstly, the principle of these materials is explained. Doped PBG materials are then presented with their main properties and applications. New phenomena like super-prism or super-lens are also introduced. A review of different numerical methods used to study photonic band gap materials and to analyze their properties is given next. Manufacturing processes are then briefly described and foreseen applications are presented. Finally, the new field of the controllable photonic band gap materials is introduced.