Selected Topics in Photonic Crystals and Metamaterials

The following sections are included:

• FOREWORD

• PREFACE

• CONTRIBUTORS

• CONTENTS

Photonic crystals have the fundamental characteristic of manipulating light at a scale on the order of the wavelength or even shorter. This property allows to develop new functional devices for a wide range of applications. PhCs have been investigated, both theoretically and experimentally, for telecom devices and sensing because of their peculiar properties, such as the capability of realizing high Q-factor cavities, enhancing field-matter interaction and controlling the group velocity. In this chapter the basic physics of photonic crystals, with specific reference to the origin of the photonic band gap, and their main applications are reviewed. A brief description of fundamentals of metamaterials and their applications is also reported in the chapter.

In this chapter, we review the salient results of our recent investigations on in-plane wave propagation in photonic quasi-crystals. Via full-wave numerical simulations and microwave measurements, we illustrate the band-gap, mode confinement, and focusing properties of two-dimensional structures made of dielectric or metallic cylindrical rods arranged according to diverse aperiodic-tiling geometries.

This chapter deals with the out-of-plane electromagnetic wave propagation in aperiodically-ordered "photonic quasi-crystals" (PQCs). With specific reference on PQC slabs based on the quasi-periodic, 8-fold-symmetric Ammann-Beenker geometry, we review a body of results from our recent studies. More specifically, we study via full-wave numerical simulations the excitation of "guided resonances" in defect-free and point-defected supercells, by looking at the transmittance response for normally-incident plane-wave excitation as well as at the modal structure, and highlighting similarities and differences with respect to the standard periodic case. Finally, we address the fabrication-related issues, and present some preliminary experimental results at infrared wavelengths.

The theory of optical forces and binding of a cluster of Rayleigh particles is presented in detail. The time averaged optical force acting on a Rayleigh particle is derived using a classical theory. A comprehensive account of the theory of optical forces and binding of a collection of particles is then given, with due consideration of the light scattering among the particles. While the light induced forces are in general non-conservative, an effective potential energy can be derived under the single scattering approximation for an incident standing wave. We then briefly discuss the optical forces and binding of microparticles whose sizes are beyond the Rayleigh regime.

This chapter describes electromagnetic properties of 1D- and 2D-periodic arrays of metallic nanospheres that support plasmonic modes. Current fabrication possibilities are reported, and a simple formulation to analyze array electromagnetic properties is summarized. We review these properties, provide information about mode propagation in the array plane, and we analyze transmissivity, reflectivity and absorption when the array is illuminated by a plane wave, as well as the extinction cross section. Last, we summarize possible applications of arrays of plasmonic nanoparticles.

The 3D regular lattice of bi-spherical dielectric resonant inclusions arranged in a cubic lattice as two sets of spheres made from the same dielectric material having different radii and embedded in a host dielectric material with lower dielectric permittivity was carefully investigated. The magnetic resonance corresponding to the first Mie resonance in the spherical particles is achieved by forming a regular array of effective magnetic dipoles, and the structure of the identical spherical dielectric resonators can be designed as an isotropic µ-negative 3D-metamaterial. For the electric resonance it was found experimentally and by simulation that the resonant response of the electric dipole is weakly pronounced and the ε-negative behavior is remarkably suppressed. To enhance the electric dipole contribution we considered another kind of the symmetry of the bi-spherical arrangement of the particles corresponding to the face-centered cubic symmetry instead of the symmetry of NaCl analogue considered previously. Electromagnetic properties of a volumetric structure based on a regular lattice of identical cubic dielectric particles are also considered and analyzed as µ-negative metamaterial. The cubic particle based 3D-metamaterial is preferable for practical realization as compared with the spherical inclusions. For practical realization of all dielectric metamaterial the limitation of the dielectric permittivity of spherical inclusions should be taken into account. It is shown that to get double negative behavior of bi-spherical metamaterial, resonators with permittivity higher than 100 should be used. The same estimations could be made for rod, cylindrical resonators or any kind of dielectric resonators used as components for metamaterial design.

Electromagnetic Band-Gap (EBG) materials are periodic structures with properties of confinement and filtering of electromagnetic radiation. In this work, EBGs with a simple geometry are considered, as periodic one-dimensional multilayers, and their design is presented. When the periodicity of such structures is interrupted, evanescent modes can be localized. The particular case of a periodicity break along a plane is considered in this chapter. A cavity made of two identical mirrors separated by an air-filled spacing is studied, moreover its equivalent layout obtained from the image theory is analyzed. An interesting application to directivity enhancement of planar antennas is devised. All the numerical results reported here are obtained by using a commercial software implementing the finite-element method.

We review some recent applications of changes of coordinate systems applied to the design of a novel class of metamaterials: invisibility cloaks, rotators and concentrators. These heterogeneous anisotropic media allow for a markedly enhanced control of the electromagnetic waves.

We review here some of the salient features of the plasmonic cloaking technique, which uses the anomalous properties of plasmonic metamaterial layers to suppress and cancel the scattering from a dielectric or conducting object. In particular, we focus our attention on penetrable obstacles, for which the peculiar properties of this technique ensure that the cloaked regions are not necessarily isolated from the surrounding. This may enable to exploit one of the most intriguing applications of plasmonic cloaking: the possibility to sense the surrounding from within the cloak, lowering a receiving system's scattering and near-field disturbance, without necessarily affecting its capability to measure and "sense" the external world. In other words, the plasmonic cloak may allow external fields to penetrate into the cover, but it may at the same time ensure the suppression of most of the reaction and scattered fields from the sensor. This may allow "sensing" the external world, or receive an external signal, from inside the cloak in a variety of schemes of interest for near-field sensing and imaging. We review here the main applications of this technique to several scenarios of interest, and some of their connections with anomalous scattering mechanisms and cloaking scenarios.

In this chapter, we review the theoretical analysis and the design principles of electromagnetic cloaking devices working both at microwaves and optical frequencies. The cloaking approach we use is based on the scattering cancellation principle, applied not only to canonical geometries but also to irregularly-shaped objects with anisotropic scattering response. The cloaking devices are synthesized through plasmonic or metamaterials conformal covers, coating a given object, providing a significant and uniform scattering reduction of the overall structure, independent of the angle of incidence, position and polarization of the illuminating electromagnetic radiation. The robustness of the invisibility cloak is also discussed, proposing a proper figure of merit and validating the theoretical formulation and the design procedure through full-wave numerical simulations. The simulation results confirm that the plasmonic cloaking technique may be effectively applied to highly reduce the scattered field of even strongly anisotropic dielectric, plasmonic or conducting objects.

A theory of nonradiating cancelling (NRC) currents is formulated in order to derive sufficient conditions for cloaking on the dyadic constitutive parameters of an anisotropic linear metamaterial of arbitrary shape illuminated by arbitrary sources. The link between the NRC current theory and the constitutive parameters of the cloak is established by applying the volumetric equivalence theorem. The constitutive parameters are eventually found as a function of two vector potentials satisfying simple boundary conditions. Two-dimensional and three-dimensional transformation optics cloaks are derived as particular cases of the general formulation.

Photonic crystal surfaces provide a wide range of functions that are useful for the detection of biological analytes. Label-free detection, label-free imaging, and enhancement of fluorescence assays take advantage of the ability of periodic surface structures with high refractive index contrast to strongly confine light to a surface, where it can interact with biomaterials in a variety of ways. Applications in pharmaceutical research, disease diagnostics, cell biology, and genomics are all actively being pursued.

Quantum computing has progressively become a concrete reality. This led to the need of developing q-bit high efficiency integrated sources. This paper deals with the design of a planar device able to generate twin photons through the nonlinear process of Spontaneous Parametric Down Conversion (SPDC). The aim of the device is to enhance the efficiency of the SPDC process through an integrated micro-cavity resonant structure.

The ability to slow and even stop-light is crucial for the realization of all-optical integrated circuitry. In this chapter we present a design approach for realizing slow-light devices in the microwave band of frequency. Slow light can be achieved in a simple planar waveguide cladded with single negative metamaterial. Our device consists of a planar waveguide having a dielectric core and a negative permeability metamaterial. The negative permeability is obtained by arranging periodically split ring resonators (SRRs). We introduce a theoretical model, valid for both TE and TM modes, which describes light propagation in planar waveguides with single negative cladding, then we propose a prototype structure for TE mode working at 9.87GHz. The current design strategy relies on numerical simulations of the electromagnetic properties of SRRs which provide the scattering parameters. A parameters retrieval method has been used to extract the design window for the permeability and the permittivity.

Structured optical fibres are commonplace within optical research since many phenomena can, in the first instance, be localised and studied with greater ease within the confines of an optical waveguide, seemingly offering many alternative approaches to other existing technologies. However, this apparent ease has not translated to actual technology penetration beyond a few (but important) niche areas, with their superiority over existing technologies being unclear. Here, the linear and nonlinear properties possible with these structured fibres is reviewed and evaluated, both from a scientific and applied perspective. A case for citing complex and multiple functionality as an important motivation leading to future new technology is presented.

In this chapter, the role of complex artificial structures in enhancing the power transmission through sub-wavelength apertures is discussed. Such devices are aimed at exciting highly localized resonances in order to increase the aperture equivalent magnetic and electric dipole moments. Some examples, based on epsilon-near-zero metamaterials (ENZ), frequency selective surfaces (FSSs) and split-ring resonators (SRRs) at microwaves, and silver nano-particle pairs at terahertz scale, are presented. Such structures may find applications in different fields, such as high-resolution spatial filters, ultra-diffractive imaging systems, high-capacity optical memories, enhanced light throughput tips for near-field scanning optical microscopes, etc.

In this article, material preparation, structures, and related nanofabrication technologies for the 2D and 3D photonic crystals are briefly reviewed. This article will mainly deal with semiconductor-based 2D hole slabs and 3D top-down etch structures (e.g., Yablonovite) and piled-up structures, which can be defined by electron beam lithography with vertical dry-etching.

Many research efforts are devoted to conceive, develop and fabricate new devices able to exploit the unattended physical properties coming from the collection of one or more materials arranged in a specific pattern. Nevertheless, the renewed interest towards metamaterials and photonic crystals mainly comes from recent advances in nanofabrication techniques that allow different materials to be structured on the nanometer scale.

The authors present in this chapter an introductory survey of the main fabrication techniques employed for manufacturing metamaterials and photonic crystals. Particular emphasis is devoted to nanofabrication techniques including standard photolithography, interferometric lithography techniques, electron-beam lithography, focused-ion beam lithography, soft lithography, multi-spacer patterning and self-assembly techniques. Advantages, drawbacks and challenges are also outlined.