Introduction

The electromagnetic (EM) wave propagation within a given material mainly depends on its constitutive parameters, viz. permittivity (ε), permeability (ε) and thickness of material. In macroscopic sense, these parameters describe the effects of induced electric and magnetic polarisations within the medium. These constitutive parameters can have either negative or positive values. The negative permittivity and permeability are known to be associated with the metamaterials (Veselago 1968). A metamaterial can be epsilon negative index (ENG) or mu negative index (MNG) or double negative index (DNG) materials (Shelby et al. 2001). Various analytical methods have been proposed for the plane wave analysis of EM propagation within the multilayered structures (Ziolkowski and Heyman 2001), (Kong 2002), (Cory and Zach 2004). The EM propagation within such materials exhibits negative refraction and other interesting propagation phenomena. The characteristic reflection/transmission behaviours of dielectric-metamaterial coatings have strategic applications towards the control of radar signatures of aerospace structures and, hence, low-observable platforms.

In this chapter, a systematic description of EM propagation through layered media is presented. These multilayered media include both dielectric–dielectric and dielectric-metamaterial media. The dielectric media is taken to be homogeneous. For a plane EM wave incident on planar layers having different dielectric and magnetic parameters, the reflected and transmitted fields are determined. The EM propagation within the layers is explained in terms of reflection/transmission from different types of media. This includes semi-infinite media, dielectric layers with finite thickness and lossy dielectric layers. The presence of absorption in a lossy medium is taken into account by the complex nature of wave numbers. The reflective behaviour of the multilayered media with respect to the frequency of the incident EM wave, thickness and constitutive parameters of the layers is discussed. A proper choice of design parameters would facilitate the design and development of radar-absorbing material (RAM) coatings.

EM propagation in classical multilayered media

In this section, the basic expressions for the impedance of multilayered medium, the Fresnel's coefficients for reflection and the transmission for parallel and perpendicular polarisations are discussed. The EM propagation is expressed in terms of these coefficients.

Introduction

The rapid development of research on plasmonics in recent years has led to numerous interesting applications, and many plasmonic nanostructures have been designed and fabricated to achieve novel functionalities and/or better performance. For example, optical antennas are used for biochemical sensing [1–4], plasmonic waveguides have been proposed for on-chip optical communications [5], and metamaterials are under consideration for subwavelength imaging [6]. Most of those plasmonic nanostructures are complicated, so we cannot find analytical solutions for them. Therefore numerical modeling methods are the only choice when it comes to device modeling and structural design. Many numerical methods for solving Maxwell's equations have been established. They can be generally categorized into two classes: frequency-domain methods and time-domain methods.

In frequency-domain methods we assume that the electromagnetic wave is a single-frequency harmonic wave with a time dependence term eiωt or e−iωt (most electrical engineers use eiωt, while e−iωtis more popular among physicists. They are essentially the same, except that, when a medium is lossy, the imaginary parts of its refractive index and permittivity take positive values for e−iωt and negative values for eiωt). Then the time dependence in Maxwell's equations can easily be eliminated and the fields are functions solely of space coordinates. The solutions obtained from frequency-domain methods are generally steady-state solutions. There are many frequency-domain methods available for plasmonic device modeling, among which the finite-element method (FEM) and the method of moments (MoM) are very popular.

In this chapter, the finite-difference time-domain method (FDTD) is developed and implemented for the modeling and simulation of passive and active plasmonic devices. For the simulation of passive devices, the Lorentz–Drude (LD) dispersive model is incorporated into the time-dependent Maxwell equations. For the simulation of active plasmonics, a hybrid approach, which combines the multilevel multi-electron quantum model (to simulate the solid state part of a structure) and the LD dispersive model (to simulate the metallic part of the structure), is used. In addition, the multilevel multi-electron quantum mode (solid-state model) is modified to simulate the semiconductor plasmonics. For numerical results, the methodologies developed here are applied to simulate nanoparticles, metal–semiconductor–metal (MSM) waveguides, microcavity resonators, spasers, and surface plasmon polariton (SPP) extraction from spaser. To enhance the simulation speed, graphics processing units (GPUs) are used for the computation, and, as an example, an application of a passive plasmonic device is examined.

Introduction

The diffraction limit was a challenge in the miniaturization of photonics devices, which restricted the minimum size of a component to being equivalent to λ/2. The new emerging ield of plasmonics has recently made it possible to overcome the diffraction limit of photonic devices. In plasmonics, the wave propagates at the interface of a metal and dielectric, and remains bounded. This feature allows the miniaturization of photonics devices below the diffraction limit. Some plasmonic structures, which guide and manipulate the electromagnetic signals, have been presented in the literature [1–7].

To detect an analyte, surface plasmons whose characteristics are sensitive to the refractive-index variations close to the sensor's surface are excited and measured. Binding of the target analyte onto the sensor's surface will cause changes in refractive index and hence in the measured plasmonic characteristics. Depending on what type of surface plasmon is excited (e.g. surface plasmon polariton (SPP), Fano resonance), which plasmonic characteristic is measured/modulated (e.g. resonance wavelength, transmitted light intensity), and in what manner the bio-functionalization (i.e. binding of the target analyte) is performed, there are many different configurations for plasmonic biosensors, which will be reviewed in this chapter. The ultimate goal is to increase the sensor's sensitivity and the figure of merit. To achieve this goal, one must first understand the physics of the resonances, and then implement a smart structural design. In this chapter, two design methods will be introduced: an N-layer model and a finite-element-method (FEM) model, which are further elaborated by presentation of three biosensor design examples.

Introduction

A biosensor is a device for detecting an analyte, which typically combines a biological component with a physiochemical detector. For instance, a blood-glucose biosensor uses the enzyme glucose oxidase to break blood glucose down. In doing so it first oxidizes glucose and uses two electrons to reduce the FAD (a component of the enzyme) to FADH2. Then the FADH2 is oxidized by accepting two electrons from the electrode.

Plasmons, being the electromagnetic eigenoscillations of intrinsic charges, play an important role in the electrodynamics of metals and determine the main optical properties of metal structures. Following the classification given in Section 1.3.1, there are two types of plasmons – longitudinal and transverse. Both types are inherent to any metal and appear equally in metal structures. Longitudinal plasmons define the optical response of metals to conservative fields, while transverse plasmons define the response to solenoidal fields. Therefore, transverse plasmons are more attractive for optical applications, since they provide resonant interaction with photons, in contrast to longitudinal plasmons, which require very specific conditions, such as certain electron density profiles or applied external magnetic/electric fields, in order for them to interact with photons. In this chapter, we consider transverse plasmons supported by different metal nanostructures in spherical, cylindrical, and planar geometries. By solving eigenvalue and scattering problems, we discuss the properties of these plasmons and study their coupling with incident photons.

Plasmonic modes in spherical geometry

In this section, we consider the transverse eigenmodes supported in structures with spherical geometry. Within the vector spherical-harmonics formalism, we study the plasmonic modes of a metal sphere and a spherical cavity in a bulk metal. Also, we investigate the scattering of plane waves by metal nanoparticles and make a generalization for the case of a multilayer sphere.

Data communication and information processing are driving the rapid development of ultra-high speed and ultra-compactness in nano-photo-electronic integration. Plasmonics technology has in recent years demonstrated the promise to overcome the size mismatch between microscale photonic and nanoscale electronic integration, and it likely will be crucial for the next generation of on-chip optical nano-interconnects, enabling the deployment of small-footprint and low-energy integrated circuitry.

The phenomenon of surface plasmons was first observed in the Lycurgus cup, which is a Roman glass cage cup in the British Museum, London, UK. This special cup is made of a dichroic glass that shows a different color depending on the condition of illumination. Specifically, in daylight, the cup appears to have a green color, which means that light is being reflected from the cup; however, when a light is shone into the cup and transmitted through the glass, it appears to have a red color. Today, we know that this fascinating behavior is due to nanoscopic-scale gold and silver particles embedded in the glass. However, it took 1500 years and doubtless countless fantastic interpretations for a plausible explanation to emerge. In the last few decades, the phenomenon of surface plasmons has been extensively studied both theoretically and experimentally, and there have been attempts to use it for various applications ranging from solar-cell energy and sensing to nanophotonic devices.

This chapter presents the hybrid plasmonic waveguide (HPW) platform and its components. In particular, the effective mode index, propagation distance, and mode confinement of the planar vertical hybrid plasmonic waveguides (VHPWs) are numerically characterized as functions of dimensions and materials in the near-infrared wavelengths. The chapter demonstrates that the vertical hybrid silver–silica–silicon plasmonic waveguide achieves better propagation characteristics than those of the counterpart silver–silica–silver MIM and silicon-based dielectric-loaded plasmonic waveguide. Moreover, we propose and design various passive waveguide-based components based on the optimized VHPW, including bends, power-splitters, couplers, and ring resonator filters. An important issue is how to implement these HPW-based components and devices in standard complementary metal–oxide–semiconductor (CMOS) electronic–photonic integrated circuits. To meet this requirement, two CMOS-compatible HPW platforms, namely a copper-cap VHPW and a hybrid horizontal copper–silicon dioxide–siliconsilicon dioxide–copper plasmonic waveguide, and devices based on them such as bends and ring resonator filters are subjected to further investigation both in experiments and in theory in the subsequent sections.

Introduction

In the context of communications and information processing, integration of photonic and nanoelectronic devices on the same chip would lead to a tremendous synergy by combining the ultra-compactness of nanoelectronics with the super-wide bandwidth of photonics. Such integration will benefit considerably from the application of nanotechnology for data-processing, sensing, medical, health-care, and energy purposes. In recent years, it has been demonstrated theoretically and experimentally that plasmonic devices, taking advantage of plasmon-enabled tight modal confinement, promise to overcome the size mismatch between microscale photonics and nanoscale electronics.