Introduction

In this chapter we discuss wave propagation in anisotropic media. We shall see that in such media the electric vector of a propagating wave is not in general parallel to its polarization direction, which is defined by the direction of its electric displacement vector. Further, for propagation of plane waves in a particular direction through an anisotropic medium two distinct possible polarization directions exist, and waves having these polarization directions propagate with different velocities. We shall discuss an ellipsoidal surface called the indicatrix and show how with its aid the allowed polarization directions and their corresponding refractive indices can be determined for wave propagation in a given direction. Other three-dimensional surfaces related to the indicatrix and their use in describing different optical properties of anisotropic media are also discussed. We shall concentrate our attention primarily on uniaxial crystals, which have optical properties that can be referred to an indicatrix with two equal axes, and will discuss how such crystals can be used to control the polarization characteristics of light.

Important anisotropic optical media are generally crystalline, and their optical properties are closely related to various symmetry properties possessed by crystals. To assist the reader who is not familiar with basic ideas of crystal symmetry, Appendix 8 summarizes a number of aspects of this subject that should be helpful in reading this chapter and some of those succeeding it.

Introduction

Many important laser systems operate using molecular species. The laser transition occurs between energy levels of the molecule, which may be in the gaseous, liquid, or solid state. To understand more about molecular lasers it is important to consider the additional complexity of the energy-level structure of a molecule compared with that of an atom. In this chapter we will explain the three different kinds of energy level – electronic, vibrational, and rotational – which occur for molecular species, and then go on to explain how such a complex energy-level structure allows the possibility of laser oscillation over a very broad wavelength range.

The energy levels of molecules

Electronic energy states

In an atom, the orbiting electrons move in the spherically symmetric potential of the nucleus, and the various energy levels of the system correspond, in a simple sense, to different orbital arrangements of these electrons. For example, an excited electron frequently moves into an orbit that takes it further from the nucleus. In a molecule the electrons travel in orbits that surround all the nuclei of the molecule, although quite often there will be considerable localization of some electrons near a particular nucleus. The electronic energy states of the molecule result from different arrangements of the orbiting electrons about the nuclei. Electrons that move from one electronic energy level of a molecule to another experience changes in energy that are broadly comparable to such jumps in atoms.

Introduction

Practical photonic systems can conveniently be divided into four distinct parts: (a) the optical source (or sources), (b) a passive optical structure, (c) an active optical structure, and (d) a detection system. A good example of such a system is the human eye, which is shown schematically in Fig. 13.1. In this system the source of light is the Sun, or artificial lighting that renders objects visible to the eye. The passive optical structure includes the cornea, the intraocular fluid, and other fixed structures in the eye. The active optical structure includes the deformable eye lens, whose shape is controlled by the ciliary muscles, and the iris, whose diameter is adjusted to control the amount of light entering the eye. The detector in this system is the retina, where photons are absorbed by special molecules, leading to chemical reactions that produce charges and subsequent electrical signals to the brain along the optic nerve.

We have already explored in some detail the fundamental physics, constructional details, and properties of lasers.We have also seen the connection between the amplifying medium and the optical structures that turn the laser amplifier into an oscillator. In this and the following chapters we will further examine the characteristics of various passive and active optical structures that are important in photonic systems. Initially we will discuss the characteristics of important passive optical components and systems. These will include optical materials, lenses, mirrors, prisms, diffraction gratings, interferometers, crystals, polarizers, and optical fibers.

Introduction

In this chapter we shall examine some of the characteristics of laser radiation that distinguish it from ordinary light. Our discussion will include the monochromaticity and directionality of laser beams, and a preliminary discussion of their coherence properties. Coherence is a measure of the temporal and spatial phase relationships which exist for the fields associated with laser radiation.

The special nature of laser radiation is graphically illustrated by the ease with which the important optical phenomena of interference and diffraction are demonstrated using it. This chapter includes a brief discussion of these two phenomena with some examples of how they can be observed with lasers. Interference effects demonstrate the coherence properties of laser radiation, while diffraction effects are intimately connected with the beam-like properties that make this radiation special.

Diffraction

Diffraction of light results whenever a plane wave has its lateral extent restricted by an obstacle. By definition, a plane wave traveling in the z direction has no field variations in planes orthogonal to the z axis, so the derivatives ∂/∂x or ∂/∂y operating on any field component give zero. Clearly this condition cannot be satisfied if the wave strikes an obstacle: at the edge of the obstacle the wave is obstructed, and there must be variations in field amplitude in the lateral direction. In other words, the derivative operations ∂/∂x and ∂/∂y do not give zero, and the wave after passing the obstacle is no longer a plane wave.

Introduction

In this chapter we shall continue our discussion of molecular gas lasers. Many of the lasers to be discussed here provide substantial CW and pulsed power output, or have unusual and innovative technical features. Some of the lasers to be discussed have already been encountered in another context in earlier chapters. For many lasers a change in the method of excitation enhances some important aspects of laser performance, for example providing higher power output or operation in a new wavelength range. Radical departures from traditional methods of gas-discharge excitation have been particularly important in allowing the development of many of the laser systems to be described in the present chapter.

Gas transport lasers

In many laser systems a fundamental limit to the average output power is set by the buildup of waste heat that results from inefficient laser operation. Even in the relatively highefficiency CW CO2 and CO lasers, collisions that destroy vibrationally excited molecules, rather than just leading to energy exchange from one molecule to another, cause the temperature of the laser medium to rise. In these lasers the temperature rise reduces the population inversion through thermal excitation of the lower laser level. The rise in temperature also reduces the gain through an increase in the Doppler width. Waste heat can also produce changes in the optical properties of the laser medium in a spatially inhomogeneous way. This leads to a phenomenon called thermal lensing.

Introduction

In this chapter we shall use a variety of analytic techniques to analyze periodic optical systems and understand their behavior. These are optical systems in which a ray crosses a repeating pattern of interfaces, a so-called stratified medium, or passes through a sequence of optical components that repeat in a periodic fashion along the axis.

These periodic systems include multi-layer structures that have special reflective or transmissive properties and structures whose dielectic properties vary symmetrically in two or three dimensions. Such periodic structures are often called photonic crystals. Periodic lens sequences are axisymmetric arrangements of multiple lenses arranged along an axial direction. They can be described as stable or unstable. Stable lens sequences have the ability to confine a propagating bundle of rays near to the axis in such a way that the rays never deviate by more than a certain finite distance from the axis and remain confined. Periodic lens sequences can also be used to study the paths of light rays bouncing back and forth between pairs of mirrors – optical resonators. This will allow us to deduce the stability condition for such resonators.

Plane waves in media with complex refractive indices

The relative permittivity and the relative permeability characterize a medium in terms of its difference from a vacuum. Most materials that are important in a discussion of lasers and optical devices are not strongly magnetic, and it is generally legitimate to assume that for such materials μr = 1.

Introduction

In this chapter we will review some of the fundamentals of the optical detection process. This will include a discussion of the randomly fluctuating signals, known as noise, that appear at the output of any detector. We will then examine some of the practical characteristics of various types of optical detector. The chapter will conclude with a discussion of the limiting detection sensitivities of important detectors used in various ways.

Photon detectors operate by absorbing the photons coming from a source and using the absorbed energy to produce a change in the electrical characteristics of their active element(s). This can occur in many ways. In a photomultiplier or vacuum photodiode the incoming photons are absorbed in a photoemissive surface, and free electrons are produced by the photoelectric effect. These electrons can be accelerated and detected as an electric current. In a semiconductor photodiode or photovoltaic detector, absorption of a photon at a p–n or p–i–n junction creates an electron–hole pair. The electron and hole separate because of the energy barrier at the junction – each carrier moves to the region where it can reduce its potential energy, as shown in Fig. 21.1.

Thermal radiation detectors use the heating effect produced by absorbed photons to change some characteristic of the detector element. In a bolometer, the heating of carriers changes their mobility and consequently the resistivity of the detector element. In a thermopile, the heating effect is used to generate a voltage through the thermoelectric (Seebeck) effect.

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].