Optical fibers are the backbone of the world's communication systems. They also represent the simplest example of a photonic device, where photons in waveguides replace electrons in wires. More sophisticated devices than this can be made, in which all the optical components – including multiple waveguided modes – are integrated on a chip. It is important to understand the quantum noise properties of these systems.

While in some respects these systems can be treated as one-dimensional, there are additional features. Dispersion is due not just to material properties, but also to the waveguide geometry. The nonlinearity comes from a combination of material and geometric properties as well. There is, of course, a quantum aspect to these photonic devices, in which quantum noise occurs due to random effects caused by nonlinearity and gain.

Optical devices based on waveguides are, of course, not just simple fibers. One can have multiple waveguides with various types of linear coupling. The intrinsic nonlinearity of the dielectric leads to four-wave mixing, which can be an important source of correlated photons, both for fundamental tests of quantum mechanics, and for applications in quantum information.

It is often essential to include effects due to anisotropies of various types, as well as material dispersion. In dielectrics, another effect that should be included is the coupling of vibrational modes of the (solid) dielectric to the propagating field, which gives rise to Raman and Brillouin scattering effects. This allows us to obtain a more detailed and correct theory of quantum noise than the simplified case treated in Chapter 3.

The laser

A laser is an oscillator that operates at optical frequencies. These frequencies of operation lie within a spectral region that extends from the very far infrared to the vacuumultraviolet (VUV) or soft-X-ray region. At the lowest frequencies at which they operate, lasers overlap with the frequency coverage of masers, to which they are closely related, and millimeter-wave sources using solid-state or vacuum-tube electronics, such as TRAPATT, IMPATT, and Gunn diodes, klystrons, gyroklystrons, and traveling-wave tube oscillators, whose principles of operation are quite different [1]. In common with electronic-circuit oscillators, a laser is constructed using an amplifier with an appropriate amount of positive feedback. The positive feedback is generally provided by mirrors that re-direct light back and forth through the laser amplifier. The acronym LASER, which stands for light amplification by stimulated emission of radiation, is in reality therefore a slight misnomer.

A little bit of history

The basic physics underlying light emission and absorption by atoms and molecules was first expounded by Albert Einstein (1879–1955) in 1917 [2]. Richard Chace Tolman (1881–1948) observed that stimulated emission could lead to “negative absorption.” In 1928 Rudolph Walther Landenburg (1889–1953) confirmed the existence of stimulated emission and negative absorption. It is interesting to note that a famous spectroscopist, Curtis J. Humphreys (1898–1986), who for most of his career worked at the U.S. Naval Ordnance Laboratory in Corona, California, might have operated the first gas laser without knowing it.

Introduction

The semiconductor laser, in various forms, is the most widely used of all lasers, is manufactured in the largest quantities, and is of the greatest practical importance. Every CD (compact disk), DVD (digital versatile disk or digital video disk), and Blu-ray player contains one. Most of the world's long-, and medium-, distance communication takes place over optical fibers along which propagate the beams from semiconductor lasers. Highpower semiconductor lasers are increasingly part of laser systems for engraving, cutting, welding, and medical applications. Semiconductor lasers operate by using the jumps in energy that can occur when electrons travel between semiconductors containing different types and levels of controlled impurities (called dopants). In this chapter we will discuss the basic semiconductor physics that is necessary to understand how these lasers work, and how various aspects of their operation can be controlled and improved. Central to this discussion will be what goes on at the junction between p- and n-type semiconductors. The ability to grow precisely doped single- and multi-layer semiconductor materials and fabricate devices of various forms – at a level that could be called molecular engineering – has allowed the development of many types of structure with which one can make efficient semiconductor lasers. In some respects the radiation from semiconductor lasers is far from ideal, since its coherence properties are far from perfect, being intermediate between those of a low-pressure gas laser and an incoherent line source.

In this chapter we shall explain how the distortion produced in a crystal lattice by the application of an electric field or by the passage of a sound wave affects the propagation of light through the crystal. These effects – the electro-optic and acousto-optic effects, and related effects such as field-induced changes in the absorption of a material – are of considerable practical importance since they can be used to amplitude- and phase-modulate light beams, shift their frequencies, and alter the direction in which they travel.

Introduction to the electro-optic effect

When an electric field is applied to a crystal, the ionic constituents move to new locations determined by the field strength, the charge on the ions, and the restoring force. As we saw in Chapter 17, unequal restoring forces along three mutually perpendicular axes in the crystal lead to anisotropy in the optical properties of the medium. When an electric field is applied to such a crystal, in general, it causes a change in the anisotropy. These changes can be described in terms of the modification of the indicatrix by the field – both in terms of the principal refractive indices of the medium and in terms of the orientation of the indicatrix. If these effects can be described, to first order, as being linearly proportional to the applied field then the crystal exhibits the linear electro-optic effect. We shall see that this results only if the crystal lattice lacks a center of symmetry. So, some cubic crystals can exhibit the linear electro-optic effect.

Introduction

In this chapter we shall begin our discussion of nonlinear phenomena that are important in optics. When one or more electromagnetic waves propagate through any medium they produce polarizations in the medium that, in principle, oscillate at all the possible sum and difference frequencies that can be generated from the incoming waves. These polarizations, which oscillate at these new frequencies, give rise to corresponding electromagnetic waves. Thus, we get phenomena such as harmonic generation, for example, when infrared light is converted into visible or ultraviolet light, and various other frequency-mixing processes. These nonlinear processes can be described by a series of nonlinear susceptibilities or mixing coefficients. These coefficients will be defined and their origin traced to the anharmonic character of the potential that describes the interaction of particles in the medium.

Anharmonic potentials and nonlinear polarization

When an electromagnetic wave propagates through a medium a total electric field acts on each particle of the medium. This total field contains components at all the frequencies contained in the input wave or waves. Each particle of the medium will be displaced from its equilibrium position by the action of this field. Positive ions and nuclei will be displaced in the direction of the field, while negative ions and electrons will be displaced in the opposite direction to that of the field. The resultant separation of centers of positive and negative charge creates dipoles in the medium.

Introduction

When an electromagnetic wave propagates through amedium stimulated emissions increase the intensity of the wave, while absorptions diminish it. The overall intensity will increase if the number of stimulated emissions can be made larger than the number of absorptions. If we can create such a situation then we have built an amplifier that operates through the mechanism of stimulated emission. This laser amplifier, in common with electronic amplifiers, has useful gain only over a particular frequency bandwidth. Its operating frequency range will be determined by the lineshape of the transition, and we expect the frequency width of its useful operating range to be of the same order as the width of the lineshape. It is very important to consider how this frequencywidth is related to the various mechanisms by which transitions between different energy states of a particle are smeared out over a range of frequencies. This line broadening affects in a fundamental way not only the frequency bandwidth of the amplifier, but also its gain. A laser amplifier can be turned into an oscillator by supplying an appropriate amount of positive feedback. The level of oscillation will stabilize because the amplifier saturates. Laser amplifiers fall into two categories, which saturate in different ways. A homogeneously broadened amplifier consists of a number of amplifying particles that are essentially equivalent, whereas an inhomogeneously broadened amplifier contains amplifying particles with a distribution of amplification characteristics.

Homogeneous line broadening

All energy states, except the lowest energy state of a particle (the ground state) cover a range of possible energies.

Introduction

In this chapter we will put the concept of coherence on a more mathematical basis. This will involve the formal definition of a number of functions that are used to describe the coherence properties of optical fields. These include the analytic signal, various correlation functions, and the degree of coherence for describing both temporal and spatial coherence. We shall see that the degree of temporal coherence is quantitatively related to the lineshape function and that the degree of spatial coherence between two points is determined by the size, intensity distribution, and location of an illuminating source. We will use the wave equation, and special solutions to the wave equation called Green's functions, to show how spatial coherence varies from point to point.

The chapter will conclude with a discussion of how the intensity fluctuations of a source depend on its coherence properties, and we will examine a specific scheme, namely the Hanbury Brown–Twiss experiment, by means of which this relationship is studied. This discussion will involve a discussion of “photon statistics,” namely the time variation of the “detection” of photons from a source. In a quantum-mechanical context, square-law detectors respond to these quantized excitations of the optical field, which we call photons.

In classical coherence theory it is advantageous to represent the real electromagnetic field by a complex quantity, both for its mathematical simplicity and because it serves to emphasize that coherence theory deals with phenomena that are sensitive to the “envelope” or average intensity of the field.

The author of a text generally feels obligated to explain the reasons for his or her writing. This is a matter of tradition as it provides an opportunity for explaining the development and philosophy of the text, its subject matter and intended audience, and acknowledges the help that the author has received. In the case of a second edition of a text, as is the case here, a new preface provides an opportunity for the author to explain the revisions of the second edition and to further acknowledge help from colleagues. I hope to accomplish these tasks briefly here.

The first edition of this text grew over many years out of notes that I had developed for courses at the senior undergraduate and beginning graduate student level at the University of Manchester, Cornell University, and the University of Maryland, College Park. These courses covered many aspects of laser physics and engineering, the practical aspects of optics that pertain to an understanding of these subjects, and a discussion of related phenomena and devices whose importance has grown from the invention of the laser in 1960. These include nonlinear optics, electro-optics, acousto-optics, and the devices that take practical advantage of these phenomena. The names given to the fields that encompass such subject matter have included laser physics, optical electronics, optoelectronics, photonics, and quantum electronics. The fundamentals of these subjects have not changed significantly in the years that have intervened since the publication of the first edition.