Photonics is an engineering discipline concerning the control of light, or photons, for useful applications, much as electronics has to do with electrons. Light is electromagnetic radiation of frequencies in the range from 1 THz to 10 PHz, corresponding to wavelengths between∼300 μm and ∼30 nm in free space. This optical spectral range is generally divided into infrared, visible, and ultraviolet regions, as indicated in Table 1.1. The spectral range of concern in photonics is usually in a wavelength range between 10 μm and 100 nm. The primary interest in the applications of photonic devices is in an even narrower range of visible and near infrared wavelengths. As we shall see later, this spectral range of application is largely determined by the properties of materials used for photonic devices.

The wave nature of light is very important in the function of photonic devices. In particular, the propagation of light in a photonic device is completely characterized by its wave nature. However, in the spectral range of interest for practical photonic devices, the quantum energies of photons are in a range where the quantum nature of light is also important. For example, photons of visible light have energies between 1.7 and 3.1 eV, which are in the range of the bandgaps of most semiconductors. Photon energy is an important factor that determines the behavior of an optical wave in a semiconductor photonic device. The uniqueness of photonic devices is that both wave and quantum characteristics of light have to be considered for the function and applications of these devices.

In many applications, it is necessary to control opticalwaves with externally applied signals to perform such functions as modulation, switching, deflection, isolation, frequency shifting, and polarization rotation of optical signals. Depending on the nature of the external control signal, these functions can be accomplished through the interactions of an optical wave with an electric field, a magnetic field, an acoustic wave, or another optical wave. Generally speaking, these interactions are all nonlinear optical phenomena. Nevertheless, electro-optic, magneto-optic, and acousto-optic effects each have very specific characteristics. Many useful devices have been developed based specifically on these effects for many important functions, such as optical modulation and optical switching. The electro-optic, magneto-optic, and acousto-optic devices are discussed separately in this and the following two chapters. The discussions in Chapter 9 then focus on nonlinear optical devices based solely on the interactions between optical waves.

Electro-optic effects

The optical property of a dielectric material can be changed through an electro-optic effect in the presence of a static or low-frequency electric field E0. The result is a field-dependent susceptibility and thus a field-dependent electric permittivity:

and

where field-independentχ(ω) = χ(ω, E0 = 0) and ∈(ω) = ∈(ω, E0 = 0) represent the intrinsic linear response of the material at the optical frequency ω, while Δχ and Δ∈ represent changes induced by the low-frequency field E0. We can write D(ω, E0) = D(ω) + ΔP(ω, E0), where ΔP(ω, E0) = Δ∈(ω, E0) E(ω).

Over the past two decades, photonics, the use of photons for engineering applications, has gradually become established as a well-defined engineering discipline. Photonics has developed from studies in crystal optics, guided-wave optics, nonlinear optics, lasers, and semiconductor optoelectronics. Though many excellent books exist on each of these subjects, and several have been written specifically to address photonics, it is still difficult to find one book where the diverse core subjects that are central to the study of photonic devices are presented with a good balance of breadth and depth of coverage. Through my teaching of undergraduate courses, I have found it very effective to introduce the field of photonics to undergraduate students using the rigorous, systematic approach of this book. Through my experience of working with graduate students in research, I have found that such a book is very much needed to prepare a solid foundation for graduate students who intend to major, or minor, in photonics. Through my teaching experience, I have found it highly desirable and beneficial for both instructors and students to have ample examples and problems that are well thought out and fully integrated with the subjects covered in the text. This book is written to address these needs.

I began this project in early 1994 after many years of teaching undergraduate and graduate courses in lasers, nonlinear optics, quantum electronics, and quantum mechanics. Though I had already accumulated a large collection of classnotes and problem sets when I started this project, it still took me exactly nine years to finish writing this book, with fully one-third of that time devoted to the work on examples and problems.

The principles of many photonic devices are based on the coupling between optical fields of different frequencies or different spatial modes. In general, the coupling mechanism can be described by a polarization ΔP on top of a background polarization representing the property of the medium in the absence of the coupling mechanism. In this chapter, we present the general coupled-wave and coupled-mode formalisms, which provide the foundation for understanding the functions of many devices in the following chapters. The coupled-wave formalism deals with the coupling of optical waves of different frequencies, whereas coupled-mode theory applies to the coupling of optical fields of different spatial modes.

Coupled-wave theory

In this section, the general formulation of the coupled-wave formalism for coupling of optical waves of different frequencies is presented. For simplicity, we consider only coupling among plane optical waves, but the formulation can be easily extended for nonplane waves, such as optical waves of Gaussian beam profiles.

As discussed in Section 1.3, coupling among opticalwaves of different frequencies is possible only if the optical property of the medium in which the optical waves propagate is either time varying or optically nonlinear. Time-varying optical properties can be induced by time-varying electric, magnetic, or acoustic fields through electro-optic, magneto-optic, or acousto-optic effects, which are discussed in Chapters 6, 7, and 8, respectively. In particular, an acoustic wave always induces time-varying changes in the optical property of a medium, whereas changes induced by electro-optic or magnetooptic effects can be static when they are caused by static electric or magnetic fields. Nonlinear optical properties are discussed in Chapter 9.

The word laser is an acronym for light amplification by stimulated emission of radiation. However, the term laser generally refers to a laser oscillator, which generates laser light without an input light wave. A device that amplifies a laser beam by stimulated emission is called a laser amplifier. Laser light is generally highly collimated with a very small divergence and highly coherent in time and space. It also has a relatively narrow spectral linewidth and a high intensity in comparison with light generated from ordinary sources. Due to the process of stimulated emission, an optical wave amplified by a laser amplifier preserves most of the characteristics, including the frequency spectrum, the coherence, the polarization, the divergence, and the direction of propagation, of the input wave. In this chapter, we discuss the characteristics of laser amplifiers. Laser oscillators are discussed in Chapter 11. Optical fiber amplifiers are of particular interest in photonics applications. They are specifically discussed in Section 10.5. Semiconductor laser amplifiers are discussed in Chapter 13.

Optical transitions

Optical absorption and emission occur through the interaction of optical radiation with electrons in a material system that defines the energy levels of the electrons. Depending on the properties of a given material, electrons that interact with optical radiation can be either those bound to individual atoms or those residing in the energy-band structures of a material such as a semiconductor. In any event, the absorption or emission of a photon by an electron is associated with a resonant transition of the electron between a lower energy level |1〉 of energy E1 and an upper energy level |2〉 of energy E2, as illustrated in Fig. 10.1.

Optical waveguides are the basic elements for confinement and transmission of light over various distances, ranging from tens or hundreds of micrometers in integrated photonics to hundreds or thousands of kilometers in long-distance fiber-optic transmission. They are used to connect various photonic devices. In many devices, they form important parts or key structures, such as thewaveguides providing optical confinement in semiconductor lasers. Furthermore, they form important active or passive photonic devices by themselves, such as waveguide couplers and modulators. In this chapter, we consider the basic characteristics of linear, lossless dielectric waveguides. Optical fibers are discussed in Chapter 3. Other waveguide devices are discussed in later chapters.

Waveguide modes

The basic structure of a dielectric optical waveguide consists of a longitudinally extended high-index optical medium, called the core, which is transversely surrounded by low-index media, called the cladding. A guided optical wave propagates in the waveguide along its longitudinal direction. We consider a straight waveguide whose longitudinal direction is taken to be the z direction, as shown in Fig. 2.1(a). The characteristics of a waveguide are determined by the transverse profile of its dielectric constant ∈(x, y)/∈0, which is independent of the z coordinate. For a waveguide made of optically isotropic media, we can simply characterize the waveguide with a single spatially dependent transverse profile of the index of refraction, n(x, y).

In a nonplanar waveguide of two-dimensional transverse optical confinement, the core is surrounded by cladding in all transverse directions, and n(x, y) is a function of both x and y coordinates. The channel waveguides, discussed in Section 2.8, and the circular optical fibers, discussed in Chapter 3, are such waveguides.

Magneto-optic materials have unique physical properties that offer the opportunity of constructing devices with many special functions not possible from other photonic devices. The most significant of these properties are that the linear magneto-optic effect can produce circular birefringence and that, unlike other optical effects in dielectric media, it is nonreciprocal. All practical magneto-optic devices exploit one or both of these two properties. Important applications of these devices include polarization control, optical isolation, optical modulation, and magneto-optic recording. The basic principles of magneto-optic effects, as well as the functions of various magneto-optic devices based on these effects, are considered in this chapter.

Magneto-optic effects

Because magneto-optic effects are intimately connected to the magnetic properties of materials, we first briefly summarize the fundamental magnetic properties of materials. To a certain degree there is a parallelism between the electric and the magnetic properties of materials, but this parallelism is not complete. We shall pay attention to the similarities and differences between these properties in order to gain an appreciation of the uniqueness of magneto-optic devices.

Following the similarity between (1.1) and (1.2), a magnetic susceptibility tensor, χm, analogous to the electric susceptibility tensor χ can be defined to describe the magnetization induced by a magnetic field.

There are a wide variety of lasers, covering a spectral range from the soft X-ray to the far infrared, delivering output powers from microwatts to terawatts, operating from continuous wave to femtosecond pulses, and having spectral linewidths from just a few hertz to many terahertz. The gain media utilized include plasma, free electrons, ions, atoms, molecules, gases, liquids, solids, and so on. The sizes range from microscopic, of the order of 10 μm3, to gigantic, of an entire building, to stellar, of astronomical dimensions. An optical gain medium can amplify an optical field through stimulated emission. If the gain medium is sufficiently long, it is possible to generate laser light at one end of the medium through amplification of some initial optical field from spontaneous emission produced at the other end of the gain medium. Astrophysical laser action in space has been found to occur naturally, for example at the deep ultraviolet wavelength of 250 nm from the star Eta Carinae, at the near-infrared H2 wavelength of 2.286 μm from the star NGC 7072, at the far-infrared wavelength of 169 μm in a disk of hydrogen gas surrounding the star MWC349 in the constellation Cygnus, and at the mid-infrared CO2 wavelength of 10.6 μmin the Martian atmosphere. In a practical laser device, however, it is generally necessary to have certain positive optical feedback in addition to optical amplification provided by a gain medium. This requirement can be met by placing the gain medium in an optical resonator. The optical resonator provides selective feedback to the amplified optical field.

Lasers are indeed fascinating, but not all of them are of practical usefulness as photonic devices.