Optical nonlinearity emerges from nonlinear interaction of light with matter. In this chapter, the basic concept and formulation of light‒matter interaction are discussed through a semiclassical approach with the behavior of the optical field classically described by Maxwell’s equations and the state of the material quantum mechanically described by a wave function governed by the Hamiltonian of the material. An optical field interacts with a material through its interaction with the electrons in the material. A Schrödinger electron is nonrelativistic with a nonzero mass, and a Dirac electron is relativistic with a zero mass. The interaction Hamiltonian can be expressed in terms of the vector and scalar potentials by using the Coulomb gauge. It can be expressed in terms of the electric and magnetic fields through multipole expansion as a series of electric and magnetic multipole interactions, with the first term being the electric dipole interaction. The electric polarization of a material induced by an optical field is obtained through density matrix analysis. The optical susceptibility of the material is then obtained from the electric polarization.

Bistability is a phenomenon that has two stable states under one condition. A bistable device has two possible stable output values for one input condition. The necessary conditions for optical bistability are optical nonlinearity and positive feedback. Depending on whether the optical nonlinearity that is responsible for the bistable function comes from the real or the imaginary part of a nonlinear susceptibility, a bistable optical device can be classified as either dispersive or absorptive. Depending on the type of feedback, a bistable optical device can also be classified as either intrinsic or hybrid. After a general discussion on the condition for optical bistability, this chapter covers dispersive optical bistability, absorptive optical bistability, and hybrid optical bistability of passive optical systems in three sections. The final chapter covers optical bistability in the active optical system of a laser oscillator.

All-optical modulation of an optical wave is accomplished through a nonlinear optical process that involves one or multiple optical waves. A nonlinear optical modulator can be based on either self-modulation or cross-modulation. Such nonlinear optical modulators and switches are also known as all-optical modulators and all-optical switches, respectively. Most all-optical modulators and switches are based on third-order nonlinear optical processes, but some rely on the high-order process of optical saturation, either absorption saturation or gain saturation. There are two fundamentally different types of all-optical modulators and switches: the dispersive type and the absorptive type. All-optical modulation of the dispersive type, which is based on the optical Kerr effect, is discussed in this chapter. In the first four sections, the physics, phenomena, and measurement of the optical Kerr effect are discussed. The last two sections cover all-optical modulators and switches in the bulk form and those in the waveguide form.

Supercontinuum generation is a nonlinear optical process that produces a broad continuous spectrum, often spanning over an octave, when an intense laser beam of an initially narrow bandwidth propagates through a nonlinear medium. Given a sufficiently high laser power, supercontinuum generation can be observed in any material. In general, many nonlinear processes are involved, including self-phase modulation, cross-phase modulation, four-wave mixing, modulation instability, self-focusing, stimulated Raman scattering, soliton dynamics, and dispersive wave generation. The specific nonlinear optical processes that are involved depend on the optical properties of the material and on the wavelength and the temporal characteristics of the laser beam. The usage of optical fibers greatly facilitated the development of supercontinuum generation because an optical fiber provides the favorable combination of both high intensity and long interaction length for efficient supercontinuum generation.

Optical nonlinearity manifests nonlinear interaction of an optical field with a material. The origin of optical nonlinearity is the nonlinear response of electrons in a material to an optical field. Macroscopically, the nonlinear optical response of a material is described by an optical polarization that is a nonlinear function of the optical field. This optical polarization is obtained through density matrix analysis by using the interaction Hamiltonian, which can be approximated with electric dipole interaction in most cases. When the interaction Hamiltonian is small compared to the Hamiltonian of the system, it can be treated as a perturbation to the system by expanding the density matrix in a perturbation series and the total optical polarization in terms of a series of polarizations. In most nonlinear optical processes of interest, the perturbation expansion of the polarization is valid and only the three terms of linear, second-order, and third-order polarizations are significant. The perturbation expansion is not valid in the cases of high-order harmonic generation and optical saturation. Then, a full analysis is required.

There are basically two types of nonlinear optical frequency converters. The majority are based on parametric processes, which require phase matching. Devices that use the nonparametric third-order processes of stimulated Raman or Brillouin scattering to shift the optical frequency are the other type. In this chapter, only those based on parametric processes are considered. The first six sections cover practical optical frequency converters that are based on second-order parametric processes, including second-harmonic generation, sum-frequency generation, difference-frequency generation, optical parametric up-conversion, optical parametric down-conversion, optical parametric amplification, optical parametric generation, and optical parametric oscillation. Frequency conversion based on the third-order parametric four-wave mixing of small frequency shifts is discussed in Section 10.7. The generation of high-order harmonics is discussed in Section 10.8.

In a nonlinear process of multiphoton absorption, the multiple photons are simultaneously absorbed. These photons can have either the same photon energy or different energies. This chapter begins with a general discussion of multiphoton absorption. The simplest of multiphoton absorption is two-photon absorption. It is a third-order nonparametric nonlinear optical process, in which two photons of the same or different photon energies are simultaneously absorbed. By comparison, three photons of the same or different photon energies are simultaneously absorbed in three-photon absorption, which is a fifth-order nonparametric nonlinear optical process. The detailed characteristics of the typical scenarios of two-photon absorption and three-photon absorption are discussed in this chapter.

Practical electro-optic modulators are based on the Pockels effect. The electro-optic effects are generally discussed in the first section, and the Pockels effect is specifically addressed in the second section. The operational principles and characteristics of basic electro-optic modulators, including phase modulators, polarization modulators, and amplitude modulators, are discussed in the third section. In the fourth section, the structures, principles, characteristics, and advantages of guided-wave electro-optic modulators are discussed and shown through the forms of some well-established device structures, including Mach–Zehnder waveguide interferometers, directional coupler switches, polarization-mode converters, and traveling-wave modulators.

Many techniques have been developed for the generation of laser pulses over a wide range of pulsewidths from the order of milliseconds to femtoseconds. The generation of a laser pulse is inherently a nonlinear optical process because all of the techniques utilize some form of optical nonlinearity that is coupled to the dynamics of a laser. In this chapter, the basic concepts of the primary techniques for the generation of laser pulses are covered, including gain switching, active and passive Q switching, active and passive mode locking, and synchronous pumping.

A brief introductory chapter puts synchrotron radiation in the context of other radiation sources, includes a short historical survey of particle accelerators and then provides an introduction of the origins and basic theory of synchrotron radiation.

Chapter 4 describes the range of methods used to determine the atomic scale structure of crystalline solids based on X-ray diffraction. It includes a brief introduction to the basic theory of X-ray diffraction but focuses on applications that go beyond those achievable using conventional laboratory X-ray sources. Extensions of the methods to study the structure of surfaces are also included

Chapter 3 describes the key components of the beamlines that deliver synchrotron radiation to experimental users. These include the use of mirrors and other focusing optical components to direct the radiation and monochromators for both the X-ray and vacuum ultraviolet spectral ranges.