The mineralogical composition of a metamorphic rock can be used to determine pressures, temperatures, and fluid compositions during metamorphism. However, this is only part of the record these rocks preserve. Their textures are also a source of valuable information and can be diagnostic of a particular type of metamorphism – contact versus regional, for example.

The coupled-wave theory deals with the coupling of waves of different frequencies in nonlinear optical interactions. In the first section, the general coupled-wave equation is derived. Its form under the slowly varying amplitude approximation is then obtained, followed by a form under the transverse approximation. In the second section, the coupled-wave equations for a parametric process are formulated by using three-frequency parametric interaction and second-harmonic generation as two examples. In the third section, the coupled-wave equations for a nonparametric process are formulated by using stimulated Raman scattering and two-photon absorption as two examples.

Most parametric frequency-conversion processes are not automatically phase matched, thus requiring arrangements to achieve phase matching. If a parametric frequency-conversion process is perfectly phase matched, optical power can be efficiently converted from one frequency to another. Otherwise, the conversion efficiency is reduced. The geometric arrangement and the conditions for collinear phase matching and noncollinear phase matching are discussed in the first section. The second section addresses the concept and techniques of birefringent phase matching, which employs the birefringence of a uniaxial or biaxial crystal to accomplish phase matching of a nonlinear optical process. It is the most commonly used method of obtaining collinear phase matching for a second-order frequency-conversion process. The third section covers the concept and techniques of quasi-phase matching, which uses periodic modulation of the nonlinear susceptibility for phase matching. Phase matching in an optical waveguide is discussed in the fourth section.

The fact that people who rank high on one dimension of inequality (e.g., income, wealth) tend to rank high on other dimensions (e.g., power, prestige) suggests a permanence in social inequality that extends beyond the individuals in the structure. Structured inequality refers to the fact that inequality is not arbitrary. Rather, inequality tends to be systematic, and it is usually the case that the same people and groups who have more economic resources also have more prestige and power.

In this chapter we discuss common igneous rock associations. Since the end of the Archean, most, but not all, igneous rock associations can be related to their plate tectonic settings. The Earth’s largest igneous-rock factory has been at divergent plate boundaries in oceanic regions, where MORBs and associated intrusive rocks have been generated as a result of decompression melting.

Before we discuss the sociology of sex inequality, we must first address the definitions of sex and gender. Some might ask, “Are the two not the same? There are two sexes and men are masculine and women are feminine, right?” This common perception fails to acknowledge the complexities associated with both sex and gender. We will investigate these differences as well as explain how social construction affects gender.

When asked, nearly 70 percent of American’s say they are middle class (Northwestern Mutual 2019) compared to 90 percent just over a decade ago (Taylor et al. 2008). But ask them to clarify what it means to be middle class, and they often reply it is because some people have more, and some people have less than they do. Being middle class, then, is a default category that says little about what class membership holds.

Most prograde metamorphic reactions involve dehydration or decarbonation. The large increase in entropy that accompanies the liberation of a fluid phase from a mineral ensures that rising metamorphic temperatures will favor reactions that produce a separate fluid phase.

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.

Metamorphism is the sum of all the changes that take place in a rock as a result of changes in the rock’s environment; that is, changes in temperature, pressure (directed as well as lithostatic), and composition of fluids. The changes in the rock may be textural, mineralogical, chemical, or isotopic. These changes proceed at varying rates, so time is an important factor in metamorphism.

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.

In this chapter we discuss how magmas differentiate to produce the wide range of igneous rocks. Many processes have been invoked, but fractional crystallization is undoubtedly the most important of these. After dealing with the chemical evidence for fractional crystallization, we discuss the actual mechanisms by which crystals can be segregated from liquid in magmas. Historically this was thought to be due to gravitative crystal settling.