Optical interactions can generally be categorized into parametric processes and nonparametric processes. A parametric process does not cause any change in the quantum-mechanical state of the material, whereas a nonparametric process causes some changes in the quantum-mechanical state of the material. Phase matching among interacting optical fields is not automatically satisfied in a parametric process but is always automatically satisfied in a nonparametric process. All second-order nonlinear optical processes are parametric in nature. The nonlinear polarization and phase-matching condition of each second-order process are discussed in the second section. Some third-order nonlinear optical processes are parametric, and others are nonparametric. The nonlinear polarization and phase-matching condition of each third-order process are discussed in the third section.

This chapter deals with the classification of igneous rocks. This reduces the thousands of rock names found in the literature down to a manageable number and links them to a logical classification based on their mineral content and chemical composition. The chapter presents the classification adopted by the International Union of Geological Sciences (IUGS), which uses the abundance of the major rock-forming minerals (the mode) to place rocks in compositional fields for which there are commonly accepted names. Some rocks are too fine-grained, or even glassy, for this modal classification to be applied.

Stimulated Raman scattering leads to Raman gain for a Stokes signal at a frequency that is down-shifted at a Raman frequency, and stimulated Brillouin scattering leads to Brillouin gain at a frequency that is down-shifted by a Brillouin frequency. This chapter begins with a general discussion of Raman scattering and Brillouin scattering. After a discussion of the characteristics of the Raman gain, Raman amplification and generation based on stimulated Raman scattering are addressed through their applications as Raman amplifiers, Raman generators, and Raman oscillators. After a discussion of the characteristics of the Brillouin gain, Brillouin amplification and generation based on stimulated Brillouin scattering are addressed through their applications as Brillouin amplifiers, Brillouin generators, and Brillouin oscillators. This chapter ends with a comparison of Raman and Brillouin devices.

What does it mean to be poor? Or more precisely, what material things make up “what is enough?” This is the central question to scholars who study poverty. The number of people living in poverty varies by the agency that collects these data, and the percentage of poor used by government agencies is generally only an estimate. This chapter will consider the definition of poverty and how this construction affects who is considered poor and able to receive assistance. We then turn to the determinants of poverty and sociological theories that seek to explain who are the poor and predict how many people will fall below the poverty line in any given period. We conclude with the consequences associated with poverty as well as broad national policies and their effectiveness at reducing poverty.

The general formulation for optical propagation in a nonlinear medium is given in this chapter. In the first section, the general equation for the propagation in a spatially homogeneous medium is obtained. This equation can be expressed either in the frequency domain or in the time domain. In the second section, the general pulse propagation equation for a waveguide mode is obtained in the time domain. In the third section, the propagation of an optical pulse in an optical Kerr medium is considered for three useful equations: nonlinear equation with spatial diffraction for propagation in a spatially homogeneous medium, nonlinear Schrödinger equation without spatial diffraction for propagation in a spatially homogeneous medium or in a waveguide, and generalized nonlinear Schrödinger equation for the nonlinear propagation of an optical pulse that has a pulsewidth down to a few optical cycles or that undergoes extreme spectral broadening.

Most Americans have thought about the chance that they will change social positions during their life. Trying to improve social status – that is, to move up the status hierarchy over time – is usually considered a desirable objective and a positive individual trait. It is common for young people to imagine that they can achieve more in their life than their parents, and many elements of the way we socialize children encourages or assumes that social mobility is a real possibility. Although we have begun to take for granted that social mobility is at least possible, the potential for change of this type is relatively recent. Throughout most of history and in most societies, people grew up to occupy the same social positions as their parents: peasants remained peasants, elites remained elites, and those in the middle remained in the middle. People even had surnames to indicate their social position (e.g., Bishop, Carpenter, Miller, and Wainwright). Today, we accept that through education, occupational change, entrepreneurship, and other processes, at least some people will not follow the same patterns as their parents. However, determining who is socially mobile and why is not a simple task.

This chapter addresses optical wave propagation in isotropic and anisotropic media. This chapter begins with general discussions on the energy flow and power exchange as an optical wave propagates through a medium. The next two sections respectively address the propagation of plane waves in isotropic and anisotropic homogeneous media. The polarization normal modes of propagation are defined for a birefringent crystal, which can be uniaxial with only one optical axis or biaxial with two optical axes. The concepts and characteristics of phase velocity, group velocity, and various types of dispersion are then discussed.

The coupled-wave theory is used in the analysis of the interactions among optical waves of different frequencies. In the analysis of the coupling of waveguide modes, coupled-mode theory has to be used. In general, both the interaction among different optical frequencies and the characteristics of the waveguide modes have to be considered for a nonlinear optical interaction in an optical waveguide. In the first section, a combination of coupled-wave and coupled-mode theories is formulated for the analysis of nonlinear optical interaction in a waveguide. In the second section, the coupled equations for a parametric nonlinear interaction in a waveguide are formulated by using three-frequency parametric interaction, second-harmonic generation, and the optical Kerr effect as three examples. In the third section, the coupled equations for a nonparametric nonlinear interaction in a waveguide are formulated by using stimulated Raman scattering and two-photon absorption as two examples.

This chapter outlines what is known about the pressures and temperatures in the Earth. We start by discussing pressure and see that although rocks near the surface are strong, they become weak and flow plastically at depth. As a result, reasonable pressures can be calculated by treating them as extremely viscous liquids; we refer to this pressure as lithostatic. Exceptions to this approximation occur if fluids are released by metamorphic reactions or melt is generated at rates that exceed the rate at which surrounding rock can deform.

This chapter introduces rocks and petrology, the science that attempts to explain the origin and distribution of rocks. Rocks are the solid material constituting the Earth, and it is essential to know what composition the planet has. We begin with a brief review of the planetary formation process and how it determined the Earth’s composition and major divisions into core and mantle.

This chapter addresses the physics and applications of optical saturation, including optical absorption saturation and optical gain saturation. Optical saturation is a nonlinear optical process that usually cannot be approximated with a perturbation expansion as a second-order or third-order nonlinear process. Instead, a fully nonlinear analysis is required. Following a discussion on the general physics and characteristics of absorption saturation and gain saturation in the first section, the properties and applications of saturable absorbers and saturated amplifiers are discussed in the second and third sections. The last section covers laser oscillation as a consequence of optical gain saturation.