In Chapter 4, we look at nonresonant scattering, specifically Rayleigh and Raman scattering from linear molecules. We continue with the semiclassical (quantum) treatment, leading to the induced dipole moment and associated differential scattering cross section. Explicitly adding vibrational and rotational manifolds of the ground state, we show the results for all three regimes: Rayleigh, rotational Raman, and vibrational Raman scattering. We then apply these results to nitrogen and oxygen molecules and associate the results with macroscopic quantities, such as the index of refraction of an ensemble, or gas. From this point, we focus specifically on Rayleigh + vibrational Raman spectra of O2 and N2, determining vibrational and rotational constants and the thermal populations of the states, based on their molecular energies, which leads to the spectral strengths of individual lines. We finish this chapter with a description of the Cabannes spectrum and the effect of the density fluctuations on its lineshape, considering the success of theoretical models in reproducing these spectra in Knudson (low-density), kinetic (medium-density) and hydrodynamic (high-density) regimes.

In Chapter 6, we concentrate on the broadband lidars, from the point of view of the lidar equation as described in Chapter 5. Here, we describe in detail Rayleigh–Mie (elastic backscattering) lidars in regions with and without the presence of aerosols. Next, we move to polarization lidars for the study of aerosols and cloud particles. Here, we use Stokes vectors to describe the transmitting beam and Mueller matrices for optical elements and the individual scatterers in the atmosphere. We move from polarization lidar to Raman and DIAL lidar for monitoring minor species, carrying out a detailed comparison of the two techniques, including analysis of their relative uncertainties. We close with a brief overview of lidars not presented in this book, but which are nevertheless important and worth mentioning. These include airborne and spaceborne systems, particulate and air pollution monitoring systems, and those used for 3–D mapping and profiling, archeology, and other hard–target applications.

In Chapter 8, we give an overview of the optics that control beam transmission and signal reception. We open with a description of the use and benefits of a beam expander to control the output beam divergence. From there, we move to describing receiver optics, starting with the telescope and importance of size, field of view, and using high-quality optics. This includes using an optical fiber to transport the received photons to the downstream filtering and detection optics. Next, we discuss detector characteristics and the trade-offs one must consider when selecting an appropriate photon counting sensor. We follow with a short section on the value of computer modeling the receiver optics. We close the chapter with a concise discussion of atmospheric turbulence and of laser guide stars and adaptive optics for the mitigation of atmospheric turbulence effects on astronomical telescopes.

In this chapter, the characteristics of pulse propagation in an isotropic and spatially homogeneous Kerr medium are discussed. The general optical pulse propagation equation and its form under the rate equation approximation are presented in the first section. The second section addresses the effect of dispersion on the propagation of an optical pulse in a linear optical medium where the nonlinear susceptibility does not exist. The third section addresses the effect of self-phase modulation on the propagation of an optical pulse in a nonlinear optical Kerr medium without the effect of dispersion. The following two sections cover the phenomena and characteristics of spectral stretching, pulse stretching, pulse compression, soliton formation, and soliton evolution that appear under different conditions in the propagation of an optical pulse in a nonlinear optical Kerr medium with the effect of dispersion. The final section addresses the process of modulation instability from the viewpoint of nonlinear wave propagation.

The optical response of a material is described by an electric polarization through an optical susceptibility. In the presence of optical nonlinearity, the total optical susceptibility is generally a function of the optical field. When the electric polarization can be expressed as a perturbation series of linear and nonlinear polarizations, field-independent linear and nonlinear susceptibilities can be defined. The linear susceptibility is a second-order tensor, and the second-order and third-order nonlinear susceptibilities are respectively third-order and four-order tensors. Each tensor element of these susceptibilities satisfies the reality condition. All tensor elements as functions of interacting optical frequencies generally possess intrinsic permutation symmetry. A full permutation symmetry exists when the material causes no loss or gain at all of the optical frequencies, and Kleinman’s symmetry exists when the medium is nondispersive at these frequencies. The spatial symmetry of a linear or nonlinear susceptibility tensor depends on the structure of the material.

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.

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.

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.

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 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.

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.