In Chapter 5, having introduced the physics behind light scattering, we present the lidar equation. This sets the stage for consideration and simulation of various types of lidar. These include the following broadband lidars: Rayleigh–Mie, polarization, vibrational Raman and fluorescence, and differential absorption. They also include high–spectral resolution (narrowband) lidars: Lidar ratio and aerosol properties, temperature profiling by integration Rayleigh+Raman, temperature profiling with rotational Raman and Cabannes scattering, Rayleigh–Mie wind profiling, and mesopause–region resonance fluorescence wind+temperature profiling.

In Chapter 7, we present lidars for profiling atmospheric parameters such as aerosol optical properties, temperatures, and winds. We start with a description of methods for profiling the lidar aerosol-molecular ratio and determining aerosol optical properties. We present and compare techniques for these measurements, including Rayleigh and vibrational Raman integration, rotational Raman technique, and the use of multiple receiver channels with custom-built interference filters. We follow with a description of high-spectral resolution lidar (HSRL), including a detailed discussion of notch (atomic or molecular vapor) filters in the Cabannes scattering detection channels and what is required to make an “ideal” or near-ideal filter. From there, we describe wind profiling methods using Cabannes–Mie scattering, comparing coherent versus incoherent lidars. For HSRL, we describe a near-ideal filter based on absorption in potassium vapor at 770 nm. Following parameter profiling with Cabannes–Mie lidar, we close by describing temperature and wind profiling with laser-induced fluorescence. Here, we focus on Na and Fe lidars. We give summaries of daylight measurements and data processing algorithms, including uncertainty in measurements. We close by discussing scientific contributions by and challenges for these lidars.

In Chapter 2, we present classical light scattering theory. We show the classical electric dipole and how it leads to a model of atomic polarizability and differential scattering cross section. This leads us to the two principal divisions of atomic and molecular scattering, resonant and nonresonant. From here, we close with the causes of broadening of the scattering spectrum, as compared to the laser excitation.

Chapter 1 is an introduction, reviewing the current state of instructional texts on atmospheric lidar. We point to the lack of a treatment of light scattering as employed by lidar from fundamental physics, the motivation for writing this book. We then summarize the scattering processes, Rayleigh, Raman, Mie, and fluorescence, that enable us to probe the state of the atmosphere with lidar. We include a description of the structure and content of the chapters that follow.

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.