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Coherent anti-Stokes Raman scattering (CARS) spectroscopy is a technique that has been widely applied for temperature measurements in combustion and for microscopic imaging of cell structures. CARS spectroscopy is discussed in detail in this chapter as an example of a nonlinear optical technique. The concept of the nonlinear susceptibility is introduced, and the derivation of the susceptibility tensor appropriate for CARS spectroscopy is described in detail. A key aspect of this derivation is the incorporation of the electric dipole transition matrix elements for the Raman scattering process into the susceptibility tensor. CARS spectral modeling and collisional narrowing of CARS spectral features are discussed in detail. The emerging field of femtosecond CARS is discussed. The chapter concludes with detailed examples of CARS intensity calculations.
The structure of diatomic molecules is discussed in this chapter. The electronic structure of diatomic molecules is then discussed in detail. The coupling of the orbital and spin angular momenta of electrons and the angular momentum associated with nuclear rotation are discussed, with an emphasis on Hund’s cases (a) and (b). The rotational wavefunctions for diatomic molecules in the limits of Hund’s cases (a) and (b) and in the case intermediate between Hund’s cases (a) and (b) are then discussed in detail. For molecules that are of importance in combustion diagnostics, such as OH, CH, CN, and NO, the electronic levels are intermediate between Hund’s cases (a) and (b). We use Hund’s case (a) as the basis wavefunctions, and linear combinations of these wavefunctions are used to represent wavefunctions for electronic levels intermediate between cases (a) and (b). The choice of case (a) wavefunctions as the basis set is typical in the literature although case (b) wavefunctions can also be used as a basis set.
Raman scattering spectroscopy is widely used in analytical chemistry, for structural analysis of materials and molecules and, most importantly for our purposes, as a gas-phase diagnostic technique. Raman scattering is a two-photon scattering process, and the mathematical treatment of Raman scattering is very similar to the mathematical treatment of two-photon absorption. Many of the molecules of interest for quantitative gas-phase spectroscopy are diatomic molecules with non-degenerate 1Σ ground electronic levels, including N2, CO, and H2. In this chapter, the theory of Raman scattering is developed based on Placzek polarizability theory and using irreducible spherical tensor analysis. Herman–Wallis effects are discussed in detail. The chapter concludes with detailed examples of Raman scattering signal calculations.
For the engineer or scientist using spectroscopic laser diagnostics to investigate gas-phase media or plasmas, this book is an excellent resource for gaining a deeper understanding of the physics of radiative transitions. While a background in quantum mechanics is beneficial, the book presents a comprehensive review of the relevant aspects, extensively covering atomic and molecular structure alongside radiative transitions. The author employs effective Hamiltonians and Hund's case (a) basis wavefunctions to develop the energy level structure of diatomic molecules. These techniques also form the basis for treating radiative transitions in diatomic molecules. Recent advancements in quantum chemistry, enabling readers to calculate absolute single-photon and Raman transition strengths, are also presented. Illustrated with detailed example calculations of molecular structure and transition rates, this self-contained reference for spectroscopic data analysis will appeal to professionals in mechanical, aerospace, and chemical engineering, and in applied physics and chemistry.