Nonlinear optical susceptibilities of free atoms and molecules

Yuratich, Michael Andrew (1976) Nonlinear optical susceptibilities of free atoms and molecules. University of Southampton, Doctoral Thesis.

Abstract

The properties of electric dipole nonlinear optical susceptibilities, hypcrpolarisabilities and transition hyperpolarisabilities for free atoms and molecules are studied theoretically. Emphasis is placed on symmetry based conclusions. The major theoretical tool is the W=,ner-Eckartl theorem and the method of irreducible tensors both are applied to the full rotation-reflection group and finite point groups. Particular emphasis is placed on the statement and uses of selection rules; including those due to time reversal.Among the general results obtained is orientation averaging of tenth order tensors, which decomposes these into a set of irreducible linearly independent tensors, each characterised by an angular factor that depends on the electric field polarisation' vectors - this allows i one to choose optimum geometries for gain, or to determine arbitrary depolarisation ratios. When attention is focussed on singly-resonant susceptibilities, such as Raman scattering, and atoms or rotating molecules are considered, then the irreducible tensors often divide into the product of a reduced line strength (which for many purposes can be regarded as an adjustable parameter) and a multiplet factor. This latter allows relative intensities and/or gains to be determined for transitions between multiplets, and is-evaluated for atoms, diatomic molecules (Hund's cases (a) and (b)) and symmetric and spherical tops (ground vibronic stat(Zs). The absolute calculation of line strengths, even when a multiplet factor--cannot be split off, is discussed for atoms and rotating molecules, and the summation over intermediate state spatial degeneracies carried out in closed form.1Third order processes are discussed at length for.atoms and rotating diatomic molecules (in particular with'Z- ground electronic states) with fine structure calculations of stimulated Raman scattering in the alkali and alkaline earth atoms and including a description of the 'polarisation flips phenomenon when resonant scattering occurs. Hyper-Raman scattering is also treated as a special case, and fine structure calculations for the alkali and alkaline earth atoms made for the stimulated process, numerical results being presented for Na and Cs.

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