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Theory of Molecular Nonlinear Optics

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Author:  Mark G. Kuzyk, Kenneth D. Singer, and George I. Stegeman 
















Description 
The theory of molecular nonlinear optics based on the sumoverstates (SOS) model is reviewed. The interaction of radiation with a single wtpisolated molecule is treated by firstorder perturbation theory, and expressions are derived for
the linear (alpha) polarizability and nonlinear (beta_{ijk},y_{ijkl}) molecular hyperpolarizabilities in terms of the properties of the molecular states and the electric dipole
transition moments for lightinduced transitions between them. Scale invariance is used to estimate fundamental limits for these polarizabilities. The crucial role
of the spatial symmetry of both the single molecules and their ordering in
dense media, and the transition from the single molecule to the dense medium
case (susceptibilities Chi_1, Chi_2), is discussed. For example, for
beta, symmetry determines whether a molecule can support secondorder nonlinear processes
or not. For asymmetric molecules, examples of the frequency dispersion based
on a twolevel model (ground state and one excited state) are the simplest pos
sible for beta
and examples of the resulting frequency dispersion are given. The
thirdorder susceptibility is too complicated to yield simple results in terms of
symmetry properties. It will be shown that whereas a twolevel model suffices
for asymmetric molecules, symmetric molecules require a minimum of three
levels in order to describe effects such as twophoton absorption. The frequency
dispersion of the thirdorder susceptibility will be shown and the importance of
one and twophoton transitions will be discussed. 

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