Optical Polarizabilities of a Molecule with No Permanent Dipole

Linear Optical Polarizabilities of a Molecule with No Permanent Dipole 

To obtain explicit expressions for the Unear and nonlinear polarizabilities nd Yytft, consider the solution of py /) to the corresponding order. To simplify the calculations, we consider a single moleeule illuminated by anophcal field E t) of the form 

For example, if there are three frequency components i, (O2, and 3 in E(t), Equation (10.17) gives 

The zeroth-order solution of is From Equation (10.11), the solu- 

We make a simplifying assumption that there is initially no coherence among the molecular states that is, all the oflf-diagonal elements 0 for ii j. [Note that the diagonal elements Pjf give the population of the ith state and some of them are nonvanishing.] In this case the commutator in Equation (10.20) gives 

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