Abstract
The exact formula is derived from the "sum over states" (SOS) quantum mechanical model for the frequency dispersion of the nonlinear refractive index coefficient n₂ for centrosymmetric molecules in the off-resonance and non-resonant regimes. This expression is characterized by interference between terms from two-photon transitions from the ground state to the even-symmetry excited states and one-photon transitions between the ground state and odd-symmetry excited states. When contributions from the two-photon terms exceed those from the one-photon terms, the non-resonant intensity-dependent refractive index n₂>0, and vice versa. Examples of the frequency dispersion for the three-level SOS model are given. Comparison is made with other existing theories.
Highlights
IntroductionThere have been ongoing discussions since the early days of nonlinear optics about the dispersion and sign of the non-resonant value of n2 (when the photon energies are all much smaller than the energy to the first excited state), the Kerr nonlinear refractive index coefficient due to transitions between the electronic states of atoms and molecules [1,2,3,4]
There have been ongoing discussions since the early days of nonlinear optics about the dispersion and sign of the non-resonant value of n2, the Kerr nonlinear refractive index coefficient due to transitions between the electronic states of atoms and molecules [1,2,3,4]
We have used the widely accepted “sum over states” model for molecular nonlinear optics to calculate a general formula for the third-order nonlinearity n2 in the off-resonance and nonresonant regimes
Summary
There have been ongoing discussions since the early days of nonlinear optics about the dispersion and sign of the non-resonant value of n2 (when the photon energies are all much smaller than the energy to the first excited state), the Kerr nonlinear refractive index coefficient due to transitions between the electronic states of atoms and molecules [1,2,3,4]. It includes only two photon “resonance” contributions to n2 and is labeled here as the “two photon resonance model” Neither of these approaches describe completely the third order nonlinearity of symmetric molecules, nor does the two level SOS model, since such molecules have zero permanent dipole moment. In this paper we use the SOS general expressions to extend the results for the three-level model to an arbitrary number of excited states for symmetric molecules or atoms in the offresonant and non-resonant regimes. This leads to general analytical results for the dispersion with frequency of n2 in terms of electric dipole transition moments and locations of the excited states which for simple atoms and molecules can be calculated from first principles. It will be shown that the relative importance of the contributions of the one- and two-photon transitions still determines the sign of the non-resonant nonlinearity
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