Nonlinear response of individual molecules to strong electric fields is of considerable current interest as it ultimately determines nonlinear optical effects in gaseous media interacting with focused laser pulses. From a phenomenological standpoint, the molecular response is described by the polarizability and hyperpolarizability. The former corresponds to the linear response of the molecule and determines the refractive index of the medium whereas the latter corresponds to the nonlinear response. In particular, second harmonic generation (SHG) in non-centrosymmetric systems is governed by the second-order term in the refractive index, that is, by the first hyperpolarizability. The third-order term (the second hyperpolarizability) is responsible for Kerr lensing and is of broader interest.The expected fundamental changes in nonlinear optical properties of a molecule upon its ionization can be gleaned by considering response to a quasistatic electric field. The change of the molecular energy, E, in the electric field is related to the polarizability and hyperpolariability as,Ei (F) = E0i-? �i Fi-1/2?aij Fi Fj-1/6? �ijk Fi Fj Fk-1/24? ?ijkl Fi Fj Fk Fl-�Here, Fi are components of the electric field, Ei0is the energy of the molecule in the absence of electric field, �i is dipole moment, aij is the polarizability, �ijk is the first order hyperpolarizability and ?ijkl corresponds to the second order hyperpolarizability. According to Eq. (1), the latter four characteristics can be expressed as derivatives of the energy with respect to the electric field. Further, applying weak and homogeneous electric field, second order hyperpolarizability can be written as the derivative of first order hyperpolarizability and calculated by numerical differentiation. A complementary approach for the calculation of the second-order hyperpolarizability is to calculate the polarizability as a function of the external electric field and to fit the result with second-order polynomial, a*=a0 + a1F + a2F2.We report the theoretical changes to the linear and nonlinear polarizability of nitrogen molecule undergoes upon ionization. Using auxiliary electric field approach, we calculated the nonzero components of the second-order polarizabiltiy tensor and the fourth-order hyperpolarizability tensor at HF, MP2, MP4(SDQ), and CCSD levels of theory, with aug-cc-pvqz basis set. The results obtained have direct application to Kerr lensing and laser filamentation in pure nitrogen and in atmospheric air.The results reflect the enhanced role of excitations in the polarization response of the ion. At realistic laser pulse intensities of 1014 W/cm2, the calculated nonlinear contribution to the induced dipole moment of nitrogen ion is more than 10 times greater than that of the neutral molecule. This increase of nonlinearity may play a considerable role in the processes of laser filamentation and microplasma channel formation.

Theoretical study of polarizability and second-order hyperpolarizability   for N<sub>2</sub> and N<sub>2 </sub>ion

244th National Meeting (2012)

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Theoretical study of polarizability and second-order hyperpolarizability for N2 and N2 ion

Theoretical study of polarizability and second-order hyperpolarizability for N₂ and N₂ion