Molecular second- and third-order polarizabilities from measurements of second-harmonic generation in gases

Computer simulation of the linear and nonlinear optical properties of liquid benzene: Its local fields, refractive index, and second nonlinear susceptibility

“…7 and 8͒ quantum chemical approaches. Experimentally, the electric field-induced second-harmonic generation ͑EFISH͒ technique [9][10][11] and, more recently, the hyperRayleigh scattering ͑HRS͒ technique 12 have been developed and exploited to estimate molecular hyperpolarizabilities in the liquid phase. Gas-phase measurements, 13 which would allow for a direct comparison between experimentally and quantum chemically obtained hyperpolarizabilities, are often not possible, since NLO-active molecules have very high dipole moments, which do not allow evaporating them into the gas phase.…”

Rigorous theory of molecular orientational nonlinear optics

“…Equation (68) is exactly the same as that of literatures. 7,26,28,[30][31][32][33][34][35][36]40 Similar to the EFISH, we can also predict the dc electric field induced sum (and difference) frequency generation (EFISFG 42 and EFIDFG) within the framework of our theory. The corresponding effective third-order nonlinear susceptibility for EFISFG (EFIDFG) may be written as…”

“…This is attributed to the fact that the hyperpolarizabilities responsible for molecular orientational polarizations may be deduced from the temperature dependent measurements in dc Kerr effect 8,13,44,45 and EFISH. 8,31,46 The physical origin of the molecular orientational nonlinearity is the tendency of molecules to orient in a preferable direction to the applied electric field in a way to minimize the free energy. This results in the change of the molecular nonlinear polarization by the molecular orientation.…”

“…Isotropic medium or randomly oriented molecules under the action of an electric field including optical wave undergo molecular orientational polarization and pure electronic polarization, and this breaks the symmetry of center of inversion due to the field induced partial orientation of induced and/or permanent electric dipole moments. Combining effects of both molecular orientational and pure electronic polarizations lead to new classes of thermal energy dependent nonlinear optical processes which include the static dielectric constant, 11,12 dc Kerr effect, 9,13-20 OKE, 10,[21][22][23][24][25] dc field induced second harmonic generation (EFISH), [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] self-focusing, 41 dc field induced sum frequency generation (EFISFG), 42 and others. Among them, the EFISH is one of the most popular experimental techniques for determining the first hyperpolarizability tensor β, where a strong dc field is applied to the isotropic medium and breaks the centrosymmetry of the medium, allows second harmonic wave generation.…”

“…Among them, the EFISH is one of the most popular experimental techniques for determining the first hyperpolarizability tensor β, where a strong dc field is applied to the isotropic medium and breaks the centrosymmetry of the medium, allows second harmonic wave generation. The total (effective) contribution to the EFISH is expressed a Electronic mail: chkwak@ynu.ac.kr as [26][27][28][29][30][31][32][33] χ (3) eff ∝ ⟨γ⟩ + µ · β/5k B T, where χ (3) eff is the effective third-order nonlinear susceptibility, ⟨γ⟩ is the orientational averaged scalar part of the molecular second hyperpolarizability tensor γ, µ is the permanent electric dipole moment vector of the polar molecule, β is the vector part of the molecular first hyperpolarizability 7,33,34,43 and k B T is the thermal energy of the medium where k B is the Boltzmann constant and T is the temperature. The first term, ⟨γ⟩ , represents the contribution from the electronic cloud distortion of molecules, while the thermal energy dependent second term, µ · β/5k B T, depicts the contribution of the partial reorientation of the polar molecules interacting with the vector part of the molecular first hyperpolarizability.…”