The Origins of the Nonlinear Refractive Indices of Liquids and Glasses

Abstract

Nonlinear refractive index changes in isotropic media are a consequence of two distinct types of mechanisms. An mechanism arises from the nonlinear distortion of the electron orbits about the nuclei and a mechanism arises from an electric-field-induced change in the motions of nuclei. A general treatment of nonlinear optical phenomena involving a polarization cubic in the electric field strength is given with the topic of nonlinear index changes treated as a special case. A central result of this theory is the following expression for the nonlinear polarization P 3(t) in terms of the electric field E (t), the parameter σ and the response functions a(t) and b(t): P 3(t) = σ-2 E (t)▪ E (t) E (t) + ∫ a(t-τ) E (τ)▪ E (τ)dτ E (t) + ∫ b(t-τ) E (τ)▪ E (t) E (τ)dτ In the theory the relationship between these parameters and the nonlinear susceptibility tensor X 3, is established. Several experiments in nonlinear optics are analyzed; in particular, it is shown that Kerr effect measurements lead to a determination of the quantity σ + β (where β = ʃ b(t)dt) whereas measurements of the intensity dependent of the polarization of a monochromatic optical beam yield the quantity σ + 2β. Hence together these two techniques offer a means of uniquely determining both the parameter a and the parameter β in any isotropic medium. The nonlinear susceptibility element X31221 (-ω,ω,ω,-ω) = σ+2β/24 is calculated from measurements in fused quartz, BK-7 borosilicate crown glass, and SF-7 dense flint glass giving values of 1.5, 2.3, and 9.9 x 10-15 esu at λ = 6943A, respectively. These measurements constitute the first observations of in any solid and (with an absolute accuracy of 11%) are the most accurately known of any nonlinear optical parameter in glasses. Although the interpretation of these results along with Kerr, three-wave mixing, and third harmonic generation data nominally indicate that σ ˃˃ β for glasses, we hesitate to conclude that the nonlinear refractive indices in glasses are purely in origin until the uncertainties in the latter measurements are reduced. If it is assumed however that electronic contributions are dominant, these experimental data would indicate that the nonlinear refractive index n2 for a linearly polarized beam in fused quartz, BK-7 glass, and SF-7 glass is 1.2, 1.7, and 6.9 x 10-13 esu respectively. Parallel investigations of ellipse rotation in the symmetric molecule liquid CC14 show that X31221 (-ω,ω,ω,-ω) = 6.1 x 10-15 esu. This value when interpreted along with very accurate Kerr measurements indicate that the fractional electronic contribution to the Kerr constant of CC14 is given by σ/σ+β = 0.54 ± 0.17. Hence both electronic and nuclear contributions are significant to nonlinear refractive index changes in CC14.