Relation between nonlinear refractive index and third-order susceptibility in absorbing media

Abstract

Expressions relating complex third-order optical susceptibility (χ(3)=χR(3)+iχI(3)) with nonlinear refractive index (n2) and nonlinear absorption coefficient (β) have been formulated that eliminate the commonly used approximation of a negligible linear absorption coefficient. The resulting equations do not show the conventional linear dependence of χR(3) with n2 and χI(3) with β. Nonlinear refraction and absorption result instead from the interplay between the real and imaginary parts of the first- and third-order susceptibilities of the material. This effect is illustrated in the case of a metal–dielectric nanocomposite for which n2 and β values were experimentally obtained by Z-scan measurements and for which the use of the new formulas for χR(3) and χI(3) yield a large correction and a sign reversal for χI(3).