Effect of inhomogeneous band broadening on the nonlinear optical properties of hydrazones

Abstract

It is well known that an electroabsorption (EA) spectrum can be described as a linear combination of the zero-, first-, and second-order derivatives of an absorption spectrum on the basis of a theoretical formula derived by Liptay (Liptay equation). According to the Liptay equation, the coefficients of the zero-, first-, and second-order derivatives (these coefficients are abbreviated as D, F, and H terms, respectively) indicate the following three nonlinear optical properties of a material: (1) transition dipole-moment polarizability and its hyperpolarizability, (2) polarizability change upon photoexcitation $(\ensuremath{\Delta}\ensuremath{\alpha}),$ and (3) static dipole-moment change upon photoexcitation $(\ensuremath{\Delta}\ensuremath{\mu}).$ The Liptay equation can be applied only in the case when nonlinearity of an entire absorption band is supposed to be uniform. If this is not the case, for example, due to inhomogeneous band broadening, the nonlinear optical properties of the material cannot be simply derived from the D, F, and H values. In this study, we explicitly included the effect of inhomogeneous band broadening and reformulated the Liptay equation. On the basis of our formula, we analyzed the EA spectra of a series of hydrazones derived from biological polyenes. Even in the case when the effect of inhomogeneous band broadening is predominant, the nonlinearity of these hydrazones can be correctly evaluated.