Quasi-three-level model applied to measured spectra of nonlinear absorption and refraction in organic molecules

Materials with a large nonlinear refractive index (n2) and relatively small linear and nonlinear absorption losses, namely, two-photon absorption (2PA, of coefficient α2), have long been sought after for applications such as all-optical switching (AOS). Here we experimentally determine the linear and 2PA properties of several organic molecules, which we approximate as centrosymmetric, and use a simplified essential-state model (quasi-three-level model) to predict the dispersion of n2. We then compare these predictions with experimental measurements of n2 and find good agreement. Here “quasi”-three-level means using a single one-photon allowed intermediate state and multiple (here two) two-photon allowed states. This also allows predictions of the figure-of-merit (FOM), defined as the ratio of nonlinear refractive phase shift to the 2PA fractional loss, that determines the viability for such molecules to be used in device applications. The model predicts that the optimized wavelength range for a large FOM lies near the short wavelength linear absorption edge for cyanine-like dyes where the magnitude of n2 is quite large. However, 2PA bands lying close to the linear absorption edge in certain classes of molecules can greatly reduce this FOM. We identify two molecules having a large FOM for AOS. We note that the FOM is often defined as the ratio of real to imaginary parts of the third-order susceptibility (χ(3)) with multiple processes leading to both components. As explained later in this paper, such definitions require care to only include the 2PA contribution to the imaginary part of χ(3) in regions of transparency.