Dispersion of x⁽³⁾in fused aromatic ladder polymers and their precursors probed by third-harmonic generation

Probing Structure−Property Relationships in Third-Order Nonlinear Optical Polymers: Third Harmonic Generation Spectroscopy and Theoretical Modeling of Systematically Derivatized Conjugated Aromatic Polyimines

“…This excitonic theory has been used successfully to reproduce the χ (3) spectra of polyacetylene and polydiacetylenes 10a,,,, molecular excitons are central to the SOS theory. Experimentally, site-selective fluorescence spectroscopy on p -phenylenevinylene polymers and oligomers has been used to show that the lowest energy optically allowed transitions in the absorption and emission spectra of these materials are excitonic in nature. 62b,c We have similarly employed site-selective fluorescence spectroscopy to probe the excited states of the conjugated polyimines of Chart 1 and confirm that they are best described as molecular excitons.…”

“…The magnitude of the third-order susceptibility χ (3) (−3ω;ω,ω,ω) of the sample (thin polymer film on a fused silica substrate) is obtained relative to fused silica by comparing the Maker fringe patterns of the sample and fused silica. , The resulting approximate χ (3) value is then used as a starting value for the exact fitting procedure. , However, the large optical nonlinearity of the polymer films studied in this work made the use of the exact fitting technique impractical for some samples. Therefore, only the magnitude and not the phase of χ (3) (−3ω;ω,ω,ω) is reported here.…”

“…As a result, a second pathway, which contributes to the optical nonlinearity with an opposite sign from that of the first one, becomes manifest. It has been suggested that an interference between these two paths, which may lead to a sharp decrease of the optical nonlinearity at some frequencies, can be expected. , The optical channels contributing to γ(−3ω;ω,ω,ω) in a three-level SOS model are …”

“…Our SOS theoretical model analysis of the χ (3) dispersion data involves the inclusion of a hyperbolic secant function to account for inhomogeneous and vibronic broadening of electronic transitions. This approximation along with the derivation of eq 3 has been described in detail elsewhere. , After Kramer−Kronig transformation, eq 3 is obtained as a substitute for the Lorentzian line-shape term in the time-dependent SOS equation (2) for the second hyperpolarizability. , Equations 2 and 3 coupled with the above optical channels are used to calculate the second hyperpolarizabilty (γ) for each SOS model. The macroscopic frequency-dispersed χ (3) is calculated from the second hyperpolarizability by including the Lorentz−Lorenz local field factors according to: In this expression, the number density ( N ) was calculated independently from a theoretical consideration of atomic contributions to the physical density of the materials, , and the refractive indices, n (ω) and n (3ω), were obtained from the refractive index dispersion data .…”

“…In this way, the structural origins of observed χ (3) variations can be isolated and structure−χ (3) functions applicable to the polymers extracted. We have previously applied such an approach to a number of different classes of conjugated polymers, including polyquinolines,22a polyanilines, 21a,22b poly(benzobisazoles), , and poly(benzimidazolebenzophenanthrolines) …”