Measurement and analysis of molecular hyperpolarizability in the two-photon resonance regime

Abstract

The frequency dependent hyperpolarizability of typical donor–acceptor organic nonlinear optical molecules is commonly represented by a nonresonant two-level model, first presented by Oudar and Chemla. We discuss how this model can be extended into the resonant regime, including cases where the molecular transition is described by an inhomogeneously broadened peak. A resonant measurement of hyperpolarizability by electric field induced second harmonic generation (EFISH) is demonstrated, as well as the more conventional off-resonance EFISH. The theoretical model correctly predicts both the amplitude and phase of the resonant hyperpolarizability measured by EFISH. We also show that both on-resonance and off-resonance EFISH yield the same hyperpolarizability extrapolated to the zero frequency limit.

Compromise between conjugation length and charge-transfer in nonlinear optical η5-monocyclopentadienyliron(II) complexes with substituted oligo-thiophene nitrile ligands: Synthesis, electrochemical studies and first hyperpolarizabilities

“…It is observed that b increases much less upon going from 1.550 lm to 1.064 lm for 1a than for 2a and 3a. This behaviour cannot be explained by the difference in resonance conditions (values of k eg relative to 532 nm: 1a is closer to resonance than 3a), within the TLM, not even if homogeneous damping [31] is taken into account. Clearly, near to resonance the dispersion of the b values of compounds 1a-3a is not well described by this simple model.…”

“…The deshielding observed for the complexes containing L1 and L2 derivatives are lower than those found in the related p-benzonitrile complexes [10,28], which can be a result of the enhanced p-backdonation in the present compounds with thiophene ligands. 31 P NMR data of the complexes showed the expected deshielding of the phosphines upon coordination. The dppe ligand was characterized by a singlet and (+)-diop by two doublets due to its inequivalent phosphorus atoms.…”

“…1 H, 13 C and 31 P NMR spectra were recorded on a Varian Unity 300 spectrometer at probe temperature. The 1 H and 13 C resonances are reported in parts per million (ppm) downfield from internal Me 4 Si and the 31 Electronic spectra were recorded at room temperature on a Shimadzu UV-1202 spectrometer. Melting points were obtained using a Reichert Thermovar.…”

Intrinsic Hyperpolarizabilities as a Figure of Merit for Electro-optic Molecules

“…Indeed, the excited state transition moments and energies for many states are often needed to accurately calculate the dispersion of the hyperpolarizability [33,34] and there are wellknown problems associated with extrapolating β 0 to zero frequency. [35,36] Even when only two electronic states dominate the response, the damping correction must be carefully taken into account [37,38] and vibronic overtones may complicate the analysis. [39,40] Secondly, there is nothing intrinsic about β 0 as we can argue from the fact that it can be large for very different underlying reasons.…”

A General Theory of Inhomogeneous Broadening for Nonlinear Susceptibilities: The Polarizability and Hyperpolarizability

“…Robert J. Kruhlak is at the Department of Physics, University of Auckland, Auckland, NZ E-mail: r.kruhlak@auckland.ac.nz Mark G. Kuzyk is at the Department of Physics, Washington State University Pullman, Washington 99164-2814 E-mail: kuz@wsu.edu Dirk et al [3] and Berkovic et al [4] showed that it was important to take damping into account by using a complex energy in the Orr and Ward SOS expression even when considering off-resonance susceptibilities. The distribution of molecules, when embedded in a polymer, are randomly perturbed by virtue of the fact that each molecule experiences a different local environment due to microscopic inhomogeneities.…”