Accurate Determination and Modeling of the Dispersion of the First Hyperpolarizability of an Efficient Zwitterionic Nonlinear Optical Chromophore by Tunable Wavelength Hyper-Rayleigh Scattering

Abstract

The wavelength-dependent molecular first hyperpolarizability β of the zwitterionic nonlinear optical (NLO) chromophore picolinium quinodimethane (PQDM) is determined by hyper-Rayleigh scattering (HRS) and used to test and improve theoretical β dispersion models. Experimental HRS data are obtained over a very wide fundamental wavelength range (780−1730 nm), spanning the entire range of two-photon resonance with the intramolecular charge-transfer (ICT) transition and reaching the onset of a higher energy resonance. Reliable calibration against the pure solvent (dimethylformamide, DMF, and DMF-d 7 at the longest wavelengths) was achieved over the full spectral range as a result of the high sensitivity of the HRS setup. Extremely high resonant β values are obtained (up to 4560 × 10-30 esu at 1360 nm) and also away from resonance β remains very large (1210 × 10-30 esu at 1730 nm). The two-photon resonance with the ICT band shows a pronounced red shift (∼33 nm in second-harmonic wavelength) relative to the absorption maximum. The various two-level β dispersion models available in the literature are considered, and some important improvements are introduced. Furthermore, a vibronic model including a single vibrational mode and incorporating inhomogeneous broadening is developed and contrasted to the other extreme of a continuum of vibronic lines without inhomogeneous broadening. The red shift of the β maximum can be largely explained by either an improved inhomogeneous broadening model or by vibronic coupling. However, the vibronic models are physically more realistic and lead to a better description of the observed β dispersion. In general, models with more inhomogeneous broadening result in a narrower β resonance, whereas incorporating more homogeneous broadening yields a broader resonance. Hence, the derived static electronic hyperpolarizability β0 depends very critically on the precise modeling of the broadening mechanisms. Upper and lower bounds to the true β0 are estimated from the two limiting vibronic models.

Dispersion of quadratic nonlinearity of polarized films of chromophore-containing polyimides in the range of resonance absorption

“…The comparison of our data obtained by the Maker fringes method with data from [9] leads to a good coincidence with the experimental accuracy. In [10] a red shift of the nonlinear response dispersion with respect to the linear absorption spectrum was observed for the picolinium quinodimethane chromophore. A detailed discussion of the reasons for such behavior is presented in [10].…”

“…In [10] a red shift of the nonlinear response dispersion with respect to the linear absorption spectrum was observed for the picolinium quinodimethane chromophore. A detailed discussion of the reasons for such behavior is presented in [10]. Taking into account these data the red shift of the nonlinear response can be explained by a well-developed vibrational structure of electronic levels of the chromophore with predominantly populated lower vibrational levels of the ground electronic state.…”

N-Methylquinolinium derivatives for photonic applications: Enhancement of electron-withdrawing character beyond that of the widely-used N-methylpyridinium

“…The HRS measurements were performed at the long laser wavelength of 1550 nm, well beyond (one-and) two-photon resonance for all three compounds, so that the simple undamped two-level model (TLM) of Oudar and Chemla [43] can be used to reliably extrapolate the experimental b values to the static ('resonance free') limit b 0 [44], needed for correct comparison between different molecules.…”

Practical Model for First Hyperpolarizability Dispersion Accounting for Both Homogeneous and Inhomogeneous Broadening Effects

“…In the purely homogeneous vibronic-like (HV) model, 10 the intramolecular charge-transfer (ICT) absorption band is described as a weighted sum of many narrow vibronic lines, so that β becomes an integral over all vibronic transitions contributing to the hyperpolarizability: 10…”

“…This typically results in an overestimation of the tails of the β resonance (see Figure 1). 10 Another approach to include vibrational levels in a simple β dispersion model is to consider an electronic transition coupled linearly to just one normal mode and combine this with a maximal amount of inhomogeneous broadening G (giving a realistic description of the experimental absorption spectrum). In this inhomogeneous single-mode vibronic (IV) model, 10 absorption is described by a series of inhomogeneously broadened vibrational lines: 10…”