Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and thomas-kuhn sum rules

Successfully predicting the frequency dispersion of electronic hyperpolarizabilities is an unresolved challenge in materials science and electronic structure theory. We show that the generalized Thomas-Kuhn sum rules, combined with linear absorption data and measured hyperpolarizability at one or two frequencies, may be used to predict the entire frequency-dependent electronic hyperpolarizability spectrum. This treatment includes two- and three-level contributions that arise from the lowest two or three excited electronic state manifolds, enabling us to describe the unusual observed frequency dispersion of the dynamic hyperpolarizability in high oscillator strength M-PZn chromophores, where (porphinato)zinc(II) (PZn) and metal(II)polypyridyl (M) units are connected via an ethyne unit that aligns the high oscillator strength transition dipoles of these components in a head-to-tail arrangement. We show that some of these structures can possess very similar linear absorption spectra yet manifest dramatically different frequency dependent hyperpolarizabilities, because of three-level contributions that result from excited state-to excited state transition dipoles among charge polarized states. Importantly, this approach provides a quantitative scheme to use linear optical absorption spectra and very limited individual hyperpolarizability measurements to predict the entire frequency-dependent nonlinear optical response. Copyright © 2010 American Chemical Society.

Separating the scattering and absorption coefficients using the real and imaginary parts of the refractive index with low-coherence interferometry.

We present an analytical method that yields the real and imaginary parts of the refractive index (RI) from low-coherence interferometry measurements, leading to the separation of the scattering and absorption coefficients of turbid samples. The imaginary RI is measured using time-frequency analysis, with the real part obtained by analyzing the nonlinear phase induced by a sample. A derivation relating the real part of the RI to the nonlinear phase term of the signal is presented, along with measurements from scattering and nonscattering samples that exhibit absorption due to hemoglobin.

Molecular characterization of chordoma xenografts generated from a novel primary chordoma cell source and two chordoma cell lines.

OBJECT: Chordoma cells can generate solid-like tumors in xenograft models that express some molecular characteristics of the parent tumor, including positivity for brachyury and cytokeratins. However, there is a dearth of molecular markers that relate to chordoma tumor growth, as well as the cell lines needed to advance treatment. The objective in this study was to isolate a novel primary chordoma cell source and analyze the characteristics of tumor growth in a mouse xenograft model for comparison with the established U-CH1 and U-CH2b cell lines. METHODS: Primary cells from a sacral chordoma, called "DVC-4," were cultured alongside U-CH1 and U-CH2b cells for more than 20 passages and characterized for expression of CD24 and brachyury. While brachyury is believed essential for driving tumor formation, CD24 is associated with healthy nucleus pulposus cells. Each cell type was subcutaneously implanted in NOD/SCID/IL2Rγ(null) mice. The percentage of solid tumors formed, time to maximum tumor size, and immunostaining scores for CD24 and brachyury (intensity scores of 0-3, heterogeneity scores of 0-1) were reported and evaluated to test differences across groups. RESULTS: The DVC-4 cells retained chordoma-like morphology in culture and exhibited CD24 and brachyury expression profiles in vitro that were similar to those for U-CH1 and U-CH2b. Both U-CH1 and DVC-4 cells grew tumors at rates that were faster than those for U-CH2b cells. Gross tumor developed at nearly every site (95%) injected with U-CH1 and at most sites (75%) injected with DVC-4. In contrast, U-CH2b cells produced grossly visible tumors in less than 50% of injected sites. Brachyury staining was similar among tumors derived from all 3 cell types and was intensely positive (scores of 2-3) in a majority of tissue sections. In contrast, differences in the pattern and intensity of staining for CD24 were noted among the 3 types of cell-derived tumors (p < 0.05, chi-square test), with evidence of intense and uniform staining in a majority of U-CH1 tumor sections (score of 3) and more than half of the DVC-4 tumor sections (scores of 2-3). In contrast, a majority of sections from U-CH2b cells stained modestly for CD24 (scores of 1-2) with a predominantly heterogeneous staining pattern. CONCLUSIONS: This is the first report on xenografts generated from U-CH2b cells in which a low tumorigenicity was discovered despite evidence of chordoma-like characteristics in vitro. For tumors derived from a primary chordoma cell and U-CH1 cell line, similarly intense staining for CD24 was observed, which may correspond to their similar potential to grow tumors. In contrast, U-CH2b tumors stained less intensely for CD24. These results emphasize that many markers, including CD24, may be useful in distinguishing among chordoma cell types and their tumorigenicity in vivo.