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In multicolor time resolved pump probe techniques used to investigate molecular dynamics the interacting electromagnetic waves propagate at different group velocities and thus get separated after propagating some distance in the spectroscopic sample. This problem is especially pronounced when pumping in the UV. The group velocity mismatch (GVM) is a quantitative evaluation of this effect.
An obvious consequence of the GVM is that the time resolution of the spectroscopic measurements deteriorates. Although widely tunable UV pulses and extremely short UV pulses are readily available - and used - for time resolved spectroscopic applications, the crucial role of GVM is often overlooked.
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To estimate the GVM, the wavelength dependence of the refractive index of the sample must be known. Unfortunatelly, reference books do not cover the entire range of matter, illumination wavelength and temperature. In the literature one definitely can find data for the 589.3 nm sodium D2 resonance line at 20 °C. Further published data of neat liquids show significant scatter or typically do not exist at all for the UV. Measurement of the refractive index, on the other hand, remains a challenge at the shorter wavelengths.
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 To overcome this deficiency, we developed a new method for the direct measurement of the GVM in the UV. It is based on a standard pump probe arrangement in which the pulses are propagating parallel to each other before being focused to an interaction region, in our case a BBO crystal, in which intensity cross correlation (CC) is measured. The principle of our method is very simple: a thick sample cell is positioned before the focusing optics, and CC is recorded when the cell is empty, and when it is filled with the solvent. Since the pulse with the shorter central wavelength has a longer optical path in the solvent, the path of the other pulse has to be adjusted with the help of the variable optical delay line to maintain the temporal overlap between the two pulses in the nonlinear crystal. The shift of the optical delay line is equal to the GVM and sample thickness product.
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 We measured the GVM in the 230 to 640 nm spectral range for toluene, cyclohexane and water (indicated by symbols in the figure) and compared the obtained results with values calculated from previously published dispersion formulae (lines). There is an excellent agreement in the visible spectral range. In the UV, however, the measured GVM is always significantly higher than the predicted values, when the dispersion curves were obtained by extrapolation of refractive index data outside the measured wavelength range (below 405 nm for toluene, and below 326 nm for cyclohexane).
We also showed that a straightforward way exists to derive a function describing the wavelength dependence of the refractive index from the measured GVM data. The GVM was measured and dispersion formulae were derived at room temperature in the 230 to 640 nm spectral range for 2-propanol, acetonitrile, cylcohexane, dimethyl sulfoxide, ethanol, ethyl acetate, ethylene glycol, methanol, n-hexane, toluene, and water - supplying data useful for the most common spectroscopic situation.
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"Direct measurement of the group velocity mismatch and derivation of the refractive index dispersion for a variety of solvents in the ultraviolet"
Ida Z. Kozma, Patrizia Krok, and Eberhard Riedle
J. Opt. Soc. Am. B 22, 1479-1485 (2005)
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