Simultaneous All-Optical Determination of Molecular Concentration and Extinction Coefficient

Absolute molecular number concentration and extinction coefficient are simultaneously determined from linear and nonlinear spectroscopic measurements. This method is based on measurements of absolute femtosecond pump–probe signals. Accounting for pulse propagation, we present a closed form expression for molecular number concentration in terms of absorbance, fluorescence, absolute pump–probe signal, and laser pulse parameters (pulse energy, spectrum, and spatial intensity profile); all quantities are measured optically. As in gravimetric and coulometric determinations of concentration, no standard samples are needed for calibration. The extinction coefficient can then be determined from the absorbance spectrum and the concentration. For fluorescein in basic methanol, the optically determined molar concentrations and extinction coefficients match gravimetric determinations to within 10% for concentrations from 0.032 to 0.540 mM, corresponding to absorbance from 0.06 to 1. In principle, this photonumeric method is extensible to transient chemical species for which other methods are not available.