We have devised an accurate method to measure multiphoton excitation cross sections in order to establish a reliable data base of excitation cross sections in the visible and near IR for two photon fluorescence microscopy. Because quantum mechanical parity selection rules modify transition probabilities it is not possible to predict two-photon (even parity) excitation spectra by simple doubling the wave lengths of the one-photn (odd parity) excitations. However, three-photon (odd parity) excitation spectra do follow at three times the one-photon spectra. The figures below show a sampling of our measured data for the wavelength ranges of the most promising mode-locked lasers as nonlinear excitation sources are plotted below for comparison.

Multiphoton Fluorophore cross sections. The molecular MPE nonlinear cross section relates the average rate of n-photon absorption per fluorophore W_n to the average power of the photon flux density: W_n=s_n<I_n>. For example depends on the pair density of photons and thus on the average squared photon flux: W₂=s₂<I₂> and W₃=s₃<I₃>. Two-photon cross sections are cited in GM units (after Maria Goeppert-Mayer who first predicted two photon absorption as a single quantum event) in which 1 GM = 10-50 cm⁴sec. The units of can be understood in terms of the one-photon cross section and a time scale of simultaneity. The energies of two photons can combine only if those photons interact with the same fluorophore at the same time. Thus s₂=s₁DADt where DA is the molecular area of electronic interactions: AD @ s₁ @ 10^-17-10^-16cm². The time interval Dt is the time scale of molecular energy fluctuations at photon energy scales, as determined by the Heisenberg uncertainty principle: Dt @ 10^–16 sec. Thus is on the order of 10 GM. This same argument can be generalized to higher order processes: s_n @ s₁ⁿDt^n–1.

Two vs one photon cross sections

More two photon cross sections

Fluorophore photostability