Fluorescence microscopy, is an important tool in modern cell biology. A variation on this technique depends on a phenomenon known as two-photon excitation. If two photons are absorbed simultaneously (i.e., within about \(10^{-16} \mathrm{~s}\) ), their energies can add. A molecule that is normally excited by a \(350 \mathrm{~nm}\) photon can be excited by two photons each having half as much energy. For this process to be useful, photons must illuminate the sample at the very high rate of at least \(10^{29}\) photons \(/ \mathrm{m}^{2} \cdot \mathrm{s}\). This is achieved by focusing a laser beam to a small spot and by concentrating the power of the laser into very short \(\left(10^{-13} \mathrm{~s}\right)\) pulses that are fired \(10^{8}\) times each second. Suppose a biologist wants to use two-photon excitation to excite a molecular species that would be excited by \(500 \mathrm{~nm}\) light in normal one-photon fluorescence microscopy. What minimum intensity \(\left(\mathrm{W} / \mathrm{m}^{2}\right)\) must the laser beam have during each pulse?