So, in multi photon excitation several photons may interact with the molecules
simultaneously and make them reach the excited state. Then relax back with emitting photons. So, will those photons be with longer wavelength than the excited ones?.
In single photon excitation, the energy of the photon used for excitation matches the S0-S1 energy gap whereas in multi-photon the energy of the photon used for excitation is either half or one third of the S0-S1 energy gap in a molecule.
Since the wavelength of excitation is different, dye photobleaching rates are different and light penetration depths can also be different.
Multiple photons are used to cause excitation from S0 state to S1 state. For example, in two photon excitation two photons of half the energy would be needed to excite an electron from S0 to S1 state.whereas in three photon excitation three photons of one-time third energy would be needed to excite an electron from S0 to S1 state.
Since multiple photons need to be absorbed simultaneously by a molecule, higher intensity of light would be needed. It is a non-linear process.
In the case of multi photon excitation one need high intensity laser to provide more number of photons to be absorbed simultaneously to excite atoms or molecules. However if the laser intensity is even more than the required for excitation. Then it can ionize the atoms or molecules and produce plasma. This indicates that multi photon absorption is mainly dependent on laser intensity. That is on number of photons available for interaction.
" So, will those photons be with longer wavelength than the excited ones?."
This is bit complicated to explain. In one part, it is possible the emission can be at longer wavelength. But it is the combination of following factors:, the material properties, its dimension, shape, excitation wavelength and temperature.