Threephoton absorption (3PA) is a nonlinear absorption process whereby three photons are absorbed simultaneously by an atom, ion or molecule and an electron is promoted from a lower energy level to a higher energy level. For example, threephoton absorption can excite an electron from the ground state to an excited state. The total energy of the transition is equal to the sum of the three photon energies.
The equation describing the intensity attenuation of a light beam passing through a material undergoing singlephoton, twophoton and threephoton absorption is given by
∂I / ∂z = − α I − β I^{2} − γ I^{3}  (prop equation) 
where α, β and γ are constants. The constant γ for threephoton absorption is related to the fifthorder susceptibility. The absorbed power in a thickness element dz for singlephoton absorption is proportional to light intensity, whereas the absorbed power for twophoton absorption is proportional to the intensity squared and the absorbed power for threephoton absorption is proportional to the intensity cubed.
Threephoton absorption constant γ is usually found for a certain (known) concentration of photoactivated material (species). The main assumption is that during interaction of laser beam with the material the concentration of photoactivated species (molecules, ions, QDs etc) remains constant most of the time (e.g., it reaches equilibrium in a fraction of the beam duration). However, for ultrafast processes this assumption is no longer valid and a more detailed model is usually used for numerical calculations. The central parameter of the new model is a threephoton absorption molecular crosssection σ_{3PA} , while the concentration (or, population density) of the species being in ground state N_{0} is is “detached” from the absorption constant as follows:
∂I(z,t) / ∂z = − σ_{3PA} N_{0}(z,t) I^{3}(z,t)  (detailed PROP) 
For simplicity, we left many other important terms out of this example equation – which may include singlephoton, twophoton, or, generally speaking, multiphoton absorption, linear absorption, stimulated emission etc. Each multiphoton absorption term will have a factor of population density of the energy state from which the absorption occurs. The function of concentration N_{0}(z,t) follows the following corresponding rate equation:
∂N_{0} / ∂t = − σ_{3PA} N_{0}(z,t) I^{3}(z,t) /3 h ω_{0} + k_{10} (NN_{0})  (RATE equation) 
where N is the initial concentration of species and k_{10} attributes to the rate of relaxation of species from the excited state.
See also: Singlephoton absorption, Twophoton absorption, Relaxation.
SimphoSOFT® supports modeling twophoton (as well as single and threephoton) absorption. Its mathematical model includes propagation equation, written in the terms of electromagnetic field, coupled with timeresolved radiallydependent rate equations. 
SimphoSOFT® can be purchased as a single program and can be also configured with Energy Transfer addon , MultiBeam addon , Optimization addon , Zscan addon , and MPA Info+ addon for an additional charge. Please, contact our sales staff for more information


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