Singlephoton absorption (SPA or 1PA) is a linear absorption process whereby one photon excites an atom, ion or molecule from a lower energy level to a higher energy level, for example, from the ground state to the first excited state.
The equation describing the intensity attenuation of a light beam passing through a material undergoing singlephoton absorption is given by
∂I / ∂z = − α I  (PROP equation) 
where α is a constant. The absorbed power in a thickness element dz for singlephoton absorption is proportional to light intensity.
Singlephoton absorption constant α 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 However, for ultrafast processes this assumption is no longer valid and a more detailed model is usually used for numerical calculations.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 singlephoton absorption molecular crosssection σ_{SPA} , 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_{SPA} N_{0}(z,t) I(z,t)  (detailed PROP) 
The function of concentration N_{0}(z,t) follows the following corresponding rate equation:
∂N_{0} / ∂t = − σ_{SPA} N_{0}(z,t) I(z,t) / 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: Twophoton absorption, Threephoton absorption, Relaxation.
SimphoSOFT® supports modeling singlephoton (as well as two and threephoton) absorption. Its mathematical model includes a variant of PROP equation, written in the terms of electromagnetic field, coupled with timeresolved radiallydependent RATE equations.
SimphoSOFT® case study of excitedstate singlephoton absorption in a chromophore AF455. Video describing how to build energy level diagram for optical limiter, containing single and twophoton absorption transitions, and how to optimize its performance in SimphoSOFT®. 
App Notes 
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