Single-photon 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.

single-photon absorption

The equation describing the intensity attenuation of a light beam passing through a material undergoing single-photon absorption is given by

I  / z = − α I (PROP equation)

where α is a constant. The absorbed power in a thickness element dz for single-photon absorption is proportional to light intensity.

Single-photon absorption constant α is usually found for a certain (known) concentration of photo-activated material (species). The main assumption is that during interaction of laser beam with the material the concentration of photo-activated 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 However, for ultra-fast processes this assumption is no longer valid and a more detailed model is usually used for numerical calculations.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 single-photon absorption molecular cross-section σSPA , while the concentration (or, population density) of the species being in ground state N0 is is “detached” from the absorption constant as follows:

I(z,t)  / z = − σSPA N0(z,t) I(z,t) (detailed PROP)

The function of concentration N0(z,t) follows the following corresponding rate equation:

N0  / t = − σSPA N0(z,t) I(z,t) / h ω0 + k10 (N-N0) (RATE equation)

where N is the initial concentration of species and k10 attributes to the rate of relaxation of species from the excited state.

See also: Two-photon absorption, Three-photon absorption, Relaxation.

SimphoSOFT logo SimphoSOFT® supports modeling single-photon (as well as two- and three-photon) absorption. Its mathematical model includes a variant of PROP equation, written in the terms of electromagnetic field, coupled with time-resolved radially-dependent RATE equations.

SimphoSOFT® case study of excited-state single-photon absorption in a chromophore AF455.

Video describing how to build energy level diagram for optical limiter, containing single- and two-photon absorption transitions, and how to optimize its performance in SimphoSOFT®.
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