Two-Photon Absorption Calculator

Created by Luciano Mino
Last updated: Jun 26, 2022

Using the two-photon absorption calculator, you can find the amount of two-photon excitations per molecule given a Gaussian beam laser source.

In this short article, we will explain:

  • What two-photon absorption is; and
  • The two-photon absorption equation.

Keep reading to learn more!

What is two-photon absorption?

Two-photon absorption is a phenomenon discovered by Maria Goppert-Mayer in 1931. In this scenario, an atom or molecule absorbs two photons at once, taking the particle from the ground state (E0E_{0})to a higher virtual energy state (EnE_{n}).

These photons can have equal or different wavelengths, and the difference between the energy in the two states matches the sum of the energy of both photons.

Difference in the energy between both states
Difference in the energy between ground state and the excited state

Two photon absorption equation

The two-photon absorption calculator finds the number of two-photon excitations per molecule NN by using the following formula:

N=12δϕ2τ\quad N = \frac{1}{2} \cdot \delta \cdot \phi^2 \cdot \tau

where:

  • δ\delta – Cross-section in GM. One GM is 1050 cm4sph110^{-50}\ \rm cm^4 \cdot s \cdot ph^{-1};
  • τ\tau – Exposure time; and
  • ϕ\phi – Photon flux at the center of the Gaussian beam.

Finding two-photon excitations number without photon flux

You'll notice the two-photon absorption calculator has a few other parameters.
These come in handy if you don't know ϕ\phi since you can calculate it with the following equation:

ϕ=Ihν=Iλhc\quad \phi = \frac{I}{h\nu} = \frac{I \lambda}{hc}

where:

  • ν\nu and λ\lambda are the photon's frequency and wavelength, respectively;
  • II is the beam's intensity; and
  • cc is the speed of light.

And we can write the intensity using its power PP and beam radius ww as:

I=2Pπw2\quad I = \frac{2P}{\pi w^2}

Lastly, we can replace the beam radius with the laser's full width at half-maximum (FWHM) value:

w=FWHM2 ln2\quad w = \frac{\rm FWHM}{\sqrt{2\ \ln 2}}

Using the two photon absorption calculator

Let's assume we have the following data:

  • ϕ=7.41024phcm2s\phi = 7.4\cdot 10^{24} \frac{ph}{cm^{2}s} for a given laser.
  • δ=200 GM\delta = 200\ \text{GM}.
  • τ=1.2s\tau = 1.2 s

This is all we need to find the number of two-photon excitations according to the two-photon absorption equation.

We can plug that information into the calculator to find that N=65.71N = 65.71.

Luciano Mino
Cross-section (δ)
GM
Laser power (P)
W
Wavelength (λ)
nm
Focus size FWHM
μm
Exposure time (τ)
ns
Photon flux (ϕ)
x10²⁴
ph/(cm²•s)
Excitations per molecule (N)
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