# Two-Photon Absorption Calculator

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 ($E_{0}$)to a higher virtual energy state ($E_{n}$).

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

## Two photon absorption equation

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

where:

- $\delta$ – Cross-section in GM. One GM is $10^{-50}\ \rm cm^4 \cdot s \cdot ph^{-1}$;
- $\tau$ – Exposure time; and
- $\phi$ – 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** $\phi$ **since you can calculate it with the following equation**:

where:

- $\nu$ and $\lambda$ are the photon's frequency and wavelength, respectively;
- $I$ is the beam's intensity; and
- $c$ is the speed of light.

And we can write the intensity using its $P$ and beam radius $w$ as:

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

## Using the two photon absorption calculator

Let's assume we have the following data:

- $\phi = 7.4\cdot 10^{24} \frac{ph}{cm^{2}s}$ for a given laser.
- $\delta = 200\ \text{GM}$.
- $\tau = 1.2 s$

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 $N = 65.71$.