TwoPhoton Absorption Calculator
Table of contents
What is twophoton absorption?How to calculate twophoton excitation rate – Twophoton absorption equationHow to use the twophoton absorption calculator – TPA calculation exampleFAQsOmni's twophoton absorption calculator allows you to determine the number of twophoton excitations per molecule for a given laser source.
Continue reading this article to know what twophoton absorption (TPA) is and how to calculate the excitation rate using the twophoton absorption equation. You will also find an example of TPA calculation.
What is twophoton absorption?
Twophoton absorption (TPA) is a process where an atom or a molecule absorbs two photons simultaneously. The energy of the two photons can be identical or different. This absorption results in the excitation of the atom or molecule from one energy state (usually the ground state) to a higherenergy state via an induced virtual state (shown by the dashed horizontal line in Figure 1).
As shown in Figure 1, the difference in the energy of the two states is equal to the sum of the energy of the two absorbed photons.
The phenomenon was first predicted by Maria GoppertMayer in 1931, and Kaiser and Garret experimentally verified it in 1963.
How to calculate twophoton excitation rate – Twophoton absorption equation
To calculate the number of twophoton excitations per molecule $N$, we will use the formula:
where:
 $\delta$ – Twophoton absorption (TPA) crosssection measured 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 a Gaussian beam.
💡 Do you know the twophoton absorption crosssection is expressed in units of GM to honor Maria GoppertMayer?
Since the energy carried by a photon is $h\nu$, the number of photons crossing a unit area per unit time (i.e., the photon flux) is related to the intensity of the beam $I$ by the expression:
The intensity of the laser beam with power $P$ and the beam radius $w$ can be described as:
Where the beam radius is related to the full width at half maximum (FWHM) as (see figure 2):
In the next section, we will use the twophoton absorption calculator to calculate the number of excitations per molecule for a given laser pulse.
How to use the twophoton absorption calculator – TPA calculation example
Let's calculate the photon flux and number of excitations per molecule when a sample is irradiated for $1\ \rm s$ with a $10\ \rm W$ laser source of wavelength $840\ \rm nm$. The twophoton absorption crosssection is $210\ \rm GM$, and the FWHM of the focussed laser beam is $20 \ \rm\mu m$.

Enter the twophoton absorption crosssection in GM ($210\ \rm GM$).

Type the power of the laser source ($10\ \rm W$), the wavelength of the beam ($840\ \rm nm$), and the FWHM of the focussed beam ($20 \ \mu \rm m$). You can also use the wavelength calculator or the energy to wavelength calculator to find out the wavelength if you know the frequency or energy of the laser source.

Enter the exposure time ($1\ \rm s$).

The twophoton absorption calculator will give you the photon flux at the center of the beam ($9.33 \times 10^{24}\ \rm ph/(cm^2·s)$) and the number of excitations per molecule ($91.4$).
What does photon absorption mean?
Photon absorption is a process in which an atomic electron absorbs the energy of an incident photon. If the photon's energy is higher than the binding energy of the electron, the electron is ejected from the atom. Otherwise, the electron gets excited to a higher energy state within the atom.
Can a free electron absorb a photon?
No, a free electron cannot absorb or emit a photon. The conditions for conservation of energy and momentum are not satisfied in the process if the electron is free. Hence, only electrons that are bound to atoms can absorb photons.
How do you measure twophoton absorption crosssection?
Some of the techniques used to measure twophoton absorption crosssection are:
 Twophoton excited fluorescence (TPEF) spectroscopy;
 Zscan approach;
 Masssedimentation approach; and
 Nonlinear transmission method.
What are the applications of twophoton absorption?
The twophoton absorption technique has several applications, including:

The study of novel materials and investigate the relationship between their molecular structure and electronic and optical properties.

Performing highresolution imaging of live cell and tissue samples.
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