Two-Photon Absorption (TPA) Calculator
Two-photon absorption (TPA) is a nonlinear optical process in which a molecule simultaneously absorbs two photons to reach an excited state. Enter the TPA cross-section in Göppert-Mayer (GM) units, the laser wavelength, sample concentration, peak intensity, and path length to get the bulk absorption coefficient, sample transmittance, and per-molecule excitation rate.
GM
nm
mM
GW/cm²
mm
Fraction of laser power transmitted through the sample (thin-sample open-aperture approximation)
How does this calculator work?
Given TPA cross-section σ [GM], laser wavelength, sample concentration, peak intensity, and path length, this calculator computes the bulk TPA coefficient β = N·σ/ℏω, the sample transmittance T = 1/(1 + β·I₀·L), and the per-molecule TPA excitation rate R = σ·Φ². TPA scales as intensity squared, so transmittance drops rapidly at high peak powers.
Formula
How this is calculated
The TPA cross-section σ (in Göppert-Mayer units: 1 GM = 10⁻⁵⁰ cm⁴·s) quantifies how strongly a molecule absorbs two photons simultaneously. The bulk TPA coefficient β [m/W] is obtained by multiplying σ by the molecular number density N and dividing by the single-photon energy ℏω = hc/λ. β connects material properties to measurable nonlinear loss.
Sample transmittance follows the open-aperture z-scan approximation T = 1/(1 + β·I₀·L), valid when the nonlinear loss per unit length is small compared with linear propagation effects. The factor β·I₀·L gives the effective nonlinear optical depth; values above ~0.3 indicate significant TPA attenuation. At higher intensities or longer path lengths the transmittance drops sharply, demonstrating the intensity-squared dependence characteristic of a two-photon process.
The per-molecule TPA excitation rate R = σ·Φ² (where Φ = I₀/ℏω is the photon flux) gives the number of two-photon events per molecule per second at peak intensity. For pulsed lasers, multiply by the pulse duration to get the excitation probability per pulse. Assumptions: thin-sample limit (no significant beam reshaping), negligible linear absorption at the laser wavelength, and no excited-state or multi-photon effects beyond second order.
Frequently asked questions
1 GM = 10⁻⁵⁰ cm⁴·s (sometimes written cm⁴·s·photon⁻¹). The unit was named after Maria Göppert Mayer, who predicted two-photon absorption in 1931. Typical TPA cross-sections range from < 1 GM for simple molecules to tens of thousands of GM for purpose-designed chromophores used in TPA microscopy or photodynamic therapy.
TPA excitation is confined to the focus of a tightly focused pulsed laser, because absorption scales as I², giving intrinsic 3-D optical sectioning without a confocal pinhole. Wavelengths in the near-infrared (700–1100 nm) also penetrate tissue more deeply with less scattering and phototoxicity than the UV/visible photons that would produce the same excited state via one-photon absorption.
The formula assumes a plane wave with uniform intensity and negligible beam diffraction, linear refractive-index changes, and no linear absorption at the laser wavelength. For Gaussian beams or high-NA focusing, the result overestimates TPA because intensity varies across the beam profile. Significant nonlinear loss (β·I·L ≫ 1) also pushes the regime where higher-order effects and excited-state absorption matter.
Also known as
TG we-Calculate Editorial Team. (2026). Two-Photon Absorption (TPA) Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/two-photon-absorption-calculator
TG we-Calculate Editorial Team. "Two-Photon Absorption (TPA) Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/two-photon-absorption-calculator.
TG we-Calculate Editorial Team, "Two-Photon Absorption (TPA) Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/two-photon-absorption-calculator
@misc{wecalculate_two_photon_absorption_calculator, title = {Two-Photon Absorption (TPA) Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/two-photon-absorption-calculator}}, year = {2026}, note = {TG we-Calculate} }
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