Two-Photon Absorption Calculator
Calculate the two-photon excitation rate per molecule for any laser source using TPA cross-section, laser power, wavelength, focus size, and exposure time. Free online TPA calculator with photon flux and breakdowns.
About This Calculator
The Two-Photon Absorption Calculator helps researchers, physicists, chemists, and microscopy professionals determine the number of two-photon excitations per molecule for a given laser source. By entering the TPA cross-section (in GM units), laser power, wavelength, focused beam size, and exposure time, you can quickly compute the photon flux at the center of a Gaussian beam and the resulting excitation rate per molecule.
Two-photon absorption (TPA) is a nonlinear optical process where an atom or molecule simultaneously absorbs two photons. The total energy of both photons must match the energy gap between the ground and excited states. The phenomenon was first predicted by Maria Goppert-Mayer in 1931 and was experimentally verified by Kaiser and Garret in 1963. The rate is calculated using N = ½ × δ × φ² × τ, where δ is the TPA cross-section, φ is the photon flux derived from the beam intensity I = 2P/πw², and τ is the exposure time. The quadratic dependence on photon flux means TPA only occurs significantly at the focal point of a tightly focused beam, enabling intrinsic 3D resolution in microscopy.
This calculator supports real-world laser parameters: typical two-photon microscopy uses femtosecond Ti:sapphire lasers with 700-1100 nm wavelength, 10-100 mW average power at the sample, and pulse widths of 100-200 fs. The cross-section δ varies widely — from ~1 GM for small organic molecules to over 10,000 GM for specially designed chromophores. Default values (210 GM, 10 W, 840 nm, 20 μm FWHM, 1 s exposure) represent a typical experimental configuration.
Results include the photon flux in ph/(cm²·s), the number of excitations per molecule, the beam radius at focus, the beam intensity, and the photon energy. The breakdown table reveals all intermediate calculation steps, making this an ideal educational tool for students learning nonlinear optics, microscopy, and photophysics.
Frequently Asked Questions
What is two-photon absorption (TPA)?
Two-photon absorption (TPA) is a nonlinear optical process where an atom or molecule simultaneously absorbs two photons, combining their energy to reach an excited state. First predicted by Maria Goppert-Mayer in 1931 and experimentally verified in 1963, TPA requires extremely high photon flux densities typically achieved with pulsed lasers. The sum of the two photon energies equals the energy gap between the ground and excited states.
How do you calculate the two-photon excitation rate?
The number of two-photon excitations per molecule is N = ½ × δ × φ² × τ, where δ is the TPA cross-section in GM (1 GM = 10⁻⁵⁰ cm⁴·s·ph⁻¹), φ is the photon flux in ph/(cm²·s), and τ is the exposure time in seconds. The photon flux is derived from laser intensity I = 2P/πw² and beam radius w = FWHM/√(2×ln 2), giving φ = Iλ/hc.
What units are used for the TPA cross-section?
The two-photon absorption cross-section δ is expressed in GM units (Goppert-Mayer), named after Maria Goppert-Mayer. 1 GM = 10⁻⁵⁰ cm⁴·s·ph⁻¹. Typical organic fluorophores have TPA cross-sections ranging from 10 to 1000 GM. The unit reflects the extremely small probability of simultaneous two-photon absorption events.
What are the applications of two-photon absorption?
Two-photon absorption has numerous applications including: high-resolution fluorescence microscopy of live cells and tissues (three-dimensional imaging with deep penetration), photodynamic therapy, 3D optical data storage, microfabrication and lithography, optical power limiting, and the study of electronic structure and optical properties of novel materials.
Why is TPA useful for microscopy compared to single-photon excitation?
Two-photon microscopy offers several advantages over single-photon (confocal) microscopy: deeper tissue penetration due to the use of near-infrared wavelengths (700-1100 nm), reduced photobleaching and phototoxicity since excitation is confined to the focal plane, and intrinsic 3D sectioning capability without a pinhole. The quadratic dependence on intensity means fluorescence only occurs at the focal spot.
What laser parameters affect two-photon absorption?
Key laser parameters affecting TPA include: peak power (higher power increases intensity quadratically), wavelength (near-infrared 700-1100 nm is common for biological applications), pulse duration (femtosecond pulses provide high peak powers at low average power), repetition rate, and focus size (a tighter focus increases intensity). The excitation rate scales as 1/w⁴ with beam radius, making tight focusing critical for efficient TPA.
How does photon flux relate to the TPA excitation rate?
The two-photon excitation rate scales quadratically with photon flux (N ∝ φ²), unlike linear absorption which scales linearly with intensity. This quadratic dependence means that doubling the laser intensity quadruples the TPA excitation rate. It also confines TPA to the focal volume of a tightly focused beam, as the photon flux falls off rapidly away from focus, providing intrinsic three-dimensional resolution.