Two-Photon Absorption Calculator

How to use the two-photon absorption calculator

What this calculator does. It estimates the photon flux at the center of a focused Gaussian beam and the expected number of two-photon excitations per molecule during a stated exposure. The result is useful for checking orders of magnitude in nonlinear-optics experiments, comparing fluorophores or absorbers with different two-photon cross-sections, exploring how tighter focusing changes excitation, and preparing a reproducible calculation for a lab note. It does not predict fluorescence yield, photobleaching, saturation, heating, pulse-shape effects, propagation losses, or biological response. Those effects require additional experimental parameters.

When to use it. Use the calculator to compare candidate wavelengths for a known absorber, estimate how changing objective focus affects central excitation, perform a quick plausibility check before microscopy or spectroscopy work, or document the assumptions behind a classroom or research calculation. The underlying idea is consistent with the standard description of two-photon absorption in nonlinear optics, where excitation depends quadratically on photon flux.

How to calculate. The page opens with a complete demonstration: 210 GM, 10 W, 840 nm, 20 μm FWHM, and 1 s. Its results and XLSX workbook are available immediately. To run your own case:

1. Replace each demonstration value with a plain decimal number using a period as the decimal separator. Do not enter scientific notation, unit symbols, commas, or negative values.
2. Read the live Excitations per molecule (N) result first, then inspect Photon flux (ϕ), Beam radius (w), Peak intensity (I), and Photon energy to understand how the result was formed.
3. Use the calculation-detail table to copy canonical values with more precision. Select Download Excel to create a fresh workbook from the current validated inputs.
4. Select Reset to clear the demonstration and all calculated content. Reset intentionally leaves required fields empty and disables Excel export until a complete valid input set is entered again.

Input guide. Cross-section (δ) is required, measured in Göppert-Mayer units, and must be greater than zero; 210 GM is a realistic example. Increasing it raises excitations linearly. A common mistake is entering a value already converted to cm⁴·s/photon instead of the numerical GM value. Laser power (P) is required in watts and must be positive; 10 W is the demonstration value. Excitations scale with the square of power because photon flux is proportional to power. Do not substitute pulse energy unless it has first been converted into a model-appropriate power. Wavelength (λ) is required in nanometers and must be positive; 840 nm is shown. At fixed power and focus, a longer wavelength means lower photon energy and therefore more photons per second, increasing photon flux in this simplified model. Focus size FWHM is required in micrometers and must be positive; 20 μm is shown. A smaller FWHM increases peak intensity strongly, and because excitation is quadratic in flux, the final count changes approximately with the inverse fourth power of FWHM. Exposure time (τ) is required in seconds and may be zero or positive; 1 s is shown. It scales excitations linearly. Zero exposure correctly yields zero excitations while the beam quantities remain defined.

Output guide. Excitations per molecule (N) is a dimensionless expected count from the idealized rate equation. Zero means no modeled exposure or effectively no two-photon events; a high value does not by itself prove that saturation or depletion can be ignored. Photon flux (ϕ) is reported in photons per square centimeter per second and is driven by power, wavelength, and focus. Beam radius (w) is the Gaussian 1/e²-style radius used by this formulation, converted from the entered FWHM. Peak intensity (I) is the modeled central intensity in W/cm². Photon energy is an exact conversion from wavelength using the defined SI values of the speed of light and Planck constant; the NIST fundamental constants reference explains those constants. The summary pills repeat photon flux and excitations from the same canonical model, while the detail table provides the same quantities at higher displayed precision.

Worked example. For δ = 210 GM, P = 10 W, λ = 840 nm, FWHM = 20 μm, and τ = 1 s, the beam radius is 20/√(2 ln 2) = 16.986 μm. The peak intensity is 2P/(πw²) = 2.206356 × 10⁶ W/cm². A photon at 840 nm carries 2.364826 × 10⁻¹⁹ J, so the central photon flux is 9.329925 × 10²⁴ ph/(cm²·s). Substituting δ = 210 × 10⁻⁵⁰ cm⁴·s/photon into N = ½δϕ²τ gives 91.399871 excitations per molecule, displayed as 91.400.