Two Photon Absorption Calculator
Calculate two photon absorption with our free science calculator. Uses standard scientific formulas with unit conversions and explanations.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
T = 1 / (1 + beta * I * L) | beta = sigma2 * N
T is the transmission, beta is the TPA coefficient (sigma2 times number density N), I is the laser intensity in W/cm2, and L is the path length. Sigma2 is the TPA cross section in GM units (10^-50 cm^4 s/photon). The absorption rate is proportional to intensity squared.
Worked Examples
Example 1: Fluorescent Dye TPA
Problem:A fluorescent dye with sigma2 = 50 GM at 800 nm, concentration 0.01 mol/L, path length 0.1 cm, laser intensity 10^9 W/cm2.
Solution:sigma2 = 50e-50 cm4 s/photon\nN = 0.01 * 6.022e23 / 1000 = 6.022e18 /cm3\nbeta = 50e-50 * 6.022e18 = 3.011e-28 cm/W\nbeta*I*L = 3.011e-28 * 1e9 * 0.1 = 3.011e-20\nT is essentially 100% (very small absorption)
Result:Negligible absorption at this intensity
Example 2: High Cross-Section Molecule
Problem:A designed chromophore with sigma2 = 5000 GM, concentration 0.1 mol/L, 1 cm path, intensity 10^12 W/cm2.
Solution:sigma2 = 5000e-50 cm4 s/photon\nN = 6.022e19 /cm3\nbeta = 5000e-50 * 6.022e19 = 3.011e-27 cm/W\nbeta*I*L = 3.011e-27 * 1e12 * 1 = 3.011e-15\nStill very small absorption per pass
Result:Significant TPA only at extreme intensities
Frequently Asked Questions
What is two-photon absorption?
Two-photon absorption (TPA) is a nonlinear optical process where a molecule simultaneously absorbs two photons to reach an excited electronic state. Unlike single-photon absorption, the transition energy equals the sum of the energies of both photons, so each photon typically has half the energy (twice the wavelength) needed for a one-photon transition. TPA was first predicted theoretically by Maria Goeppert-Mayer in 1931 and experimentally observed after the invention of lasers. The probability of TPA depends on the square of the light intensity, making it significant only under high-intensity laser illumination.
What are the applications of two-photon absorption?
Two-photon absorption has numerous important applications across science and technology. In microscopy, two-photon fluorescence microscopy provides superior depth penetration and reduced photobleaching for imaging biological tissues. In photodynamic therapy, TPA enables activation of photosensitizers deep within tissue using near-infrared light. TPA is also used in 3D microfabrication and lithography, where the quadratic intensity dependence allows writing features smaller than the diffraction limit. Additional applications include optical data storage, optical power limiting for laser protection, and upconversion lasing.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy