Two-Photon Absorption Calculator
Calculate two-photon excitation rates and photon flux for laser-induced molecular absorption
Calculate Two-Photon Absorption
Cross-section in GM units (1 GM = 10⁻⁵⁰ cm⁴⋅s⋅ph⁻¹)
Average power of the laser beam
Wavelength of the laser light
Full width at half maximum of the focused beam (μm)
Duration of laser exposure
Two-Photon Absorption Results
Formula: N = (1/2) × δ × φ² × τ
Beam radius: w = FWHM / (2√ln2) = 12.0 μm
Analysis: Intense two-photon absorption events - Very high efficiency
Common Laser Examples
Ti:Sapphire Laser
Standard two-photon microscopy laser
λ: 800 nm, P: 10 W, FWHM: 15 μm, δ: 200 GM
Nd:YAG Laser (doubled)
Frequency-doubled Nd:YAG
λ: 532 nm, P: 5 W, FWHM: 25 μm, δ: 150 GM
Er:Glass Laser
Near-infrared applications
λ: 1540 nm, P: 15 W, FWHM: 30 μm, δ: 300 GM
Femtosecond Ti:Sapphire
Ultrafast two-photon processes
λ: 840 nm, P: 20 W, FWHM: 10 μm, δ: 250 GM
TPA Cross-Section Values
Small Molecules
1-100 GM
Organic dyes, simple aromatics
Fluorescent Proteins
10-200 GM
GFP, RFP, and variants
Optimized Dyes
100-1000 GM
Specially designed TPA chromophores
Quantum Dots
1000-10000 GM
Semiconductor nanocrystals
Key Formulas
Where: δ = cross-section (GM), φ = photon flux (ph/cm²/s), τ = time (s), I = intensity (W/cm²), P = power (W)
TPA Applications
Understanding Two-Photon Absorption
What is Two-Photon Absorption?
Two-photon absorption (TPA) is a nonlinear optical process where an atom or molecule simultaneously absorbs two photons to reach an excited state. The energy of both photons combined equals the energy difference between the ground and excited states.
Key Characteristics
- •Simultaneous absorption of two photons
- •Quadratic dependence on light intensity
- •Virtual intermediate state involvement
- •Confined to focal volume (3D localization)
Historical Background
The phenomenon was first theoretically predicted by Maria Göppert-Mayer in 1931 as part of her doctoral dissertation. It was experimentally verified by Kaiser and Garrett in 1963 using a ruby laser, confirming the quadratic intensity dependence.
Mathematical Framework
En - E0 = 2hc/λ
N = (1/2) × δ × φ² × τ
φ = Iλ/(hc)
Parameters
- δ: Two-photon absorption cross-section (GM units)
- φ: Photon flux at beam center (ph/cm²/s)
- τ: Exposure time (s)
- I: Laser intensity (W/cm²)
- λ: Wavelength (m)
- N: Number of excitations per molecule
Note: The GM unit honors Maria Göppert-Mayer. 1 GM = 10⁻⁵⁰ cm⁴⋅s⋅photon⁻¹
Applications and Advantages
Two-Photon Microscopy
Deep tissue imaging with reduced photobleaching and improved 3D resolution due to nonlinear excitation.
Photodynamic Therapy
Precise spatial control of therapeutic activation, minimizing damage to surrounding healthy tissue.
3D Microfabrication
Sub-diffraction-limited manufacturing through precise two-photon polymerization processes.