Two-Photon Absorption Calculator

Model two-photon excitation rates for fluorescence microscopy. Enter laser parameters (power, wavelength, pulse width, repetition rate, NA) and fluorophore properties to calculate single-molecule and total fluorescence rates.

Average power at the sample

Two-photon excitation wavelength

Laser pulse duration in femtoseconds

Laser pulse repetition rate

Objective numerical aperture

Two-photon absorption cross section (1 GM = 10⁻⁵⁰ cm⁴·s/photon)

Concentration of fluorophore (optional for total signal)

Two-Photon Excitation Rate: ⟨n_a⟩ = (P² × δ × NA⁴) / (τ × f² × λ² × h² × c²) × (2/π) Where: • ⟨n_a⟩ = Excitation rate (photons/s/molecule) • P = Average laser power (W) • δ = 2PA cross section (m⁴·s) • NA = Numerical aperture • τ = Pulse width (s) • f = Repetition rate (Hz) • λ = Wavelength (m) • h = Planck's constant (6.626×10⁻³⁴ J·s) • c = Speed of light (3×10⁸ m/s) Peak Power: P_peak = P_avg / (τ × f) Focal Volume (approximate): V_focal = (4π/3)(λ/2NA)³ Molecules in Focus: N = C × V_focal × N_A Total Signal: F_total = ⟨n_a⟩ × N × η Key Properties: • Scales as NA⁴ • Quadratic power dependence • Confocal-like sectioning • Deep tissue penetration
Example 1: Standard 2P Microscope Laser Power: 10 mW at 800 nm Pulse Width: 100 fs, 80 MHz NA: 1.0 (water immersion) Cross Section: 100 GM (GFP) Peak Power = 0.01 W / (100e-15 × 80e6) = 1,250 W Excitation Rate ≈ 0.15 photons/s/molecule Focal Volume ≈ 0.67 fL If [GFP] = 10 µM: Molecules = ~4000 in focus Total Rate ≈ 600 photons/s (good signal for imaging) Example 2: High NA Comparison Change NA from 1.0 to 1.4: Rate increases by (1.4/1.0)⁴ = 3.84× Excitation Rate ≈ 0.58 photons/s/molecule Better signal but shallower imaging depth Example 3: Low Power Imaging Power: 5 mW, NA: 0.8, all else same Rate = 0.15 × (5/10)² × (0.8/1.0)⁴ = 0.15 × 0.25 × 0.41 = 0.015 photons/s/molecule (Reducing power by half reduces signal to 1/4 due to quadratic scaling) Example 4: Dye Comparison Rhodamine B (δ ≈ 150 GM at 800 nm): Rate ≈ 0.23 photons/s/molecule eGFP (δ ≈ 100 GM at 920 nm): Rate ≈ 0.15 photons/s/molecule Quantum dots (δ ≈ 5000 GM): Rate ≈ 7.5 photons/s/molecule (50× brighter than GFP!) Common 2P Dyes: • GFP (920 nm): ~100 GM • Rhodamine B (800 nm): ~150 GM • Alexa 488 (760 nm): ~80 GM • Cy5.5 (800 nm): ~200 GM • Quantum Dots: 1000-10000 GM

What is two-photon absorption (2PA) and how does it differ from one-photon absorption?

Two-photon absorption occurs when two photons are simultaneously absorbed by a molecule, with the combined energy matching an electronic transition. Unlike one-photon absorption which depends linearly on intensity, 2PA scales quadratically with excitation intensity. This nonlinearity confines excitation to a tiny focal volume (~1 femtoliter), enabling unparalleled 3D resolution in fluorescence microscopy without out-of-focus bleaching.

What is a GM unit for two-photon cross sections?

The GM unit (named after Maria Göppert-Mayer, who predicted two-photon absorption in 1931) is 1 GM = 10⁻⁵⁰ cm⁴·s/photon. Typical two-photon cross sections range from 1-100 GM for common fluorophores. Specialized dyes engineered for 2PA can have cross sections of 10,000 GM or more. The small value reflects the inherently weak nature of two-photon absorption, which is why high-intensity pulsed lasers are needed.

Why are femtosecond pulsed lasers used for two-photon microscopy?

Two-photon absorption requires extremely high photon density to achieve measurable excitation rates. Femtosecond lasers concentrate the same average power into ultra-short pulses (~100 fs) with very high peak power, creating the necessary instantaneous photon density. A typical Ti:Sapphire laser with 100 fs pulses at 80 MHz produces peak powers about 100,000 times higher than its average power, making 2PA practical.

How does numerical aperture (NA) affect two-photon excitation?

The excitation rate scales with NA⁴, making high-NA objectives critical for efficient two-photon excitation. A 1.4 NA objective produces about (1.4/0.5)⁴ ≈ 61 times more excitation than a 0.5 NA objective at the same laser power. Higher NA also produces a tighter focal volume, improving spatial resolution. Water immersion objectives are often preferred for deep tissue imaging to match refractive index.

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