What is a Göppert-Mayer unit?

Named after Maria Göppert-Mayer who predicted TPA in 1931, 1 GM = 10⁻⁵⁰ cm⁴·s·photon⁻¹. It measures the probability of simultaneous two-photon absorption. Values range from 10,000 GM for designed chromophores.

Why use two-photon instead of one-photon excitation?

TPA uses near-IR light (~700-1100 nm) which penetrates tissue deeper (up to ~1 mm), causes less photodamage, and provides inherent 3D sectioning because absorption only occurs at the tight focal volume where photon density is highest. This keeps planning practical and lowers the chance of preventable errors.

What lasers are used for TPA microscopy?

Ti:sapphire lasers (tunable ~680-1080 nm, ~80 MHz, ~100 fs pulses) are standard. Newer options include OPO systems for extended wavelength range and fiber lasers for specific fixed wavelengths.

How does concentration affect TPA?

TPA rate scales linearly with concentration (like OPA), but quadratically with photon flux. Doubling the laser power quadruples the TPA signal, unlike one-photon where it only doubles.

What is the action cross-section?

Action cross-section = σ₂ × quantum yield (σ₂φ). It's the practical figure of merit for fluorescence microscopy because it combines absorption probability with emission efficiency.

Can TPA be used for photodynamic therapy?

Yes, TPA-PDT uses near-IR light that penetrates deeper into tissue. The photosensitizer absorbs two photons to reach the excited state that generates reactive oxygen species. Requires high σ₂ values (>100 GM) for practical efficacy.

Two-Photon Absorption Calculator

Calculate two-photon absorption cross-sections, excitation wavelengths, action cross-sections, and fluorescence rates. Covers GM units, power density, and comparison of TPA fluorophores.

Common TPA Fluorophores

One-Photon Absorption Peak

TPA Cross-Section (σ₂)

Quantum Yield (φ)0 to 1

Laser Parameters

Average Power

Repetition Rate

MHz

Pulse Width

Focal Diameter

µm

Fluorophore Concentration

µM

λ_OPA = 490 nm → λ_TPA = 980 nm (near-IR)

σ₂φ = 38.0 × 0.93 = 35.3 GM

TPA Wavelength

980 nm

Near-IR (tissue window)

Photon Energy

1.266 eV

Two-photon total: 2.532 eV

Action Cross-Section

35.3 GM

σ₂ × quantum yield

Peak Power

1.3 kW

Instantaneous power during pulse

Photon Flux

3.14e+30 cm⁻²s⁻¹

Peak photon flux at focal point

TPA Rate per Molecule

3.74e+12 s⁻¹

Absorption events per molecule per second

Wavelength Spectrum

OPA 490 nm

TPA 980 nm

300 nm (UV)550 nm (Vis)800+ nm (NIR)

Fluorophore Comparison

Fluorophore	OPA λ (nm)	TPA λ (nm)	σ₂ (GM)	QY	σ₂φ (GM)
DAPI	358	700	0.16	0.58	0.1
Fluorescein	490	780	38	0.93	35.0
EGFP	489	920	6	0.6	3.6
YFP	514	960	4.2	0.61	2.6
Rhodamine B	543	840	210	0.5	105.0
Rhodamine 6G	530	830	130	0.95	124.0
Alexa 488	495	780	96	0.92	88.0
Texas Red	596	780	89	0.51	45.0
Cy5	649	820	11	0.27	3.0
Coumarin 307	395	776	14	0.56	7.8
Stilbene 3	350	600	12	0.85	10.0
tdTomato	554	1050	13	0.69	9.0

Planning notes, formulas, and examples

About the Two-Photon Absorption Calculator

Two-photon absorption (TPA) is a nonlinear optical process where two photons are simultaneously absorbed to excite a molecule to a higher electronic state. The energy of the two photons together equals the transition energy: E = hν₁ + hν₂. In practice, two identical photons at twice the wavelength of the one-photon absorption are used, enabling deep-tissue imaging with near-infrared light.

The TPA cross-section (σ₂) is measured in Göppert-Mayer units (GM), where 1 GM = 10⁻⁵⁰ cm⁴·s/photon. Typical fluorescent proteins have σ₂ of 1–100 GM, while specially designed organic fluorophores can exceed 10,000 GM. The action cross-section (σ₂ × φ, where φ is quantum yield) determines practical brightness for microscopy.

This calculator converts between one-photon and two-photon wavelengths, computes photon flux and TPA rates from laser parameters, calculates action cross-sections, and provides a comparison database of common TPA fluorophores used in multiphoton microscopy and photodynamic therapy.

When This Page Helps

Calculate TPA excitation parameters, action cross-sections, and compare fluorophores for multiphoton microscopy, photodynamic therapy, and nonlinear optical applications.

How to Use the Inputs

Enter the one-photon absorption wavelength to find the TPA excitation wavelength.
Enter the TPA cross-section (σ₂) in GM units.
Enter laser parameters: average power, repetition rate, and pulse width.
Specify the fluorescence quantum yield for action cross-section.
View the TPA rate, photon flux, and action cross-section.
Compare with common TPA fluorophores in the reference table.

Formula used

TPA wavelength: λ_TPA = 2 × λ_one-photon\nPhoton energy: E = hc/λ\n\nPhoton flux: F = P_avg / (E_photon × f_rep × τ_pulse × A)\n where P_avg = average power, f_rep = repetition rate, τ = pulse width, A = focal area\n\nTPA rate: R_TPA = σ₂ × F² × C\n where σ₂ = TPA cross-section, C = concentration\n\nAction cross-section: σ₂φ = σ₂ × quantum yield\n1 GM = 10⁻⁵⁰ cm⁴·s·photon⁻¹ This keeps planning practical and lowers the chance of preventable errors.

Example Calculation

Result: TPA λ = 976 nm, action σ₂φ = 90 GM

For a fluorophore with one-photon peak at 488 nm: TPA wavelength = 976 nm (near-IR). With σ₂ = 100 GM and QY = 0.9, the action cross-section is 90 GM. Using 10 mW average power at 80 MHz rep rate with 100 fs pulses, the instantaneous photon flux and TPA rate are computed.

Tips & Best Practices

For microscopy, action cross-section (σ₂φ) matters more than σ₂ alone.
TPA signal scales with I² — use pulsed lasers to get high peak power at low average power.
The TPA wavelength is approximately (not exactly) 2× the one-photon peak due to different selection rules.
Background-free detection: only the focal volume fluoresces, giving inherent z-sectioning.
Common TPA dyes: fluorescein (38 GM), rhodamine B (210 GM), DAPI (0.16 GM), GFP (~6 GM).
For three-photon excitation, use λ ≈ 3× the OPA wavelength and even shorter pulses.

Physics of Two-Photon Absorption

TPA is a third-order nonlinear optical process. The transition probability is proportional to the square of the light intensity (I²), which is why it only occurs at the laser focal point where photons are most concentrated. The TPA cross-section tensor connects to molecular properties through the imaginary part of the third-order susceptibility χ⁽³⁾.

Fluorophore Design for TPA

High σ₂ values come from extended π-conjugation, donor-acceptor-donor (D-A-D) architecture, and planar molecular geometry. Push-pull chromophores with strong intramolecular charge transfer have the largest TPA cross-sections. Quantum dots and conjugated polymers can exhibit σ₂ > 10⁴ GM per particle.

Applications Beyond Microscopy

Two-photon absorption enables 3D microfabrication (two-photon polymerization), optical data storage, photodynamic therapy with deeper tissue penetration, upconversion lasing, and optical power limiting for eye/sensor protection against intense laser pulses.

Sources & Methodology

Last updated: June 1, 2026

Frequently Asked Questions

Named after Maria Göppert-Mayer who predicted TPA in 1931, 1 GM = 10⁻⁵⁰ cm⁴·s·photon⁻¹. It measures the probability of simultaneous two-photon absorption. Values range from <1 GM for simple molecules to >10,000 GM for designed chromophores.