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Two-Photon Absorption Calculator

Chemistry

Calculate two-photon absorption rate and excitation probability from TPA cross-section (GM units), laser intensity, and fluorophore concentration.

Reviewed by the thecalcu.com team · Last updated August 16, 2025

10 GM
GM
100 mW
mW
1 μm
μm
1 μM
μM
800 nm
nm

Photon Flux (I)

12,810,000,000,000,000,000,000,000
TPA Absorption Rate
16.41
Irradiance
3,183,098.9
Excitation Probability
0

This calculator computes your Photon Flux (I), TPA Absorption Rate, Irradiance, Excitation Probability from the values you enter.

Inputs
TPA Cross-Section (δ)Laser Peak PowerBeam Waist (w₀)Fluorophore ConcentrationLaser Wavelength
Outputs
Photon Flux (I)TPA Absorption RateIrradianceExcitation Probability

What is a Two-Photon Absorption?

The Two-Photon Absorption Calculator computes photon flux, irradiance, TPA absorption rate, and excitation probability per pulse for a focused pulsed laser interacting with a TPA-active fluorophore. Enter the TPA cross-section (δ, in GM), laser peak power (mW), beam waist (μm), fluorophore concentration (μM), and wavelength (nm).

Two-photon absorption (TPA) is a nonlinear optical phenomenon where a molecule simultaneously absorbs two photons, requiring the high photon densities available only at the focus of pulsed femtosecond lasers. The TPA rate scales as R = δ × I², where δ is the molecular cross-section in Göppert-Mayer units and I is the photon flux. This quadratic intensity dependence confines excitation to the laser focus, enabling 3D-selective imaging and microfabrication at sub-diffraction volumes.

For the single-photon limit (Beer-Lambert Law for linear absorption), the Beer-Lambert Law Calculator applies A = ε × l × c. For chromophore concentration from UV-Vis absorbance measurements used to verify TPA sample preparation, the Beer-Lambert calculator provides the linear analogue. The Calibration Curve Calculator builds standard curves for quantifying fluorophore concentrations.

Why Use a Two-Photon Absorption Calculator?

The TPA photon flux formula requires converting laser power to irradiance (W/cm²), then to photon flux (photons/cm²/s) using E_photon = hc/λ, then squaring and multiplying by δ in SI units (converting GM = 10⁻⁵⁰ cm⁴·s to SI). Each step involves different unit systems that are easy to confuse. This calculator handles all conversions transparently.

Who Should Use This Calculator?

Photophysics and nonlinear optics researchers at TIFR, RRI, IISc, and JNCASR designing TPA experiments and choosing laser parameters for two-photon microscopy.

Biophotonics researchers at AIIMS and NCBS computing excitation conditions for two-photon fluorescence microscopy of live biological samples.

Materials scientists at CSIR-NCL and IIT Bombay designing TPA-active organic dyes, quantum dots, and MOFs for sensing and 3D printing applications.

Optical engineering students learning nonlinear optics and laser physics, TPA is a standard topic in photonics engineering courses at IIT Madras, IIT Delhi, and NIT Trichy.

What Insights Does the Two-Photon Absorption Calculator Give You?

Photon Flux (photons/cm²/s) is the primary output, the spatial photon density at the laser focus, the key driver of TPA.

Irradiance (W/cm²), the focal intensity in familiar units; values of 10⁶–10¹⁰ W/cm² are typical for TPA experiments.

TPA Absorption Rate (events/molecule/s), how many two-photon absorption events occur per fluorophore molecule per second.

Excitation Probability per Pulse, for pulsed lasers; values of 0.001–0.1 per pulse are typical for efficient imaging.

How to use this Two-Photon Absorption calculator

  1. Enter TPA Cross-Section (δ, GM), from literature for your fluorophore at the laser wavelength. Fluorescein: 37 GM at 800 nm; Rhodamine B: 10–100 GM; Quantum dots: 10,000–50,000 GM.
  2. Enter Laser Peak Power (mW), for a Ti:sapphire laser: 10–500 mW typical average power. For pulsed systems, enter peak power = average power / (repetition rate × pulse width).
  3. Enter Beam Waist (w₀, μm), the 1/e² radius at the focal point. For a 1.4 NA objective: w₀ ≈ 0.3–0.5 μm.
  4. Enter Fluorophore Concentration (μM), for calculating the expected excitation events per volume.
  5. Read Photon Flux and Absorption Rate, if rate is very low (< 0.01 events/s), the signal will be undetectable; increase power or use a higher-δ dye.
Show formula & methodology ↓Show less ↑

Formula & Methodology

TPA absorption rate:

Irradiance:   I = P / (π × w₀²)     [W/cm²; w₀ in cm]  Photon flux:  Φ = I / E_photon      [photons/cm²/s]               E_photon = h × c / λ  [J; λ in m]  TPA rate:     R = δ × Φ²            [events/molecule/s]               δ in GM = δ × 10⁻⁵⁰ cm⁴·s  Excitation probability per pulse (τ_pulse = 100 fs):               P_exc = R × τ_pulse

Worked example, GFP two-photon imaging in brain tissue:

Ti:sapphire laser, 930 nm, 100 mW average, 80 MHz rep rate, 100 fs pulses, focused to w₀ = 0.35 μm (1.0 NA water objective). GFP δ ≈ 6 GM at 930 nm.

Peak power = 100 mW / (80 × 10⁶ Hz × 100 × 10⁻¹⁵ s) = 12,500 W = 12.5 kW  w₀_cm = 0.35 × 10⁻⁴ cm Irradiance = 12,500 / (π × (0.35×10⁻⁴)²) = 12,500 / 3.85×10⁻⁹ = 3.25×10¹² W/cm²  E_photon = (6.626×10⁻³⁴ × 3×10⁸) / (930×10⁻⁹) = 2.14×10⁻¹⁹ J Φ = 3.25×10¹² / 2.14×10⁻¹⁹ = 1.52×10³¹ photons/cm²/s  R = 6×10⁻⁵⁰ × (1.52×10³¹)² = 6×10⁻⁵⁰ × 2.31×10⁶² = 1.39×10¹³ events/s → 0.14 events per 10 fs

This rate is adequate for two-photon fluorescence microscopy of GFP-expressing neurons. TIFR's Neuroscience group uses this configuration for imaging mouse cortical neurons expressing channelrhodopsin (for optogenetics) and GFP reporter proteins, part of India's neurotechnology research programme.

Frequently Asked Questions

What is two-photon absorption (TPA)?
Two-photon absorption (TPA) is a nonlinear optical process where a molecule simultaneously absorbs two photons to undergo an electronic transition, the combined energy of both photons equals the energy gap (ΔE = 2hν, where ν = laser photon frequency). Unlike single-photon absorption (Beer-Lambert law, linear in intensity), TPA rate is proportional to the square of laser intensity: R_TPA = δ × I², requiring high photon densities available only from pulsed femtosecond or picosecond lasers. TPA was theoretically predicted by Maria Göppert-Mayer (1931) and experimentally confirmed after the laser's invention (1960s).
What is the Göppert-Mayer unit (GM) and what values are typical?
The Göppert-Mayer unit (GM, named after Maria Göppert-Mayer) is the unit for TPA cross-section (δ): 1 GM = 10⁻⁵⁰ cm⁴·s·photon⁻¹. The TPA cross-section δ measures how efficiently a molecule absorbs two photons. Typical values: Common organic dye molecules: 1–100 GM. Specially designed TPA dyes (for bioimaging): 100–10,000 GM. Quantum dots (CdSe, CdTe): 10,000–50,000 GM. Metal-organic frameworks (MOFs) for TPA: 1,000–100,000 GM. Stilbene derivatives and push-pull π-systems often have large TPA cross-sections. Higher δ → more sensitive TPA detection → better imaging contrast.
How do I use the Two-Photon Absorption Calculator?
Enter TPA Cross-Section (δ, in GM), Laser Peak Power (mW), Beam Waist (w₀, in μm, the 1/e² radius at the focal point), Fluorophore Concentration (μM), and Laser Wavelength (nm). The calculator returns Photon Flux (photons/cm²/s), Irradiance (W/cm²), TPA Absorption Rate (events/molecule/s), and Excitation Probability per pulse (for 100 fs pulses). Default: δ=10 GM, 100 mW, w₀=1 μm, 800 nm wavelength, typical Ti:sapphire laser two-photon microscopy conditions.
What laser systems are used for two-photon absorption studies?
TPA requires high peak intensity but can use average powers acceptable for biological samples. Common TPA laser systems: Ti:sapphire laser (700–1050 nm, 100 fs pulses, 80 MHz repetition rate, 100–1000 mW average power), the gold standard for two-photon microscopy. OPO (Optical Parametric Oscillator) extending range to 1300 nm, for deep tissue imaging. Ytterbium fibre laser (1030–1040 nm), lower cost, compact. In India: Raman Research Institute (RRI, Bangalore), TIFR (Mumbai), IISc (Bangalore), and JNCASR have ultrafast laser systems for nonlinear optics and two-photon microscopy research, often in collaboration with Indian Institute of Chemical Technology (IICT) for TPA dye synthesis.
What are the applications of two-photon absorption?
Two-photon absorption applications: (1) Two-photon fluorescence microscopy (2PFM): sub-micron resolution imaging of live cells and tissues up to 1 mm deep, advantage over single-photon confocal microscopy is reduced phototoxicity and better tissue penetration. (2) 3D microfabrication: two-photon polymerisation (2PP) achieves sub-100 nm resolution by photo-polymerising only at the laser focus, used in microfluidics, photonic crystals, MEMS. (3) Photodynamic therapy (PDT): TPA sensitisers with large cross-sections for deep tumour treatment, avoiding superficial light absorption. (4) Optical data storage: 3D data recording using TPA-active materials. (5) Two-photon optogenetics: selective neural activation in deep brain tissue. Indian research groups at TIFR, NCL, and JNCASR are active in all these areas.
How is photon flux calculated for a focused Gaussian laser beam?
For a Gaussian beam focused to a beam waist w₀ (1/e² radius): Irradiance at focus = I = P / (π × w₀²), where P = peak power (W), w₀ in cm. Photon flux = I / E_photon = I × λ / (h × c), where λ is in m, h = 6.626×10⁻³⁴ J·s, c = 3×10⁸ m/s. Example: 100 mW average power, 100 fs pulses, 80 MHz repetition rate, focused to w₀ = 1 μm. Peak power ≈ 100 mW × 1/(80 MHz × 100 fs) = 100 mW / 8 × 10⁻³ = 12.5 kW peak. For TPA, it is the PEAK power that drives the quadratic process, not the average power.
What is the difference between one-photon and two-photon excitation for fluorescence microscopy?
One-photon (confocal) microscopy: excite at λ/2 (e.g., 488 nm for GFP); excitation occurs along the entire laser path through the sample, causes photobleaching and phototoxicity outside the focal plane. Two-photon microscopy: excite at λ (e.g., 930 nm for GFP, using TPA); excitation occurs ONLY at the focal point (where photon flux is high enough for TPA quadratic process), inherently 3D-selective, no out-of-focus bleaching. Additional advantage: NIR wavelengths (700–1000 nm) penetrate biological tissue more deeply (less scattering and absorption) than UV-Vis, can image 500–1000 μm into intact brain slices. This is why two-photon microscopy is used at TIFR's neuroscience division for in-vivo brain imaging in mice.
What TPA-active dyes are commonly used in bioimaging research?
Common TPA fluorophores in bioimaging: Rhodamine B (δ ≈ 10 GM at 840 nm): classic dye, moderate TPA. FITC/fluorescein (δ ≈ 37 GM at 780 nm): cell labelling. Calcein (δ ≈ 40 GM): intracellular Ca²⁺ imaging. BODIPY dyes (δ = 20–200 GM): lipid membrane and organelle labelling. Genetically encoded fluorescent proteins: GFP (δ ≈ 6 GM), mCherry, mCerulean. Quantum dots (δ ≈ 50,000 GM): extremely bright TPA probes; CdSe/ZnS core-shell nanocrystals, being explored at CSIR-NCL Pune and JNCASR. Near-IR dyes: cyanine dyes (Cy5, Cy7) and aggregation-induced emission (AIE) materials with δ > 1000 GM for deep tissue imaging.
What is two-photon polymerisation (2PP) and how is it used in India?
Two-photon polymerisation (2PP / direct laser writing) uses TPA to locally polymerise photoinitiator-containing resins at the laser focus: only the voxel (3D pixel) at the focus reaches the threshold dose to polymerise, enabling truly 3D structures with sub-micron resolution (100–200 nm features). Applications: microlenses, photonic waveguides, biomedical scaffolds, microfluidics, MEMS. Indian institutions active in 2PP: IIT Bombay (femtosecond laser microfabrication lab), IISc Bangalore (Centre for Nanoscience), RRCAT Indore (Indus-2 synchrotron, also runs ultrafast laser labs), TIFR (femtosecond spectroscopy group). Commercial 2PP systems (Nanoscribe, UpNano) enable < 200 nm feature fabrication, not yet widely available in India but growing with AIC-IITB and BIRAC-supported deep-tech startups.
How is TPA cross-section measured experimentally?
Measurement methods for δ: (1) Two-photon excited fluorescence (TPEF): compare two-photon fluorescence from the sample to a reference dye with known δ (e.g., fluorescein in water, δ = 37 GM at 800 nm). δ_sample = δ_ref × (F_sample / F_ref) × (φ_ref / φ_sample) × (c_ref / c_sample) × (η_ref² / η_sample²), where F = TPEF signal, φ = fluorescence quantum yield, c = concentration, η = refractive index. (2) Z-scan technique: measures non-linear absorption by scanning a sample through the laser focus. (3) Pump-probe spectroscopy: time-resolved measurement of excited state population. Most δ measurements worldwide are done by TPEF relative to fluorescein, the reference standard used by Drobizhev, Makarov, and Webb's comprehensive tables.