Unlock the potential of two-photon absorption (TPA) with our advanced online calculator. Easily determine the fluorescence photon rate induced by TPA processes, crucial for applications in multiphoton microscopy, biophotonics, and materials science. Simplify complex calculations involving TPA cross-sections, laser power, and molecular properties for accurate, instantaneous results. This tool helps researchers and students understand and predict two-photon excited fluorescence yields with ease.
Formula:
The two-photon induced fluorescence photon rate (Sf) can be estimated using the following formula, assuming a Gaussian temporal and spatial pulse profile:
Sf = η × C × NA × V × (σ₂ × 10-50) × Pavg² / (2 × Ephoton² × frep × τp × Aeff²)
Where:
- Sf = Two-Photon Induced Fluorescence Photon Rate (photons/second)
- η = Fluorescence Quantum Yield (dimensionless, 0-1)
- C = Concentration (mol/L)
- NA = Avogadro's Number (6.022 × 1023 mol-1)
- V = Interaction Volume (Liters)
- σ₂ = Two-Photon Absorption Cross-Section (Goeppert-Mayer, GM)
- Pavg = Average Laser Power (Watts)
- Ephoton = Energy per Photon (Joules)
- frep = Laser Repetition Rate (Hz)
- τp = Laser Pulse Duration (seconds)
- Aeff = Effective Excitation Area (cm²)
And Ephoton = hc/λ, Aeff = π × ω₀², where h is Planck's constant (6.626 × 10-34 J·s), c is the speed of light (2.998 × 108 m/s), λ is excitation wavelength, and ω₀ is the beam waist radius.