Third-Harmonic Generation Microscopy Calculator

THG wavelength, focal intensity and source size, and signal scaling with power and depth, for label-free interface imaging.

Model: Textbook approximation

Excitation λ (nm)NAAvg Power (mW)Pulse Width, FWHM (fs)Rep. Rate (MHz)Refractive IndexScattering Coeff (cm⁻¹)

THG wavelength

400 nm

Peak intensity at focus

1.64 TW/cm²

Gaussian pulse and focus

Pulse energy

1.25 nJ

Peak power 11.7 kW

Focal radius w (1/e²)

0.676 µm

2ω_xy (Zipfel fit)

THG source, lateral FWHM

459 nm

FWHM of I³

THG source, axial FWHM

2.29 µm

FWHM of the I³ source (point object)

Fundamental, lateral FWHM

796 nm

FWHM of I = THG × √3

Fundamental, axial FWHM

3.97 µm

An interface responds over ≈ the fundamental axial FWHM (confocal parameter), 3.97 µm (Barad et al. 1997).

Physics

λ_THG = λ/3, I_THG ∝ |χ⁽³⁾|² I³; FWHM of I³ = FWHM of I / √3 (Gaussian focus)

I_peak = P_peak/(2π ω_xy²), P_peak = 2√(ln 2/π)·E/τ

In a homogeneous medium with normal dispersion (Δk = 3k_ω − k_3ω < 0), the third-harmonic fields generated before and after a tight focus cancel because of the Gouy phase, so no THG leaves the focus. A signal appears only where χ⁽³⁾ or n changes within the focal volume: interfaces, membranes, lipid bodies (Boyd, Nonlinear Optics, §2.10; Barad et al., Appl. Phys. Lett. 70, 922, 1997). The signal therefore can't be predicted from the intensity alone. The charts show only how it scales.

Focal radii from the Gaussian fit of Zipfel, Williams & Webb, Nat. Biotechnol. 21, 1369 (2003). The depth chart counts only ballistic excitation photons.

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

Focal size from Zipfel's Gaussian fit (I³ source). The signal is not predicted: in a homogeneous medium the Gouy phase cancels THG, so it appears only at interfaces, and the charts show scaling only. An interface responds over ≈ the confocal parameter (Barad 1997), wider than the I³ source.

Zipfel W. R., Williams R. M., Webb W. W. (2003). Nonlinear magic: multiphoton microscopy in the biosciences. Nat. Biotechnol. 21, 1369–1377. Gaussian fit to the squared illumination PSF. doi:10.1038/nbt899
Boyd R. W. (2008). Nonlinear Optics, 3rd ed., §2.10. Academic Press. Gouy-phase cancellation of the third harmonic.
Barad Y. et al. (1997). Nonlinear scanning laser microscopy by third harmonic generation. Appl. Phys. Lett. 70, 922–924. Cited for THG appearing only where χ⁽³⁾ or n changes within the focus. doi:10.1063/1.118442

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