A femtosecond laser is focused through a lens into a droplet of liquid photoresist. Ordinary single-photon polymerization triggers wherever the light intensity crosses a threshold — since intensity falls off gradually away from focus, the cured region is a blurry hourglass far wider than the beam waist (see the "1-photon UV" toggle).
Two-photon absorption is different: its probability scales with the square of intensity, I². Intensity outside the tight focal spot is far too low to trigger absorption at all, but right at the focus — where photon density peaks — I² crosses threshold in a volume orders of magnitude smaller than the diffraction-limited spot itself. Only that tiny voxel polymerizes.
rate_1photon ∝ I(r)
rate_2photon ∝ I(r)²
I(r) = I₀·exp(−r²/w₀²) (Gaussian focus)
- Scan speed — how fast the focal point sweeps through the resist to trace out each layer of the structure.
- Laser intensity — scales I₀; push it up and the 1-photon exposure zone balloons while the 2-photon voxel grows only slightly (√ scaling of the nonlinear threshold radius).
- 2-photon vs 1-photon toggle — same focused beam, same optics; only the absorption physics differs, and it's the reason 2PP prints features far below the wavelength of the light used.
Real-world relevance: two-photon polymerization (direct laser writing) is used today to print micro-lattices, photonic crystals, microfluidic scaffolds and even single-element micro-lenses with ~100 nm resolution — far finer than the ~400-800 nm laser wavelength that writes them, because it is the focus, not the wavelength, that sets the resolution.