Physics · the subject of my PhD
One photon or two
Two-photon excitation is a quadratic effect, and that one square changes everything: where light acts, how deep it reaches, and how precisely it can treat tissue. Move the sliders; the optics are computed live.
01 · The focus
Gaussian beam in water
Same lens, two very different glows
One-photon excitation of a molecule at 400 nm, and two-photon excitation of the same transition at 800 nm, focused by the same objective. Seen from the side, as a camera would.
Why the cone glows for one photon. The same power crosses every plane of the beam, and one-photon excitation is linear in intensity, so every plane is excited equally: the glow fills the whole hourglass.
Why only the focus glows for two. Excitation per plane follows intensity squared integrated over the spot, which falls as 1/w². It is confined to about two Rayleigh ranges: axial sectioning without a pinhole.
The waist trade-off. At the same NA the 800 nm spot is twice as wide, but squaring the intensity narrows the excitation by √2. The gain is not lateral sharpness; it is that nothing outside the focus is excited.
w₀ = λ / (π·NA) is the paraxial Gaussian estimate; z_R = π·w₀²·n / λ with n = 1.33. At high NA the paraxial model is approximate.
02 · Penetration
the optical window
Why near-infrared reaches deeper
Below about 600 nm, blood absorption and scattering stop light within a short distance. Between roughly 600 and 1300 nm sits tissue's optical window. Fluence falls as exp(−z/δ).
A subtlety worth knowing: two-photon excitation follows fluence squared, so its depth signal decays twice as fast as the 800 nm light itself (δ/2 ≈ 3.3 mm here), similar to 630 nm one-photon light. Its advantage at depth is not more signal; it is that the excitation stays confined to the focus, wherever that focus is placed.
δ values: 630 nm ≈ 4.0 mm (brain-tumour tissue phantom, μ_eff 0.25 mm⁻¹); 750 to 800 nm ≈ 6.6 mm (breast tissue, μ_eff ≈ 1.5 cm⁻¹). Real tissue varies widely.
03 · Photodynamic therapy
illustrative model
Treating a tumour without touching what is above it
In photodynamic therapy a photosensitiser collects in the tumour; light excites it, and its triplet state makes singlet oxygen, which kills nearby cells. The same molecule, the same 1270 nm glow as the lab agent's experiment.
Standard PDT illuminates everything in the beam, so healthy tissue above the tumour, and the skin most of all, receives dose wherever photosensitiser is present. Two-photon PDT scans a focus through the tumour and excites only there. Its practical limits are real: it needs femtosecond lasers, and most photosensitisers absorb two photons weakly, which is why new high-cross-section molecules are an active research area.
Model: photosensitiser 1.0 in tumour, 0.35 elsewhere; 630 nm δ = 4.0 mm; 800 nm δ = 6.6 mm with excitation ∝ fluence²; focus drawn at 0.12 mm for visibility (a real two-photon focal volume is around 1 µm³ and is scanned). It shows the principle, not a dosimetry calculation.
Sources
- Penetration depth definitions and the 750 to 800 nm breast-tissue value: J. Biomed. Opt. 9(1).
- 630 nm penetration in brain-tumour phantoms: Proc. Estonian Acad. Sci. (2022).
- Two-photon PDT confinement and photosensitiser cross-sections: Analyst (2019); Photonics.com.