Physics · the subject of my PhD
One photon or two
Two-photon excitation grows with the square of the light's intensity. That one square decides where light acts and how precisely it can treat tissue. Move the slider and the optics update live.
Why it mattered for my PhD: the research in four steps.
Part of Work · What I've done
Two-photon excitation was at the heart of my PhD. A molecule can be excited by one particle of light, or by two arriving at the same moment. With two, the effect grows with the square of the brightness, so it happens only at the focus of a lens. That confinement lets two-photon microscopes image in 3D, and could let light treat a tumour while leaving the tissue above it alone.
Move the aperture slider and watch the focus change, then follow red and near-infrared light into tissue. The one result to remember is that two-photon excitation fades with depth twice as fast as the 800 nm light itself (about 3.3 mm against 6.6 mm). Its strength is confinement. The therapy panel at the end is an illustration of the principle.
Terms used here
- Photon
- A single particle of light. Shorter wavelengths carry more energy, so one 400 nm photon carries as much as two 800 nm photons.
- One- and two-photon excitation
- With one photon, excitation grows in proportion to intensity (∝ I). With two, it grows with the square (∝ I²).
- Numerical aperture (NA)
- How steeply a lens focuses light. The higher the NA, the smaller the focus.
- Beam waist (w₀)
- The radius of the beam at its narrowest point, the focus.
- Rayleigh range (z_R)
- How far from the focus, along the beam, it stays nearly as narrow.
- Penetration depth (δ)
- The depth at which light in tissue has fallen to about a third (1/e) of its strength.
- Optical window
- Roughly 600 to 1300 nm, where blood and tissue absorb and scatter least, so light gets furthest.
- Photodynamic therapy
- Treatment with light, a light-sensitive drug and oxygen. The drug only switches on where the light shines.
- Femtosecond laser
- A laser that fires pulses a millionth of a billionth of a second long, packing photons close enough together for two to be absorbed at once. See inside one.
01 · The focus
Gaussian beam in water
Same lens, two very different glows
The same molecule excited by one 400 nm photon or by two 800 nm photons, through the same lens, seen from the side. Press inside a focus to place the molecule yourself, then drag it out of the waist.
Press inside either focus to place a molecule.
Why. The same power crosses every plane of the beam, so linear one-photon excitation is equal in each. Two-photon excitation per plane follows intensity squared over the spot, which falls as 1/w², so 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, and squaring the intensity narrows the excitation by √2. So the excited spot ends up slightly wider than with one photon. What two photons buy 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).
Drag along the depth axis to read the light at any depth.
Two photons therefore gain nothing at depth. What they offer is confinement: excitation stays at the focus, wherever you place it.
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
Killing a tumour without harming the tissue above it
- A drug collects in the tumour. It does nothing in the dark. Some also reaches healthy tissue, here a third as much.
- Light switches the drug on. The switched-on drug turns oxygen into singlet oxygen, which kills the cell it is in.
- The light has to get in. Red light switches the drug on in every cell it passes. A single 800 nm photon is too weak to do it; two must arrive at once, and that only happens in a tiny focus. Scan the focus through the tumour and the cells above it are left alone. Press on the two-photon view to take the focus yourself.
Both treatments run until every tumour cell is killed, because any cell left alive can regrow. The deepest tumour cells decide how long the red light stays on, and by then it has switched on the drug in all the healthy tissue it crossed. The focus only ever sits inside the tumour; the few healthy cells it harms touch the tumour's edge.
Two-photon PDT has a cost. It needs femtosecond lasers, and most photosensitisers absorb two photons weakly, so chemists are designing new molecules with larger cross-sections. My PhD measured the singlet oxygen these treatments produce.
Model (pdt-core.js): drug 1.0 in the tumour, 0.35 elsewhere; 630 nm δ = 4.0 mm; 800 nm δ = 6.6 mm with excitation ∝ fluence²; cells every 0.25 mm, each killed or harmed once its dose passes the same threshold. The focus is drawn at 0.12 mm so it can be seen; a real two-photon focal volume is around 1 µm³. It illustrates the principle, and the doses are not to scale.
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.