Upconversion Nanoparticle Imaging Simulator

Excitation

NIR pump power 80 mW/mm²

Nanocrystal

Yb:Er doping ratio 18:1

Tissue depth 4.0 mm

Live Readouts

Local irradiance

— mW/mm²

Power-law slope n

—

Detected surface intensity (green : red)

—

How it works

β-NaYF₄:Yb,Er nanocrystals convert two low-energy near-infrared photons into one higher-energy visible photon — the opposite of normal (Stokes) fluorescence — via energy-transfer upconversion (ETU). A steady-state rate-balance model drives this sim:

Yb³⁺ sensitizer population N₁ (²F₅/₂):
  0 = σP·(N₀−N₁) − k₁N₁ − 2W·N₁²

Er³⁺ emitting population N₂ (⁴S₃/₂ / ⁴F₉/₂):
  0 = W·N₁² − k₂N₂
  ⇒ I_UC = k₂N₂ = W·N₁²

σ is the NIR absorption cross-section, P the local irradiance, k₁/k₂ spontaneous decay rates, and W the Yb→Er energy-transfer rate. Because N₂ depends on N₁², emitted intensity scales as I ∝ Pⁿ with n ≈ 2 at low pump power — the classic upconversion fingerprint — falling toward n ≈ 1 as the sensitizer population saturates (N₁ → N₀) at high pump power. The live "power-law slope n" readout is measured directly from the model, exactly as it is measured on a real microscope by fitting log(intensity) vs log(power).

Green (⁴S₃/₂ → ⁴I₁₅/₂, ~540 nm) vs red (⁴F₉/₂ → ⁴I₁₅/₂, ~660 nm) branching shifts with Er³⁺ content: denser Er doping (lower Yb:Er ratio) increases Er–Er cross-relaxation, which preferentially feeds the red channel. Excitation attenuates through tissue as P(depth) = P₀·e^(−μ_ex·depth); the emitted visible light re-attenuates on its way back out, with green scattered/absorbed more strongly than red — the same physics that makes red-shifted, NIR-in/NIR-window-out probes preferable for deep-tissue optical imaging, and why an alternative 808 nm pump (absorbed less by water, so it heats tissue less, at the cost of a lower effective cross-section without Nd³⁺ co-sensitization) is used in living-tissue work instead of the more efficient but more strongly water-absorbed 980 nm line.

980/808 nm NIR pump beam Green upconverted emission (⁴S₃/₂) Red upconverted emission (⁴F₉/₂)

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