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Purcell Factor

A quantum emitter near a nanosphere: total and radiative decay enhancement, modified quantum yield, and lifetime — exact multipole theory with the emitter's intrinsic quantum yield folded in.

v0.1.0·Updated 2026-07-18
Model & Assumptions Beta
Model
Exact multipole decay rates of a point dipole at distance d from a sphere (Kim, Leung & George, Surf. Sci. 195, 1 (1988)), ℓmax = 20. Emitter bookkeeping: τ′ = τ₀/(q₀Ftot + 1 − q₀), q′ = q₀Frad/(q₀Ftot + 1 − q₀).
Assumptions
Point dipole; homogeneous lossless host; local response of the sphere material (tabulated n,k). Isotropic orientation = (radial + 2·tangential)/3.
Limitations
No nonlocal/quantum corrections at sub-nm gaps — below ~1 nm the local model overestimates quenching. Single sphere only (no substrate, no dimer gaps).
Parameters

Reading the numbers. Ftot is the Purcell factor; the gap between Ftot and Frad is light absorbed in the particle (quenching). A good antenna raises q′ of a poor emitter; quenching kills it at small gaps.

Ftot (Purcell) — Γ/Γ₀
Frad — Γrad/Γ₀
q′ — quantum yield
τ′ — ns
Decay enhancement vs gap at λem (log scale)
Decay enhancement vs wavelength at gap d (log scale)
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