A quantum dot (QD) sitting inside a planar Fabry–Pérot microcavity — two Distributed Bragg Reflector (DBR) stacks facing each other, exactly the geometry used in VCSELs and pillar/micropost single-photon sources — does not decay at its free-space spontaneous emission rate Γ₀. The electromagnetic mode density it sees is reshaped by the cavity, and its decay rate is enhanced or suppressed: the Purcell effect.
F_P,max = (3 / 4π²) · (λ/n)³/V · Q
F_P(z, Δ) = F_P,max · sin²(π z/L) · κ²/4 / (Δ² + κ²/4)
Γ_total / Γ₀ = 1 + F_P κ = E_cav / Q (cavity linewidth)
β = F_P / (1 + F_P) (fraction of photons emitted into the cavity mode)
- QD position (z/L) — the standing wave inside the cavity has a field antinode at the centre and (approximate) nodes at the mirrors, so coupling scales as sin²(πz/L). Placing the dot off-antinode throttles the Purcell enhancement even at perfect spectral resonance — visible as the glowing "field profile" beads dimming away from centre.
- Detuning Δ — the cavity resonance is a Lorentzian of linewidth κ = Ecav/Q. Moving the QD's emission line away from the cavity mode falls off this Lorentzian, cutting FP even at the antinode.
- DBR mirror pairs N — more quarter-wave layer pairs raise mirror reflectivity and hence the cavity Q (modelled here as Q ≈ 200·N, a realistic order of magnitude for micropillar/microdisk QD cavities). Higher Q means a narrower spectral window and a narrower escape cone in the far field, because only near-normal wavevector components build up enough round trips to leak out — the beam you see above the top mirror visibly narrows as N increases.
- Cyan streaks are photons emitted into the cavity mode (probability β) — they leave nearly collimated, straight up through the top DBR, the vertical-cavity emission this sim is named for. Dim grey streaks are photons that escape into free space instead (probability 1−β), in random directions, exactly as an uncoupled dipole would radiate.
Mode volume V and the escape-cone scaling are held to fixed, physically reasonable idealisations (a wavelength-scale cavity, V ≈ 1.5(λ/n)³) so the sliders isolate the three quantities that matter most in a real device: spatial overlap, spectral detuning, and mirror quality — the same three knobs epitaxial growers and lithographers spend years optimizing to build efficient quantum-dot single-photon sources and VCSELs.