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PolskiThe Purcell Effect (2D): Cavity Density of States
A 2D companion to the 3D cavity-QED lab: the same Fermi's-golden-rule Purcell factor, driven by a flat top-down cavity view, a live density-of-states plot and a real-time photon-emission stream.
This 2D companion runs the exact same Purcell-effect physics as the 3D version — a real Fermi's-golden-rule calculation, not a decorative stand-in — through a flat top-down canvas built for reading the numbers rather than orbiting a rendered scene. An emitter sits between two cavity mirrors (or floats free in open space, in "No Cavity" mode); dragging the quality factor Q, mode volume V or detuning slider recomputes the on-resonance Purcell factor FP = (3/4π²)·Q/V and its Lorentzian line-shape fall-off live, and that number drives everything else on screen: how fast photons stream from the emitter, how brightly the mirrors glow, and the shape of the density-of-states curve traced in the side panel. Switch to "Cavity Detuned" and push the detuning slider outward to watch the emission rate fall below the free-space baseline — the photonic-bandgap-style suppression regime the 3D lab also demonstrates.
2D Purcell-effect lab: live Fermi's-golden-rule computation of the Purcell factor from cavity quality factor Q, mode volume V and detuning, driving a density-of-states plot, photon-emission animation and decay-rate readout in real time.
2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install
FAQ
The cavity only couples strongly to the emitter when its resonant frequency matches the emitter's transition frequency. The Lorentzian line shape L(δ) = 1/(1+(δQ)²) falls off sharply as the fractional detuning δ grows, especially for a high-Q cavity, so the Purcell factor drops toward 1 (the free-space rate) the further you detune.
Identical underlying physics and formula — this page trades the orbiting 3D cavity render for a flat, always-fully-visible 2D view with a dedicated density-of-states plot, which makes it easier to read the numbers while you drag the sliders.
Free space always has some vacuum density of photonic states available for the emitter to decay into, so the Purcell factor is fixed at exactly 1 — the reference baseline every cavity configuration is measured against.