A Fabry-Pérot cavity has one fixed mirror and one mirror mounted on a spring (the mechanical oscillator, frequency ω_m). A laser drives the cavity field a(t); moving the mirror by x shifts the cavity's resonance frequency, coupling light to motion:
ȧ = [ i(Δ₀ + G·x) − κ/2 ] a + η
m·ẍ = −m·ω_m²·x − m·Γ_m·ẋ + ħ·G·|a|²
κ is the cavity linewidth (photon leak rate), Δ₀ = ω_laser − ω_cavity is the static detuning, G = dω_cavity/dx is the optomechanical coupling, and ħ·G·|a|² is the radiation-pressure force from the circulating photons.
Dynamical backaction: because the cavity field takes a moment (∼1/κ) to catch up to the mirror's motion, the radiation-pressure force lags slightly behind x(t). That lag has two effects, set entirely by the sign of Δ₀:
- Red detuning (Δ₀ < 0) — the lagging force opposes the mirror's velocity on average, adding extra damping. This is the basis of laser (radiation-pressure) cooling of mechanical resonators, used to cool micro- and nano-mechanical oscillators toward their quantum ground state. Watch the strip chart: the vibration envelope rings down.
- Blue detuning (Δ₀ > 0) — the force reinforces the velocity instead, pumping energy in (anti-damping / parametric instability, the mechanism behind optomechanical amplification and self-oscillation). The strip chart envelope grows instead.
- Either sign also produces an optical spring effect: the position-dependent force shifts the mirror's effective spring constant, so the oscillation frequency itself shifts with Δ₀ and drive power.
This is the real linear-response model used across the field of cavity optomechanics (Aspelmeyer, Kippenberg & Marquardt, Rev. Mod. Phys. 86, 1391 (2014)) — the same physics behind LIGO's suspended mirrors and laboratory ground-state cooling of micromechanical membranes. This 2D companion swaps the 3D perspective view for a flat schematic side-view of the cavity plus a scrolling x(t) strip chart, which makes the cooling-vs-heating envelope trend easier to read at a glance than a 3D camera view.