PDH Locking — Interactive Teaching Lab

A browser-based teaching app that builds up the Pound–Drever–Hall (PDH) laser frequency-stabilization technique one idea at a time, then unlocks a full control-systems simulator. Built with Vite + React + TypeScript; all physics runs client-side from a small, dependency-free simulation engine.

Running it

npm install
npm run dev        # development server (hot reload)
# or
npm run build && npm run preview   # production build + static preview

Then open the printed local URL (e.g. http://localhost:5173).

Progress is saved to localStorage, so you can close the tab and pick up where you left off. Use Reset (top-right) to start over.

What it teaches

Ten guided stages, each introducing exactly one new concept with an interactive Plotly figure and a guided "Try this" experiment:

Stage	Idea
0	Why a free-running laser must be locked at all
1	The Fabry–Pérot cavity and the Airy reflection dip
2	Why reflected power alone is ambiguous (it is symmetric)
3	Adding sidebands with an EOM (Bessel-weighted spectrum)
4	The antisymmetric reflected-phase S-curve
5	Turning phase into a measurable RF beat note
6	Demodulation, the demod-phase knob, and RAM
7	Reading the S-curve: discriminant slope vs. capture range
8	Closing the loop with a PI controller (lock acquisition)
9	Real limits: actuator bandwidth and loop delay

After Stage 9, Free Play unlocks: a four-tab dashboard (S-curve · Bode · live Time Domain · Noise/PSD) with every cavity, modulation, actuator, controller and noise parameter exposed at once, plus named presets. The time-domain simulation streams from a Web Worker so the UI stays responsive.

A Theory & Derivations appendix (top-right) states the actual mathematics the simulator implements, with references.

Physics fidelity

The engine (src/sim/) is not a cartoon — it computes the real quantities:

• Cavity reflection from the exact two-mirror Fabry–Pérot coefficient F(ω) = [r₁ − r₂ e^{−iφ}] / [1 − r₁r₂ e^{−iφ}], giving the true Airy dip and the antisymmetric reflected phase.
• Sidebands from Bessel functions Jₙ(β) (series for J₀, J₁; Miller's downward recurrence for higher orders), validated against reference values.
• The PDH error signal as the demodulated beat, ε ∝ Im{F(ω)F*(ω+Ω) − F*(ω)F(ω−Ω)}·cos φ_LO + …·sin φ_LO, keeping both quadratures so the demod-phase knob behaves like a real lock-in.
• Residual Amplitude Modulation (RAM) as a first-class effect. This matters: for an ideal lossless cavity one can show D(−δ) = −D(δ), so every demod quadrature is antisymmetric and a 90°-wrong demod phase merely flattens the discriminant. The familiar symmetric dip only appears with RAM present — the app models this explicitly rather than faking the classic textbook cartoon.
• A genuine closed loop in the time domain: error → PI (with anti-windup) → finite-bandwidth actuator → transport-delay ring buffer → detuning, with a seeded noise/disturbance model for reproducible runs.
• Open-loop Bode analysis using the same gains as the time-domain loop, with numerically located gain/phase margins — so the "delay collapses the phase margin" lesson is quantitative, not asserted.

Project layout

src/
  sim/           pure simulation modules (no React)
    cavity.ts        Fabry–Pérot reflection, finesse/linewidth, finesse→R
    modulation.ts    Bessel functions, sideband powers
    errorSignal.ts   PDH error signal, quadratures, S-curve analysis
    controller.ts    PI(D) with anti-windup
    plant.ts         actuator low-pass + delay line
    noise.ts         seeded RNG, white + flicker noise, disturbance
    integrator.ts    time-domain closed-loop engine
    loopAnalysis.ts  open-loop Bode + margins
    fft.ts           radix-2 FFT + periodogram (PSD)
    presets.ts       default params + named Free Play presets
  content/       stage text + slider configuration
  components/    SignalChainMap, StagePanel, StageVisual, FreePlay, TheoryModal, …
  simWorker.ts   Web Worker wrapping the integrator for Free Play
  store.ts       Zustand store + localStorage persistence

References

• E. D. Black, An introduction to Pound–Drever–Hall laser frequency stabilization, Am. J. Phys. 69, 79 (2001).
• R. W. P. Drever et al., Appl. Phys. B 31, 97 (1983).
• T. Day, E. K. Gustafson, R. L. Byer, IEEE J. Quantum Electron. 28, 1106 (1992).