Spatial measurements of light
Interactive phasor simulation
By default every curve is divided by its own peak value \((1-R^N)^2\), so you compare line shapes. Untick Normalise each curve to its peak to see the absolute transmission. For a few phasors and high \(R\) that number is tiny, because most of the light is still bouncing inside the etalon.
Fabry–Pérot etalon: phasor sum and transmission spectrum
Move the sliders, press Scan, or click and drag on the spectrum
Number of phasors N (log scale)
Reflectivity R
OPD between successive phasors
Scan window
Scan duration (one sweep)
Things to try
- Michelson limit. Set \(N = 2\) and \(R = 0.99\). The two phasors are almost equal in length, so the spectrum is a full-contrast \(\cos^2\) fringe, exactly what a Michelson interferometer gives. The dashed line is what the same mirrors give once all reflections are included. (At lower \(R\) the two phasors differ in length and the fringe contrast \(2R/(1+R^2)\) drops.)
- From Michelson to Fabry–Pérot. Keep \(R = 0.99\) and click Hold curve at \(N = 2, 10, 50, 300\). Each extra phasor sharpens the peak. The curve only lands on the dashed Airy line once \(R^N \ll 1\), here after a few hundred round trips (the readout gives the number). The finesse is really a count of how many beams interfere.
- Weakly decaying phasors. At \(R = 0.99\) and \(N = 10\) the phasors hardly decay, so the chain is close to a regular polygon. You get \(N-2\) small secondary maxima between the main orders, just like an \(N\)-slit grating.
- Watch the chain while you scan. On resonance the chain is a straight line. At \(\delta = \pi\) it zig-zags back and forth. Close to resonance it curls into a spiral. A high-\(R\) chain is long, so a very small phase error per step is enough to close the spiral. That is why high finesse means narrow peaks.
- Zoom in. At high finesse the peaks are narrower than one pixel of the 3-order view. Use the 0.9 – 1.1 λ window to resolve them.