Interference
Fabry–Pérot cavity
Two partial mirrors facing each other trap light that bounces between them many times. Only when a whole number of half-wavelengths fits between the mirrors do all the bounces add up, and then nearly all the light gets through. Otherwise almost none does.
What you are looking at
The laser shines through two 95% mirrors 50 mm apart onto a photodiode. The tracer follows the beam round many round trips and the compositor adds every pass with its own phase.
How the bench is set up
A laser with a wide beam (3 mm across), two partial mirrors (R = 95%) 50 mm apart and a large photodiode. The second mirror has a piezo. The wide beam matters: a narrow one spreads a little on every round trip, so the late bounces stop overlapping the first and the peaks blur.
The theory
For two mirrors of reflectance and spacing , the transmission against the round-trip phase is the Airy function
Peaks are one free spectral range apart, in frequency or in spacing, and the finesse is
What to measure
Transmission peaks every λ/2 of spacing; finesse π√R/(1 − R)
- Select the second mirror and move its piezo in steps of 20 nm until the photodiode jumps, then in steps of 1 nm across the peak.
- Find two peaks: they should be 316.4 nm apart. The width of a peak over that spacing is one over the finesse.
What the model leaves out
- The mirrors are perfectly flat and parallel; a real etalon’s finesse is also limited by flatness and tilt.
Things to try
- Raise the reflectance to 99%: the peaks get sharper.
- Tilt one mirror by 100 µrad and watch the transmission fall as the bounces walk off.
- Narrow the laser to a 0.3 mm waist: each round trip spreads the beam, and the finesse drops well below the mirrors’ value.
References
- E. Hecht (2017), Optics, 5th edition, Pearson.
- C. Fabry and A. Pérot (1899), Théorie et applications d’une nouvelle méthode de spectroscopie interférentielle, Annales de Chimie et de Physique 16, 115.
More experiments, and how the lab works, are in the laser lab’s overview.