A Fabry-Perot cavity has an air gap of length between two mirrors

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Interference and diffraction · Interference and diffraction

What an Instrument Can See, Ch Multiple beams: the stack as a matrix and the etalon as a filter

Problem

A Fabry-Perot cavity has an air gap of length

d = 0.300\ \mathrm{m}

between two mirrors, each of power reflectance

\mathcal{R} = 0.995

. There is no other loss. The light is at

633\ \mathrm{nm}

. ((a)) Find the round-trip time

T = 2nd/c

(take

n=1

). ((b)) Find the finesse

\mathcal{F} = \pi\sqrt{\mathcal{R}}/(1-\mathcal{R})

, the free spectral range, and the linewidth

\Delta\nu

. ((c)) Predict the photon (energy) lifetime

\tau_p

that a ringdown measurement of this cavity would report, using

\Delta\nu = 1/(2\pi\tau_p)