A telecommunications engineer builds a narrowband filter from two identical

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

Optics and Photonics, Ch Multiple-beam interference: thin films, multilayers and the Fabry-Perot etalon

Problem

A telecommunications engineer builds a narrowband filter from two identical, lossless, parallel mirrors, each of reflectance R=0.90\mathcal{R} = 0.90, facing each other to form a Fabry-Perot etalon. Each mirror alone transmits T=1−R=0.10\mathcal{T} = 1 - \mathcal{R} = 0.10 of the light incident on it. The engineer reasons: "light must get through the first mirror, then through the second, so at best only T×T=0.10×0.10=1%\mathcal{T}\times\mathcal{T} = 0.10\times0.10 = 1\% of the incident light can ever be transmitted by the pair." ((a)) Explain what is wrong with this reasoning. ((b)) Using the Airy function, find the actual transmittance TFP\mathcal{T}_{\rm FP} of the etalon at a transmission peak (δ=2mπ\delta = 2m\pi). ((c)) Find the coefficient of finesse FF for these mirrors.

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