Finesse F = π√R/(1−R) quantifies how many sharp transmission peaks fit within one free spectral range. Higher R (and higher F) gives narrower resonances.

What is the free spectral range?

FSR = λ/(2n) is the cavity-length spacing between adjacent transmission peaks at fixed wavelength. In frequency, FSR = c/(2nL).

How is linewidth related to finesse?

Approximately ΔL ≈ FSR/F. High-finesse cavities transmit only a very narrow range of lengths or wavelengths near resonance.

Mirror absorption, surface figure, walk-off at angle, thermal drift, and frequency-dependent dispersion in the medium are not modeled.

Fabry–Pérot Cavity / Etalon

A Fabry–Pérot cavity consists of two partially reflecting mirrors enclosing a medium of refractive index n and length L. For normal incidence the round-trip phase is δ = 4πnL/λ, and the transmitted intensity follows the Airy function T(δ) = (1−R)²/[(1−R)² + 4R sin²(δ/2)] for symmetric mirror reflectivity R. Sharp resonances appear when δ is a multiple of 2π. The amplitude finesse F = π√R/(1−R) measures how narrow the transmission peaks are; the free spectral range in cavity length is FSR = λ/(2n), and the FWHM linewidth is approximately ΔL ≈ FSR/F. Scanning L (or wavelength) through a resonance is the basis of etalon filters, laser cavities, and high-resolution spectroscopy. This simulator plots T(L), displays F, FSR, and linewidth, and animates a cavity-length scan with a schematic etalon and transmitted beam brightness proportional to T.

Who it's for: Undergraduate optics students after two-beam interference (Michelson/Mach–Zehnder) and before laser cavities or high-finesse spectroscopy.

Key terms

Fabry–Pérot etalon
Airy function
Finesse
Free spectral range
Linewidth
Optical cavity
Multiple-beam interference

Live graphs

How it works

Fabry–Pérot etalon: Airy transmission, finesse, free spectral range, and linewidth as you scan cavity length L.

Key equations

T(δ) = (1−R)² / [(1−R)² + 4R sin²(δ/2)]

δ = 4πnL/λ · F = π√R/(1−R) · FSR = λ/(2n) · ΔL ≈ FSR/F

Frequently asked questions

What is finesse?: Finesse F = π√R/(1−R) quantifies how many sharp transmission peaks fit within one free spectral range. Higher R (and higher F) gives narrower resonances.
What is the free spectral range?: FSR = λ/(2n) is the cavity-length spacing between adjacent transmission peaks at fixed wavelength. In frequency, FSR = c/(2nL).
How is linewidth related to finesse?: Approximately ΔL ≈ FSR/F. High-finesse cavities transmit only a very narrow range of lengths or wavelengths near resonance.
What is left out?: Mirror absorption, surface figure, walk-off at angle, thermal drift, and frequency-dependent dispersion in the medium are not modeled.

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Live graphs

How it works

Key equations

Frequently asked questions

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Live graphs

How it works

Key equations

Frequently asked questions