How does a Fabry-Pérot cavity select specific frequencies?

The cavity resonates when the round-trip optical path length equals an integer number of wavelengths: 2nL = mλ, where m is the mode number. At these resonant frequencies, successive reflections add constructively and the cavity transmits nearly all incident light. Between resonances, the multiply-reflected beams interfere destructively and the cavity reflects most light. This frequency selectivity is the basis for laser modes and wavelength-division multiplexing filters.

What is finesse and how does it affect performance?

Finesse F = π√R/(1−R) is a dimensionless figure of merit for the cavity. It equals the ratio of the free spectral range to the full-width-half-maximum (FWHM) of a transmission peak. High finesse (achieved with high reflectivity mirrors, R → 1) means very narrow, well-resolved peaks—essential for separating closely spaced spectral lines or achieving low-phase-noise laser oscillation. Super-polished mirrors in gravitational-wave detectors achieve finesse values of 300,000 or more.

What is the free spectral range (FSR)?

The FSR is the frequency spacing between adjacent transmission peaks: FSR = c/(2nL). It sets the bandwidth over which the interferometer can be used without ambiguity—a signal at frequency f cannot be distinguished from one at f + FSR. Shorter cavities have larger FSR (wider unambiguous range) but fewer modes in a given bandwidth. Longer cavities pack more modes into the FSR, enabling higher frequency resolution at the cost of narrower operating range.

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🔭 Fabry-Pérot Interferometer

Simulate a Fabry-Pérot etalon: resonant transmission peaks, Free Spectral Range (FSR), Finesse, and how mirror reflectivity shapes the cavity modes.

Optics & Light3DAdvanced60 FPS

About this simulation

This model recreates the multiple-beam interference that occurs inside a Fabry-Pérot etalon: two parallel, partially-reflective mirrors bouncing light back and forth until it either escapes as a sharp transmission peak or is reflected away. The Airy function governs the shape of every peak, whilst reflectivity alone decides how narrow those peaks become. Watching the standing wave build inside the cavity makes the abstract resonance condition 2nL = mλ genuinely visible.

🔬 What it shows

The live transmission spectrum T(λ) traced by the Airy formula, alongside the standing-wave pattern forming between the two mirrors whenever the cavity is near resonance. Colour on both the beams and the spectrum panel reflects the true visible-light hue of the chosen wavelength.

🎮 How to use

Drag Mirror reflectivity R, Cavity length L, Refractive index n and Wavelength λ. Watch the Finesse, FSR, FWHM, T(λ) and mode-order m readouts update instantly, and note how the orange marker on the spectrum tracks the current wavelength against the Airy envelope.

💡 Did you know?

Fabry-Pérot cavities with ultra-high reflectivity mirrors underpin gravitational-wave detectors such as LIGO, where finesse values in the hundreds of thousands allow laser light to make hundreds of round trips before it leaks out, vastly amplifying the effective path length.

Frequently asked questions

Why do the transmission peaks get narrower as R increases?

The coefficient of finesse F = 4R/(1−R)² grows very rapidly as R approaches 1, which sharply increases the denominator of the Airy function away from resonance whilst leaving the peak itself at T = 1. That squeezes the linewidth down, so raising the slider from 0.90 towards 0.999 turns broad humps into razor-thin spikes.

What determines the spacing between adjacent peaks?

The free spectral range, FSR = λ²/(2nL), sets that spacing. Increasing the cavity length L or the refractive index n packs more resonance orders into the same wavelength window, shrinking the FSR, whilst a shorter cavity spreads the peaks further apart.

Why does the mode order m change when I move the sliders?

The order m is simply the nearest integer to 2nL/λ, the number of half-wavelengths that fit in one round trip. Changing L, n or λ shifts that ratio continuously, so m jumps between integers as the cavity passes through successive resonances.

Why does the cavity glow brighten and dim as I drag the wavelength slider?

The glow intensity is tied directly to the instantaneous transmission T(λ) from the Airy function. Near a resonance, T rises towards 1 and the cavity appears bright; between resonances T falls towards zero and the glow all but disappears, mirroring how little light actually gets through off-peak.

How is finesse related to FSR and FWHM?

Finesse is defined as the ratio of the free spectral range to the peak linewidth, F = FSR/FWHM. It is a dimensionless measure of how many resolvable peaks could theoretically fit inside one FSR, and the simulation computes it directly from the mirror reflectivity as π√R/(1−R).

⚙ Under the hood

Explore resonant transmission in an optical cavity: Airy function, Finesse, FSR, and linewidth.

opticsinterferencecavitylaserspectroscopyAiry function

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install