Glossary entry

Fabry-Perot resonator (FP cavity)

The optical resonator formed by two parallel partially reflecting mirrors: light bounces back and forth, the round trips interfere, and the cavity transmits only at frequencies spaced by the free spectral range c/2nL, each resonance narrowed by the finesse. Laser diode chips, etalons, fiber cavities, reference cavities and VCSELs are all Fabry-Perot resonators; the transmission formula, the linewidth, Q and photon lifetime, the lossy and asymmetric cases, and a calculator.

Optics fundamentals Lasers & gainUpdated October 2026

A Fabry-Perot resonator is two mirrors of power reflectivity $R_{1}$ and $R_{2}$ facing each other across a length $L$ of a medium of refractive index $n$ . Light that enters through the first mirror makes repeated round trips, and each round trip adds a partial wave to the transmitted and reflected fields with a phase delay of $2 π \times 2 n L / λ$ . When that delay is a whole number of cycles the partial waves add in phase and the cavity transmits; a little off resonance they cancel and it reflects. The resonator was described by Charles Fabry and Alfred Perot in 1899 as a spectroscopic interferometer, and it has since become the cavity of nearly every laser, the etalon in every wavelength locker, and the reference against which the narrowest lasers are stabilized. The Fabry-Perot Cavity Calculator evaluates everything below for any length, index, reflectivities and internal loss and draws the spectra from the exact field sums.

The transmission formula

Summing the round trips gives the transmitted field as a geometric series. With the round-trip amplitude factor $ρ = \sqrt{R_{1} R_{2}} e^{- α_{i} L}$ , where $α_{i}$ is the internal power loss per unit length, the transmitted and reflected powers at a round-trip phase $δ = 2 π (ν - ν_{m}) / F S R$ from the nearest resonance are

T (δ) = \frac{(1 - R_{1}) (1 - R_{2}) e^{- α_{i} L}}{∣ 1 - ρ e^{i δ} ∣^{2}}

R (δ) = \frac{∣ \sqrt{R_{1}} - \sqrt{R_{2}} e^{- α_{i} L} e^{i δ} ∣^{2}}{∣ 1 - ρ e^{i δ} ∣^{2}}

For equal lossless mirrors this collapses to the Airy function that most textbooks quote,

T (ν) = \frac{1}{1 + F \sin^{2} (π ν / F S R)}, F = \frac{4 R}{(1 - R)^{2}}

with $F$ the coefficient of finesse, so the transmission peaks at 1 and falls to $1 / (1 + F)$ halfway between resonances. The resonances sit where the round-trip phase is a multiple of $2 π$ , at $2 n L = m λ$ , with $m$ the longitudinal mode number, which for a 1 cm air cavity at 1550 nm is 12,903 and for a 300 µm laser chip about 1,240.

Quantity	Expression
Free spectral range	$F S R = c / (2 n_{g} L)$ , or $λ^{2} / (2 n_{g} L)$ in wavelength
Finesse	$F = π \sqrt{ρ} / (1 - ρ)$ , which is $π \sqrt{R} / (1 - R)$ for equal lossless mirrors
Resonance linewidth (FWHM)	$Δ ν = F S R / F$ to first order; exactly $(2 F S R / π) \arcsin [(1 - ρ) / 2 \sqrt{ρ}]$
Quality factor	$Q = ν_{0} / Δ ν = (2 n_{g} L / λ_{0}) F$ , which is $m F$ when $n_{g} = n$
Photon lifetime	$τ_{p} = 1 / [v_{g} (α_{i} + α_{m})] \approx 1 / (2 π Δ ν)$ , with $v_{g} = c / n_{g}$
Mirror loss coefficient	$α_{m} = \ln (1 / R_{1} R_{2}) / 2 L$
Peak transmission	$(1 - R_{1}) (1 - R_{2}) e^{- α_{i} L} / (1 - ρ)^{2}$
Intracavity power on resonance	$(1 - R_{1}) / (1 - ρ)^{2}$ times the incident power

The free spectral range uses the group index because it is the spacing of resonances in frequency, which depends on how the round-trip phase changes with frequency; the mode number uses the phase index. The exact linewidth and the first-order one agree within 0.01 % at $R = 0.99$ but differ by 2 % at $R = 0.5$ , and below $ρ = 0.17$ the fringes are shallower than half their height and a linewidth is no longer defined. Two consequences of the formulas are worth carrying around. A lossless cavity with equal mirrors transmits everything on resonance, however small $1 - R$ is, because the reflected partial waves cancel exactly; that is impedance matching, and unequal mirrors or any internal loss spoil it. And the power circulating inside a matched cavity is $1 / (1 - R)$ times the incident power, a hundredfold for $R = 0.99$ , which intracavity frequency doubling exploits; cavity ring-down and cavity-enhanced absorption spectroscopy use the matching gain in effective path length, $L / (1 - R) \approx F L / π$ .

Worked cases

A cleaved InGaAsP laser chip 300 µm long has facets of $R = 0.31$ from the Fresnel reflection of the semiconductor-air interface, $n_{g} = 3.6$ and an internal loss of about 10 cm⁻¹: its FSR is 139 GHz, or 1.1 nm, its mirror loss 39 cm⁻¹, its photon lifetime 2.4 ps, and 80 % of the light generated above threshold leaves through the facets rather than being absorbed, which is the differential efficiency's cavity factor. Its finesse is only 2, so its fringes are broad, and that broad Fabry-Perot comb under the gain curve is why an uncoated chip lases on several longitudinal modes at once; a DFB grating or a coated facet is needed to select one. A 5 mm fused-silica etalon with 90 % coatings has an FSR of 20.5 GHz, a finesse of 30 and a linewidth of 690 MHz, a narrow filter; a telecom wavelength locker uses the opposite, a finesse of about 3 and an FSR equal to the 50 or 100 GHz channel spacing. A 10 cm fiber cavity between 99 % reflectors has an FSR of 1.0 GHz and a 3.3 MHz linewidth, and a 10 cm ULE reference cavity with 99.999 % mirrors has an FSR of 1.5 GHz, a finesse of 314,000, a linewidth of 4.8 kHz, a Q of $4 \times 10^{10}$ and a photon lifetime of 33 µs, which is why lasers locked to such cavities reach hertz linewidths. A 5 mm silicon waveguide with uncoated facets ( $R = 0.30$ ) and 2 dB/cm of loss shows fringes with a contrast of 0.45, and that contrast, measured as a function of wavelength, is the Fabry-Perot method for measuring waveguide loss without cleaving the chip.

Applications

Every edge-emitting semiconductor laser is a Fabry-Perot resonator between its facets, and the VCSEL is one between two Bragg mirrors a wavelength apart, which pushes its FSR beyond the gain bandwidth and makes it single-mode by construction. Ultrastable reference cavities are Fabry-Perot resonators built for the highest finesse and the lowest thermal noise. Scanning Fabry-Perot interferometers sweep the mirror spacing with a piezo to read a laser's longitudinal mode structure with megahertz resolution, and are usually built confocal, with curved mirrors separated by their radius of curvature, which makes them insensitive to alignment at the cost of halving the free spectral range to $c / 4 L$ . Thin-film bandpass filters are Fabry-Perot cavities with dielectric-stack mirrors and a spacer layer, and the characteristic matrix method computes them layer by layer. Plane-mirror cavities are marginally stable and need curved mirrors for a confined transverse mode in free space; the plane-wave theory above describes the longitudinal behavior that all of these share.

References: A. E. Siegman, Lasers (University Science Books, 1986), chapter 11. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019), chapter 11. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), section 7.6. C. Fabry and A. Perot, "Théorie et applications d'une nouvelle méthode de spectroscopie interférentielle," Annales de Chimie et de Physique 16, 115 (1899). N. Ismail, C. C. Kores, D. Geskus, and M. Pollnau, "Fabry-Pérot resonator: spectral line shapes, generic and related Airy distributions, linewidths, finesses, and performance at low or frequency-dependent reflectivity," Optics Express 24, 16366 (2016).