Glossary entry

Fabry–Pérot resonator (FP)

An optical resonator formed by two parallel reflecting surfaces. The simplest and most fundamental resonator geometry; ubiquitous as laser cavities, optical filters, and spectroscopic reference standards.

A Fabry–Pérot resonator consists of two highly-reflecting mirrors (reflectivities $R_1$ , $R_2$ ) separated by a distance $L$ . Light entering one mirror undergoes multiple round trips, with interference between the partial waves determining the transmitted and reflected fields.

Transmission spectrum. For matched-mirror reflectivities ( $R_1 = R_2 = R$ ) and lossless intracavity medium:

T(\nu) \;=\; \frac{1}{1 + F \sin^2(\pi \nu / \text{FSR})},

where $F = 4R / (1-R)^2$ is the cavity coefficient of finesse. The transmission peaks at frequencies satisfying the resonance condition:

2 n L \;=\; m \lambda \;\Leftrightarrow\; \nu_m = m \cdot \frac{c}{2 n L},

where $m$ is an integer (the longitudinal mode number) and $n$ is the index of the intracavity medium.

Key spectral quantities:

Parameter	Expression
Free spectral range	$\text{FSR} = c / (2 n_g L)$
Finesse	$\mathcal{F} = \pi \sqrt{R} / (1 - R)$
Resonance linewidth	$\Delta\nu = \text{FSR} / \mathcal{F}$
Quality factor	$Q = \nu_0 / \Delta\nu$
Photon lifetime	$\tau_p = 1 / (2\pi \Delta\nu)$

Applications.

Laser cavities. Edge-emitting semiconductor diode lasers are FP resonators with cleaved end facets ( $R \approx 0.30$ for InP/InGaAsP, from Fresnel reflectivity of the high-index–air interface).
High-finesse reference cavities. Stabilized lasers lock to a single transmission peak of an evacuated, temperature-stabilized FP cavity. Finesse exceeds $10^5$ ; linewidth $< 100$ Hz.
Optical spectrum analyzers. Scanning FP analyzers sweep $L$ to map an optical spectrum. Sub-MHz resolution is achievable with high-finesse confocal designs.
Thin-film bandpass filters. Multi-layer dielectric stacks form FP cavities with periodic transmission, used as WDM filters.
VCSELs. Vertical-cavity surface-emitting lasers are sub-wavelength FP resonators with distributed Bragg reflector mirrors above and below the active region.
Etalons. Thick glass plates with parallel, partially-reflecting surfaces serve as static FP filters for laser wavelength locking and spectral channelization.

Confocal vs flat-mirror geometries. Two flat mirrors form an unstable cavity for any misalignment. Curved mirrors give stable confined-mode operation; the confocal FP (mirror radii of curvature equal to mirror separation) is particularly insensitive to alignment and provides degenerate higher-order transverse modes that simplify high-resolution spectroscopy.

Most diode laser characterization geometries treat the chip as a multimode FP resonator and extract internal parameters from the LIV curve, spectral envelope, and mode spacing. A DFB laser is conceptually an FP cavity with an embedded grating that breaks the degeneracy among longitudinal modes, selecting one wavelength for single-mode operation.