Optical Resonators and Cavity Modes
An optical resonator confines light between mirrors, supporting discrete longitudinal and transverse modes that shape a laser's spectrum and beam.
Definition
An arrangement of mirrors that traps light in standing or circulating waves, supporting a discrete set of resonant longitudinal and transverse modes characterized by their frequencies, spatial profiles, and losses.
Scope
This topic covers the optical cavities that provide feedback in lasers and that act as spectral filters. It includes the Fabry-Perot and confocal resonators, the longitudinal modes set by the round-trip phase condition and their spacing, the transverse modes and their Gaussian and Hermite-Gaussian profiles, the stability condition for two-mirror cavities, the quality factor and photon lifetime, the finesse and free spectral range, and the relation between resonator losses and laser linewidth. It explains how the cavity determines which frequencies and spatial patterns oscillate.
Core questions
- What frequencies and spatial patterns can resonate in a given cavity?
- What conditions make a two-mirror resonator stable?
- How do finesse, quality factor, and photon lifetime characterize a resonator?
- How does the resonator select the laser's longitudinal and transverse modes?
Key concepts
- Fabry-Perot resonator
- longitudinal modes
- transverse modes
- free spectral range
- finesse
- quality factor
- cavity stability condition
- photon lifetime
Key theories
- Longitudinal modes and the resonance condition
- Only wavelengths for which the round-trip optical path is an integer number of wavelengths resonate, giving a comb of longitudinal modes whose spacing is set by the cavity length.
- Transverse modes and cavity stability
- The transverse field forms Gaussian and higher-order Hermite- or Laguerre-Gaussian modes; a two-mirror cavity supports stable confined modes only when its mirror curvatures and spacing satisfy the resonator stability condition.
Clinical relevance
Resonator design fixes the wavelength, linewidth, and beam quality of medical and diagnostic lasers, and high-finesse optical cavities serve as the frequency-selective elements in spectroscopic sensors used for breath and blood analysis.
History
The Fabry-Perot interferometer of the 1890s became the prototype of the optical resonator. When Schawlow and Townes proposed the optical laser in 1958, the key step beyond the maser was to use such an open mirror cavity to provide feedback and select modes at optical wavelengths.
Key figures
- Charles Fabry
- Alfred Perot
- Arthur L. Schawlow
Related topics
Seminal works
- siegman1986
- salehteich2019
Frequently asked questions
- What sets the spacing between a laser's longitudinal modes?
- The spacing in frequency equals the speed of light divided by twice the optical cavity length, so longer cavities have more closely spaced modes.
- Why must a laser cavity be stable?
- In a stable resonator a ray bounces back and forth without walking off the mirrors, so a confined mode can build up; an unstable cavity lets light escape after a few passes unless that loss is deliberately exploited for high-power designs.