Optical cavity

An optical cavity (also called a resonator or oscillator) is a bounded optical region with one or more reflective surfaces that supports discrete resonant electromagnetic modes. Combined with a gain medium, a cavity converts amplification into oscillation — the defining function of a laser.

Roles of the cavity. An optical cavity serves multiple purposes:

1. Mode selection: only specific frequencies (longitudinal modes) and spatial patterns (transverse modes) satisfy the cavity boundary conditions
2. Feedback: light returns through the gain medium multiple times, accumulating amplification
3. Output coupling: the partially-transmitting output coupler extracts a fraction of the intracavity power as the laser output
4. Linewidth narrowing: high-Q cavities produce narrow emission linewidths via the Schawlow-Townes formula
5. Wavelength control: wavelength-selective cavities (DBR, DFB, external grating) determine the lasing wavelength

Standard cavity types.

Cavity type	Geometry	Use
Fabry-Perot	Two parallel mirrors	Most basic laser cavity; standard for diode lasers, He-Ne
Linear standing-wave	Two mirrors, light bounces back and forth	Most CW lasers
Ring	Multiple mirrors forming a closed loop	Unidirectional traveling-wave operation; used for fiber lasers, lower spatial hole burning
Folded	Multiple mirrors at angles	Compact packaging
Confocal	Two spherical mirrors with $R_1 + R_2 = 2L$	Easy alignment, degenerate transverse modes
Plano-concave	Flat + curved mirror	Common stable cavity
External cavity	Diode laser + external mirror/grating	Tunable, narrow linewidth
Microring	On-chip ring resonator	Integrated photonics; on-chip lasers, filters
Whispering gallery	Light circulates by TIR in a sphere or disk	Very high Q, microsphere lasers
VCSEL	Surface-emitting cavity with DBR mirrors	Vertical emission, low-cost array integration

Cavity stability. For a two-mirror cavity with mirror curvatures $R_1, R_2$ and spacing $L$:

$$g_1 \;=\; 1 - \frac{L}{R_1}, \quad g_2 \;=\; 1 - \frac{L}{R_2},$$

The cavity is stable (Gaussian beam can be contained) when:

$$0 \;\leq\; g_1 g_2 \;\leq\; 1.$$

Outside this range, the beam diverges through repeated round trips — diffraction loss exceeds gain. Stable cavities support TEM₀₀ Gaussian operation with a well-defined waist; unstable cavities (used in some high-power applications) deliberately allow some diffraction loss but extract higher output.

Cavity Q-factor. The quality factor of an optical cavity:

$$Q \;=\; \frac{\omega \tau_p} = \frac{2\pi \nu \tau_p},$$

where $\tau_p$ is the photon lifetime. High-Q cavities have low loss per round trip and store the photon for many round trips.

Cavity	Typical Q
Cleaved-facet diode laser	$\sim 10^3$
HR-coated diode laser	$\sim 10^4$
External-cavity diode laser	$\sim 10^6$
Ti:sapphire	$\sim 10^7$
HeNe	$\sim 10^8$
Ultra-stable reference cavity	$\sim 10^{11}$
Whispering-gallery microsphere	$\sim 10^9$
Silicon microring	$\sim 10^5 - 10^6$

Cavity finesse. Related to Q but emphasizing the mode spacing:

$$F \;=\; \frac{2\pi}{\text{round-trip loss}} \;\approx\; \frac{\pi\sqrt{R_1 R_2}}{1 - R_1 R_2},$$

where $R_1, R_2$ are the cavity mirror reflectivities. For a 50% Fabry-Perot with $R_1 = R_2 = 0.50$: F = $\pi \sqrt{0.25} / (1-0.25) = 2.1$. For 99% mirrors: F = 310.

Round-trip time. Light bounces between the mirrors with round-trip time:

$$T_\text{rt} \;=\; \frac{2 L n}{c},$$

where $L$ is the cavity length and $n$ is the average refractive index. The free spectral range (frequency spacing between longitudinal modes) is $1/T_\text{rt}$.

Cavity length	FSR (telecom band)
100 μm (diode laser)	1500 GHz
1 cm (microcavity)	15 GHz
10 cm (small bench laser)	1.5 GHz
1 m (large bench laser)	150 MHz
10 m (fiber laser)	15 MHz
100 m (fiber laser ring)	1.5 MHz
1 km (large astronomy reference)	150 kHz

Threshold condition. A laser cavity oscillates when round-trip gain equals round-trip loss:

$$G_\text{round trip} \cdot R_1 R_2 \;\geq\; 1,$$

or equivalently:

$$g_\text{th} \;=\; \alpha + \frac{1}{2L} \ln\!\left( \frac{1}{R_1 R_2} \right),$$

where $\alpha$ is the average intrinsic loss per unit length and $R_1, R_2$ are the mirror reflectivities. The mirror term is the "useful loss" — the fraction of power that exits as the laser beam.

Cavity design considerations for lasers.

Goal	Design choice
High output power	Low-reflectivity output coupler (5 – 30%)
Narrow linewidth	High-finesse cavity, single-mode selection
Short pulse duration	Broad-bandwidth cavity (low Q)
High pulse energy	Long upper-state lifetime gain medium + Q-switch
Single longitudinal mode	Short cavity (FSR > gain bandwidth) or intracavity filter
Tunable wavelength	External cavity with grating
Low cost	Cleaved-facet semiconductor cavity (no coatings needed)

Cavity modes and laser output. A passive cavity supports all its modes equally; with a gain medium, the cavity preferentially populates modes at the gain peak. Mode competition (homogeneous gain saturation, spatial hole burning, etc.) determines which modes actually lase.

Cavity-related effects.

• Mode hops: discrete jumps between longitudinal modes as temperature/current changes the gain peak relative to mode positions
• Mode beats: multiple longitudinal modes produce RF intensity modulation at FSR
• Spatial hole burning: standing-wave pattern of one mode depletes gain at its anti-nodes, allowing adjacent modes to lase
• Power broadening: very high intracavity intensities can broaden mode linewidths
• Frequency pulling: gain dispersion pulls the lasing frequency slightly from the empty-cavity resonance

Open vs closed cavities. Most laser cavities are "open" — they have transverse losses (diffraction past the mirror edges). The mirror size and Fresnel number determine how high-order transverse modes are suppressed by edge losses. "Closed" cavities (waveguide cavities, integrated photonics) have transverse confinement built in.

References: Saleh & Teich, Fundamentals of Photonics (3rd ed., 2019), Ch. 11 (resonator optics); Siegman, Lasers (University Science Books, 1986), Ch. 11 – 16 — the comprehensive treatment; Yariv & Yeh, Photonics (6th ed., 2007), Ch. 7.