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 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 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 $1/T_\text{rt}$.

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.

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.