Laser Cavity Modes: How Resonators Shape Laser Light

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500 MHz mode spacing, ~6 lasing modes

A 30 cm cavity with 95% reflective mirrors produces mode spacing of 500 MHz. With a 2 nm gain bandwidth centered at 632 nm, approximately 6 longitudinal modes can lase.

Formula

Δν = c / (2L)
g_threshold = −ln(R₁R₂) / (2L)
F = π√R / (1 − R)
N_modes ≈ Δλ_gain / (λ² / 2L)

Standing Waves Between Mirrors

A laser cavity is a pair of mirrors facing each other with a gain medium in between. Light bouncing between the mirrors forms standing waves — only wavelengths that fit an exact integer number of half-wavelengths into the cavity length are sustained. These are the longitudinal modes of the resonator, and their frequency spacing is simply c/(2L). For a 30 cm cavity, this spacing is 500 MHz — a tiny fraction of the optical frequency itself.

Gain, Loss, and Threshold

The gain medium amplifies light passing through it, while the mirrors let a small fraction escape as the useful laser beam. Lasing begins when the gain per round trip exceeds the total losses — mirror transmission, scattering, and absorption. This threshold condition determines the minimum pumping power needed. The threshold gain coefficient equals −ln(R₁R₂)/(2L), so higher mirror reflectivity lowers the threshold.

Multi-Mode vs Single-Mode Lasers

When the gain bandwidth is wide enough to span several mode spacings, multiple longitudinal modes can oscillate simultaneously. A helium-neon laser at 632.8 nm with a 30 cm cavity might support 5–6 modes. For applications demanding extreme spectral purity — interferometry, spectroscopy, coherent communications — single-mode operation is achieved with shorter cavities, intracavity etalons, or distributed feedback gratings.

Finesse and Stored Energy

Cavity finesse measures how many times a photon bounces between the mirrors before escaping. High-finesse cavities (F > 1000) store enormous amounts of optical energy and produce extremely narrow emission lines. This principle is exploited in ring-down spectroscopy to detect trace gases at parts-per-trillion levels, and in gravitational wave detectors like LIGO where finesse exceeds 400.

FAQ

What are longitudinal modes in a laser cavity?

Longitudinal modes are standing-wave resonances that fit an integer number of half-wavelengths between the cavity mirrors. Their frequency spacing is c/(2L), where c is the speed of light and L is the cavity length. Only modes within the gain bandwidth can lase.

How does cavity length affect laser output?

A longer cavity produces more closely spaced modes (smaller c/2L spacing), so more modes fit within the gain bandwidth. Short cavities produce fewer, wider-spaced modes. Very short micro-cavities can achieve single-mode operation.

What determines the laser threshold?

Lasing threshold occurs when the round-trip gain equals the round-trip losses. The gain must compensate for mirror transmission losses (−ln(R₁R₂)/2L), scattering, absorption, and diffraction losses. Higher reflectivity mirrors lower the threshold.

What is cavity finesse?

Finesse measures how many round trips light makes before escaping the cavity. It equals π√R/(1−R) for identical mirrors with reflectivity R. High finesse means narrow linewidth and more stored energy, critical for stable single-frequency lasers.

Sources

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