Laser Linewidth Calculator

Calculate the Schawlow-Townes linewidth of a laser based on cavity parameters, output power, and wavelength. Understand the fundamental quantum limit on laser spectral purity.

SCHAWLOW-TOWNES LINEWIDTH
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Frequency
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Cavity Linewidth
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Photon Lifetime
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Coherence Length
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What Is Laser Linewidth?

Laser linewidth describes the spectral width of the laser output, indicating how monochromatic the emitted light is. A narrower linewidth means a purer single frequency, which is critical for applications such as spectroscopy, interferometry, coherent communications, and gravitational wave detection. The fundamental lower limit on linewidth is set by quantum mechanics through the Schawlow-Townes formula.

In practice, technical noise sources such as vibrations, thermal drift, and pump noise broaden the linewidth well beyond the Schawlow-Townes limit. Modern stabilized lasers can approach sub-hertz linewidths using active feedback and ultra-stable cavities.

The Schawlow-Townes Formula

Δν = (4π h ν (Δνc)² nsp) / Pout

Where Δν is the laser linewidth (Hz), h is Planck's constant (6.626 x 10-34 J·s), ν is the laser frequency, Δνc is the cold cavity linewidth, nsp is the spontaneous emission factor, and Pout is the output power. The cavity linewidth depends on the round-trip loss and cavity length.

Δνc = -c · ln(R) / (2π L)

Factors Affecting Linewidth

ParameterEffect on LinewidthTypical Range
Output PowerInversely proportional0.1 mW - 10 W
Cavity LengthLonger cavity = narrower1 cm - 1 m
Mirror ReflectivityHigher R = narrower0.95 - 0.9999
Spontaneous EmissionHigher nsp = broader1 - 5
WavelengthShorter = broader200 nm - 10 μm

Linewidths of Common Lasers

Laser TypeWavelengthTypical Linewidth
HeNe632.8 nm1 - 1500 MHz
Nd:YAG1064 nm1 - 10 kHz (stabilized)
DFB Diode1550 nm1 - 10 MHz
External Cavity DiodeVarious10 - 500 kHz
Fiber Laser1550 nm1 - 100 kHz

Frequently Asked Questions

What is the Schawlow-Townes limit?

The Schawlow-Townes limit is the fundamental quantum noise floor for laser linewidth. It arises from spontaneous emission events that add random phase perturbations to the coherent laser field. In practice, most lasers operate well above this limit due to technical noise, but it represents the best achievable linewidth for a given set of cavity and power parameters.

How does cavity length affect linewidth?

A longer cavity has a narrower free spectral range and a higher quality factor for each longitudinal mode. This reduces the cold cavity linewidth, which enters the Schawlow-Townes formula squared, making cavity length a very effective parameter for narrowing linewidth.

Why does higher power give narrower linewidth?

Higher output power means more photons in the cavity mode. Since spontaneous emission adds one random photon at a time, the relative phase perturbation per spontaneous event decreases as the photon number increases, leading to a narrower linewidth proportional to 1/P.