Laser Linewidth and Bandwidth Calculator

Laser linewidth (Δν) is the spectral width of the laser's emission, measuring how closely it approximates a perfectly monochromatic (single-frequency) source. Even though lasers emit very narrow spectra compared to other light sources, quantum noise from spontaneous emission introduces a fundamental lower limit to this linewidth, described by the Schawlow-Townes formula.

The Schawlow-Townes linewidth formula is Δν = (π × h × ν × Γ²) / P, where h is Planck's constant (6.626×10⁻³⁴ J·s), ν is the laser frequency, Γ is the cavity photon decay rate (Hz), and P is the output power (W). This gives the fundamental quantum noise limit; in practice, technical noise sources usually broaden the linewidth further.

A narrow linewidth laser has a very small Δν, often in the kHz or even sub-Hz range. These are used in precision spectroscopy, optical coherence tomography, LIDAR, and fiber-optic communications where long coherence lengths and high frequency stability are required. Distributed feedback (DFB) and external cavity diode lasers are common narrow-linewidth designs.

Laser linewidth refers specifically to the spectral width of the laser's own emission (how monochromatic the source is), while laser bandwidth can also refer to the range of frequencies that an optical system or amplifier can handle. For a CW single-mode laser, these are closely related, but for pulsed or multi-mode lasers the bandwidth of the output spectrum is typically much wider than the Schawlow-Townes linewidth limit.

They are related by Δν ≈ (c / λ²) × Δλ, where c is the speed of light, λ is the center wavelength, and Δλ is the wavelength bandwidth. This approximation holds well for small bandwidths. For large bandwidths, the exact relationship uses the start and stop frequencies computed directly from the start and stop wavelengths.

Coherence length (L_c) is the propagation distance over which the laser's phase remains predictable and interference can be observed. It is given by L_c = c / (π × Δν), where Δν is the laser linewidth. A narrower linewidth means a longer coherence length — single-frequency lasers used in interferometry can have coherence lengths of hundreds of meters to kilometers.

A common red diode laser pointer (650 nm) typically has a linewidth of several hundred MHz to a few GHz, corresponding to a coherence length of roughly centimeters to tens of centimeters. This is far above the Schawlow-Townes quantum limit because technical noise (temperature fluctuations, current noise, mode hopping) dominates in uncontrolled diode lasers.

Optical bandwidth describes the width of a frequency (or wavelength) range associated with a light source, optical filter, amplifier, or detector. It can refer to the emission spectrum of a source, the transmission window of an optical element, or the detectable range of a photodetector. In telecommunications, standard channel spacings like 25 GHz, 50 GHz, and 100 GHz define common bandwidth windows.