Laser Linewidth and Bandwidth Calculator
Enter your laser center wavelength and either a wavelength bandwidth or a frequency bandwidth to instantly convert between the two representations, compute the coherence time and coherence length of the beam, and find the spectral quality factor. The calculator uses the exact endpoint method rather than the small-bandwidth approximation, so it stays accurate even for broadband sources.
What is laser linewidth?
Laser linewidth refers to the spectral width of the light emitted by a laser, usually measured as the full width at half maximum (FWHM) of the optical power spectrum. An ideal single-frequency laser would emit at exactly one wavelength, but in practice every real laser has a finite linewidth caused by quantum noise (spontaneous emission), thermal fluctuations, vibrations, and current noise. Linewidth can be expressed in frequency units (Hz, kHz, MHz, GHz) or in wavelength units (pm, nm). The two representations are linked through the center wavelength because the relationship between wavelength and frequency is nonlinear. A 0.1 nm bandwidth means very different things in GHz depending on whether the laser is at 400 nm (visible) or 1550 nm (telecom).
Exact vs. approximate bandwidth conversion
The most accurate way to convert a wavelength bandwidth to a frequency bandwidth is the endpoint method: compute the frequencies at the two spectral edges (lambda0 - delta_lambda/2 and lambda0 + delta_lambda/2) and subtract them. The common first-order approximation, delta_nu = (c / lambda0^2) * delta_lambda, gives the same answer only when the bandwidth is very small compared with the center wavelength. For a 0.01 nm bandwidth at 1550 nm the approximation error is negligible, but for a 50 nm bandwidth at 800 nm it can exceed 1 percent. This calculator always uses the exact method and shows the approximation error so you can judge whether the shortcut applies to your situation.
Coherence time and coherence length
Coherence time (tau_c) is the characteristic time over which the electric field of the laser output remains phase-correlated with itself. For a Lorentzian lineshape, tau_c = 1 / delta_nu. The coherence length L_c = (c / n) * tau_c is the corresponding path-length difference over which two copies of the beam can still produce visible interference fringes. In air or vacuum n is approximately 1.000, but in glass (n ~ 1.5) or optical fibre (n ~ 1.46 at 1550 nm) the coherence length is shortened by the factor 1/n. A narrow linewidth of 1 MHz gives a coherence length of about 300 mm in air, while a 1 nm bandwidth around 1550 nm corresponds to only about 1.6 mm. Knowing the coherence length is essential for designing interferometers, holographic setups, and optical coherence tomography systems.
Quality factor and spectral purity
The quality factor Q = nu0 / delta_nu is a dimensionless measure of spectral purity. A 1 MHz linewidth at 193 THz (1550 nm) gives Q ~ 2 x 10^8. Optical frequency standards and atomic clocks reach Q > 10^15. For comparison, a microwave cavity has Q ~ 10^5, and a laser operating close to the Schawlow-Townes quantum limit can approach Q values of 10^14 or higher. The Schawlow-Townes formula gives the fundamental quantum lower bound on laser linewidth: delta_nu_ST = (pi * h * nu * delta_nu_c^2) / P_out, where h is Planck's constant, nu is the optical frequency, delta_nu_c is the cold-cavity linewidth, and P_out is the output power. In most practical lasers the actual linewidth far exceeds this limit because of technical noise, and dedicated linewidth-narrowing techniques such as the Pound-Drever-Hall method are used to approach it.
Typical laser linewidths by type
| Laser type | Typical linewidth | Coherence length (approx.) |
|---|---|---|
| He-Ne (632.8 nm, single mode) | 1 MHz | ~300 mm |
| DFB telecom diode (1550 nm) | 1-10 MHz | 30-300 mm |
| Fabry-Perot multimode diode | 1-5 nm / ~100-500 GHz | ~0.3-1.5 mm |
| Nd:YAG DPSS (1064 nm) | ~100 kHz | ~3 m |
| Stabilised ECDL (780 nm) | <100 kHz | >3 m |
| Optical frequency comb tooth | <1 Hz | >300 000 km |
| SLED / ASE source (1550 nm) | 30-60 nm / ~3-6 THz | <0.1 mm |
| Ti:sapphire (fs mode-locked) | ~10 nm / ~1 THz | <0.3 mm |
Representative free-running linewidths. Stabilisation and external cavities can reduce these values by many orders of magnitude.
Frequently asked questions
What is the difference between linewidth and bandwidth?
In laser physics the two terms are usually used interchangeably: both refer to the spectral width of the emitted light, typically defined as FWHM. "Linewidth" is more common for narrow single-mode lasers measured in Hz or kHz, while "bandwidth" is often used for broader sources measured in nm or GHz. This calculator handles both, using the same formulas regardless of the label.
Why does 1 nm mean a different number of GHz at different wavelengths?
Frequency and wavelength are linked by nu = c / lambda, and this relationship is nonlinear. A 1 nm step near 1550 nm corresponds to about 125 GHz, but the same 1 nm step near 800 nm corresponds to about 469 GHz. Always use the exact endpoint conversion (as this calculator does) or the approximation delta_nu ~ (c / lambda0^2) * delta_lambda, keeping in mind that the approximation gets less accurate as the bandwidth grows.
What coherence length do I need for interferometry?
The coherence length must exceed the maximum optical path difference (OPD) in your interferometer. For a Michelson interferometer with arm lengths that differ by 10 mm, you need L_c > 10 mm, which requires a linewidth below about 30 GHz at 1550 nm. For LIDAR ranging over kilometres, you need a coherence length of kilometres, corresponding to linewidths below about 300 kHz. For optical coherence tomography (OCT), a short coherence length is actually desirable because it gives fine axial resolution.
How does the refractive index affect coherence length?
The coherence length in a medium is L_c = (c / n) * tau_c. A higher refractive index slows down the phase velocity, reducing L_c relative to free space. In standard single-mode fibre at 1550 nm (n ~ 1.47), the coherence length is about 32 percent shorter than in air. This matters for on-chip photonic circuits and fibre interferometers. Set the refractive index in this calculator to match your medium.
What is the Schawlow-Townes linewidth?
The Schawlow-Townes formula gives the quantum-limited minimum linewidth of a laser: delta_nu_ST = (pi * h * nu * delta_nu_c^2) / P_out. It is set by spontaneous emission noise coupling into the lasing mode. For a 1 mW He-Ne laser at 633 nm with a 1 GHz cavity linewidth, the Schawlow-Townes limit is around 10 mHz. In practice, technical noise (vibrations, thermal drift, current noise) raises the linewidth many orders of magnitude above this limit, which is why external frequency stabilisation is used when a narrow linewidth matters.