Laser Linewidth & Bandwidth Calculator (Δλ ↔ Δν, coherence length)

Understanding the laser linewidth calculator — concept and principle

This calculator converts a laser's linewidth between frequency, wavelength and wavenumber units, and gives the centre frequency, coherence time, coherence length and quality factor. It is used for choosing lasers for interferometry, fibre sensing, coherent communications and spectroscopy.

A narrow linewidth means a long, steady wave train: here nearly a kilometre stays in step.

How it is calculated

ν = c ÷ λ

Δν = c Δλ ÷ λ²; Δλ = λ² Δν ÷ c (valid for Δλ ≪ λ)

Coherence time τ = 1 ÷ (π Δν); coherence length L = c ÷ (π Δν) (Lorentzian line)

Rough coherence length = c ÷ Δν; quality factor = ν ÷ Δν; wavenumber width = Δν ÷ c

c = 299,792,458 m/s; linewidth is the full width at half maximum.

The principle

Frequency and wavelength are inversely related, so a small spread in one corresponds to a small spread in the other, scaled by λ²/c. A narrow linewidth means the light wave keeps a steady phase for a long time; the coherence time is how long, and the coherence length is how far light travels in that time. For a Lorentzian line, typical of single-frequency lasers, the exact relation is τ = 1/(πΔν); many texts quote the rougher c/Δν for the length.

Worked example

Default inputs: λ = 1,550 nm, linewidth 100 kHz.

Δν = 0.1 MHz; ν = c ÷ 1,550 nm = 193.414 THz.
Δλ = (1,550 × 10⁻⁹)² × 10⁵ ÷ c = 8.014 × 10⁻¹⁶ m = 0.0008014 pm.
τ = 1 ÷ (π × 10⁵) = 3.183 µs; coherence length = c × τ = 954.3 m.
Rough length c ÷ Δν = 2,998 m; quality factor = 1,934,144,890; wavenumber width = 0.000003336 cm⁻¹.

Each point is the calculator re-run with only “Linewidth (full width at half maximum)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Linewidth (full width at half maximum)	Linewidth in frequency Δν (MHz)
25	0.025
50	0.05
75	0.075
100	0.1
125	0.125
150	0.15
200	0.2

How to read the result

At 1,550 nm, 1 pm of linewidth corresponds to about 125 MHz. A 100 kHz laser is very narrow, with a coherence length of hundreds of metres, which suits long-path interferometry and coherent fibre links. Broad-area diode lasers and LEDs have linewidths of nanometres and coherence lengths of micrometres to millimetres.

Common mistakes

Mixing kHz, MHz and GHz.
Using the conversion for broad spectra where Δλ is not small compared with λ.
Comparing coherence lengths calculated with c/Δν and c/(πΔν).
Quoting the linewidth without stating whether it is FWHM.

Keep in mind: Measured linewidth depends on the measurement time and method. Check how the manufacturer specifies it.

Frequently asked questions

How do I convert pm to MHz at 1,550 nm?

Multiply by about 125: 1 pm ≈ 125 MHz.

What is coherence length?

The path difference over which light still interferes well with itself.

Why do sources quote different coherence lengths?

Some use c/Δν, others c/(πΔν) for a Lorentzian line.

Does a narrower linewidth mean higher power?

No. Linewidth and power are separate properties.

Sources: R. Paschotta, RP Photonics Encyclopedia, "Coherence Length" and "Coherence Time"

Checked 9 Nov 2026. RP Photonics Encyclopedia (R. Paschotta): “Coherence Length” (L_coh = c/(πΔν) for a Lorentzian spectrum, Δν = FWHM; c/Δν as a rough estimate) and “Coherence Time” (τ_coh = 1/(πΔν)). Δν = cΔλ/λ² follows from ν = c/λ (standard).

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