Laser Linewidth and Bandwidth Calculator

Background.

No laser is perfectly monochromatic. Its output occupies a narrow band of the spectrum, and the width of that band — the linewidth — governs how coherent the light is, how tightly channels can be packed into an optical fibre and how finely a spectroscopic measurement can resolve detail. The awkward part is that the same width is quoted in two different currencies. Grating spectrometers and optical spectrum analysers read out in wavelength, so a datasheet may say 1 pm or 0.1 nm, while telecom engineers, spectroscopists and anyone doing heterodyne measurements think in megahertz and gigahertz.

The exchange rate is not fixed. Frequency and wavelength are inversely related, ν = c/λ, so a small step in wavelength corresponds to a frequency step that depends on where in the spectrum you are: Δν ≈ cΔλ/λ². With λ squared in the denominator, one picometre is worth about 1.06 GHz at 532 nm, about 265 MHz at 1064 nm and about 125 MHz at 1550 nm. In the telecom C-band, the familiar 100 GHz channel spacing of dense wavelength-division multiplexing works out to roughly 0.8 nm.

Enter the centre wavelength and the wavelength linewidth, both in metres, and the page returns the frequency linewidth in hertz. The conversion is first-order, which is accurate whenever the band is narrow compared with its wavelength — true of essentially every laser line. It says nothing about the shape of the line, the coherence time or the bandwidth of a pulse.

What is laser linewidth and bandwidth calculator?

Laser linewidth is the spectral width of a laser's emission, usually taken as the full width at half maximum of its optical spectrum. It can be stated as a span of wavelengths, Δλ, or as a span of optical frequencies, Δν, and both describe the same physical width. The quantity calculated here is Δν in hertz, found from Δλ and the centre wavelength λ through the first-order relation Δν ≈ cΔλ/λ², where c is the speed of light in vacuum.

How to use this calculator.

1. 01Enter the centre wavelength in metres: 1550 nm is 1.55 × 10⁻⁶ m, 1064 nm is 1.064 × 10⁻⁶ m and 632.8 nm is 6.328 × 10⁻⁷ m.
2. 02Enter the wavelength linewidth in metres as well — 1 nm is 10⁻⁹ m and 1 pm is 10⁻¹² m. Use the full width at half maximum unless your datasheet defines the width another way, and keep one definition when comparing sources.
3. 03Read the frequency linewidth in hertz; divide by 10⁶ for megahertz or by 10⁹ for gigahertz.
4. 04Check that the linewidth is a small fraction of the centre wavelength. For a broadband source spanning a sizeable part of λ, convert each edge of the band to frequency separately instead.

The formula.

Frequency and wavelength are linked by ν = c/λ, with c = 299,792,458 m/s, the exact value fixed by the SI definition of the metre. Differentiating gives dν/dλ = −c/λ², so a small wavelength width Δλ corresponds to a frequency width Δν ≈ cΔλ/λ²; the minus sign only says that longer wavelengths mean lower frequencies, and widths are quoted as positive. The result is proportional to Δλ and inversely proportional to the square of λ, so halving the wavelength quadruples the frequency width for the same Δλ. Only the first-order term is kept. For a band whose edges sit Δλ/2 either side of λ, the exact width is cΔλ/(λ² − Δλ²/4), so the first-order value is low by a fraction (Δλ/2λ)²: 0.0025% when Δλ is 1% of λ and 0.25% at 10%. Both inputs must be positive.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST, 2022 CODATA Recommended Values of the Fundamental Physical Constants.
2. [2]RP Photonics Encyclopedia, Linewidth.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.