Laser Linewidth and Bandwidth Calculator
With our laser linewidth and bandwidth calculator, you will learn how much your laser pointer deviates from an ideal monochromaticity.
Coherence length200.2179 mmc/Δν — the path difference over which interference fringes stay visible, and so the depth an interferometer can measure
Linewidth in frequency1.4973 GHzΔν = cΔλ/λ² — note the λ SQUARED, which is why the same wavelength spread means a very different frequency spread in the infrared than the ultraviolet
Linewidth in wavelength2 pm
Centre frequency473.7555 THz
Coherence time667.8551 ps
Quality factor of the line3.164e+5λ/Δλ — how many wavelengths fit in the coherence length, and a direct measure of spectral purity
Fringes visible3.164e+5the number of wavelengths in a coherence length
Against a red LED (Δλ ≈ 25 nm)16.0174 µmtens of microns — which is why an LED shows fringes only with nearly equal path lengths, and a laser shows them across a room
Against sunlight (Δλ ≈ 300 nm)1.3348 µmunder a micron — white light interference needs the paths matched to within a wavelength or two, which is exactly why a soap film shows colours and a thick window does not
The line shape mattersthese are order-of-magnitudea Gaussian line and a Lorentzian one of the same width give coherence lengths differing by a factor near unity but not equal to it. Treat these as the scale, not a precise figure
The formula
Δν = cΔλ/λ²; L_c = λ²/Δλ = c/Δν
Narrow lines see far
Coherence length is the speed of light divided by the linewidth: the path difference over which two parts of a beam still interfere. A helium-neon laser with a few megahertz of linewidth stays coherent over tens of metres. A red LED, with a spread of around 25 nm, manages only tens of microns — which is why an LED shows fringes only when the two paths are nearly equal.
Sunlight is narrower still in coherence, under a micron, and that is precisely why a soap film shows colours while a window pane does not. The film is thin enough for the two reflections to stay coherent; the glass is not.
The λ² in the conversion
Converting a wavelength spread to a frequency spread carries a factor of λ², so the same nanometre of linewidth means a very different bandwidth in the infrared than in the ultraviolet. Quoting a linewidth without saying which quantity it refers to is ambiguous by orders of magnitude.