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Coherence LengthGaussian & Lorentzian Models

Broadband SLDs and narrow-linewidth lasers sit at opposite ends of the coherence spectrum — one engineered short, the other long.

Gaussian · FWHM
Coherence length Lc
Lc = 2·ln2π · λ²Δλ ≈ 0.44 · λ²Δλ Gaussian spectrum, Δλ = full width at half maximum
SLD broadband (Gaussian) wide Δλ fringe envelope dies fast → Lc in µm DFB narrow-linewidth (Lorentzian) narrow Δν envelope decays slowly → Lc of hundreds of meters
Bandwidth and coherence length are inversely related: the wider the spectrum, the shorter the interference "memory"

What coherence length is

Coherence length is the maximum path difference over which two beams still form clear interference fringes. It is set entirely by the source bandwidth: the wider the spectrum, the faster fringes from different wavelengths walk off each other. The two coefficients come from lineshape — Gaussian spectra (SLDs and most broadband sources) use (2ln2/π)·λ²/Δλ, while phase-noise-dominated single-frequency lasers use the Lorentzian c/(π·Δν).

SLDs are engineered wide on purpose: pushing coherence down to tens of microns suppresses coherent noise from Rayleigh backscatter and polarization cross-coupling in fiber gyros, and directly sets OCT axial resolution. DFB / ECL lasers are engineered narrow: stretching coherence to tens of meters or kilometers enables coherent detection, distributed sensing and heterodyne interferometry. When selecting, ask: how much path difference must your application "remember"?

Related Products

Related tools: OCT axial resolution · Spectral ripple & FSR · Δλ↔Δν converter

※ Formulas on this page assume ideal models; all device parameters shown are typical values — refer to the datasheet and the serialized factory test report shipped with each unit. For selection support, contact sales@lncetek.com.