Laser Linewidth Calculator — Δν ↔ Δλ & Coherence Length
Enter the center wavelength and either the frequency linewidth (Δν in MHz) or wavelength linewidth (Δλ in nm) to get the complementary quantity plus coherence length and coherence time.
Linewidth input type
nm
MHz
L_c = λ² / Δλ = c / Δν (rectangular lineshape)
- 1
Frequency linewidth (Hz)
1 MHz × 10⁶ = 1,000,000 - 2
Wavelength linewidth Δλ (m)
λ² ÷ c × Δν = 0 - 3
Coherence length (m)
λ² ÷ Δλ = 0.000001064² ÷ 0 = 299.7925 - 4
Coherence length (cm)
299.7925 × 100 = 29,979.246
How does this calculator work?
Convert frequency linewidth to wavelength linewidth via Δλ = λ²·Δν/c, where c = 3×10⁸ m/s. The coherence length L_c = c/Δν = λ²/Δλ (rectangular lineshape). A 1 MHz linewidth at 1064 nm gives Δλ ≈ 3.8×10⁻⁶ nm and L_c ≈ 30 cm. Narrower linewidth = longer coherence.
Formula
How this is calculated
Because frequency ν = c/λ, a small linewidth in one domain maps to the other via the derivative: Δν = (c/λ²)·Δλ, or equivalently Δλ = (λ²/c)·Δν. The conversion is wavelength-dependent — the same frequency linewidth corresponds to a larger wavelength spread at longer wavelengths. For example, 1 MHz at 1064 nm corresponds to only ~3.8×10⁻⁶ nm, while at 10 600 nm (CO₂) the same 1 MHz spans ~3.8×10⁻⁴ nm.
The coherence length L_c = λ²/Δλ = c/Δν is the path-length difference up to which two copies of the beam can still interfere with significant contrast. This calculator uses the rectangular (transform-limited) convention L_c = λ²/Δλ; for a Lorentzian lineshape (natural/pressure-broadened linewidth) the coherence length is π times smaller, and for a Gaussian lineshape it is (2·ln2/π)⁰·⁵ times different — choose the formula matching your lineshape.
The coherence time τ_c = L_c/c = 1/Δν sets the maximum temporal delay for interference. Narrow-linewidth lasers (Hz to kHz range) have coherence lengths of many kilometres; mode-locked pulses (THz bandwidth) have sub-millimetre coherence lengths. These quantities matter for interferometry, holography, optical coherence tomography (OCT), and fibre sensor systems.
Frequently asked questions
The conversion Δλ = λ²·Δν/c contains λ² — so at twice the wavelength, the same Δν gives four times the Δλ. A 1 MHz linewidth at 532 nm is ~0.94×10⁻⁶ nm but at 1550 nm it is ~8×10⁻⁶ nm. Always specify which domain your linewidth is in.
This calculator uses L_c = λ²/Δλ (rectangular/uniform lineshape), which gives the maximum coherence length for a given Δν. Lorentzian lineshapes (typical for free-running single-mode diode lasers or Schawlow-Townes limited lasers) give L_c = λ²/(π·Δλ) — about 3.14× shorter. Gaussian lineshapes give an intermediate value. Choose the formula that matches your lineshape or use this as a conservative upper bound.
You need L_c to exceed the maximum optical path difference (OPD) in your interferometer. Michelson interferometers for surface profiling often need centimetres; fibre gyroscopes need metres; Fabry-Pérot cavities for spectroscopy need tens of metres. Telecommunications-grade DFB lasers (Δν ≈ 1–10 MHz at 1550 nm) give L_c ≈ 3–30 cm; ultra-narrow ECDL or fibre lasers (sub-kHz) reach kilometres.
Also known as
TG we-Calculate Editorial Team. (2026). Laser Linewidth Calculator — Δν ↔ Δλ & Coherence Length [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/laser-linewidth-calculator
TG we-Calculate Editorial Team. "Laser Linewidth Calculator — Δν ↔ Δλ & Coherence Length." TG we-Calculate. 2026. https://we-calculate.com/calculator/laser-linewidth-calculator.
TG we-Calculate Editorial Team, "Laser Linewidth Calculator — Δν ↔ Δλ & Coherence Length," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/laser-linewidth-calculator
@misc{wecalculate_laser_linewidth_calculator, title = {Laser Linewidth Calculator — Δν ↔ Δλ & Coherence Length}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/laser-linewidth-calculator}}, year = {2026}, note = {TG we-Calculate} }
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