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Laser Linewidth & Bandwidth Calculator

Convert between frequency linewidth and wavelength bandwidth, calculate coherence time, coherence length, Q factor, and spectral purity.

Interactive calculator

Laser Linewidth & Bandwidth Calculator

Convert between frequency linewidth and wavelength bandwidth, calculate coherence time, coherence length, Q factor, and spectral purity.

Try an example

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose: frequency linewidth, wavelength bandwidth, coherence time, coherence length, Q factor, or spectral purity.
  • Use presets for HeNe, DFB, ECDL, and LED sources.
  • Click Calculate for complete spectral analysis.

Table of Contents

Key Takeaways

  • Δf and Δλ are related by Δf = c·Δλ/λ² (or equivalently Δλ = c·Δf/f²).
  • Coherence time τc = 1/(π·Δf) for a Lorentzian lineshape.
  • Coherence length Lc = c·τc determines the maximum path difference for interference.
  • Q factor = f₀/Δf measures spectral purity — higher is better.
  • Narrow-linewidth lasers (kHz range) have coherence lengths of hundreds of kilometres.

Laser Linewidth

Every laser emits light over a small range of frequencies, not a single perfect frequency. This spectral width — the linewidth — determines the laser's coherence properties, spectral purity, and suitability for precision applications like interferometry, spectroscopy, and optical communications.

Key Formulas

Δf=c⋅Δλλ02\Delta f = \frac{c \cdot \Delta\lambda}{\lambda_0^2}
τc=1πΔf,Lc=c⋅τc\tau_c = \frac{1}{\pi \Delta f}, \quad L_c = c \cdot \tau_c

Where Δf is the frequency linewidth, Δλ is the wavelength bandwidth, τc is the coherence time, and Lc is the coherence length.

Coherence

Coherence is the ability of light to produce interference. Temporal coherence (measured by coherence time and length) determines how far apart two points along the beam can be and still interfere. Narrow linewidth → long coherence → better for precision measurements.

SourceΔfLc
White LED~100 THz~1 μm
Multimode laser~100 GHz~1 mm
HeNe laser~1 MHz~100 m
ECDL laser~1 kHz~100 km

How to Use

  1. Select a conversion or calculation mode.
  2. Enter linewidth or bandwidth values.
  3. Click Calculate for coherence properties and Q factor.

Examples

HeNe laser (632.8 nm, Δf = 1 MHz)

τc = 1/(π × 10⁶) ≈ 318 ns; Lc ≈ 95.5 m

LED (550 nm, Δλ = 30 nm)

Δf = 3×10⁸ × 30×10⁻⁹ / (550×10⁻⁹)² ≈ 29.8 THz; Lc ≈ 3.2 μm

FAQ

What is laser linewidth?›

Laser linewidth is the spectral width of the laser emission, typically measured as the full width at half maximum (FWHM). It can be expressed in frequency (Hz) or wavelength (nm) units. Narrower linewidth means more monochromatic light.

What is coherence length?›

Coherence length Lc = c/(π·Δf) is the maximum optical path difference over which interference fringes remain visible. A HeNe laser (Δf ≈ 1 MHz) has Lc ≈ 100 m; a 1 kHz ECDL has Lc ≈ 100 km.

Why does coherence matter?›

Coherence is essential for interferometry, holography, spectroscopy, and optical fiber sensing. Longer coherence length allows measurement of larger path differences and more precise measurements.

What is the Q factor?›

The quality factor Q = f₀/Δf measures how spectrally pure the laser output is. A HeNe laser at 474 THz with 1 MHz linewidth has Q ≈ 5×10⁸. Ultra-stable lasers achieve Q > 10¹⁴.

Sources

  1. RP Photonics – Linewidth
  2. RP Photonics – Coherence Length
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

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