Calculate frequency bandwidth from laser wavelength linewidth using the small-signal approximation.This formula is valid only for small linewidths relative to center wavelength. For broadband sources or wide linewidths, use exact formulas.
Last updated: April 2026 | Optical Engineering Tool
He-Ne (632.8), VCSEL (850, 1310, 1550 nm)
Spectral width at FWHM (Full Width Half Max)
Laser linewidth (Δλ) represents the spectral width of light emitted by a laser, measured in nanometers or angstroms. Unlike an ideal monochromatic source that emits a single frequency, real lasers emit light over a narrow range of wavelengths around a center value. The spectral width determines the coherence of the light and its ability to maintain interference patterns over distance—a fundamental property in applications ranging from fiber optics to interferometry.
Wavelength vs. Frequency Domain: The same physical property can be expressed two ways. Wavelength linewidth (Δλ in nm) describes spectral width directly. Frequency bandwidth (Δν in Hz) describes the same width in frequency space. The relationship is nonlinear: Δν = (c × Δλ) / λ². A small wavelength linewidth at infrared wavelengths can correspond to a large frequency bandwidth because frequency spacing is denser at longer wavelengths.
Types of Lasers by Linewidth: He-Ne lasers achieve <0.001 nm through optical cavities. Fabry-Perot semiconductor lasers: 1–10 nm. Distributed Feedback (DFB) lasers: 0.1–1 nm. External Cavity lasers (ECL): <0.001 nm. Fiber lasers and solid-state lasers can achieve <0.01 nm. Narrower linewidth enables longer coherence length and better spectroscopic resolution, but increases cost and complexity.
The OSA measures laser power across frequency and displays a spectral curve. Linewidth is defined as the Full Width at Half Maximum (FWHM) of this curve—the width at 50% of peak power. Typical OSA resolution: 0.01 nm.
Pass laser light through a scanning Fabry-Perot cavity. The cavity produces interference fringes whose width reveals linewidth. High finesse cavities can resolve <0.001 nm. Common in research labs for precise measurements.
Beat the laser against a narrow-linewidth reference laser. The beat frequency and width directly reveal the unknown laser's linewidth. Requires access to an ultra-narrow reference (research-grade DFB laser or fiber laser).
In an interferometer, reduce visibility as path difference increases. Coherence length Lc ≈ λ² / Δλ. When visibility drops to 50%, you've reached coherence length, revealing linewidth indirectly. Quick lab technique.
Laser manufacturers typically specify typical linewidth values. For semiconductor lasers: 1–10 nm. DFB: 0.1–1 nm. He-Ne: <0.01 nm. Use datasheet values for initial design; measure experimentally if tight specs are critical.
Calculate frequency bandwidth for a He-Ne laser:
Wavelength linewidth (Δλ) and frequency bandwidth (Δν) describe the same physical property but in different domains. The nonlinear relationship Δν = (c × Δλ) / λ² means a narrow wavelength linewidth at longer wavelengths (IR) corresponds to a broader frequency bandwidth than at shorter wavelengths (visible).
FWHM = Full Width Half Maximum. On a spectral power curve, it's the width of the emission at 50% of peak power. This standard measure defines laser linewidth. A narrower FWHM indicates better coherence and spectral purity.
Narrower linewidth increases coherence length (distance over which interference patterns persist), enabling longer baselines in interferometry, better spectroscopic resolution, improved optical communication channel stability, and higher quality factor (Q) for laser-cavity resonance applications.
A laser's linewidth is inversely related to its optical cavity finesse and stability. External cavities, temperature stabilization, and feedback mechanisms reduce phase noise and narrow linewidth. Free-running semiconductor lasers have poor cavity quality and broad linewidth; external cavities reduce it 10-100×.
DFB (Distributed Feedback) lasers have linewidth ~0.1–1 nm due to distributed feedback mechanism. VCSELs (Vertical Cavity Surface-Emitting Lasers) have broader linewidth 1–10 nm but are cheaper and easier to integrate. DFBs dominate telecom; VCSELs suit short-reach data centers.
An Optical Spectrum Analyzer can measure linewidth if its resolution is sufficiently high (typically < 0.1× the linewidth being measured). High-end OSAs achieve 0.01 nm resolution, sufficient for most commercial lasers. Ultra-narrow DFB/fiber lasers (< 0.001 nm) require Fabry-Perot or heterodyne techniques.
Coherence length Lc ≈ λ² / Δλ. Narrower linewidth → longer coherence. A He-Ne laser with 0.001 nm linewidth has ~4 m coherence. A broad LED with 100 nm linewidth has ~0.003 m (3 mm) coherence. This directly impacts interferometer visibility and measurement range.
Fiber ring lasers and phase-stabilized solid-state lasers achieve < 100 Hz linewidth (requiring ultra-stable cavities and frequency locks). For commercial systems: External cavity DFB lasers < 0.001 nm, commercial DFB ~0.1 nm, He-Ne ~0.001 nm. Semiconductor lasers without feedback: 1–10 nm.
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