Laser Linewidth Calculator

About the Laser Linewidth Calculator

Laser linewidth, the spectral width of a laser's emission, determines its coherence properties, spectroscopic resolution, and suitability for applications like interferometry, holography, and telecommunications. A narrow-linewidth laser maintains phase coherence over long distances, while a broad-linewidth laser is suitable for illumination and materials processing where coherence is less important.

The linewidth can be expressed in wavelength (nm or pm), frequency (Hz, MHz, GHz), or wavenumber (cm⁻¹), and converting between these representations requires knowledge of the center wavelength. The relationship Δν = c·Δλ/λ² connects frequency and wavelength linewidths. From the linewidth, critical derived quantities follow: coherence length L_c = c/Δν tells you the maximum path difference for interference, and coherence time τ_c = 1/Δν sets the temporal window for phase-stable experiments.

This calculator converts linewidth between all common units, computes coherence length and time, estimates the number of longitudinal cavity modes, and provides a comprehensive unit conversion table. Presets for common laser types from LEDs (30 nm) to ultra-narrow DFB diodes (1 MHz) let you quickly explore the vast range of spectral purities available in modern photonics.

When This Page Helps

Use this page to convert laser linewidth between units and estimate coherence length, coherence time, and cavity-mode context from one spectral-width input. It helps keep the linewidth in the same frame as the laser cavity and the intended application, which makes comparisons easier. That makes it easier to compare sources that report linewidth in Hz, nm, or cm⁻¹ without losing the physical meaning of the number.

How to Use the Inputs

1. Select a preset laser type or enter a custom center wavelength.
2. Input the linewidth value and select its units.
3. Optionally enter the cavity length to compute FSR and mode count.
4. Review the linewidth in multiple units, coherence metrics, and quality factor.
5. Use the conversion table for quick reference across all unit systems.
6. The coherence length scale shows your laser in context from LED to ultra-narrow.

Example Calculation

Tips & Best Practices

• A very small linewidth in wavelength units can still correspond to a much larger frequency linewidth depending on the center wavelength.
• Coherence length is often the more intuitive output if you care about interference path matching.
• Cavity length affects free spectral range, which in turn helps you judge whether a source is likely to support many longitudinal modes.
• Narrow-linewidth sources are valuable for spectroscopy and interferometry, but many illumination and processing tasks do not need extreme coherence.

Why Linewidth Matters

Laser linewidth is a compact way to describe spectral purity and phase stability. Narrower linewidth generally means longer coherence time and a larger path difference over which interference can remain stable.

Unit Conversion Needs Context

Frequency linewidth, wavelength linewidth, and wavenumber linewidth are not interchangeable without the center wavelength. That is why a calculator helps here: the same physical source can look numerically very different depending on which unit system you start from.

Practical Interpretation

For interferometers, coherence length is often the headline output. For cavity design, free spectral range and mode count can matter more. For telecom or spectroscopy, the frequency linewidth is often the most natural quantity to compare across sources.

Frequently Asked Questions

• What determines a laser's linewidth?

  Fundamentally, spontaneous emission (Schawlow-Townes limit). Practically: cavity length, mirror reflectivity, gain medium properties, and environmental vibrations all contribute.

• What is coherence length used for?

  It sets the maximum path difference for interference. Holography requires coherence lengths longer than the scene depth. Fiber sensors need long coherence for distant reflections.

• How narrow can a laser linewidth be?

  The narrowest stabilized research lasers can reach sub-hertz linewidths, leading to enormous coherence lengths and making them useful in optical clocks and precision metrology. Most practical systems are much broader, but still narrow enough for interferometry or spectroscopy.

• What is free spectral range?

  FSR = c/(2L) is the frequency spacing between adjacent longitudinal modes of a laser cavity. A longer cavity has more closely spaced modes.

• Why convert between frequency and wavelength linewidth?

  Spectroscopists often work in wavenumbers, telecom engineers in GHz, and optical designers in nm. The conversion depends on center wavelength, making a calculator essential. Using the same calculator keeps the unit choice explicit and reduces mistakes when comparing sources.

• Does linewidth affect focusing ability?

  Not directly — focusing is determined by beam quality (M²). However, chromatic optics perform better with narrower linewidths since there's less chromatic aberration.