Laser Linewidth and Bandwidth Calculator

Calculate laser spectral linewidth, bandwidth conversion, and coherence properties

Calculate Laser Linewidth and Bandwidth

Calculate Linewidth

Find spectral linewidth from laser parameters

Convert Bandwidth

Convert between wavelength and frequency bandwidth

Laser Linewidth Parameters

Fundamental frequency of the laser emission

Q-factor of the cold laser cavity (damping strength)

Power of the laser mode

Corresponding wavelength: 632.80 nm

Laser Linewidth Results

Spectral Linewidth

9.86e-1
Hz
Full width at half maximum (FWHM)

Coherence Properties

Coherence length:303991.19 km
Q-factor:4.80e+14
Wavelength:632.80 nm

Key Formula: Δν = (π × h × ν × Γ²) / P

Coherence length: Lc = c / Δν (distance over which laser maintains phase coherence)

Laser Quality Analysis

✅ Excellent monochromaticity - very narrow linewidth

🎯 Ultra-high Q-factor - exceptional spectral purity

🌟 Excellent coherence - suitable for interferometry

Example Calculation

He-Ne Laser (632.8nm, 1W)

Frequency: ν = 473.755 THz

Cavity linewidth: Γ = 1 GHz

Power: P = 1 W

Linewidth: Δν = (π × h × 473.755×10¹² × (1×10⁹)²) / 1 = 0.986 Hz

Coherence length: Lc = 3×10⁸ / 0.986 = 304 million meters

Typical Laser Pointer (635nm, 5mW)

• Frequency: 472.114 THz, Cavity: 10 GHz, Power: 5 mW

• Linewidth: ~19.7 kHz (much broader due to lower power)

• Coherence length: ~15 km (still excellent for most applications)

• Q-factor: ~2.4×10¹⁰ (high spectral quality)

Typical Laser Linewidths

Ultra-stable lasers:< 1 Hz
He-Ne laboratory:1-10 Hz
Laser pointers:1-100 kHz
Laser diodes:1-100 MHz
LED (comparison):10-100 THz

Narrower linewidth = better monochromaticity

Laser Coherence Facts

Linewidth is FWHM of optical spectrum

Narrower linewidth = longer coherence length

Higher power generally reduces linewidth

Quantum noise sets fundamental limit

Technical noise often dominates in practice

Q-factor = ν/Δν measures spectral purity

Understanding Laser Linewidth and Bandwidth

What is Laser Linewidth?

Laser linewidth measures how much a real laser deviates from perfect monochromaticity. It's defined as the full width at half maximum (FWHM) of the optical spectrum, quantifying the spread of frequencies in the laser output around the central frequency.

Quantum vs Technical Noise

  • Quantum noise: Fundamental limit from spontaneous emission
  • Technical noise: Cavity vibrations, temperature fluctuations
  • Mode competition: Multiple longitudinal modes
  • Phase noise: Random phase fluctuations

Key Formulas

  • Δν = (π × h × ν × Γ²) / P
  • Lc = c / Δν
  • Q = ν / Δν
  • Δν = c/(λ₀-Δλ/2) - c/(λ₀+Δλ/2)
  • Δν: Laser linewidth (Hz)
  • h: Planck constant (6.626×10⁻³⁴ J⋅s)
  • ν: Laser frequency (Hz)
  • Γ: Cavity linewidth (Hz)
  • P: Laser power (W)
  • Lc: Coherence length (m)

Applications and Importance

Interferometry

Ultra-narrow linewidths enable coherent interference over vast distances, crucial for gravitational wave detection and precision measurements.

Spectroscopy

Narrow linewidth lasers resolve fine spectral features in atomic and molecular systems, enabling high-resolution spectroscopic analysis.

Optical Communication

Low phase noise and narrow linewidths enable coherent optical communication systems with high data rates and long transmission distances.