Laser Linewidth and Bandwidth Calculator
Calculate laser spectral linewidth using the Schawlow-Townes formula Δν = πhνΓ²/P. Enter wavelength, cavity linewidth, and power to get accurate linewidth results with charts.
About This Calculator
The Laser Linewidth and Bandwidth Calculator computes the spectral linewidth of a laser using the quantum-derived Schawlow-Townes formula Δν = πhνΓ²/P. This formula relates the fundamental laser frequency ν (derived from the operating wavelength), the cold cavity linewidth Γ (a measure of the resonator Q-factor), and the laser output power P to the resulting spectral linewidth at full width at half maximum (FWHM).
Understanding laser linewidth is critical for applications requiring high coherence and spectral purity including coherent optical communications, precision metrology, LIDAR systems, atomic clock spectroscopy, quantum computing, and medical diagnostic equipment. Narrower linewidths enable longer coherence lengths and higher signal-to-noise ratios in interferometric systems.
How It Works
This calculator first converts the input wavelength to frequency using ν = c/λ where c is the speed of light. The Schawlow-Townes formula then computes the linewidth from the frequency, cavity linewidth squared, and Planck constant, divided by the mode power. Results are automatically scaled to the most appropriate unit (Hz, kHz, MHz, GHz, or THz) for readability.
The laser linewidth equation fundamentally arises from the energy-time uncertainty principle: spontaneous emission events introduce random phase fluctuations that broaden the laser spectrum. The inverse relationship with power Δν ∝ 1/P explains why high-power lasers tend to have narrower intrinsic linewidths, though practical devices also face technical noise sources.
Regional Notes
All regions (SI units): This calculator uses standard SI units: nanometers for wavelength, Hz for cavity linewidth and frequency, mW for power. The physics formulas and Planck constant are universal, so defaults are identical across all regions.
Typical reference values: He-Ne laser (632.8 nm, 1 GHz cavity linewidth, 1 mW) → ~0.99 Hz linewidth. Red laser pointer (635 nm, 10 GHz, 5 mW) → ~19.7 kHz linewidth. These values help users validate their inputs and understand expected linewidth magnitudes.
Applications
Essential for laser physicists, optical engineers, telecommunications specialists, and researchers in quantum optics, spectroscopy, and interferometry who need to estimate or verify laser spectral purity from basic operating parameters.
Frequently Asked Questions
What is laser linewidth?
Laser linewidth is the full width at half maximum (FWHM) of the optical power spectrum of a laser. It measures how much the laser output deviates from perfect monochromaticity due to quantum and technical noise sources. A narrower linewidth means a more coherent and pure single-frequency output.
How is laser linewidth calculated?
Laser linewidth is calculated using the Schawlow-Townes formula Δν = πhνΓ²/P where h is the Planck constant, ν is the laser fundamental frequency, Γ is the cavity linewidth (Q-factor), and P is the laser mode power. The formula shows that linewidth decreases with higher power and lower cavity losses.
What causes laser linewidth broadening?
Laser linewidth is broadened by quantum phase noise from spontaneous emission, technical noise from temperature fluctuations and mechanical vibrations, cavity length instabilities, pump power fluctuations, and mode hopping between competing longitudinal modes. Narrow linewidth lasers minimize these sources.
What is a narrow linewidth laser?
A narrow linewidth laser emits light with linewidth typically below 1 kHz to a few MHz. These lasers use advanced cavity designs, feedback stabilization, and noise reduction techniques. Applications include coherent optical communications, precision metrology, LIDAR, atomic physics, and medical sensing.
How do I convert wavelength bandwidth to frequency bandwidth?
Frequency bandwidth Δν is calculated from wavelength bandwidth Δλ and central wavelength λ₀ using Δν = c/(λ₀ - Δλ/2) - c/(λ₀ + Δλ/2). For small bandwidths relative to wavelength, the approximation Δν ≈ c·Δλ/λ₀² is often used.
What is a typical laser linewidth for common lasers?
Typical laser linewidths vary widely: He-Ne lasers ~1 MHz, diode lasers ~1-100 MHz, fiber lasers ~1-100 kHz, external cavity diode lasers ~1-100 kHz, and stabilized lab lasers can reach sub-Hz linewidths. A typical red laser pointer has linewidth around 20 kHz.
How does laser power affect linewidth?
Higher laser power reduces linewidth because the Schawlow-Townes formula shows linewidth is inversely proportional to power Δν ∝ 1/P. More power means a higher photon number which reduces the relative phase noise contribution from spontaneous emission events.