Even an ideal laser has a finite spectral width because of spontaneous emission. The Schawlow–Townes formula gives this quantum limit. Bandwidth conversion is used for pulsed lasers, filters and spectroscopy.
How to use the Laser Linewidth and Bandwidth Calculator
- Calculate
- Laser frequency ν
- Cavity linewidth Δν_c
- Power P
- Fundamental wavelength λ
- Wavelength bandwidth Δλ
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the calculation. For bandwidth conversion, enter the central wavelength and the wavelength width.
Inputs explained
| Field | What to enter |
|---|---|
| Calculate | Choose one: Linewidth (Schawlow–Townes), Bandwidth from wavelength width |
| Laser frequency ν | Units: THz, GHz, Hz |
| Cavity linewidth Δν_c | Units: MHz, kHz, GHz, Hz |
| Power P | Units: mW, W |
| Fundamental wavelength λ | Units: nm, µm, mm, m, pm, Å |
| Wavelength bandwidth Δλ | Units: nm, µm, mm, m, pm, Å |
What each result means
- Linewidth Δν = 6.62607e-34×pi×[Laser frequency ν]×[Cavity linewidth Δν_c]^2÷[Power P]
- Frequency bandwidth Δν = 2.99792e+08×[Wavelength bandwidth Δλ]÷[Fundamental wavelength λ]^2
Example values
How the main result changes when Laser frequency ν changes and everything else stays at the example values above:
| Laser frequency ν (THz) | Linewidth Δν (Hz) |
|---|---|
| 237 | 0.0005 |
| 355.5 | 0.0007 |
| 474 | 0.001 |
| 592.5 | 0.0012 |
| 711 | 0.0015 |
| 948 | 0.002 |
Formula
Δν_ST = π·h·ν·Δν_c² / P · Δν = c·Δλ / λ²
Worked example
Inputs — Calculate: Linewidth (Schawlow–Townes); Laser frequency ν: 474 THz; Cavity linewidth Δν_c: 1 MHz; Power P: 1 mW.
Results — Linewidth Δν = 0.000987 Hz.
Key terms
- Linewidth
- Spectral width of a laser's output.
Frequently asked questions
What limits a laser's linewidth?
Spontaneous emission noise sets the quantum (Schawlow–Townes) limit.
Why do real lasers have wider lines?
Mechanical vibration, temperature drift and pump noise.
How are Δλ and Δν related?
Δν = c·Δλ/λ².
What is a narrow-linewidth laser used for?
Interferometry, atomic clocks and coherent communications.