How this calculator works
Frequency and wavelength are reciprocals, so a narrow spectral interval changes by the local derivative c/λ². The exact comparison uses symmetric wavelength endpoints and is not an exact conversion of arbitrary line-shape FWHM. The modified Schawlow-Townes relation here uses FWHM for both the cavity and laser. It assumes above-threshold operation, no parasitic cavity losses and a unity spontaneous-emission factor. Technical noise often dominates a real laser.
Formula
Δν ≈ cΔλ/λ². For symmetric wavelength edges, Δνexact = cΔλ/[λ²-(Δλ/2)²]. Ideal FWHM Δνlaser = πhν(Δνcavity)²/P.
Worked example
At 1000 nm, a 1 nm wavelength bandwidth is approximately 299.792458 GHz. Reversing that narrowband calculation recovers 1 nm.
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Frequently asked questions
Which linewidth convention is used?
The quantum-limited model uses full width at half maximum throughout. A half-width convention changes numerical factors.
Why does the exact width differ?
Frequency is nonlinear in wavelength, so equally spaced wavelength edges are not equally spaced in frequency.
Will the quantum result match a measured laser?
Only if the simplifying quantum-noise assumptions hold. Vibration, drift and other noise can broaden the line.