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 Incoming links: Gain bandwidth limit on a laser pulse

Past exam of the quantum condensed matter course of the University of Cambridge / 2004 / Section A / 6 / Solution Created 2026-10-18 Updated 2026-10-20

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The gain bandwidth must be expressed as a frequency range:

Δ ν = c (\frac{1}{600 nm} - \frac{1}{700 nm}) ≃ 7.14 \times 1 0^{13} Hz .

(1)

The gain bandwidth limit on a laser pulse then gives

Δ t \sim \frac{1}{Δ ν} ≃ 1.4 \times 1 0^{- 14} s, of order 10 fs .

(2)

The numerical coefficient depends on the pulse shape and width definition. For example a Gaussian pulse whose intensity spectral FWHM actually filled this width would have a transform-limited intensity duration about

6.2 fs

. A hard gain interval does not by itself specify such a FWHM. Reaching the estimated scale requires coherent mode locking and control of group velocity dispersion; the cavity round-trip time determines the pulse separation. An intensity autocorrelation measurement can estimate the pulse duration once its shape is specified.

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