= Solution
The <gain bandwidth> must be expressed as a <frequency> range:
$$
\Delta\nu=c\left(\frac1{600\,\mathrm{nm}}-\frac1{700\,\mathrm{nm}}\right)\simeq7.14\times10^{13}\,\mathrm{Hz}.
$$
The <gain bandwidth limit on a laser pulse> then gives
$$
\boxed{\Delta t\sim\frac1{\Delta\nu}\simeq1.4\times10^{-14}\,\mathrm s,\quad\text{of order }10\,\mathrm{fs}.}
$$
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 $6.2\,\mathrm{fs}$. 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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