### Pulse elongation with known GDD

For given GDD, dispersed pulse length $$\Delta t$$ is related to the initial pulse length $$\Delta t_0$$ as $$\Delta t = \Delta t_0 \sqrt{1 + \left (4 \ln 2 \frac{\mathrm{GDD}}{\Delta t_0^2}\right)^2}.$$ For fixed GDD, the shortest dispersed pulse is equal to $$\Delta t = \sqrt{2} \Delta t_0$$, when $$\Delta t_0 = 2\sqrt{\ln 2 \cdot \mathrm{GDD}}.$$

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