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I really need your help.

I got the following task:

"Sketch the output spectrum of a mode-locked Ti-Sapphire laser (assuming eg. gaussian shape) and calculate the shortest possible pulse duration by Fourier transformation."

So the spectrum is gauss shaped but I have no clue how to get the shortest possible pulse duration.

I thought about starting with something like

But the first equation does not contain the mode-locking thing and I have no idea how to calculate the stuff.

I am an absolute beginner without any knowledge about lasers (and bad english).

I hope that somebody understands my question and is able to help me.

Have a nice day

ATY