Does the light pulse broadens in time when passing bandpass filter?

Question

What I don't understand about relationship between laser pulse width in time and frequency, is where these rules apply, namely rules of Bandwidth-limited pulses.

Say, I have a femtosecond laser making 100fs pulses with central wavelength 900nm, and FWHM of 20nm. I pass it through something like Ultra Narrow Bandpass Filters at the central wavelength 900nm and very narrow range.

Will my pulse broaden in time more than if I passed it through a clear glass plate of similar material and width as the filter?

Answer 1

Usually, femtosecond pulses are produced by a mode-locking. A laser cavity has a certain number of modes at different frequencies, which usually illuminate with a random phase relationship between each other. The mode-locking is a process that results in a certain phase shift between the modes. Imagine that you have a lot of sinusoidal waves with the same amplitude. When you make them in phase, by means of the Fourier transform it could be shown that the sum of the waves will give $sinc$ function in time which indeed looks like a pulse. Note that, the more frequencies you have, the less is the pulse duration.

Now, when you cut several frequencies with a filter, the pulse gets broader. Indeed, imagine you cut all the frequencies except one. Then you end up with one sinusoidal wave which is infinite in time. Moreover, you could disrupt the phase relationship by means of reflection and scattering.

The last thing that should be mentioned is the material dispersion. If you pass a laser beam through a simple glass plate you don't cut frequencies. However, different frequencies have different velocities in glass, so the pulse again gets broader in this case.