# Wave packet frequency change

1. Oct 12, 2013

### leroyjenkens

1. The problem statement, all variables and given/known data

A laser with λ = 1 μm is pulsed (turned on and then back off) with a duration of 100
fs. What is the resulting frequency spread Δf in output of the pulsed laser? Assume that
the pulse has a Gaussian envelope.

2. Relevant equations

Not really sure, but possibly
ψ(x,0) = Ae-Δk2x2cos(k0x)

$$f=\frac{c}{λ}$$

3. The attempt at a solution
I'm not sure what I'm being asked to find here. The change in frequency? Is there an initial frequency and then there's a change in the frequency after the pulse is released from the laser? Does the frequency change from what it was at the beginning of the pulse, to when the pulse ends?

I converted the units to find that during the duration of the laser being on, 30 wavelengths of light was released. Not sure if that matters. Pretty lost here.

Thanks.

2. Oct 12, 2013

### UltrafastPED

The original wavelength is the central line; the really short pulses (100 fs = ultrafast laser).

They are asking for the bandwidth required to support a 100 fs pulse. Since your pulse is given as Gaussian you should know something about the time-bandwidth product, which is a Fourier analysis theorem.

See http://chirality.swarthmore.edu/PHYS81/UltrafastPulses.pdf [Broken]

Last edited by a moderator: May 6, 2017