1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Time Evolution of a Square Pulse - Fourier

  1. Oct 21, 2008 #1
    Hi There,
    A square pulse of light has the form f(x) = A exp(ik0x) for |x| < L/2
    and f(x) = 0 everywhere else.

    I want to know how that pulse evolves overtime. I want to graph it in Mathematica.

    I did a fourier transform to find the wave number spectrum, with the general form:

    F(k) = Sin((k - k0) L/2) / (k - k0)

    this is a sinusoid that decays inversely, centered on k0. I figure that this wave packet will disperse over time, due to the different wave number components.

    my question is "how do I calculate the time evolution of this pulse?

    my attempted answer (thanks to Lewis A. Riley): calculate the inverse transformation, with the addition of a factor to account for the time progression of the wave:

    y(x,t) = Integral[ { sin((k-k0) L/2) / (k-k0) } * exp (ik {x - vt}) ] dk

    this is not a trivial calculation (I'm using Mathematica) and it returns an answer in the form of the exponential integral. I'm not sure how to make sense of this. I expect I should be able to graph a real function here, since we are talking about the evolution of real waves. I don't know how to do that.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted



Similar Discussions: Time Evolution of a Square Pulse - Fourier
Loading...