p214_dispersion_simulation - How does dispersion affect the...

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How does dispersion affect the shape of a periodic pulse train? We take the pulse train to be an even function of x (symmetric about x=0 at t=0), so that its Fourier series co Each term will have the form a_n cos (k_n x- omega_n t) = a_n cos (k_n (x - v_n t) where v_n is the phase velocity when the wavevector is k_n and the frequency is omega_n. The Fourier coefficients a_n = w/lambda [sin( n pi w/lambda )] / (n pi w/lambda) We approximate the rectangular pulse train by the first 20 terms in its Fourier series. In the spreadsheet below, the "duty cycle" of the pulse train is w/lambda, and the dispersion is given by v_n = v_1 + n (disp factor) The phase velocity then varies linearly with frequency, with a slope set by (disp factor). You can set the pulse duty cycle, dispersion factor, and time t at which you observe the pulse. Start with the dispersion factor =0, and plot y versus x for a few different t's. What happens to the shape of t Then set a small dispersion positive factor (say, +0.01) and do the same thing. In this case, the higher k (hig Then set a small negative dispersion factor (say, -0.01) and do the same thing. In this case the higher k com
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This note was uploaded on 03/31/2009 for the course PHYS 214 taught by Professor Thorne during the Spring '08 term at Cornell University (Engineering School).

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p214_dispersion_simulation - How does dispersion affect the...

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