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p214_dispersion_simulation

# 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 We approximate the rectangular pulse train by the first 20 terms in its Fourier series. the dispersion is given by v_n = v_1 (1 + n d) The phase velocity then varies linearly with frequency, with a slope set by d. 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 d k_1 v_1 dx t 0.2 0.01 1 1 0.01 4 . n kn an vn 1 6.28 0.19 1.01 2 12.57 0.15 1.02 3 18.85 0.1 1.03 4 25.13 0.05 1.04 5 31.42 0 1.05 6 37.7 -0.03 1.06 7 43.98 -0.04 1.07 8 50.27 -0.04 1.08 9 56.55 -0.02 1.09 10 62.83 0 1.1 11 69.11 0.02 1.11 12 75.4 0.03 1.12 13 81.68 0.02 1.13 14 87.96 0.01 1.14 15 94.25 0 1.15 16 100.53 -0.01 1.16 17 106.81 -0.02 1.17 18 113.1 -0.02 1.18 19 119.38 -0.01 1.19 20 125.66 0 1.2 x

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p214_dispersion_simulation - How does dispersion affect the...

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