p214_dispersion_simulation - How does dispersion affect the...

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Unformatted text preview: 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 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 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 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 1.2 x We can resolve a pulse train of spatial period and pulse width w into a sum of cosine functions with k_n =...
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This note was uploaded on 04/01/2009 for the course PHYS 2214 taught by Professor Giambattista,a during the Spring '07 term at Cornell University (Engineering School).

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p214_dispersion_simulation - How does dispersion affect the...

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