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Assignment 06

# Assignment 06 - tions centered around the origin but...

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Electromagnetic Theory, PHYS 441B Due: Wednesday, 11.March 2009, 10:30 100 Points Assignment 6 Problem 1: Wave packet propagation 100 P Use your favorite math program (Maple, Mathematica, Matlab) to make a wave packet simulation in one dimension. Choose an initial wave and see how it propagates in free space, so that ω ( k ) = kc and also in a wave guide for some TE(n,m) or TM(n,m) modes in a quadratic wave guide with dimensions a and b, so that ω ( k ) = c p k 2 + ( a ) 2 + ( b ) 2 . Tasks: 1. Find parameters and choices of times that demonstrate the propagation behaviour in both cases, especially for cases that show the distortion in the wave packet form. You might want to work with rescaled dimen- sionless parameters in the numerics, but relate your ﬁnding to physical values working either in the microwave or in the optical domain. 2. Include also the situation where initially two modes in the wave guide are excited. 3. Include the situation where you have initially two Gaussian distribu-
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Unformatted text preview: tions centered around the origin, but centered around diﬀerent k in the Fourier transform. What happens to the wave packets after suﬃciently long time in free space and in the wave guide? For your handing in, please provide the analytic form of the physical wave (real valued amplitude, and initial time derivative), the complex valued initial function for the ﬁeld. All with a suitable set of parameters. Also add a print-out of your short code. Provide plots for t=0 and suitable chosen follow-up times to show how the pulse propagates in time. Remark: with the mathematics packages it should not be too hard to im-plement the numerics with the standard mathematics tools, but you will have to spend some thought to ﬁnd which parameter regime which demonstrates the expected eﬀects without running into numerical problems. 1...
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