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# HW7 - UNIVERSITY OF CALIFORNIA Santa Barbara Department of...

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UNIVERSITY OF CALIFORNIA Santa Barbara Department of Electrical and Computer Engineering Problem Set No. 7 Issued: November 16, 2007 Fall 2007 Due: November 21, 2007 ECE 201A 1. You have a one dimensional beam at a free space wavelength of 1.3 μm with a Gaussian profile given as ( ) 2 2 64 9 ( ,0) x E x e = , where x and the numbers have units of μm. In other words at z=0 μm the beam is a Gaussian centered at x= 64 μm with a full width at half maximum of 7.5 μm. (a) Using your favorite software sample this profile at 256 equally spaced points in the range 1 to 128 μm and plot it. (b) Obtain plots of the magnitude and phase of the digital Fourier transform of this profile. (c) Calculate and plot the magnitude and phase of this beam 150 μm and 500 μm later, i.e., at z=150 and z=500 μm. Comment on the result. 2. You have a one dimensional beam at a free space wavelength of 1.3 μm with a Gaussian profile given as ( ) 2 2 64 9 ( ,0) x E x e = , where x and the numbers have units of μm. In other words at z=0 μm the beam is a Gaussian centered at x= 64 μm with a full width at half maximum of 7.5 μm. Calculate the following:

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