# HW6 - 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. 5 Issued: November 5, 2008 Fall 2008 Due: November 19, 2008 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 Ex 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: (a) This beam is normally incident on a planar dielectric interface located at z = 150 μm. Both media are non magnetic and the indices of refraction for z<150 μm and z>150μm are 1 and 1.5 respectively. Using plane wave decomposition, calculate the magnitude and phase profiles of the transmitted and reflected beams at z = 300 μm and z = 0 μm respectively. (b) Calculate the power of the incident, reflected and transmitted beams and the associated power reflection and transmission coefficients. Do they add up as expected?

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## This note was uploaded on 12/02/2009 for the course ECE 000 taught by Professor O during the Spring '09 term at UCSB.

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HW6 - UNIVERSITY OF CALIFORNIA Santa Barbara Department of...

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