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# HW2 - HomeworkAssignment#2...

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ECE 437 – Fiber and Integrated Optics Homework Assignment #2 Due date: Thursday, February 18, 2010 at 5:00pm 1. Properties of Mode profile Consider the equation for solving the mode profile (electric field) in a planar wave guide (Equation 3.3 in the text book) ݀ ݀ݔ ܧ ൅ ሾ݇ ݊ ሺݔሻ െ ߚ ሿܧ ൌ 0 a) For E y1 (x) and E y2 (x) corresponding to two different values of β show that the functions E y1 (x) and E y2 (x) are orthogonal. b) Show that for slabs with symmetric refractive index profile n(x)= n(‐x), the modal profiles can be chosen to have either even or odd under reflection symmetry. i.e Ey(x)=+ Ey(‐x) 2. Angle of propagation of modes Consider a solution to the above equation E(x) for a symmetric planar wave guide. a) Express the above plane wave solution inside the waveguide as a superposition of two plane waves. b) Find the direction of propagation (θ) of the planar waves for a mode with a specific β.

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