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# HW6 - ECE 437 Fiber and Integrated Optics Homework...

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ECE 437 – Fiber and Integrated Optics Homework Assignment #6 Due date: Thursday, April 1st, 2010 at 5:00pm 1. Modes in a Parabolic Graded Index Fiber (Bonus Question) Consider a parabolic graded index circular fiber with an infinitely extended medium with refractive index Where r is the radius in the cross section, a, Δ are constants and n 1 axial refractive index. a) Write the Eigen Equation for finding the mode profile. b) Using the one dimensional result for a parabolic graded index medium [3], solve for modes of this parabolic graded index optical fiber. c) Write the function for eigenvalues of the modes. d) Draw (or plot) the first mode profile. e) As we know, the modes are orthogonal, use this fact to write the integral for orthonormality of modes. Hence derive the orthonormality condition for Hermite-Gaussian functions. Hints: [1] Define the plane of cross section as, say, XY plane. The radial vector r is in this plane.

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