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)
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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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 '04
 LIPSON
 South African National Roads Agency, numerical aperture, Asymmetric planar waveguide, planar slab waveguide

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