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a. Write a MATLAB program to follow the progress of the rays
through the fiber, properly choosing the δz increment.
b. Trace these rays going through the fiber.
Figure 8.5 shows the answer that you should obtain for a fiber length of
3 cm.

FIGURE 8.5
Traces of rays, originally parallel to the fiber’s axis, when propagating inside an optical fiber.

Pb. 8.33 Using Sylvester’s theorem, derive Eq. (8.112). (Hint: Define the
θ

angle θ, such that sin  = αδz , and recall that while δz goes to zero, its
 2  2
product with the number of iterations is finite and is equal to the distance of
propagation inside the fiber.)
Pb. 8.34 Find the maximum angle that an incoming ray can have so that it
does not escape from the fiber. (Remember to include the refraction at the
entrance of the fiber.)

8.11 MATLAB Commands Review
det Compute the determinant of a matrix.
expm Computes the matrix exponential.

© 2001 by CRC Press LLC