Fiber Optic Communications: Fundamentals and Applications

Appendix B

From Maxwell's equations, we have

B.1

From Eq. (10.24), we have

B.2

Let us consider the case of a single polarization:

B.3

From Eq. (10.42), we have

B.4

where

B.5

B.6

Here, we have ignored the subscripts 'xx' and 'xxxx'. For a dispersive medium, the first-order susceptibility is a function of frequency (see Eq. (10.22)). Since the product in the frequency domain becomes a convolution in the time domain, for a dispersive medium, Eq. (B.5) should be modified as

B.7

or

B.8

where denotes convolution. An optical pulse propagating down the fiber has rapidly varying oscillations ...