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APPENDIX E. Pulse Propagation in Optical Fiber

APPENDIX E

Pulse Propagation in Optical Fiber

In mathematical terms, chromatic dispersion arises because the propagation constant β is not proportional to the angular frequency ω, that is, dβ/dω ≠ constant (independent of ω). dβ/dω is denoted by β1, and β1 −1 is called the group velocity. As we will see, this is the velocity with which a pulse propagates through the fiber (in the absence of chromatic dispersion). Chromatic dispersion is also called group velocity dispersion.

If we were to launch a pure monochromatic wave at frequency ω into a length of optical fiber, the magnitude of the (real) electric field vector associated with the wave would be given by

image (E.1)

Here the z coordinate is taken to be along the fiber axis, and J (x, y) is the distribution of the electric field along the fiber cross section and is determined by solving the wave equation. This equation can be derived as follows.


  

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