Warren Koontz


Dispersion or pulse spreading is a basic topic in an undergraduate engineering technology course in fiber optic communication systems. Students need to understand what causes dispersion and to be able to calculate pulse spread and determine how it limits the length and data rate of a communications system. Chromatic dispersion, which results from the wavelength dependency of the velocity of light in an optical fiber, is the primary source of pulse spread in modern communications systems. The standard formula for calculating pulse spread due to chromatic dispersion can be derived using basic calculus and the derivation is comprehensible by most engineering technology students. However, although this formula is quite useful, it does not quantify all of the effects of chromatic dispersion on optical pulses. To get the total picture, one can always solve the pulse propagation equation, but this kind of rigorous analysis is more suited for engineering graduate students. A reasonable compromise between these two extremes is to model an optical fiber as a linear system and many texts do so using a Gaussian impulse response and pointing to references to justify the choice of Gaussian. A typical open foot race, which often has 1000 or more participants, provides a model of the dispersion process. At the start the runners are tightly packed and it takes only a few minutes for all of the runners to cross the start line. By the finish, however, the runners are widely dispersed and the gap between the winner and the last runner can be an hour or more for a long race. Moreover, a plot of finishing time versus place for such a race resembles a Gaussian cumulative distribution function. This foot race analogy can be used to model chromatic dispersion in terms of the fiber impulse response. In the “photon marathon”, the runners are photons with wavelength-dependent paces. The photon marathon has a perfect start – N photons are launched into the fiber simultaneously, corresponding to an optical power impulse. The “race results” define the impulse response of the fiber. The model and the associated mathematics are well within the capability of third and fourth year engineering technology students. This paper is organized as follows: • Overview of chromatic dispersion • Customary approaches to modeling chromatic dispersion o First-order pulse spread formula “Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright © 2005, American Society for Engineering Education” o Pulse propagation equation o Linear system model • The photon marathon model • Summary and conclusions

Date of creation, presentation, or exhibit



Paper given at 2005 American Society for Engineering Education Annual Conference & Exposition, Portland, OR, June 12-15, 2005 Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type

Conference Proceeding

Department, Program, or Center

Electrical, Computer and Telecommunications Engineering Technology (CAST)


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