As seen earlier, the optical pulse broadens due to dispersion. On a single mode optical fiber, the pulse broadening is due to chromatic dispersion.

The pulse broadening affects the system performance in two ways:

Part of the bit energy spreads in the neighboring bits causing inter-symbol-interference (ISI).

The reduction in the pulse energy because there is energy spread due to dispersion.

Due to reduction in the pulse energy inside a bit, causes reduction in SNR and consequently reduction in BER. To get the same BER back, the signal power has to be increases, giving dispersion induced power penalty.

The dispersion induced power penalty depends upon many factors like, the pulse shape, spectral profile of laser, fiber dispersion etc. The analysis however, generally carried out assuming that the pulse broadening is Gaussian.

The dispersion induced power penalty then is related to the reduction in the peak of the Gaussian due to dispersion.

Let a Gaussian pulse of width be launched inside a fiber. The pulse is given as

Due to dispersion the pulse will broaden to have a width of

where D is the dispersion of the fiber, and is the spectral width of the source. L is the length of the fiber.

The output pulse is

The reduction in the peak amplitude of the pulse is

Now the ISI is minimized if , where B is the bit rate. Even for the equality sign we get,

Substituting in above equation we get

The power penalty due to dispersion is

The system sensitivity degrades rapidly with the dispersion.