1. Chromatic Dispersion (CD)

Chromatic Dispersion occurs because different wavelengths (colors) of light travel at slightly different speeds through an optical fiber. Since even the most precise laser has a finite spectral width (it isn't just one single frequency), the "blue" end of the pulse may travel faster or slower than the "red" end.

In standard G.652 single-mode fiber (SMF), the dispersion becomes zero near 1310 nm. However, most long-haul networks operate in the C-Band (1550 nm), where dispersion is typically around $17 \text{ ps/nm/km}$.

2. Quantifying Pulse Spread

The amount of pulse broadening ($\Delta t$) depends on the dispersion coefficient ($D$), the distance traveled ($L$), and the spectral width of the source ($\Delta \lambda$).

3. Polarization Mode Dispersion (PMD)

While CD is deterministic and relatively stable, Polarization Mode Dispersion (PMD) is a stochastic (random) effect. It happens because a "single-mode" fiber actually carries two orthogonal polarization modes. If the fiber isn't perfectly circular (due to bending, stress, or manufacturing), these two modes travel at different speeds.

4. Modern Compensation Strategies

In the past, we used Dispersion Compensation Modules (DCMs)—coils of specialty fiber with negative dispersion. In modern 100G and 400G systems, we use Coherent Detection and Digital Signal Processing (DSP).

• CD Compensation: The DSP uses an inverse mathematical filter to "rewind" the dispersion in the digital domain. It can compensate for thousands of kilometers of CD.
• PMD Compensation: Adaptive filters in the DSP continuously track the polarization state and real-align the "fast" and "slow" modes in real-time.

Conclusion

Dispersion is the "friction" of the fiber optic world. While it once limited the reach of our networks to a few dozen kilometers, the combination of advanced fiber chemistry and high-speed silicon has allowed us to overcome these physical limits, pushing data across oceans without a single bit being lost to time-blurring.