ength of the propagating wave. The varia- tion is small and is known either as the "waveguide dispersion," or formally, "the wave- guide component of chromatic dispersion." The Chromatic Dispersion Coefficient of Single-Mode Fibers Let us now turn to digital optical communications, which consist of pulses to constitute the 1s and (ideally) no light during the Os. Whether the required pulses are created by directly modulating the current injected into a semiconductor laser or by following a CW laser with an external modulator, the presence of the modulation broadens the bandwidth of the emitted light, as explained in the earlier section on RZ and NRZ signals. Therefore, even a single-channel optical transmission system has a spread of wavelengths. Moreover, a high- bitrate channel requires shorter pulses, which have greater bandwidths. We have seen that there are two mechanisms by which the refractive indices can vary with the wavelength of light: the material dispersion and the waveguide dispersion. However, a pulse code-modulated signal has a spread of wavelengths and SO experiences a corresponding spread of each of the core, cladding, and effective refractive indices. This means that each pulse experiences a range of speeds as it passes through the optical fiber. The variation is small but accumulates over the many kilometers of transmission and SO becomes significant. Sometimes the shorter-wavelength components travel faster than the long-wavelength components; sometimes the opposite occurs. However, in both cases the pulses are broadened in the time domain as they travel in the fiber. High-datarate channels have shorter pulses and therefore wider spectral bandwidths. The result is greater broadening. Dispersion is often explained in terms of group velocity. A pulse can be regarded as consisting of a "group" or a "packet" of wavelengths. The group velocity quantifies how fast the entire group travels, as distinct from the wavefronts within the group. As the dif- ferent wavelength components of the group encoun