 fiber system because of modal noise. After a pulse propagates in a fiber the r.m.s. pulse broadening S given by (5.36) where Omat is the material (chromatic) dispersion, OW is the waveguide dispersion (discussed in the next section), and Omod is the intermodal dispersion (for step index or graded index Single-Mode Fibers fiber). For multimode transmission the material and waveguide dispersion terms are negli- gible compared to the intermodal dispersion, and they are usually ignored. Therefore, the pulse in the output of the fiber has an r.m.s. width given by (5.37) where Tinp is the r.m.s. width of the input pulse. Single-Mode Fibers In the section The Structure and Physics of an Optical Fiber, the concept of the single-mode fiber was introduced, and the most important physical feature of a single-mode fiber is its small core. For a useful image of how a single-mode fiber operates, one can use the idea that only the axial mode propagates in the fiber. The bandwidth of single-mode fiber is SO large compared to that of the multimode fiber that single-mode fiber is used in all long-haul communications today, terrestrial and submarine. Concepts used to arrive at a reasonable understanding of the propagation features of multimode fiber cannot be used in single- mode fibers, and the solution of Maxwell equations in the context of the geometry and materials is required. Only the results of the mathematical analysis based on Maxwell equa- tions will be presented in this section. The spectral loss of a single-mode fiber is that shown in Figure 5.8. This is a research result, but we will see that single-mode fibers are available with these loss characteristics as products for terrestrial and submarine applications. The most striking difference between multimode and single-mode fibers is in the dispersion. In multimode fibers the total dispersion is dominated by the intermodal dispersion. In single-mode fibers only one propagation mode is supported, SO the total dispersion consists of three components: material dispersion,