ion has different requirements and in this section we will only analyze optical fibers used in telecommunications. 4.2.1 Single-Mode Transmission Fibers A single-mode fiber used for transmission is characterized, from the point of view of elec- tromagnetism, by the condition of being a weakly guiding waveguide, that is, the refrac- tion index variation along the fiber section radius is very small (generally less than 1%). The fiber section of the simpler transmission fiber, the so-called step index fiber, is reported in Figure 4.1: it is constituted by a central cylindrical core with a refraction index nc and a coaxial cladding with a refraction index Ne. Examples of indexes values used telecommunications are n =1.4600 and Ne = 1.4592, SO that An/n = 2(nc - n)/(nc +ne) 22 0.55%. The field propagation in the fiber can be studied by solving the Maxwell equations in the structure [1,2]. Exploiting the weakly guiding approximation [3] it is possible to solve the propaga- tion problem by individuating propagation modes that constitute a complete set for the description of the guided field. In long transmission systems, the optical power that is not guided by the fiber is irradiated in the first fiber segment; thus, a description of the guided field is sufficient. The generic propagation mode in a perfectly cylindrical step index fiber in the absence of field sources can be described with the following expression of the electrical field: Radius Cladding Protection Protection Cladding Refraction index FIGURE 4.1 Section and refraction index distribution of an optical fiber. Technology for Telecommunications: Optical Fibers, Amplifiers, and Passive Devices (4.1) where p represents the radial coordinate in the fiber section B(a) is the dispersion function, that is obviously mode dependent Z is the axial coordinate The individual propagation mode can be identified through one of the three mode classes, represented by the footer S in Equation 4.1 and by two progressive numbers: l and m. The mode classes are generally indica