WDM OPTICAL NETWORKS Connection Oriented Network

186 OPTICAL FIBERS AND COMPONENTS Cladding Cladding Core Figure 8.9 Path of a light ray in a graded-index fiber.

8.2.1 Multi-mode and Single-mode Optical Fibers

Both multi-mode fiber and single-mode fiber are used in communication systems. Single- mode fiber is used in long-distance telephony, CATV, and packet-switching networks. Multi-mode fiber is often cheaper than single-mode fiber, and is used in short distance networks, such as LANs. Both fiber types have the same diameter 125 µm, but they have different core diameters. Specifically, the single-mode fiber has a very small core diameter, whereas the multi-mode fiber has a large core diameter. Corecladding diameters are given in Table 8.1. In order to understand the difference between multi-mode and single-mode fibers, we have to first introduce the concept of a fiber mode. Let us consider two incident rays, Rays 1 and 2, which are launched into the fiber at the same launch angle θ l see Figure 8.10. Ray 1 is reflected for the first time at Point A, and Ray 2 is reflected at Point B. Recall that a ray, whether an incident ray launched into the fiber or a reflected ray, has an electric field which is vertical to the direction of its path. This electric field is depicted in Figure 8.10 by the sinusoidal curve along the ray’s path. For presentation purposes, we assume a step-index optical fiber. The electric field of the reflected Ray 1 suffers a phase-shift at the interface between the core and the cladding. This phase-shift depends on a number of factors, such as the ratio of the refractive index of the core and the cladding and the angle of incidence θ i . A similar phase-shift applies to the electric field of the reflected Ray 2. However, the electric field of the incident Ray 1 traveling upwards is in phase with the electric field of the reflected Ray 2 which is also traveling upwards. Likewise, the electric field of the incident Ray 2 traveling downwards is in phase with the electric field of the reflected Ray 1 which is also traveling downwards. The electric fields of the incident rays and the reflected rays interfere with each other, and depending upon the case, they either reinforce each other or they extinguish each other. The electric fields of the two upwards or the two downwards traveling rays are in-phase see Figure 8.10. As a result, they reinforce each other; the fiber is excited; and a light beam is formed, which is guided through the core of the fiber. On the other hand, Table 8.1 Corecladding diameters. Fiber type Corecladding diameters Multi-mode fiber 50125 µm, 62.5125 µm, 100140 µm Single-mode fiber 9 or 10125 µm HOW LIGHT IS TRANSMITTED THROUGH AN OPTICAL FIBER 187 Cladding Cladding Core 1 A B 2 Figure 8.10 Electric fields. the electric fields of a downward and an upward traveling ray are in-phase, and so they interfere with each other and no light beam is formed. Due to these interactions, the electrical fields cancel each other out at the interface of the core and the cladding, but they reinforce each other in the center of the core. The resulting light beam has an electric field whose amplitude varies as shown in Figure 8.11, case m = 0. The pattern of the electric field is called a fiber mode. Different fiber modes can be created by launching the two rays at a different launch angle θ l see Figure 8.10. The amplitude of the electric field for each mode is 0 at the interface between the core and the cladding, as in the case of m = 0, discussed above. However, zero amplitude points known as null points can be also created inside the core. For instance, in Figure 8.11, we show examples of the amplitude of the electric field of a formed beam where it has a null point in the center of the core m = 1, and where it has two null points inside the core m = 2. In general, the different modes in a fiber are numbered 0, 1, 2, and so on. Also, the number of a mode is equal to the number of null points inside the core of the fiber associated with the mode. As shown in Figure 8.8, a lens is used to focus the launched light onto a small area of the core. As a result, there are many different rays that enter the fiber at different launch angles, and thus many different fiber modes are created and propagated down the core of the fiber. In other words, the propagation of the light through the fiber core, is done in terms of different modes all propagating down the fiber core. In Figure 8.12, various modes for a step-index and a graded-index fiber are shown. As mentioned above, the path of a ray through a step-index fiber is a straight line until it gets reflected into another straight line. On the other hand, the path of a ray through a graded-index fiber is a curve. Cladding Cladding Core m = 0 m = 1 m = 2 Figure 8.11 Electric field amplitudes for various fiber modes. 188 OPTICAL FIBERS AND COMPONENTS a Step-index fiber b Graded-index fiber Cladding Cladding Cladding Cladding Figure 8.12 Propagation of modes. Cladding Cladding Figure 8.13 Single-mode fiber. The number of modes in a fiber is related to the diameter of the core. As shown in Table 8.1, multi-mode fibers have a large core diameter, and the light propagates through the core in different modes, as explained above. Single-mode fibers see Figure 8.13 have a core with a very narrow diameter that only permits the propagation of the single ray with mode 0 i.e., m = 0.

8.2.2 Impairments

The transmission of light through an optical fiber is subjected to optical effects, known as impairments. There are linear and non-linear impairments. Linear impairments are due to attenuation and dispersion. Attenuation is the decrease of the optical power along the length of the fiber. Dispersion is the distortion of the shape of a pulse. These impairments are called linear because their effect is proportional to the length of the fiber. Non-linear impairments can be due to the dependency of the refractive index on the intensity of the applied electrical field. The most important non-linear effects in this category are: self-phase modulation and four-wave mixing. Another category of non-linear impairments includes the stimulated Raman scattering and stimulated Brillouin scattering. These two impairments are due to the scattering effects in the fiber medium because of the interaction of light waves with phonons molecular vibrations in the silica medium. All of these impairments are called non-linear because when they occur the response of a medium such as silica, is a non-linear function of the applied electric and magnetic field amplitude.