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Connection Oriented Networks - Perros H.G

Perros H.G Connection Oriented Networks - John Wiley & Sons, 2005. - 359 p.
ISBN 0-470-02163-2
Download (direct link): connectionorientednetworks2005.pdf
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Interestingly, an angle Oc, known as the critical angle, exists, past which the incident light will be reflected entirely. That is, if Ot > Oc, then the entire incident ray will be
HOW LIGHT IS TRANSMITTED THROUGH AN OPTICAL FIBER
185
ray
Figure 8.6 Refraction and reflection of a light ray.
reflected. For a light ray to be transmitted through an optical fiber, it has to hit the interface between the core and the cladding at an angle 6 which is greater than the critical angle 6c. In order for this to happen, the light ray must be launched at the end of the fiber at an angle 61, which is less than a critical angle 6a (see Figure 8.7(a)). The angle 61 is referred to as the launch angle. This results into a cone of acceptance within which a light ray must be launched (see Figure 8.7(b)). Typically, a lens is used to focus the launched light onto a small area of the core (see Figure 8.8).
In Figure 8.7(a), we see that the light ray travels through the core in a straight line until it is reflected at the interface between the core and the cladding. The reflected ray also continues on in a straight line. This is because we assumed a step-index optical fiber, and as mentioned above, the refractive index for the core remains constant from the center of the core to the cladding. In the case of a graded-index fiber, however, the refractive index changes with the distance from the center of the core following a parabolic function. In this case, the path of a light ray will be a curve (see Figure 8.9).
Figure 8.7 Angle of launching a ray into the fiber.
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OPTICAL FIBERS AND COMPONENTS
Cladding
>
Core
Cladding
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. Singlemode 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 ^m), 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. Core/cladding 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 (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 rays 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 et. 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 Core/cladding diameters.
Fiber type Core/cladding diameters
Multi-mode fiber 50/125 |xm, 62.5/125 |xm, 100/140 |xm
Single-mode fiber 9 or 10/125 |xm
HOW LIGHT IS TRANSMITTED THROUGH AN OPTICAL FIBER
187
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.
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