RSVP-TE Extensions THE RESOURCE RESERVATION PROTOCOL – TRAFFIC

184 OPTICAL FIBERS AND COMPONENTS a Step-index fiber b Graded-index fiber Radial distance n 1 n 2 Core Cladding Radial distance Refractive index n 2 n 1 Cladding Core Refractive index Figure 8.5 Step-index and graded-index fibers. is n = cv. The value of the refractive index of the cladding is always less than that of the core. There are two basic refractive index profiles for optical fibers: the step-index and the graded-index. In the step-index fiber, the refractive index of the core is constant across the diameter of the core. In Figure 8.5a, we show the cross-section of an opti- cal fiber and below the refractive index of the core and the cladding has been plotted. For presentation purposes, the diameter of the core in Figure 1, Figure 5, and some of the subsequent figures is shown as much bigger than that of the cladding. In the step-index fiber, the refractive index for the core n 1 remains constant from the cen- ter of the core to the interface between the core and the cladding. It then drops to n 2 , inside the cladding. In view of this step-wise change in the refractive index, this pro- file is referred to as step-index. In the graded-index fiber, the refractive index varies with the radius of the core see Figure 8.5b. In the center of the core it is n 1 , but it then drops off to n 2 following a parabolic function as we move away from the center towards the interface between the core and the cladding. The refractive index is n 2 inside the cladding. Let us investigate how light propagates through an optical fiber. In Figure 8.6, we see a light ray is incident at an angle θ i at the interface between two media with refractive indices n 1 and n 2 , where n 1 n 2 . Part of the ray is refracted – that is, transmitted through the second medium – and part of it is reflected back into the first medium. Let θ i be the angle between the incident ray and the dotted line, an imaginary vertical line to the interface between the two media. This angle is known as the incidence angle. The refracted angle θ f is the angle between the refracted ray and the vertical dotted line. We have that θ i θ f . Finally, the reflected angle θ r is the angle between the reflected ray and the vertical dotted line. We have that θ r = θ f . Interestingly, an angle θ c , known as the critical angle, exists, past which the incident light will be reflected entirely. That is, if θ i θ c , then the entire incident ray will be HOW LIGHT IS TRANSMITTED THROUGH AN OPTICAL FIBER 185 Incident ray Reflected ray Refracted ray q i q r q f n 2 n 1 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 θ i which is greater than the critical angle θ c . In order for this to happen, the light ray must be launched at the end of the fiber at an angle θ l , which is less than a critical angle θ α see Figure 8.7a. The angle θ l is referred to as the launch angle. This results into a cone of acceptance within which a light ray must be launched see Figure 8.7b. Typically, a lens is used to focus the launched light onto a small area of the core see Figure 8.8. In Figure 8.7a, 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. a q l q a b Cone of acceptance Cladding Cladding Core Core Cladding Cladding q i q r q l Figure 8.7 Angle of launching a ray into the fiber. Optical transmitter Cladding Cladding Core Figure 8.8 A lens is used to focus the launched light. 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