The RSVP-TE Path and Resv Messages

HOW LIGHT IS TRANSMITTED THROUGH AN OPTICAL FIBER 183 A typical WDM optical network, as operated by a telecommunication company, con- sists of WDM metro i.e., metropolitan rings, interconnected by a mesh WDM optical network, i.e. a network of OXCs arbitrarily interconnected. An example of such a network is shown in Figure 8.2. There are many different types of optical components used in a WDM optical network, and some of these components are described in Section 8.3. We now proceed to examine some of the basic principles of light transmission through an optical fiber.

8.2 HOW LIGHT IS TRANSMITTED THROUGH AN OPTICAL FIBER

Light radiated by a source can be seen as consisting of a series of propagating electromag- netic spherical waves see Figure 8.3. Along each wave, one can measure the electric field, indicated in Figure 8.3 by a dotted line, which is vertical to the direction of the light. The magnetic field not shown in Figure 8.3 is perpendicular to the electric field. The intensity of the electrical field oscillates following a sinusoidal function. Let us mark a particular point, say the peak, on this sinusoidal function. The number of times that this particular point occurs per unit of time is called the frequency. The frequency is measured in Hertz. For example, if this point occurs 100 times, then the frequency is 100 Hertz. An electromagnetic wave has a frequency f , a speed v, and a wavelength λ . In vacuum or in air, the speed v is approximately the speed of light which is 3 × 10 8 meterssec. The frequency is related to the wavelength through the expression: v = f λ. An optical fiber consists of a transparent cylindrical inner core which is surrounded by a transparent cladding see Figure 8.4. The fiber is covered with a plastic protective cover. Both the core and the cladding are typically made of silica SiO 2 , but they are made so that to have different index of refraction. Silica occurs naturally in impure forms, such as quartz and sand. The index of refraction, known as the refractive index, of a transparent medium is the ratio of the velocity of light in a vacuum c to the velocity of light in that medium v, that Source Electric field Wave Figure 8.3 Waves and electrical fields. Core Cladding Cladding Figure 8.4 An optical fiber. 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