Fiber Optics
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FIBER OPTICS Prof. R.K. Shevgaonkar Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture: 3 Propagation of Light in an Optical Fiber Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 1 Light energy can be modelled in three different forms which relate the particular model of light to the context in which it is talked about. Light can be characterized in any one of the following models Ray Model Wave Model Quantum Model In the simplest possible context, light is treated as a ray and the different phenomena exhibited by light are explained in terms of the ray-model of light. Some phenomena exhibited by light are not adequately explained by the Ray-Model of light. In that case, we resort to the more advanced nature of light such as the wave and the quantum models. In this section we shall mainly deal around the ray model of light and attempt to explain the propagation of light in an optical fiber treating light as a ray. Constructionally, an optical fiber is a solid cylindrical glass rod called the core, through which light in the form of optical signals propagates. This rod is surrounded by another coaxial cylindrical shell made of glass of lower refractive index called the cladding. This basic arrangement that guides light over long distances is shown in figure 2.5. Fig. 3.1: Constructional Details of an Optical Fiber The diameter of the cladding is of the order of 125 µm and the diameter of the core is even smaller than that. Thus it is a very fine and brittle glass rod that we are dealing with. In order to provide mechanical strength to this core-cladding arrangement, other coaxial surrounding called the buffer coating and jacketing layers are provided. They do not play any role in the propagation of light through the optical fiber, but are present solely for providing mechanical strength and support to the fiber. The light energy in the form of optical signals propagates inside the core- cladding arrangement and throughout the length of the fiber by a phenomenon called the Total Internal Reflection (TIR) of light. This phenomenon occurs only when the refractive index of core is greater than the refractive index of cladding and so the cladding is made from glass of lower refractive index. By multiple total internal Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 2 reflections at the core-cladding interface the light propagates throughout the fiber over very long distances with low attenuation. We shall now discuss the essential requirements of the propagation of light through an optical fiber, over long distances with minimum loss, in detail. Figure 3.2 shows a section of the core of an optical fibre. If a ray of light is incident on the core of an optical fibre from the side, the ray of light simply refracts out from the fibre on the other side. The ray shown in figure 3.2(in green) demonstrates the situation. Figure 3.2: Launching of light into an optical fiber. No matter what the angle of incidence of the light is, any light that enters the fiber from the side does not propagate along the fiber. The only option thus available with us is to launch the light through the tip of the fiber. That is, in order to guide light along the fiber, the light must be incident from the tip of the optical fiber. The red ray of light in figure 3.2 explains this situation. In other words, if the tip of the optical fiber is not exposed to light, no light will enter the fiber. Although there may be ambient light, as long as the tip is protected, no light from the sides propagates along the fiber. Equivalently, if there was propagation of light through the fiber, no light would emerge from the sides of the fiber. This characteristic of the optical fiber imparts the advantage of information security to the Optical Fiber Communication Technology. At this juncture, one basic question that may come to the reader’s mind is that whether a partial reflection at the core-cladding interface suffices the propagation of light along the fiber over long distances? The answer to this question is very clearly a no. The reason is that, at each reflection a part of the optical energy launched into the optical fiber would be lost and after a certain distance along the length of the fiber the optical power would be negligibly low to be of any use. Thus total internal reflection is an absolute necessity at each reflection for a sustained propagation of optical energy over long distance along the optical fiber. This precisely is the sole reason of launching light into the fiber at particular angles so that light energy propagates along the fiber by multiple total internal reflections at the core-cladding interface. Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 3 We have already stated that for explaining propagation of light in an optical fiber, the Ray-Model of light shall be used. The Ray-Model of light obeys the Snell’s laws. Following figure depicts a situation of a typical refraction phenomenon taking place at the interface of two optically different media having refractive indices n1 and n2: Figure 3.3: Refraction of light at a media interface The angles measured in the expression for Snell’s law are measured with respect to the normal to the media interface at the point of incidence. If n2 > n1 , then the angle of refraction is greater than the angle of incidence and the refracted ray is said to have moved away from the normal. If the angle of incidence (θ1) is increased further, the angle of refraction (θ2) also increases in accordance with the Snell’s law and at a particular angle of incidence the angle of refraction becomes 90o and the refracted ray grazes along the media interface. This angle of incidence is called the critical angle of incidence (θc) of medium 2 with respect to medium 1. One should note here that critical angle is media-relative. That means, the same optically denser medium may have different critical angles with respect to different optically rarer media. If θ1 is increased beyond the critical angle, there exists no refracted ray and the incident light ray is then reflected back into the same medium. This phenomenon is called the total internal reflection of light. The word ‘total’ signifies that the entire light energy that was incident on the media interface is reflected back into the same medium. Total Internal Reflection (TIR) obeys the laws of reflection of light. This phenomenon shows that light energy can be made to remain confined in the same medium when the angle of incidence is greater than the angle of reflection. Thus we can see that there are two basic requirements for a TIR to occur: 1. The medium from which light is incident, must be optically denser than the medium to which it is incident. In figure 3.3 n2 > n1. 2. The angle of incidence in the denser medium must be greater than the critical angle of the denser medium with respect to the rarer medium. Fiber Optics, Prof. R.K. Shevgaonkar, Dept. of Electrical Engineering, IIT Bombay Page 4 LAUNCHING OF LIGHT INTO AN OPTICAL FIBER Light propagates inside an optical fiber by virtue of multiple TIRs at the core- cladding interface. The refractive index of the core glass is greater than that of the cladding. This meets the first condition for a TIR. All the light energy that is launched into the optical fiber through its tip does not get guided along the fiber. Only those light rays propagate through the fiber which are launched into the fiber at such an angle that the refracted ray inside the core of the optical fiber is incident on the core- cladding interface at an angle greater than the critical angle of the core with respect to the cladding. But before delving into rigorous mathematical calculations, let us first visualise how light energy can be launched into a fiber. Figure 3.4 shows one of the possibilities of launching light into an optical fiber where the light ray lies in a plane containing the axis of the optical fiber. Such planes which contain the fiber axis are called meridional-planes and consequently the rays lying in a meridional-plane are called meridional-rays. Meridional rays always remain in the respective meridional plane. Figure 3.4: Launching of Meridional Rays There may be infinite number of planes that pass through the axis of the fiber and consequently there are an infinite number of meridional planes. This indirectly indicates that there are an infinite number of meridional rays too, which are incident on the tip of the fiber making an angle with the fiber-axis as shown in the above figure. These meridional rays which get totally internally reflected at the core- cladding boundary meet again at the axis of the optical fiber as shown in the figure 3.5 below. In the figure the meridional plane is the plane of the paper which passes through the axis of the fiber and the incident rays, refracted rays and the reflected rays lie on the plane of the paper. Though only two rays are shown in the figure for the sake of clarity, in practice there would be a bunch of rays that would be Fiber Optics, Prof. R.K.