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Module 2: Propagation of Light Through Optical Fiber

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Module 2: Propagation of Light Through Optical Fiber 1 Module 2: Propagation of light through optical fiber Table of Contents 1. Introduction 2. Structure of optical fiber 3. Propagation of light through optical fiber 4. Numerical Aperture 5. Pulse broadening through optical fiber 6. Phase front analysis of propagation of light 7. Summary Learning Outcome: 1. To understand propagation of light 2. To get familiar with structure of optical fiber 3. To understand propagation of light through optical fiber 4. To understand concept of numerical aperture of optical fiber 5. To get the insight of the pulse broadening phenomenon in optical fiber 6. To know about the phase front analysis of propagation of light through optical fiber Optoelectronics Electronic Science 2. Propagation of light through optical fiber 2 1. Introduction Light is electro-magnetic wave or made up of photons and has dual nature. It can be modeled in three different ways. a. Ray Model b. Wave model c. Quantum model Such type of modeling is necessary because some of the phenomenons are only explained using ray model. The some phenomenon which are not explained by ray nature or model are well explained by wave model and quantum model. In this module, ray model is used to explain the propagation of light through optical fiber. 2. Structure of optical fiber Constructionally, an optical fiber is a solid cylindrical glass rod called the core, through which light in the form of light or optical signal propagates. This is surrounded by another coaxial cylindrical structure made of glass of lower refractive index called the cladding. This basic arrangement that guides light over long distances is shown in figure 1. Core Cladding Buffer Coating Figure 1. Constructional details of optical fiber Optical fiber has diameter of the cladding is of the order of 125 μm and the diameter of the core even smaller than that. Thus it is a very fine and brittle glass rod. 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. Optoelectronics Electronic Science 2. Propagation of light through optical fiber 3 3. Propagation of light through optical fiber Propagation of light energy in the form of optical signals inside the core-cladding arrangement and throughout the length of the fiber takes place 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 reflections at the core-cladding interface the light propagates throughout the fiber over very long distances with low attenuation. The essential requirements of the propagation of light through an optical fiber, over long distances with minimum loss, are discussed in detail. Figure 2 shows a section of the core of an optical fiber. If a ray of light is incident on the core of an optical fiber from the side, the ray of light simply refracts out from the fiber on the other side. The ray shown in figure 2 (in blue) demonstrates the situation. Figure 2. Launching light into optical fiber Any light that enters the optical fiber from the side does not propagate along the fiber. Therefore, one has 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 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 lon g as the tip is Optoelectronics Electronic Science 2. Propagation of light through optical fiber 4 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. Partial reflection at the core-cladding interface does not suffice the propagation of light along the fiber over long distances. 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. The Ray-Model of light obeys the Snell’s laws. Figure 4 depicts a situation of a typical refraction phenomenon taking place at the interface of two optically different media having refractive indices n1 and n2: Normal Medium 1 Refractive index=n1 Refracted Ray θ2 n1<n2 φ2 Medium Interface Medium 2 φ1 boundary φ1 θ1 θ1 Refractive index:n2 Incident Ray Reflected Ray n1sin1 n2sin2(Snell’s law) Figure 4 Refraction of light at medium interface boundary 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 Optoelectronics Electronic Science 2. Propagation of light through optical fiber 5 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. 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. 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 4, 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. Thus one can say that light propagates inside an optical fiber because of multiple rays undergoing TIRs at the core-cladding interface. In order to occur this, refractive index of the core glass must be 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 that 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. Figure 5 shows how to launch light into an optical fiber. The light ray lies in a plane containing the axis of the optical fiber. Such planes which contain the fiber axis are called meridional- Optoelectronics Electronic Science 2. Propagation of light through optical fiber 6 planes and consequently the rays lying in a meridional-plane are called meridional-rays. Meridional rays always remain in the respective meridional plane. Cladding(n2) Refracted Ray n Reflected Ray φ φ Θ Θ0 Core(n1) Cladding(n2) Figure 5 Launching the light into optical fiber Infinite number of planes can pass through the axis of the fiber and an infinite number of meridional planes. This proves 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 5. These meridional rays after total internal reflection at the core-cladding boundary meet again at the axis of the optical fiber as shown in the figure 6. Consider 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. For the sake of simplicity and clarity only two rays are shown in the figure . However in practice there would be a number of rays that would be convergent at the same point. One can classify these Meridional rays as bound and unbound rays. The rays that undergo TIR inside the fiber core remain inside the core at all times along the propagation and are called as bound rays.
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