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Optical fibers Optical fibers are thin, flexible strands of transparent dielectric material such as glass or plastic. They are basically used to guide infrared & visible light waves through curved paths. John Tyndall a British physicist had demonstrated in 1854 to the Royal society that light could be guided along a curved stream of water. Principle of optical fibers: rarer medium = C >C denser medium Optical fibers work on the principle of total internal reflection of light. When a beam of light traveling in an optically denser medium falls on a surface separating a relatively less denser medium at an angle of incidence greater than the critical angle (C) for the pair of media, the light undergoes total internal reflection. Total internal reflection is the most superior type of reflection. Reflection is total in the sense that the entire energy is returned to the first medium through reflection without any loss of energy. Due to this the optical fibers are able to sustain light signal transmission over very long distances despite infinite number of reflections. Construction It consists of a central cylindrical core made of pure glass or plastic of refractive index n1 surrounded by a cladding made of similar material but of lower refractive index n2 (n2 < n1). But there is a material continuity from core to cladding. The cladding is enclosed in a polyurethane jacket that protects the fiber from external damaging factors such abrasion, Page 1 of 9 crushing & chemical reactions. Many such protected fibers are grouped to form a cable. The diameter of the core varies between 10 to 200 m depending upon type of the optical fiber & that of the cladding varies between 50 to 250 m. Condition for signal propagation through an optical fiber Consider an optical fiber with refractive index of the material of the core n 1 & cladding n2 placed in a surrounding medium of refractive n0. Let a ray AO of light enter the core of the fiber at an angle 0. Let this ray after refraction through an angle at O strike the interface between the core & the cladding at the critical angle such that the refracted ray grazes the interface. sin 0 n1 sin n0 Applying snells law of refraction at O, we have, sin 0 n1 sin ….(1) n0 Applying snells law of refraction at B sin (90 ) sin 90 n2 n1 or cos n2 n1 & sin 1 n 22 n12 ….(2) substituting for sin from eqn (2) in eqn (1) sin 0 1 n0 n12 n22 If the surrounding medium is air or vacuum, n0 = 1. Page 2 of 9 0 is called the acceptance angle or half angle of the acceptance cone. The acceptance angle is generally about 5 for a single mode fiber & 10 to 15 for multi mode fibers. n0sin 0 is called the numerical aperture (NA) and it indicates the light gathering power of the optical fiber. It is evident that any ray that enters the fiber at an angle less than 0, strikes the core-cladding interface at angle greater than the critical angle & undergoes total internal reflection each time it strikes the interface. The optical fiber sustains the light signal transmission over a long distance. Fractional index change : is the ratio of the change in the refractive indices (n1n2) between the core & the cladding to the refractive index n 1 of the core. (n1 n2 ) n1 Relation between NA & n12 n 22 = (n1 n2 )(n1 n2 ) NA = n1 n2 , But (n1n2) = n1 & (n1+n2) 2 n1 NA = ( n1 ) (2n1 ) n1 2 The light accepting capacity of a fiber can be increased by making large. But there are practical limitations to this. Also a very large may cause signal distortion. Types of optical fibers Based on their refractive index profile, geometry & ability to support the number of modes for propagation, optical fibers may be broadly classified into a) single mode step index optical fibers b) multi mode step index optical fibers c) multi mode graded index (GRIN) optical fibers Number of modes of transmission through an optical fiber Depending on the launch angle into the fiber, there can be hundreds of ray apaths or modes by which energy can propagate down the core. An optical fiber permits a discrete number of modes to propagate through it. Not all the rays that enter the acceptance cone sustain propagation. Only those modes that satisfy the coherent phase condition are successfully propagated. The rays belonging to the same propagating wave front must remain in step despite the phase changes that occur on reflection & traversing different optical paths. Page 3 of 9 The number of modes supported for propagation through an optical fiber is determined by a parameter called the V number that is given by V d n0 where d is the diameter of the core & is the wavelength n12 n22 of the light propagated. If V >>1 then the number of successfully 2 propagated modes is V 2 Skip distance Ls Skip distance is the distance between two successive reflections of a ray of light propagating through the optical fiber. Consider a portion of the optical fiber through which a light signal is transmitted. Ls d 0 From the figure Ls d cot d Ls d cos ec 2 1 n12 1 n02 sin 2 0 sin n0 sin 0 n1 To estimate the number of reflections occurring when the signal traverses a given distance, consider n0 = 1, n1 = 1.6, = 15 & d = 50m Then Ls = 305 m no of reflections per meter = 1 = 3278 Ls Single mode step index optical fiber n core diameter 5-10m 0 distance from the axis Cladding diameter Refractive index profile 50- 70 m Geometrical dimensions core Mode of propagation Page 4 of 9 A single mode optical fiber consists of a core having a uniform refractive index n1 that abruptly decreases at the core-cladding interface to a lower value n2 the refractive index of the cladding. The diameter of the core is narrow (5-10m) generally a few times the wavelength of the light propagating through it. Only rays nearly parallel to the fiber axis will travel through. It supports a single mode propagation because of its narrow core. Single mode optical fibers 1. need laser as the source of light. 2. are less expensive 3. have least signal attenuation & highest transmission speed & are free from modal dispersion. 4. are the most extensively used constituting about 80% of the total world manufacture of the fibers. 5. have low information carrying capacity 6. are difficult to splice Step-Index Multimode fiber In this case also the refractive index profile is similar to step index fiber i.e., fiber consists of a core having a uniform refractive index n1 that abruptly decreases at the core-cladding interface to a lower value n2 the refractive index of the cladding. But the diameter of the core is much larger (50200m). The comparatively large central core makes it rugged and easily infused with light, as well as easily terminated and coupled. It is the least expensive but also the least effective of the lot, and for long range applications, it has some serious drawbacks especially intermodal dispersion. It supports a large number of modes for propagation because of its large core diameter. n core diameter 50-200m 0 distance from the axis Refractive index profile Cladding diameter 100- 200m Geometrical dimensions Mode of propagation Page 5 of 9 Step-index multi mode optical fibers 1 accept either laser or a LED as the source of light. 2 are least expensive of all the three types of fibers 3 are used in data links that have lower band width requirements. 4 not free from modal dispersion. 5 have higher information carrying capacity. Graded-Index Multimode fiber (GRIN) It consists of a core whose refractive index decreases gradually from its axis radially outward & becomes equal to the refractive index of the cladding at the core-cladding interface. The refractive index of the cladding remains uniform. Dimensions of the core and cladding are similar to that of step index multimode fibers. It supports a large number of modes for propagation because of its large core diameter. n 0 distance from the axis Refractive index profile core diameter 50-200m Cladding diameter 100- 200 m Geometrical dimensions Fig. from E. Hecht P.No.198 Mode of propagation Graded-index multi mode optical fibers 1 accept either laser or a LED as the source of light. 2 are the most expensive of all the three types of fibers. 3 are used in telephone trunks between central offices. 4 Have lower modal dispersion. 5 have higher information carrying capacity. Page 6 of 9 Attenuation: Attenuation is the loss of power of the light signal that occurs during its propagation through the optical fiber. The main sources of attenuation are 1. absorption 2. scattering 3. other losses Absorption Absorption of light during propagation occurs due to the impurities present in the fiber material & also due to the intrinsic nature of the material itself. Absorption by impurities: Photons from the propagating signal are absorbed by the impurity atoms. The impurities generally present are a) transition metals such as iron,chromium,cobalt, copper etc. b) the hydroxy ions (OH) that enter into the fiber material at the time of fabrication due to the reaction between the starting material & the oxy hydrogen flame. The photons absorbed by the impurities may be lost as heat or may be reemitted as light energy of different wavelength & different phase from the one that is propagated. Hence it results in a loss. Though in the past, the greatest loss in the fiber optic propagation had been due to impurity absorption, improved methods of production from time to time have reduced such losses remarkably. Intrinsic absorption: Intrinsic absorption occurs by the pure material itself even if the material is free from impurities & inhomogeneities. These losses are wavelength dependent. Absorption loss due to a material over a length L of the fiber can be estimated from I = I0 e L where, I is the intensity of the signal after traversing a length L of the fiber, I0 is the intensity of the signal entering the fiber & is the attenuation coefficient for the fiber material. is a function of wavelength & also a function of the angle of incidence. The rays that strike the fiber at smaller angles of incidence travel a lesser distance of the fiber & thus the absorption is less. Intrinsic absorption though quite less compared to the loss due to the impurities, it cannot be eliminated. Attenuation due Scattering Glass is a heterogenous mixture of oxides of silicon, phosphorus, germanium etc. Structural inhomogeneities in the core index will set in the fiber material during solidification of glass from its molten state. It will also result in a fluctuation of the molecular density. These inhomogeneities act Page 7 of 9 as scattering centers. Since their dimensions are smaller than the wavelength of the light propagated through the fiber, the energy loss that occurs due to such scattering resemble Rayleigh scattering that is 1 4 . An optical fiber transmitting longer wavelength say 1.3m represents roughly 7 times lesser scattering than transmitting wavelength of 800nm. The losses due to these scattering cannot be eliminated by any process. There are other structural inhomogeneities & defects that set in during fabrication of the fiber that contribute to the loss due to scattering. Their sources are trapped gas bubbles, unreacted starting materials etc. However these can be reduced to a great extent by improved methods of manufacturing. Other losses a) Due to dimensional irregularities & imperfections in the fibers (that are called microscopic bends) the light may not sustain total internal reflection. The energy will escape from the core. b) Losses due the restrictions of the fiber numerical aperture, inevitable reflections at the interface. These are called the Fresnel losses. c) Radiation pattern & the size of the light source if not well adapted to the fiber ends reduce the efficiency both at the input & the output ends. Mismatch of the coupled fiber ends, alignment also lead to losses if not properly taken care of. d) Loses due to connectors, couplers & splices which become inevitable over long distances. e) Macroscopic bends occur during wrapping the fiber on a spool or negotiating a curve during cable laying. They have a large radius of curvature large as compared to the fiber diameter. Fibers can withstand bends of curvature up to about 10cm without significant loss. For bends smaller than this the loss increases exponentially up to a critical radius of Page 8 of 9 curvature & suddenly increases to a very large value showing the total absence of the total internal reflection at the bends. Due to the losses that occur due to various causes during propagation as explained above an amplification is needed in communication applications at regular intervals in order to compensate for the losses that occur despite all precautions. An optical repeater is used to boost the signal. Applications & Advantages of optical fibers 1. The simplest & the most important use of optical fibers is their use as flexible light pipes. It can transmit light to otherwise inaccessible areas & even provide information about such regions by returning images. The fiberscope, a bundle of fibers end-equipped with objective lens & eye piece is used by doctors to examine regions of the stomach, lungs, duodenum. 2. The rods & the cones of the human eye function as light pipes transmitting light as in optical fibers. 3. Voice or video communication & data transmission. 4. Optical fibers are smaller in size & light in weight compared to conventional metallic cables. Since optical frequencies are much higher than the conventional electrical signals, replacement of copper coaxial cables by fiber optic cables offers greater communication capacity in smaller space. Their maintenance cost is much lower. 5. In contrast with the metallic conduction techniques, communication by light through optical fibers offers complete electrical isolation, immunity to electromagnetic interference, radio frequency interference & voltage surge. Optical fibers are free from signal leakage, electric sparks & fire hazards. They are useful in laying cables near electronic hardware in industrial equipment. 6. Communication through optical fibers is especially important & advantageous where security of information is vital. 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