Optical Fibres PDF

**Optical Fibres** Optical fibres are thin cylindrical wires made of glass or any transparent dielectric material. They are essentially wave guides used in optical communication. An optical fibre consists of three parts. 1. Core 2. Cladding 3. Buffer Jacket (Polyurethane jacket) The core i...

**Optical Fibres** Optical fibres are thin cylindrical wires made of glass or any transparent dielectric material. They are essentially wave guides used in optical communication. An optical fibre consists of three parts. 1. Core 2. Cladding 3. Buffer Jacket (Polyurethane jacket) The core is the inner cylindrical part of the fibre made of glass or plastic having higher refractive index, the outer part which is concentric cylinder surrounding core is called cladding. It is also made of same material as core but of lesser refractive index. The cladding is surrounded by a polyurethane jacket which safeguards the fibre against chemical reaction with surroundings, moisture, abrasion and crushing. **Principle** The working of optical fibres is based on principle of Total internal reflection.  Consider a ray of light travelling in a denser medium of refractive index n~1~. Let XX¹ be the surface separating two media of refractive indices n~1~ and n~2~ (n~1~\> n~2~). The ray AO is incident on the surface with an angle of incidence θ~1~ and gets refracted in the second medium along OAࢭ¹ with an angle of refraction θ~2.~ Since the ray is entering from denser to rarer medium θ~2~ \> θ~1~. If θ~1~ is increased, θ~2~ increases and for certain value of θ~1~ = θ~c~ called critical angle, the refracted ray grazes the surface along O Bࢭ. For any angle of incidence which is greater than θ~c~, the ray is reflected back into the first medium. The light is completely reflected and this phenomenon is called total internal reflection. (TIR) **Conditions for TIR** 1. Light must travel from denser to rarer medium̍ 2. The angle of incidence must be greater than the critical angle. In case if TIR, there is absolutely no loss(absorption) of energy at the reflecting surface, the entire incident energy is returned along the reflected light, because of this, the optical fibres are able to sustain the light signal transmission over very long distances **Numerical Aperture and Angle of Acceptance** Numerical aperture is defined as the light gathering capacity or light collecting ability of the fibre. It is given by the sine of the angle of acceptance. N.A. = sin θ~0~ Consider a ray of light moving along AO entering into the fibre with an angle θ~0~ to the fibre axis, then it is refracted along OB at an angle θ~1~ in the core and then proceeds to fall at critical angle θ~c~ at B on the surface between core and cladding, since the angle of incidence is equal to the critical angle, the ray is refracted at 90° and grazes the surface along BC. It is clear from the figure that any ray that enters into the core at an angle of incidence less than θ~0~ , will have the angle of refraction less than θ~1~ because of which its angle of incidence (90 -- θ~1~) will be greater than critical angle and hence undergo total internal reflection. If OA is rotated around the fibre axis keeping θ~0~ same, then it describes a cone. All those rays which are entering the fibre within this cone will only be totally internally reflected. The angle θ~0~ is called acceptance angle. **Angle of acceptance** is the maximum angle of incidence at the entrance of the fibre below which the rays can propagate through fibre by undergoing total internal reflection. **Acceptance cone**: Any ray incident within the cone angle of 2θ~0~ are accepted by the fibre and transmitted through it. This cone of angle 2θ~0~ is called acceptance cone. All those rays which are entering the cone are available for TIR, the amount of light that can enter the cone is given by Numerical Aperture. Let n~0,~ n~1~ and n~2~ be the refractive indices of surrounding medium, core and cladding of the fibre respectively. For the refraction at the entrance of the fibre, from Snell's law n~0~ sin θ~0\ =~ n~1~ sin θ~1\.............(1)~ At the point B on the surface, the angle of incidence = (90 -- θ~1~) Applying Snell's law n~1~ sin (90 -- θ~1~) ~=~ n~2~ sin 90 n~1~ cosθ~1\ =~ n~2~ cosθ~1~ = [\$\\frac{n\_{2}}{n\_{1}}\$]{.math.inline} ~.............(2)~ [ cos^2^*θ*~1 ~]{.math.inline}~=~ [\$\\frac{n\_{2}\^{2}}{n\_{1}\^{2}}\$]{.math.inline} ~1\ -~ [cos^2^*θ*~1 ~ ]{.math.inline}~=\ 1\ -~[\$\\text{\\ \\ }\\frac{n\_{2}\^{2}}{n\_{1}\^{2}}\$]{.math.inline} [ sin*θ*~1 ~]{.math.inline}~=~ [\$\\sqrt{1\\ - \\frac{n\_{2}\^{2}}{n\_{1}\^{2}}}\$]{.math.inline}~......\.......(3)~ Substituting (3) in (1) n~0~ sin θ~0\ =~ n~1~ [\$\\sqrt{1\\ - \\frac{n\_{2}\^{2}}{n\_{1}\^{2}}}\$]{.math.inline} sin θ~0~ = [\$\\frac{n\_{1}}{n\_{0}}\\sqrt{1\\ - \\frac{n\_{2}\^{2}}{n\_{1}\^{2}}}\$]{.math.inline} sin θ~0~ = [\$\\frac{n\_{1}}{n\_{0}}\\sqrt{\\frac{{n\_{1}\^{2} - n}\_{2}\^{2}}{n\_{1}\^{2}}}\$]{.math.inline} sin θ~0~ = [\$\\frac{n\_{1}}{n\_{0}}\\text{\\ x\\ }\\frac{1}{n\_{1}}\$]{.math.inline} [\$\\sqrt{{n\_{1}\^{2} - n}\_{2}\^{2}}\$]{.math.inline} sin θ~0~ = [\$\\frac{\\sqrt{{n\_{1}\^{2} - n}\_{2}\^{2}}}{n\_{0}}\\ \$]{.math.inline} since [the surrounding medium is air *n*~0~ = 1]{.math.inline} sin θ~0~ =[\$\\sqrt{{n\_{1}\^{2} - n}\_{2}\^{2}}\$]{.math.inline} N.A. = [\$\\sqrt{{n\_{1}\^{2} - n}\_{2}\^{2}}\$]{.math.inline} is the expression for numerical aperture. **Modes of Propagation**: **V -- Number:** The number of modes supported for propagation in the fibre is determined by a parameter called V-number denoted as V. It is given by, V = [\$\\frac{\\text{πd\\ }\\sqrt{\\left( {n\_{1}\^{2} - n}\_{2}\^{2} \\right)}}{\\lambda}\$]{.math.inline} d is the diameter of the core [*n*~1~]{.math.inline} is the refractive index of core [*n*~2~]{.math.inline} is the refractive index of cladding [*λ*]{.math.inline} is the wavelength of light But N.A. =[\$\\sqrt{\\left( {n\_{1}\^{2} - n}\_{2}\^{2} \\right)}\$]{.math.inline} V = [\$\\frac{\\text{πd\\ }}{\\lambda}\\ (N.A)\$]{.math.inline} If the fibre is surrounded by a medium of refractive index [*n*~0~]{.math.inline} [\$V = \\frac{\\text{πd\\ }}{\\lambda}\$]{.math.inline} [\$\\frac{\\sqrt{\\left( {n\_{1}\^{2} - n}\_{2}\^{2} \\right)}}{n\_{0}}\$]{.math.inline} The number of modes supported by the fibre is given by [\$number\\ of\\ modes = \\ \\frac{V\^{2}\\ }{2}\$]{.math.inline} The optical fibres are classified into 3 types, 1)Single mode fibre 2)Step index multimode fibre 3)Graded index multimode fibre **Single mode fibre:**  This type of fibre has a smaller diameter of 8-10μm and larger cladding diameter 60 -100μm. Since the size of the core is very small it can support only one mode for propagation. In this fibre degradation of the signal is minimum. They are used for long distance communication. The refractive index profile is as shown in the figure. **Step-index Multimode fibre** It is similar to single mode fibre, but has much larger core diameter. The core diameter ranges from 50 - 200 μm and cladding diameter ranges from 100 -- 250 μm. Its refractive index profile is similar to that of a single mode fibre. The refractive index of the core remains constant from the axis to the cladding and suddenly decreases at the cladding as a step function, hence it is called step index fibre. The degradation is high due to destructive interference between many modes; hence it is not suitable for long distance communication. Laser and LED are used as source of signal. **Graded index multi-mode fibre (GRIN)**  The geometry of GRIN is same as step index multi-mode fibre. The core diameter ranges from 50 - 200 μm and that of cladding ranges from 100 -- 250 μ m. The refractive index of the core decreases continuously from the axis to the cladding and remains constant throughout the cladding. The refractive index profile is as shown in the figure. Either Laser or LED can be used as the source to transmit the signal. It is used in the telephone trunk between the central offices. **Attenuation** The loss of power by light signal as it propagates through the fibre is called attenuation. There are three mechanisms by which an optical signal suffers attenuation. They are, 1)Absorption loss 2)Scattering loss 3)Radiation loss **Absorption loss:** When light passes through the fibre**,** the light photons are absorbed by the material of the fibre resulting in attenuation. There are two types of absorption. 1) Impurity absorption and 2) Intrinsic absorption **Impurity absorption:** The glass optical fibre usually contains transition metal ions like copper, cobalt, chromium and iron as impurities. The electrons of these impurities absorb photons and get excited to higher energy state, during de excitation these photons are re emitted but in the different wavelength region or different phase, hence these photons cannot reach the end so it is a loss. **Intrinsic absorption:** The base material of the fibre itself has a tendency to absorb the light to some extent. This absorption is called intrinsic absorption. This absorption is small in case of highly transparent glass fibres. **Scattering loss** When the signal travels the fibre, the photons may scatter due to sharp changes in refractive index values inside the glass. The variation in the refractive index is induced by the localized structural inhomogeneity. This type of scattering is same as Rayleigh scattering, the intensity of Rayleigh scattering is inversely proportional to λ^4.^ It increases enormously with decrease in wavelength^.^ This can be minimised by limiting the wavelength value, the intensity increases if the wavelength is greater than 0.8 μ m. The minimum wavelength is 0.8 μ m. **Radiation losses** Thera are two types of radiation losses. 1)Macroscopic bends and 2) Microscopic bends **Macroscopic bends:** They are the bends due to bending of the fibre, if the fibre is bent sharply with small radius of curvature the total internal reflection may not be satisfied and the ray escapes from the fibre as shown in the figure**.**  **Microscopic bends:** This is a small-scale distortion found in optical fibre due to fluctuations in the linearity of the fibre axis. The micro bending is due to lack of cylindrical geometry of fibre during the manufacturing process. Micro bending may also arise due to variation in the temperature and tensile stress. The lack of cylindrical geometry results in failure of total internal reflection and the light escape as shown in the figure. **Expression for attenuation coefficient** The expression for attenuation coefficient is given by, α = - [\$\\frac{10}{L}\\log\_{10}\\ \\left( \\frac{P\_{\\text{out}}}{P\_{\\text{in}}} \\right)\\ dB/Km\$]{.math.inline} L is the length in Km [ *P*~out~]{.math.inline} is the output power in watt [ *P*~in~ ]{.math.inline} is the input power in watt **Application of Optical Fibres** **Point to pint communication** Optical fibre communication is the transmission of information by propagation of optical signal through optical fibres over the distance. The Block diagram of point to point communication is as shown in the figure. It consists of mainly two parts Transmitter and receiver connected by fibre.  The information (Voice) in electrical signal in analog form from the transmitter section enters the coder where it is converted into (digital) binary data. The binary data comes out as a stream of electrical pulses from the coder. These electrical pulses are converted into optical pulses by modulating the light emitted by an optical source such as LED or laser diode in the binary form. this unit is called optical transmitter. The optical signals from the optical transmitter propagates through optical fibres by undergoing total internal reflection and it reaches a photodetector where it is transformed into pulses of electrical signal which is then fed to decoder which converts the sequence of binary data into an analog signal and received as the original information (voice) at the other end (receiver) **Fiber optic networking** Optical transmission system usually refers to a point-to-point optical link between a transmitter and a receiver. Communication network is much more general. It is a communication among a large number of users at many different locations and with various different types of services and applications. There are many types in network) and communication network is shared by many end users (sender-receiver) where lines connecting different nodes can be cables, optical fibers, wavelengths channels etc. With the rapid increase of the number of users and the types of applications, the complexity of networks increases exponentially. Fortunately optical fibers introduction into communication networks has drastically increased the networking capacity (compared to the use of copper wires). An optical network is a type of data communication network built with optical fiber technology. Optical fibers are used for passing (transmitting) data as light pulses between sender and receiver nodes. Here an optical transmitter device is used to convert an electrical signal received from a network node into light pulses, which are then placed on a fiber optic cable for transport to a receiving device. An optical network is less prone to external inference and attenuation and can achieve substantially higher bandwidth speeds. The block diagram is as follows. Components of a fiber-optical networking system include: Optical transmitter (Laser or LED)-- to convert electrical signals into optical pulses Multi-mode or single-mode optical fiber -- to carry optical signals Multiplexer- to receive multiple signal and combine them Demultiplexer -- to receive single signal (input) and generate multiple signals (outputs) Optical switch - to direct light between ports without an optical-electrical-optical conversion Optical splitter- to send a signal down different fiber paths (not shown in block diagram) Optical amplifier- to enhance the signal strength **Merits of optical fibres (Advantages** 1. Optical fibres have wide band width and hence can transmit large amount of information at fast rate. 2. They are resistant to electromagnetic interference between different communication channels so free from noise 3. They have low attenuation and hence low power loss, thereby allowing for longer transmission distances. 4. There is no signal radiation and hence are secure, physically tapping of the signal is ruled out, if done leads to loss of signal and easily be detected. 5. No sparks are generated hence are resistant to corrosive elements and flammable environments. 6. They are flexible and small in size, 7. They have light weight so easy to transport. 8. They have long life **DeMerits of optical fibres (Limitations)** 1. Fibre material is poor in mechanical strength 2. Too much bending of fibre leads to breaking or loss in signal transmission 3. Since glass fibres can be easily broken, essential care must be taken during installation 4. The cost of manufacturing optical cables is high. 5. Fibres undergo expansion and contraction with temperature which leads to loss in signal power