Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
REF: Optics by Ajoy Ghatak Chapter -27 Optical fiber vs Copper Fiber has these advantages compared with metal wires • Bandwidth – more data per second • Longer distance • Faster • Lower loss • Immunity to crosstalk • Special applications like medical imaging and other sensors are only possible with fiber because they use light directly Disadvantage • Optical fiber is more expensive per meter than copper • Optical fiber can not be join together as easily as copper cable. • requires training , expensive measurement equipment TOTAL INTERNAL REFLECTION (a) For a ray incident on a denser medium (n2 > n1 ), the angle of refraction is less than the angle of incidence. (a) For a ray incident on a rarer medium (n2 < n1 ), the angle of refraction is greater than the angle of incidence. ϕ1 n2 n 1 1 c sin 1 (a) The angle of incidence, for which the angle of refraction is 90o, is known as the critical angle and is denoted by c. the angle of refraction 2 = 90o. When the angle of incidence exceeds the critical angle (i.e., when 1 > c), there is no refracted ray and known as total internal reflection. THE OPTICAL FIBER A (glass) fiber consists of a cylindrical central core cladded by a material of slightly lower refractive index. Refractive index distribution for a step-index fiber. n1 0<r<a n r>a n2 where n1 and n2 (< n1) represent, respectively, the refractive indices of core and cladding and a represents the radius of the core. Light rays incident on the core-cladding interface at an angle greater than the critical angle are trapped inside the core of the fiber. critical incident angle (ϕC) critical propagation angle (θC) for a ray entering the fiber, if the angle of incidence (at the core-cladding interface) is greater than the critical angle c, then the ray will undergo TIR at that interface. n2 c sin n1 1 Or should be less than c: (θC=90- ϕC) n2 c cos n1 1 • all the energy in the ray is reflected back to the core. • The ray then crosses to the other side of the core and will meet the cladding on the other side at an angle which again causes TIR. • The ray is then reflected back across the previous side of the core again. • Through multiple TIR, ray guided from one end to another end of fiber with out loss Types of optical fibers: 1. Step-index fibre depending on refractive index: 2. Graded or variable index fiber depending on modes: Modes in fibre all rays with propagation angle less than αc will propagate through the fibre. • no. Of possible ways for a ray propagating in fibre. • depends upon αc (n1 & n2 ) • increases as the RI difference increases. • lower modes are having angles much less than αc . • higher order modes travel a larger path length and hence lag behind the lower order modes and produce distortion called intermodal distortion. • number of modes is determined by V parameter • V number depends on numerical aperture, source wavelength, and diameter of core Numerical Aperture The numerical aperture of the fiber is closely related to the critical angle and is used in the specification for optical fiber and the components The quantity sin im is known as the numerical aperture (NA) of the fiber and is a measure of light-gathering power of fiber. • if a cone of light is incident on one end of the fiber, it will be guided through it provided the semi angle of the cone is less than im (Acceptance Angle) • The angle of acceptance is twice that given by the numerical aperture THE NUMERICAL APERTURE a ray incident on the entrance aperture of the fiber, making an angle i with the axis. Assuming the outside medium to have a refractive index n0 sin i n1 sin n0 ray has to suffer total internal reflection. z n2 sin ( cos ) n1 n sin i 1 n0 n2 1 n 1 2 or, sin i n12 n22 no2 THE NUMERICAL APERTURE a ray incident on the entrance aperture of the fiber, making an angle i with the axis. Assuming the outside medium to have a refractive index n0 sin i n1 sin n0 ray has to suffer total internal reflection. z n2 sin ( cos ) n1 n sin i 1 n0 n2 1 n 1 2 or, n12 n22 no2 sin i If the outside medium is air, i.e., n0 = 1; and therefore the maximum value of sin i for a ray to be guided is given by N . A. sin im n n 2 1 2 2 Numerical Aperture for graded Index Fiber In the graded index fiber , the numerical aperture is a function of position across the core. (n n ) r x 1 2 nr n 1 x NA n (r ) n 2 2 2 r NA(r 0) 1- for r a a =0 for r>a 1 2 n 1 a = x :the refractive index profile variation NA(r=0): numerical aperture at the centre of the fibre core. NA(0)= n 2 (0) n22 n12 n22 For a graded index fiber numerical aperture decrease from axial numerical aperture NA(r=0) to zero as r increases from zero to core radius ' a '. Numerical Aperture for graded Index Fiber In the graded index fiber , the numerical aperture is a function of position across the core. (n n ) r x 1 2 nr n 1 x NA n (r ) n 2 2 2 r NA(r 0) 1- for r a a =0 for r>a 1 2 n 1 a = x :the refractive index profile variation NA(r=0): numerical aperture at the centre of the fibre core. NA(0)= n 2 (0) n22 n12 n22 For a graded index fiber numerical aperture decrease from axial numerical aperture NA(r=0) to zero as r increases from zero to core radius ' a '. Number of Modes and Cut-off Parameters of Fibers The number of modes cut-off parameter (normalized cut off frequency) d 2 2 d d 2 2 d n1 n2 or, V V n1( NA n)2 or, V ( NA) V number V o o o o The approximate total number of modes V2 Number of Modes (N) 2 If the external medium around the fiber has a refractive index no then d V no ( NA) o n12 n22 as NA= no Attenuation and Signal Losses in Optical Fibers The reduction in amplitude (or power) and intensity of a signal as it is guided through an optical fibre is called attenuation. loss depends on the wavelength of the light and on the propagating material. For silica glass, the shorter wavelengths are attenuated the most The loss /decrease in signal strength along a fibre are due to •bending losses •scattering losses •absorption losses (due to material or impurities) •connector loss, splice loss, loss at terminals etc. Attenuation and Signal Losses in Optical Fibers •Bending losses: Macro-bending losses Micro-bending loss macro-bending loss is caused by micro-bending loss is caused by the curvature of entire fiber axis micro deformations of the fiber axis. •Absorption losses: •Molecules/atoms/electrons vibrates at particular frequency •Source frequency matches with these frequency (IR region) •Selective absorption can happen by these molecules of material •Absorption losses increases with the impurities in material of fiber or wapor/water/gas in the core of fiber Scattering losses (1) Due to Rough and irregular surface: even at the molecular level of the glass, can reflect rays in many random directions. (2) Due to irregular refractive index: small change in core’s refractive index as an optical obstacle for ray which change the direction of the original beam. Attenuation and Signal Losses in Optical Fibers •connector loss, splice loss, loss at terminals • In fiber-optic systems, the losses from splices and connections can be more than in the cable itself – Axial or angular misalignment – Air gaps between the fibers – Rough surfaces at the ends of fibers Attenuation coefficient Attenuation losses in optical fibers are generally measured in terms of the decibel dB . Due to attenuation, the power output ( Pout ) at the end of 1 km of optical fibre drops to some fraction say k of the input power ( Pin ) , that is, Pout k Pin After 2 km Pout k 2 Pin Similarly after L km Pout =k L Pin or, Pout kL Pin Taking log of both sides and then multiply by 10 gives power loss in dB as P Power Loss (dB) =10 log out 10log k L L10log k L Pin where is the attenuation coefficient of the fiber in dB/km. Pout 10 = log L Pin dB / km Pout 10 To indicate loss we introduce negative sign in the expression log dB / km L Pin Attenuation coefficient Attenuation losses in optical fibers are generally measured in terms of the decibel dB . Due to attenuation, the power output ( Pout ) at the end of 1 km of optical fibre drops to some fraction say k of the input power ( Pin ) , that is, Pout k Pin After 2 km Pout k 2 Pin Similarly after L km Pout =k L Pin or, Pout kL Pin Taking log of both sides and then multiply by 10 gives power loss in dB as P Power Loss (dB) =10 log out 10log k L L10log k L Pin where is the attenuation coefficient of the fiber in dB/km. Pout 10 = log L Pin dB / km Pout 10 To indicate loss we introduce negative sign in the expression log dB / km L Pin Attenuation coefficient Attenuation losses in optical fibers are generally measured in terms of the decibel dB . Due to attenuation, the power output ( Pout ) at the end of 1 km of optical fibre drops to some fraction say k of the input power ( Pin ) , that is, Pout k Pin After 2 km Pout k 2 Pin Similarly after L km Pout =k L Pin or, Pout kL Pin Taking log of both sides and then multiply by 10 gives power loss in dB as P Power Loss (dB) =10 log out 10log k L L10log k L Pin where is the attenuation coefficient of the fiber in dB/km. Pout 10 = log L Pin dB / km Pout 10 To indicate loss we introduce negative sign in the expression log dB / km L Pin Attenuation coefficient Attenuation losses in optical fibers are generally measured in terms of the decibel dB . Due to attenuation, the power output ( Pout ) at the end of 1 km of optical fibre drops to some fraction say k of the input power ( Pin ) , that is, Pout k Pin After 2 km Pout k 2 Pin Similarly after L km Pout =k L Pin or, Pout kL Pin Taking log of both sides and then multiply by 10 gives power loss in dB as P Power Loss (dB) =10 log out 10log k L L10log k L Pin where is the attenuation coefficient of the fiber in dB/km. Pout 10 = log L Pin dB / km Pout 10 To indicate loss we introduce negative sign in the expression log dB / km L Pin Attenuation coefficient Attenuation losses in optical fibers are generally measured in terms of the decibel dB . Due to attenuation, the power output ( Pout ) at the end of 1 km of optical fibre drops to some fraction say k of the input power ( Pin ) , that is, Pout k Pin After 2 km Pout k 2 Pin Similarly after L km Pout =k L Pin Taking log of both sides and then multiply by 10 gives power loss in dB as P Power Loss (dB) =10 log out 10log k L L10log k L Pin where is the attenuation coefficient of the fiber in dB/km. Pout 10 = log L Pin or, Pout kL Pin Pout Pin10 L 10 dB / km Pout 10 To indicate loss we introduce negative sign in the expression log dB / km L Pin Numerical : Compute the maximum value of ( relative refractive index) and n2 (cladding) of a single mode fibre of core diameter 10 m and core refractive index 1.5. The fibre is coupled to a light source with a of 1.3m. V cut-off for single mode propagation is 2.405. Also calculate the acceptance angle. n1 n2 relative difference of index n1 =0.0022 n2 (cladding)=1.497 Acceptance angle = 5.71deg