7005_1 - Optical Fiber Transmission Characteristics...

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IEG7005-Part 1: Optical Fiber Transmission Characteristics P. I-1 Optical Fiber Transmission Characteristics Outline: Basic Electromagnetic Theory: Maxwell’s Equations, Wave Equation, Group Velocity, Phase Velocity Modes in Waveguides Polarization of Light Optical Fiber Structure and Types Fiber Attenuation and Scattering Fiber Dispersion: Modal dispersion, Material Dispersion, Waveguide Dispersion, Group Velocity Dispersion, Pulse Broadening Bit-Rate Distance Limit
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IEG7005-Part 1: Optical Fiber Transmission Characteristics P. I-2 - Electric field - Electric Flux Density - Magnetic field - Magnetic Flux Density ε - permittivity, ε o = 8.8642x10 -12 F/m (in vacuum) µ - permeability, = 4 π x10 -7 N/A 2 (in vacuum) Note: where r is the relative permittivity or the dielectric constant of the medium Basic Electromagnetic Theory E r D r H r B r H B E D r r r r = = E E D r o r r r ε= = o o c 1 2 = J r Maxwell’s Equations 0 = = + = × = × B D t D J H t B E r r r r r r r ρ 0 = = + = × = × H E t E J H t H E r r r r r r r - current density - charge density
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IEG7005-Part 1: Optical Fiber Transmission Characteristics P. I-3 Basic Electromagnetic Theory Wave Equations In free space, 0 1 2 2 2 2 = t E c E r r o o o o c ε µ 1 ; ; 2 = = = 0 1 2 2 2 2 = t H c H r r For harmonic fields: t j t j e H e E ω r r ; 22 2 0 for where oo Ek E k n k k c π λ ∇+ = = == rr k o :wave constant k : propagation constant : wavelength : angular frequency 0 2 2 = + H k H r r Solution of EM wave equation: ( ) () r k t j kz t j e r e r r 1 For infinite plane wave For spherical wave
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IEG7005-Part 1: Optical Fiber Transmission Characteristics P. I-4 Phase Velocity and Group Velocity Consider a plane wave: where is a unit vector. Let real quantity Φ = ω t -kz+ ϕ o (phase of the wave) Phase velocity : velocity along z needed to observe a fixed phase, i.e. d = 0 dz/dt = /k phase velocity ( ) r Ea E e o jtk z o = −+ $ ωϕ $ a V k p =
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IEG7005-Part 1: Optical Fiber Transmission Characteristics P. I-5 ξ o Phase Velocity and Group Velocity Consider a wave packet Ψ ( z,t ) with center frequency ω (wave number ): An information - bearing signal comprises a spectrum of frequencies , each has different propagation constant, thus has different phase velocity.
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IEG7005-Part 1: Optical Fiber Transmission Characteristics P. I-6 Phase Velocity and Group Velocity Notice that the wave packet function at time t is just a time-delayed version of its initial function ( t =0). The whole wave packet propagates at the group velocity V g while each of its frequency components propagates at V p . dk d V k V g p ω = = Phase Velocity Group Velocity
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IEG7005-Part 1: Optical Fiber Transmission Characteristics P. I-7 Phase Velocity and Group Velocity Group velocity V g represents the velocity of information transmission.
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This note was uploaded on 10/02/2011 for the course BGFBGF bgfbgf taught by Professor Bgf during the Spring '11 term at N. Arizona.

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7005_1 - Optical Fiber Transmission Characteristics...

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