Introdution Optial Communiations Systems Dispersion in Optial Fibre (I) Dispersion limits available bandwidth As bit rates are inreasing, dispersion is beoming a ritial aspet of most systems Dispersion an be redued by fibre design Optial soure seletion is important Dispersion in an Optial Fibre Multimode fibre (LAN systems) Dispersion in Optial Fibres Modal dispersion Chromati dispersion Polarization Mode dispersion (PMD) Singlemode fibre (Teleom systems)
Why is dispersion a problem? Dispersion and Bit Rate Dispersion Pulse spreading Intersymbol Interferene Degrades error rate Fibre output with no Dispersion Fibre output with Dispersion Example Bit interval "T" Longer bit interval Optial Fibre The higher dispersion the longer the bit interval whih must be used A longer the bit interval means fewer bits an be transmitted per unit of time A longer bit interval means a lower bit rate Data at fibre input Data at fibre output Pulse spreading makes it more diffiult to distinguish "0" Conlusion: The higher the dispersion the lower the bit rate Dispersion Example Modal Dispersion Photo of Input and Output pulses for a 00 miron ore Polymer Clad Silia fibre showing pulse broadening (dispersion) In a multimode fibre different modes travel at different veloities If a pulse is onstituted from different modes then intermodal dispersion ours Modal dispersion is greatest in multimode step index fibres The drive to redue modal dispersion led to the development of graded index multimode fibre and singlemode fibre. A ray model an give and adequate desription of modal dispersion
Modal Dispersion Modal dispersion is greatest in multimode step index fibres The more modes the greater the modal dispersion Typial bandwidth of a step index fibre may be as low as 10 MHz over 1 km b a Step Index Analysis for Modal Dispersion Fibre Narrow pulse at fibre input Light ray (a) follows a longer path within the fibre than light ray () Broadened pulse at fibre output Estimating Modal Dispersion (Step Index Fibre) Step Index Modal Dispersion: Analysis (I) Assume: Step index fibre An impulse-like fibre input pulse Energy is equally distributed between rays with paths lying between the axial and the extreme meridional What is the differene in delay for the two extremes over a linear path length L? a n n Transmission distane = L a T max = Transmission time for extreme meridional ray T min = Transmission time for axial ray Delay differene δt = T max -T min
Step Index Modal Dispersion: Analysis (II) Step Index Modal Dispersion: Analysis (III) a h d a n a h d a n T min = Distane Veloity = L (/ ) = L To find T max realise that the ray travels a distane h but only travels a distane d toward the fibre end (d<h). So if the fibre length is L then the atual distane travelled is: h.l d T max = L os Using Snell's law: Using simple trigonometry sin = n = os Ln T max = 1 n Delay differene δt = T max -T L min = n - L Step Index Modal Dispersion: Analysis (IV) Impulse Response for Step Index Fibre δt = L -n = n Show for yourselves that: L n Assumes << 1 δt = L(NA) Impulse input Assume an impulse input to the fibre Output is a pulse of uniform amplitude over a time period T max -T min = δ t Output pulse of width δ t is thus the impulse response of the fibre. Assuming an output pulse amplitude of 1/δ t,the impulse response h(t) is given by: Fibre δ t 1/δ t δ t/ +δ t/ t h(t) = 1/δ t δ t / < t < +δ t/ h(t) = 0 elsewhere
Take the Fourier transform of the impulse response The transfer funtion of the fibre H(f) is given by: 1.0 Transfer Funtion for a Step Index Fibre H(f) = sin f δ t Plot of H(f) is sin like Note: sin x = sin πx πx Essential bandwidth, BW, for the fibre is 1 /δ t Bandwidth for a Step Index Fibre (I) Based on the previous analysis BW an be written as: BW = L(NA) BW 1st zero is at 1 /δ t, the so alled essential bandwidth for a system, BW 1 /δt /δt 3 /δt Frequeny BW get smaller as fibre length L inreases High NA fibres have lower bandwidths, eg plasti fibre has high NA: Poor bandwidth Lowering NA to improve bandwidth makes soure oupling more diffiult as the aeptane angle dereases Bandwidth Problem: Plasti Optial Fibre Conventional plasti optial fibre is step index, low bandwidth NA is about 0.4, ore refrative index is about 1.5 Show that the BW over 1 km is about 6 MHz Measured values are about 6 to 10 MHz so analysis is about right Reduing Modal Dispersion BW = L(NA)
Reduing Modal Dispersion Reduing Dispersion using a Graded Index Fibre Redue the differene between the propagation veloities of different modes Graded index fibre design b a Light ray (a) and (b) are refrated progressively within the fibre. Notie that light ray (a) follows a longer path within the fibre than light ray (b) Redue the number of modes to one Singlemode fibre design Ray (a) follows a longer path, but the muh of the path lies within the lower refrative index part of the fibre. Ray (b) follows a shorter path, but near the fibre axis where the refrative index is higher Sine the veloity inreases as the refrative index dereases the time delay between (a) and (b) is equalised The Profile Parameter and Intermodal Dispersion Reall that the profile parameter α for a graded index fibre ditates the shape of the refrative index profile Why does the profile parameter α used for graded index fibre has a ommon value of about? It an be shown that the optimum value of α that maximises the bandwidth of GI fibre is given by: Variation in Modal Dispersion with the Profile Parameter Plot below shows variation in intermodal dispersion with the profile parameter. Plot assumes a value of 1% for the fibre. Large value of α > 3 means a profile approahing step index. Dispersion drops by more tha00:1 with α ira by omparison with α > 3 Thus bandwidth of graded index is > 100 times higher than step index α =.(1- ) A ommon value for GI multimode fibre is 0.0 (%) (Luent 6.5/15 µm) For this value the optimum profile parameter α has a value of 1.96.
Quantifying Dispersion in a GI Fibre (I) Very involved analysis As in the step index ase one determines maximum time differene between the two most extreme modes Most ommon expression is: Quantifying Dispersion in a GI Fibre (II) Using the formulas below and assuming an value of 1.5, plot the maximum time delay or dispersion for a step index and a graded index fibre for values of from 0.01 to 0.05 using the units "ns per km" and using a ommon axis for. δt GI = L.8 δt GI = L.8 By omparison the equivalent value for a step index fibre has been shown to be: δt SI = L n Beause of the dependene for graded index the dispersion is muh lower sine is << 1. δt SI = L n Using Singlemode Optial Fibre to Eliminate Modal Dispersion Small No modal dispersion sine only one mode propagates Most effetive way to overome modal dispersion Potential bandwidth is in the order of 0 THz