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Optical Fibres - Dispersion Part 2 [Group Velocity Dispersion]

ECE 455 ecture 06 1 Optical Fibres - Dispersio Part [Group Velocity Dispersio] Stavros Iezekiel Departmet of Electrical a Computer Eieeri Uiversity of Cyprus HMY 445 ecture 06 Fall Semester 016 ECE 455
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ECE 455 ecture 06 1 Optical Fibres - Dispersio Part [Group Velocity Dispersio] Stavros Iezekiel Departmet of Electrical a Computer Eieeri Uiversity of Cyprus HMY 445 ecture 06 Fall Semester 016 ECE 455 ecture 06 CHROMATIC DISPERSION WHAT WE KNOW SO FAR ECE 455 ecture 06 3 If we have a pulse of liht which is ot moochromatic (it cotais a roup of waveleths), the we will have chromatic ispersio: U. of Washito Optical fibre z Material ispersio Waveuie ispersio Due to oliear relatioship betwee a Itramoal (chromatic) ispersio Dispersio ue to fact that roup velocity chaes with waveleth Due to refractive iex profile of the fibre. Chaes with. ECE 455 ecture 06 4 v p v k Phase velocity k Group velocity v v p v v p ispersio o ispersio v v p v v p v v p aomalousispersio ormal ispersio k ECE 455 ecture 06 5 GROUP VEOCITY DISPERSION ECE 455 ecture 06 6 Wavepackets So far we have cosiere just two, very closely space frequecies withi the roup emitte by a optical source such as a laser: Itesity (arbitrary uits) We ow look at the whole spectrum. 0 δ Wave packet A short pulse compose of the sum of waves over a fiite bawith. If we cosier the etire spectrum emitte by the source, we still obtai a moulate waveform, with a roup velocity a phase velocity as before. ECE 455 ecture 06 7 UCSD ECE 455 ecture 06 8 We ca prove the properties of the wavepacket by usi the Fourier trasform: f ( t) Fourier j t 1 j t F( ) e F( ) f ( t e t ) π (1) Time omai Frequecy omai F() This represets optical source spectrum; has a aussia profile 0 -δ δ peak frequecy ECE 455 ecture 06 9 We ca thik of F() as bei equal to some spectrum G() which is ietical i shape, but cetre at 0 istea of 0 : G() F() -δ 0 δ 0 -δ δ By ispectio, F ) G( ) ( 0 (13) F( ) 1 π f ( t) e t G( ) 0 1 π ( t) e j ( )t j t 1 j0 t j t ( t) e e t π (14) (15) 0 t ECE 455 ecture Hece: 0 f ( t) ( t) e j t (16) Correspos to siusoi at optical frequecy 0 1,5 Impulse respose of: G() 1 0, ,5 1 1,5-0,5-1 -1,5 0 ives: (t) 0 N.B. Fourier trasform of a aussia pulse is also aussia i shape ECE 455 ecture I other wors, the impulse respose associate with the optical source takes o the form of a wavepacket: (t) t f (t) This wavepacket represets a pulse of liht emitte by the optical source, a it cotais a rae of frequecies (i.e. waveleths). We ow ee to examie what will happe to the roup velocity of this pulse as it propaates alo a fibre. ECE 455 ecture 06 1 Cosier a optical pulse lauche ito a sile moe fibre. Due to the spectral with of the source, this pulse cosists of a roup of waveleths which travel at the roup velocity: optical power v k waveleth 0 istace ECE 455 ecture So the time take for the waveroup to travel a istace alo the fibre is ive by the roup elay τ : τ v k (17) The phase velocity of the peak waveleth 0 is ive by: v p k c k c (18) Substituti (18) ito (17): τ k + c 1 (19) ECE 455 ecture Eq. (3) shows that the roup elay per uit leth epes o both a /. It is also epeet o the frequecy. However, we prefer to work with waveleth istea: istea of... From the iverse relatioship betwee frequecy a waveleth (c f /π), we fi that: τ 1 + c c 1 (0) ECE 455 ecture τ c c c Derivatio of equatio (0): π π c c f c f c ECE 455 ecture Group Refractive Iex Imaie we have a fibre with core refractive iex. I this case, v p k c (1) If we trasmit a sprea of waveleths, the we ca rear the resulti roup as ecouteri a roup refractive iex, a this is efie via: v k c () c v (3) ECE 455 ecture τ c (4) varies with waveleth: 0 v v ispersio I fact, will also be waveleth epeet: (5) ECE 455 ecture Miimum 0 Poit of iflectio µm For silica lass: At 1.31 µm, has a poit of iflectio, is miimum, a the roup velocity is therefore maximum. ECE 455 ecture Group velocity ispersio (GVD) We kow that: A optical source emits a sprea of waveleths cetre o 0. This ca be represete by a wavepacket which travels at the roup velocity a therefore sees a roup iex. However, a thus the roup velocity v a elay τ are all waveleth epeet. Each ifferet spectral compoet emitte by the source will travel at ifferet roup velocities, a this GVD is the cause of material ispersio. ECE 455 ecture 06 0 Cosier the elay ifferece (per uit leth) for a waveleth δ away from the cetral waveleth 0 : τ c δ δτ 1 τ ( 0 ) 1 τ ( 0 + δ) δ If the waveleth ifferece is sufficietly small, we ca elect seco-orer terms i a Taylor series expasio to et: τ ( 0 + δ) τ ( 0) δ τ 0 (6) ECE 455 ecture 06 1 Cosier the elay ifferece (per uit leth) for a waveleth δ away from the cetral waveleth 0 : 1 δτ δ 1 τ 0 From (0): τ c 1 1 δτ δ c (7) Material ispersio D mat Uits: ps/( ECE 455 ecture 06 Group iex, refractive iex a material ispersio for silica lass (SiO ) material ispersio (ps/m-km) leth (km) (11) σ mat D mat σ sprea i time (ps) sprea i waveleth (m) D mat c ECE 455 ecture 06 3 DISPERSION MANAGEMENT ECE 455 ecture 06 4 Dispersio moifie fibres For covetioal sile-moe optical fibre: miimum atteuatio occurs at 1.55 µm miimum ispersio occurs at 1.3 µm Furthermore, optical amplifiers operate i the 1.55 µm reio I respose to this, ispersio moifie fibres have bee evelope to provie miimal ispersio at 1.55 µm ECE 455 ecture 06 5 Structure epeet losses (waveuie losses) have little effect o overall atteuatio, so chai the refractive iex profile i sile-moe fibre will have eliible impact o atteuatio. However, chai the refractive iex will moify the waveuie ispersio term, a this ca be use to our avatae. I fact, the refractive iex profile ca be tailore to shift the ispersio zero to 1.55 µm or to flatte the ispersio vs. waveleth profile so that ispersio is almost zero betwee 1.3 µm a 1.55 µm ECE 455 ecture 06 6 Chai the refractive iex profile chaes the waveuie ispersio: Dispersio flattee Dispersio shifte ECE 455 ecture 06 7 Dispersio shifte Dispersio flattee
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