Lecture 2-5. Optical Fiber

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1 We use qualitative desciptio athe tha quatitative desciptio. What is fibe? - Best aswe is cicula ad vey log waveguide. - Geeal ideas fo guidig i a plaa waveguide is exteded to a cylidical waveguide - Fibe is a cylidical dielectic waveguide made of low-loss mateials such as silica glass. It has a cetal coe i which the light is guided, embedded i a oute claddig of slightly lowe efactive idex. Light icidet o the coe-claddig bouday at agles geate tha the citical agle udego total iteal eflectio ad ae guided though the coe without efactio. y y Coe φ z Fibe axis 2 1 The step idex optical fibe. The cetal egio, the coe, has geate efactive idex tha the oute egio, the claddig. The fibe has cylidical symmety. We use the coodiates, φ, z to epeset ay poit i the fibe. is omally much thicke tha show.?1999 S.O. Kasap, Optoelectoics (Petice Hall) How to make fibes? Pefom feed Buffe tube: d = 1mm Thickess moitoig gauge Fuace Potective polymeic coa : d = µ Coe: d = 8-10 µm Polyme coate Ultaviolet light o fuace fo cuig Take-up dum Capsta The coss sectio of a typical sigle-mode fibe with a tig tube. (d = diamete) Schematic illustatio of a fibe dawig towe. Vapos: SiCl 4 + GeCl 4 + O 2 Fuel: H 2 Bue Deposited soot Dyig gases Poous soot pefom with hole Fuace Pefom Fuace Taget od Deposited Ge doped SiO 2 Rotate madel (a) (b) Clea solid glass pefom (c) Daw fibe Schematic illustatio of OVD ad the pefom pepaatio fo fibe dawig. (a) Reactio of gases i the bue flame poduces glass soot that deposits o to the outside suface of the madel. (b) The madel is emoved ad the hollow poous soot pefom is cosolidated; the soot paticles ae siteed, fused, togethe to fom a clea glass od (c) The cosolidated glass od is used as a pefom i fibe dawig

2 - Need vey pecise cotol of coe ad claddig dimesio SiCl4 + O2 > SiO2 + 2Cl2 GeCl4 + SiO2 - Cotol of tempeatue ad speed of spoolig detemie the chaacteistics of fibes Mode pofile i fibe (a) The electic field of the fudametal mode (b) The itesity i the fudametal mode LP 01 (c) The itesity i LP 11 (d) The itesity i LP 21 Coe E E 01 The electic field distibutio of the fudametal mod i the tasvese plae to the fibe axis z. The light itesity is geatest at the cete of the fibe. Itesity pattes i LP 01, LP 11 ad LP 21 modes. - I the claddig, field decays expoetially. - I the coe, field becomes Bessel fuctio - I the fibe (cicula solutio), we o loge have simple TEm, TMm modes. Rathe that this they ae coupled with each othe. - LP (liea polaizatio) modes exist; The cylidical guide is bouded i two dimesios ad the eflectios occu fom all the sufaces. Sice ay adial diectio ca be epeseted i tems of x ad y, eflectios i both x ad y diectios ae ivolved i costuctive itefeece of waves ad we theefoe eed two iteges l ad m to label all the possible tavelig waves o guided modes. - LP lm mode m: m maxima alog diectio l: 2l maxima alog φ diectio V paamete vs. b (omalized popagatio costat ) 2πa / 2 ( β / k) V = ( ), b = λ The effect of vayig paametes of fibe o umbe of popagatio modes ca be deduced fom V paamete - Sice popagatio costat of LP mode depeds o the waveguide popeties ad wavelegth, it is easy to descibe i tems of omalized popagatio costat. - Give V-paamete of fibe we ca fid b, ad hece β, fo allowed LP modes fom the left figues b LP 01 LP 11 LP 21 LP 02 Nomalized popagatio costat b vs. V-umbe fo a step idex fibe fo vaious LP modes. V

Why is the fibe useful? - Oe of the extemely useful popety is low loss. 10 5 OH - absoptiopeaks 1.0 0.5 0.1 0.05 Rayleigh scatteig 1310 m Lattice absoptio 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.

3 Why is the fibe useful? - Oe of the extemely useful popety is low loss OH - absoptiopeaks Rayleigh scatteig 1310 m Lattice absoptio Wavelegth ( ) Illustatio of a typical atteuatio vs. wavelegth ch of a silica based optical fibe. Thee ae two commu chaels at 1310 m ad 1550 m.?1999 S O KasapOptoelectoics (Petice Hall) 1550 m - Atteuatio coefficiet is elated to fibe iput powe to fibe output powe P out = P i exp( αl) 1 P α i db = 10 log L P out P i L P out Itisic Loss Impuity (wate) - This is due to hydoxyl ios. It is difficult to emove all taces of hydoxyl (wate) poducts duig fibe poductio. Lattice vibatio - Some of eegy fom the popagatig wave is coveted to othe foms of eegy, fo example, to heat by the geeatio of lattice vibatios. As EM wave popagated, it displaces the oppositely chaged ios i opposite diectios ad foces them to vibate at the fequecy of the wave. A solid with ios E x Light diectio k z Lattice absoptio though a cystal. The field i the wave oscillates the ios which cosequetly geeate "mechaica waves i the cystal; eegy is theeby tasfeed fom the

4 Rayleigh scatteig - Rayleigh scatteig ivolves the polaizatio of a small dielectic paticle o a egio that is much smalle tha the light wavelegth. I optical fibe, dielectic ihomogeeities aise fom fluctuatios i the elative pemitivity that is pat of the itisic glass stuctue. - Rayleigh scatteig deceases with icease wavelegth. Theefoe blue llight with shote wavelegth tha ed wavelegth is scatteed moe stogly by ai molecules. Hece the sky is blue. A dielectic paticle smalle tha wavelegth Icidet wave Though wave Scatteed waves Rayleigh scatteig ivolves the polaizatio of a small dielectic paticle o a egio that is much smalle tha the light wavelegth. The field foces dipole oscillatios i the paticle (by polaizig it) which leads to the emissio of EM waves i "may" diectios so that a potio of the light eegy is diected away fom the icidet beam Extisic loss - If icidet agle is smalle tha citical agle, the thee will be o total iteal eflectio ad substatial light powe will be adiated ito the claddig ad evetually to the outside medium. Field distibutio Micobedig θ θ Coe θ < θ θ θ > θc θ Escapig wave R Shap beds chage the local waveguide geomety that ca lead to waves escapig. The zigzaggig ay suddely fids itself with a icidece agle θ that gives ise to eithe a tasmitted wave, o to a geate claddig peetatio; the field eaches the outside medium ad some light eegy is lost.?1999 S O K Ot l t i (P ti H ll) α B (m -1 ) fo 10 cm of bed λ = 633 m V 2.08 λ = 790 m V Radius of cuvatue (mm) Measued micobedig loss fo a 10 cm fibe bet by diffeet amouts of adius of cuvatue R. Sigle mode fibe with a coe diamete of 3.9 µ m, claddig adius 48 µ m, = 0.004, NA = 0.11, V 1.67 ad 2.08 (Data extacted ad eplotted with coectio fom, A.J. Hais ad P.F. Castle, IEEE J. Light Wave Techology, Vol. LT14, pp , 1986; see oigial aticle fo discussio of peaks i α B vs. R at 790 m).?1999 S O O l ( i ll)

5 Howeve the above metioed atteuatio(loss) ca be compesated by amplifies. The, what will be aothe limit that esticts log-haul optical fibe commuicatio? That is Dispesio. Iteodal dispesio - Whe a light pulse is fed ito the fibe, it tavels dow the fibe though vaious modes. These modes popagate with diffeet goup velocities ad theefoe emege at the ed of the fibe with a spead of aival times, which meas that output pulse is a boadeed vesio of the iput pulse. This is a itemodal dispesio. - I fact, eve if sigle mode fibe, thee is small amout of dispesio. Sice thee is cetai amout of badwidth of the pulse. diffeet λ diffeet efactive idex diffeet goup velocity f 0 Waveguide dispesio - Waveguide dispesio is due to the depedece of the goup velocity of the fudametal mode o the V-paamete, which depeds o the souce wavelegth, eve if 1 ad 2 wee costat. Mateial dispesio - It is due to the vaiatio of the efactive idex 1 of the coe glass with wavelegth of light coupled ito the fibe. The popagatio velocity of the guided wave alog the fibe coe depeds o 1, which i tu depeds o the wavelegth. - This dispesio esults fom the wavelegth depedece of the mateial popeties of the guide. Iput Emitte Vey shot light pulse v g (λ 1 ) Coe v g (λ 2 ) Output Itesity Itesity Itesity Spectum, λ Spead, τ λ λ λ 1 o 2 λ 0 t τ t All excitatio souces ae iheetly o-moochomatic ad emit withi a spectum, λ, of wavelegths. Waves i the guide with diffeet fee space wavelegths tavel at diffeet goup velocities due to the wavelegth depedece of 1. The waves aive at the ed of the fibe at diffeet times ad hece esult i a boadeed output pulse.?1999 S.O. Kasap, Optoelectoics (Petice Hall)

6 Dispesio paamete (D) T1 T2 T = T 2 T1 T = DL λ time ps [ D]dim esio = = legth Badwidth km m dt d L d 1 ==> T = λ = ( ) = ( ) L λ dλ dλ v g dλ v g D!! Dispesio shifted fibe - Remembe that waveguide dispesio depeds o the V-paamete. That meas we ca chage the shape of the fibe. - Dispesio aises because of the fiite width wavelegth of the souce spectum. This type of dispesio caused by a age of souce wavelegths is geeally temed chomatic dispesio ad icludes both mateial ad waveguide dispesio sice both deped o λ. - By suitably desigig the guide, zeo dispesio wavelegth ca be shifted. Such fibes ae called dispesio shifted fibes. Dispesio coefficiet (ps km -1 m -1 ) D m 0-10 λ 1 λ 2 D ch = D m + D w -20 D w λ (µm) Thi laye of claddig with a depessed idex Dispesio flatteed fibe example. The mateial dispesio coefficiet (D m ) fo the coe mateial ad waveguide dispesio coefficiet (D w ) fo the doubly clad fibe esult i a flatteed small chomatic dispesio betwee λ 1 ad λ S O Kasap Optoelectoics (Petice Hall) Dispesio compesatio D1=16ps/km m D2=? L1 L2 D1 L1 + D2L2 = 0 L1 D2 = D1 L2 slicig

Module II: Part A. Optical Fibers

Module II: Part A. Optical Fibers Module II: Pat A Optical Fibes Optical Fibes as Tasissio Mediu Mai Liitatio: Atteuatio Although fibes have bee kow sice the 8 s as ediu fo light tasissio, thei pactical use becae evidet whe losses whee