Lecture 10. Erbium-doped fiber amplifier (EDFA) Raman amplifiers Have replaced semiconductor optical amplifiers in the course

Transcription

1 ecture 1 Two tye of otical amlifier: Erbium-doed fiber amlifier (EDFA) Raman amlifier Have relaced emiconductor otical amlifier in the coure Fiber Otical Communication ecture 1, Slide 1

2 Benefit and requirement Benefit: Eliminate the need for otoelectronic regenerator in lo-limited ytem Can imrove the receiver enitivity Can increae the tranmitted ower Can be ued at all bit rate and for all modulation format Can amlify many WDM channel imultaneouly Requirement: An ideal amlifier ha High gain, high outut ower, and high efficiency arge gain bandwidth No olarization enitivity ow noie No crotalk between WDM channel Ability to amlify broadband analog and digital ignal (khz 1 GHz) low couling loe to otical fiber Fiber Otical Communication ecture 1, Slide 2

3 Amlifier alication Four main alication: In-line: Comenate for tranmiion loe ower am: Increae the tranmitter outut ower re-am: Enhance the enitivity of the receiver (AN am: Comenate for couling loe in a network) Fiber Otical Communication ecture 1, Slide 3

4 Amlifier tye Doed fiber amlifier ue excitation of ion in the hot fiber The erbium-doed fiber amlifier (EDFA) i mot common Otically umed by laer light at higher energy (horter wavelength) Raman and Brillouin amlifier ue nonlinear rocee to tranfer energy from the um wave to the ignal Vibration (honon) in the ilica gla are involved in the roce arametric amlifier ue a nonlinear roce (FWM) to tranfer energy from the um wave to the ignal Semiconductor otical amlifier (SOA) are electrically umed Alo called emiconductor laer amlifier (SA) In rincile, a emiconductor laer biaed below threhold Fiber Otical Communication ecture 1, Slide 4

5 General concet Amlification can be lumed or ditributed An EDFA i lumed Gain occur in a hort iece of fiber Raman amlifier are often ditributed Gain occur within the tranmiion fiber itelf An EDFA relie on timulated emiion A timulated tranition to a lower energy level emiion of a hoton Energy i umed into the medium to induce oulation inverion Without oulation inverion, abortion will dominate Even in the abence of an inut hoton, ontaneou emiion occur Will add noie in otical amlifier In a Raman amlifier, ower i tranferred from a um wave um ha horter wavelength (1.45 μm for 1.55 μm ignal) uming can be done in forward or backward direction (or both) Backward uming minimize tranfer of um intenity noie Fiber Otical Communication ecture 1, Slide 5

6 umed veru ditributed amlification (7.1.2) umed amlification The otical ower decreae a out = in ex( αz) With amlifier acing A, the gain i adjuted to G = ex(α A ) Tyical acing i 3 1 km The acing mut not necearily be uniform dz [ g ( z) ] dz Denoting the gain by g (z), we get Ditributed amlification Ideally g (z) = α, but the um ower i not contant gain decreae with ditance from um ource Condition for comenation over ditance A i z A g ( z) dz A A i then known a um-tation acing Fiber Otical Communication ecture 1, Slide 6

7 Fiber Otical Communication ecture 1, Slide 7 Bidirectional uming cheme (7.1.3) In bidirectional uming, the gain i α i the lo at the um wavelength g 1 and g 2 are contant roortional to the launched um ower Auming equal um ower and that initial and final ignal ower = 1 Auming backward uming (g 1 = ) Figure how backward and bidirectional Raman amlification EDFA cae hown for comarion Raman even out ower fluctuation )] ( ex[ ) ex( ) ( 2 1 z g z g z g A z z z A A A A 2) / 2inh( 2) / inh( 2) / ( inh[ ex ) ( z z z A A 1 ) ex( 1 ) ex( ex ) (

8 We conider Gain in a umed medium A two-level ytem, i.e., there are two different energy level oulation inverion i obtained with either otical or electrical uming The gain coefficient, g [m -1 ], deend on the frequency ω and the intenity of the ignal being amlified The gain ha a orentzian hae g g T2 g i the eak gain coefficient determined by the amount of uming ω and T 2 are material arameter at The aturation ower i denoted by at When = at, we have g( 1 g ) 2 Fiber Otical Communication ecture 1, Slide 8

9 Unaturated gain When << at, we can neglect the aturation term The FWHM bandwidth of the ectrum i g g /( 2 ) 1/( T2 ) The amlifier bandwidth i of more interet Ue d dz z to get the ower gain z ex[ g( ) z The amlifier bandwidth i obtained from G and i found to be g z ] out in a g g ex[ g ln 2 ln 2 ] Fiber Otical Communication ecture 1, Slide 9

10 Study the gain at the gain eak d dz z Saturated gain z z g 1 Integrating uing () = in and () = out, we get G1 out out G at G Ge in G i the mall ignal gain The outut aturation ower i defined a the ower when G = G /2 Indeendent of G for large gain G ln 2 at G g e G 1 at ln 2. at at out at 7 G 2 Fiber Otical Communication ecture 1, Slide 1

11 Erbium-doed fiber amlifier (EDFA) (7.2) The ilica fiber act a a hot for erbium ion Erbium can rovide gain cloe to 1.55 μm Otically umed to an excited tate to obtain gain Fiber Otical Communication ecture 1, Slide 11

12 uming and gain ectrum (7.2.1) The energy level of Er 3+ ion have energy level uitable to amlify light in the 155 nm region Gain eak i at 153 nm Bandwidth i 4 nm The EDFA i otically umed at 148 nm or 98 nm 98 nm give better erformance Abortion and gain ectra are een in the figure Abortion i for unumed fiber Gain ectrum i hifted toward longer wavelength Fiber Otical Communication ecture 1, Slide 12

13 Energy level in Erbium are broadened into band The gain ectrum i continuou EDFA energy tate Tyical denity of Erbium in the fiber i 1 19 ion/cm 3 Relative concentration of 5 m comared to index-raiing doant Erbium i a mall erturbation Two oible um wavelength: 98 nm ( 4 I 15/2 4 I 11/2 tranition), decay raidly to 4 I 13/2 148 nm ( 4 I 15/2 4 I 13/2 tranition), uming to edge of the firt excited tate The 4 I 13/2 tate i called the meta-table tate, lifetime of 1 m Uually ufficient to conider only the ground tate and the meta-table tate The EDFA can be aroximated a a two-level ytem Fiber Otical Communication ecture 1, Slide 13

14 EDFA gain ectrum The EDFA gain ectrum deend on The co-doant (uually germanium) The um ower The erbium concentration Figure how tyical gain ectrum at large um ower and abortion ectrum (without uming) The tranition cro-ection decribe the medium caability of roducing gain and abortion the EDFA cro-ection i different for abortion and emiion and different for the um (σ a, σ e ) and the ignal (σ a, σ e ) Fiber Otical Communication ecture 1, Slide 14

15 EDFA characteritic Advantage High gain (u to 5 db oible) ow noie figure (3 6 db) (noie i dicued in next lecture) High aturation ower (> 2 dbm) Small couling lo to otical fiber No cavity no gain frequency deendence due to reflection No olarization deendence Doe not chir ignal ong excited tate oulation lifetime no crotalk Diadvantage Not very comact (comared to a emiconductor laer) Oerate at a fixed wavelength Relie on external otical um (not electrically umed) Fiber Otical Communication ecture 1, Slide 15

16 Two-level model (7.2.2) The erbium oulation denity i N 2 in the meta-table tate and N 1 in the ground tate N 1 + N 2 = N t = total erbium denity We here aume σ a = σ, σ e, σ a σ e = σ, lo i negligible The rate equation decribe the evolution of the denitie dn N1 ( N dt The hoton fluxe are N 2 1 2) a, are the cro-ectional area for the fiber mode Signal and um ower evolve according to Γ, are the mode d N N confinement factor dz ( ) 2 1 Thi give dn2 1 d 1 d N dt a h dz a h dz T Fiber Otical Communication ecture 1, Slide 16 N T 1 2 dn 1 dn 2 dt dt a h 1 2 d a h dz N 1

17 Fiber Otical Communication ecture 1, Slide 17 Two-level model A teady-tate olution i obtained by etting the time derivative to zero We obtain equation for the ower according to where α, = σ, Γ, N t are um and ignal abortion coefficient and Ue N 1 and N 2 olution in and eq on lat lide, integrate z = to dz d h a T dz d h a T N ' ' ' dz d ' ' ' dz d at ' at ' 1,,, at, T h a at at ex a a e 2 / 2 / ex at at a a e

18 EDFA gain modeling reult The (imlicit) analytical exreion can be ued to tudy the EDFA gain um ower increae mall-ignal gain increae Until all ion are excited, full oulation inverion, give lowet noie figure onger EDFA more ion to excite (otentially) larger gain For fixed um ower, an otimal length exit that maximize the gain horter fiber the um ower i not fully ued too long fiber art of EDFA i not ufficiently umed 35 db gain can be realized with < 1 mw um ower Fiber Otical Communication ecture 1, Slide 18

19 Multi-channel amlification in EDFA: Sytem aect of EDFA T 1,EDFA 1 m, the amlifier i low to react on changing inut ower No roblem related to gain modulation when doing WDM amlification Accumulation of ASE: In cacaded EDFA, ASE will caue two articular roblem Increaing degradation of the SNR after each amlifier Eventually gain aturation caued by the ASE le ignal gain ule amlification in EDFA: Amlification of ule in aturated EDFA do not uffer from chir or ditortion due to gain dynamic For very hort ule (< 1 ) however: Gain i reduced in the ectral wing due to the finite bandwidth GVD and nonlinearitie will influence the ule (EDFA length 1 m) Fiber Otical Communication ecture 1, Slide 19

20 Raman amlifier (7.3) Raman amlifier are baed on timulated Raman cattering The um and the ignal co-roagate ower i tranferred during tranmiion The um wavelength i horter than the ignal wavelength The exce energy i given to the medium (the fiber) A molecular vibration (otical honon) i created The um and ignal can roagate in different direction Fiber Otical Communication ecture 1, Slide 2

21 Raman gain and bandwidth (7.3.1) The Raman gain ectrum i a roerty of amorhou gla The Raman gain coefficient i roortional to the um intenity I gr( ) g(, z) gr( ) I ( z) ( z) a a i the cro-ectional area of the um beam, deend on fiber tye DCF ha a mall core diameter and a large g R /a Figure how g R /a and normalized gain Gain eak at 13.2 THz Shift between aborbed and emitted hoton i called Stoke hift Similar gain ectra for all fiber The FWHM of the gain eak i nearly 6 THz Require rather high ower Examle (ee the book): G > 2 db require > 5 W in a 1-km-long fiber Fiber Otical Communication ecture 1, Slide 21

22 Raman induced ignal gain (7.3.2) Conider a CW ignal and a CW um Frequency ratio occur ince um hoton have higher ower If the um i undeleted (affected only by lo), we have The amlifier gain i given by d d ( ) ()ex[( g / a ) () eff ] R / dz / dz eff ( g R / a ) ( / )( g [1 ex( )]/ R / a ) G A ex( g ), g g a { gr a eff R 1} Obtained a (outut ower with Raman)/ (outut ower without Raman) Figure how: Amlifier gain increae exonentially......until gain aturation occur Fiber Otical Communication ecture 1, Slide 22

23 Raman induced ignal gain The um ulie the ignal with ower When the tranferred energy i ignificant, the um i deleted The gain i decreaed, referred to a gain aturation The aturated amlified gain can be found numerically... ike in figure on reviou lide...or analytically, auming α = α, a G (1 r r )ex( ), (1 r ) G A r () () Figure how gain-aturation characteritic Gain i reduced by 3 db when G A r 1 In a ytem, Raman amlifier tyically oerate in the unaturated regime Fiber Otical Communication ecture 1, Slide 23

24 Multile-um Raman amlification (7.3.3) A WDM ytem with many channel require broadband amlifier 1 channel may require uniform gain over 7 8 nm (1 THz) Broadband amlification can be achieved with Hybrid EDFA/Raman amlification Raman amlification uing multile um laer Multile-um Raman amlification Will et u a ueroition of gain ectra I more broadband ince it i flatter Require careful election of the um wavelength Will determine the gain rile Require conideration of um um interaction The um wave are affected by the Raman interaction In general, thi i tudied numerically A large couled ytem of differential equation mut be olved Fiber Otical Communication ecture 1, Slide 24