Lecture 6. Erbium-doped fiber amplifier (EDFA) Raman amplifiers Have replaced semiconductor optical amplifiers in the course

Transcription

1 Lecture 6 wo tye of otical amlifier: Erbium-doed fiber amlifier (EDFA) Raman amlifier Have relaced emiconductor otical amlifier in the coure Fiber Otical Communication Lecture 6, 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 Large gain bandwidth No olarization enitivity Low noie No crotalk between WDM channel Ability to amlify broadband analog and digital ignal (khz 100 GHz) low couling loe to otical fiber Fiber Otical Communication Lecture 6, Slide

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 (LAN am: Comenate for couling loe in a network) Fiber Otical Communication Lecture 6, Slide 3

4 Fiber Otical Communication Lecture 6, Slide 4

5 Electrical ymbol rate: 3.4Gbd olarization multilexed 64QAM format 7 laer at 33 GHz acing (SE = 7.1 b//hz) covering 73 nm Bit rate: 3.4 G x x 6 x 7 = 105,8 b/ 66.7% overhead 63.5 b/ data rate Fiber Otical Communication Lecture 6, Slide 5

6 5380 km tranmiion Fiber Otical Communication Lecture 6, Slide 6

7 Amlifier tye Doed fiber amlifier ue excitation of ion in the hot fiber he 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 (SLA) In rincile, a emiconductor laer biaed below threhold Fiber Otical Communication Lecture 6, Slide 7

8 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 Lecture 6, Slide 8

9 Lumed veru ditributed amlification (7.1.) Lumed amlification he otical ower decreae a out = in ex( αz) With amlifier acing L A, the gain i adjuted to G = ex(αl A ) yical acing i km he acing mut not necearily be uniform dz [ g 0 ( z) ] dz Denoting the gain by g 0 (z), we get Ditributed amlification Ideally g 0 (z) = α, but the um ower i not contant gain decreae with ditance from um ource Condition for comenation over ditance L A i z LA 0 g0 ( z) dz L A L A i then known a um-tation acing Fiber Otical Communication Lecture 6, Slide 9

10 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 he gain coefficient, g [m -1 ], deend on the frequency ω and the intenity of the ignal being amlified he gain ha a Lorentzian hae g0 g 1 0 g 0 i the eak gain coefficient determined by the amount of uming ω 0 and are material arameter at he aturation ower i denoted by at When = at, we have g( 1 g 0 ) 0 Fiber Otical Communication Lecture 6, Slide 10

11 Unaturated gain When << at, we can neglect the aturation term he FWHM bandwidth of the ectrum i g g /( ) 1/( ) he amlifier bandwidth i of more interet Ue d dz z to get the ower gain z 0 ex[ g( ) z he amlifier bandwidth i obtained from G and i found to be g z ] out in a g L 0 g ex[ g ln L ln 0 L] Fiber Otical Communication Lecture 6, Slide 11

12 Study the gain at the gain eak d dz z Saturated gain z z g0 1 Integrating uing (0) = in and (L) = out, we get G1 out out G at G G0e in G 0 i the mall ignal gain he outut aturation ower i defined a the ower when G = G 0 / Indeendent of G 0 for large gain G ln at G 0 0 g e G 0 1 at ln 0. at at 0 out at 7 G0 L Fiber Otical Communication Lecture 6, Slide 1

13 Erbium-doed fiber amlifier (EDFA) (7.) he 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 Lecture 6, Slide 13

14 uming and gain ectrum (7..1) he energy level of Er 3+ ion have energy level uitable to amlify light in the 1550 nm region Gain eak i at 1530 nm Bandwidth i 40 nm he EDFA i otically umed at 1480 nm or 980 nm 980 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 Lecture 6, Slide 14

15 Energy level in Erbium are broadened into band he gain ectrum i continuou EDFA energy tate yical denity of Erbium in the fiber i ion/cm 3 Relative concentration of 500 m comared to index-raiing doant Erbium i a mall erturbation wo oible um wavelength: 980 nm ( 4 I 15/ 4 I 11/ tranition), decay raidly to 4 I 13/ 1480 nm ( 4 I 15/ 4 I 13/ tranition), uming to edge of the firt excited tate he 4 I 13/ tate i called the meta-table tate, lifetime of 10 m Uually ufficient to conider only the ground tate and the meta-table tate he EDFA can be aroximated a a two-level ytem Fiber Otical Communication Lecture 6, Slide 15

16 EDFA gain ectrum he EDFA gain ectrum deend on he co-doant (uually germanium) he um ower he erbium concentration Figure how tyical gain ectrum at large um ower and abortion ectrum (without uming) he 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 Lecture 6, Slide 16

17 EDFA characteritic Advantage High gain (u to 50 db oible) Low noie figure (3 6 db) (noie i dicued in next lecture) High aturation ower (> 0 dbm) Small couling lo to otical fiber No cavity no gain frequency deendence due to reflection No olarization deendence Doe not chir ignal Long 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 Lecture 6, Slide 17

18 wo-level model (7..) he erbium oulation denity i N in the meta-table tate and N 1 in the ground tate N 1 + N = N t = total erbium denity We here aume σ a = σ, σ e 0, σ a σ e = σ, lo i negligible he rate equation decribe the evolution of the denitie dn N1 ( N dt he hoton fluxe are N 1 ) 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 ( ) 1 hi give dn 1 d 1 d N dt a h dz a h dz Fiber Otical Communication Lecture 6, Slide 18 N 1 dn 1 dn dt dt a h 1 d a h dz N 1

19 Fiber Otical Communication Lecture 6, Slide 19 wo-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 olution in and eq on lat lide, integrate z = 0 to L dz d h a dz d h a N 1 1 ' ' ' 1 1 dz d ' ' ' 1 1 dz d at ' at ' 1,,, at, h a at at 0 0 ex 0 L L a a L e L / 0 / 0 ex 0 at at L L a a L e L

20 EDFA gain modeling reult he (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 Longer 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 < 10 mw um ower Fiber Otical Communication Lecture 6, Slide 0

21 Multi-channel amlification in EDFA: Sytem aect of EDFA 1,EDFA 10 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 100 m) Fiber Otical Communication Lecture 6, Slide 1

22 Lecture Noie from otical amlifier EDFA noie Raman noie Otical SNR (OSNR), noie figure, (electrical) SNR Amlifier and receiver noie ASE and hot/thermal noie reamlification for SNR imrovement Fiber Otical Communication Lecture 6, Slide

23 All amlifier add noie Amlifier noie o amlify (make a larger coy), a hyical device mut oberve the ignal Cannot be done without erturbing the ignal Aured by the Heienberg uncertainty rincile Lumed and ditributed amlification have different erformance Noie come from ontaneouly emitted hoton hee have random direction olarization frequency (within the band) hae Some of thee add to the ignal Caue intenity and hae noie Fiber Otical Communication Lecture 6, Slide 3

24 Otical ignal are often characterized by the otical SNR (OSNR) Eaily meaured with an otical ectrum analyzer (OSA) Make ignal monitoring in the lab eay i very oular he definition of the OSNR i Definition of the otical SNR OSNR ignal, X noie, X ignal, Y noie, Y {Foringle olarization ignal} ignal ASE he index X and Y denote the two olarization he OSNR i related to the SNR, Q, and BER OSNR i uually normalized to a 0.1 nm bandwidth Entire ignal ower i included, noie i meaured over 0.1 nm Imlie required OSNR (for given BER) i bit rate-deendent OSNR Fiber Otical Communication Lecture 6, Slide 4

25 EDFA noie (7..3) he noie i called amlified ontaneou emiion (ASE) I being amlified ince there i gain Will reach the receiver (remaining otical ath i amlified) he ASE ower at the outut of the EDFA ASE SASE o nh 0( G 1) o Δν 0 i the effective bandwidth of the otical filter ued to ure noie S ASE i the (oneided) noie ower ectral denity (SD) hi i the ower er olarization n i the ontaneou-emiion factor alo known a the oulation-inverion factor For an EDFA n e N e N N a 1 N N N 1 1 Fiber Otical Communication Lecture 6, Slide 5

26 OSNR due to EDFA noie (7.4.1) he OSNR i reduced each time a ignal i amlified Each EDFA add to the noie SD due to the generation of more ASE After N A amlifier in a link with an lo equal to the gain in each amlifier and with identical EDFA noie erformance, we have OSNR In db and dbm at 1550 nm and Δν 0 = 0.1 nm, we have OSNR N db in in N n [dbm] N A in h ( G 1) [db] n N n in h A ASE A o o A o 0. 1 [db] G[dB] 58dBm G 1 N A L EDFA A Fiber Otical Communication Lecture 6, Slide 6

27 OSNR due to EDFA noie, examle What i the max. tranmiion ditance with 100 km or 50 km EDFA acing? A 10 Gbit/ ytem with a OSNR requirement of 0 db he lo i 0.5 db/km and n = 5 db he launched ower into each an i 1 mw er WDM channel OSNR [dbm] N [db] n [db] G[dB] 58dBm db in L A = 100 km N A = 8 db = am 700 km L A = 50 km N A = 0.5 db = am 5650 km he amlifier acing lay a critical role for the OSNR Short L A : Noie accumulate lowly high OSNR at receiver Long L A : Few EDFA are needed ytem cot i lower Show trade-off between cot and erformance echnique that enable cot reduction are deirable hi can, for examle, be error correction or ditributed amlification Hint that ditributed amlification may erform better A Fiber Otical Communication Lecture 6, Slide 7

28 OSNR due to EDFA noie, amlifier acing We can exre the number of amlifier a L i the total ytem length hi give the OSNR in ln G OSNR nh 0 0.1L We ee that Figure how maximum ytem length = ytem reach OSNR = 0 db α = 0. db/km n =1.6 Δν 0 = 100 GHz ASE G 1 ln G ( G 1) N A L ln G Fiber Otical Communication Lecture 6, Slide 8

29 Electrical ignal-to-noie ratio (SNR) (7.5.1) he Q and BER are determined by the SNR in the detected current Agrawal call thi electrical ignal-to-noie ratio to earate from OSNR An EDFA can imrove the enitivity of a thermally noie limited receiver A reamlified otical receiver he added otical noie can be much maller than the thermal noie he generated hotocurrent in the receiver i E c = ASE co-olarized with ignal E o = ASE orthogonal with ignal i = Shot noie i = hermal noie he ASE ha a broad ectrum, and can be written he magnitude quare i a multilication new frequencie are generated beating I E in R d G n GE E c BF E o i receiver i M 1/ c ( SASE ) ex( im imt) m1 Fiber Otical Communication Lecture 6, Slide 9

30 Electrical ignal-to-noie ratio (SNR) he received electrical current i i ig- = ignal-ase beat noie term I R i - = ASE-ASE beat noie term he variance of the noie term are d G i ig i i i ig 4R d GS ASE f q R ( G ) f d ASE 4R d SASEf ( 0 f (4k / R ) f B L / ) Δν 0 i bandwidth of otical banda filter (reject out-of-band noie) he SNR i here defined a SNR I ig ( R d G ) Fiber Otical Communication Lecture 6, Slide 30

31 Imact of ASE on SNR (7.5.) Let u comare the SNR without and with amlification by an EDFA Amlifier and banda filter i inerted before the receiver SNR noam Notice that σ are different in the two cae (σ tay the ame) We neglect σ - and the noie current contribution to hot noie to get SNR am ( RdG ) (qrd f ) SNR (4R GS f ) (qr Gf ) ( R ) noam We ue the SD and the ideal reonivity n h ( G 1) { G 1 n h G We get SNR ( R ) d d ASE, SNR am SASE 0 } 0 SNR am noam n 1 k 1/ G k d Notice: k i ratio (thermal noie)/(hot noie) without amlification All quantitie in the denominator (qr d Δf) are ket contant! Fiber Otical Communication Lecture 6, Slide 31 d / G ig ( R G ) k R d q d /( h ) 0 qr f d

32 A thermal noie-limited receiver How i the SNR changed in the thermal limit? Firt aume that thermal noie dominate before and after amlification SNR am 1 k k G SNR n 1/ G k / G k / G noam here i a huge imrovement in the SNR Signal ower i increaed, noie ower remain contant However, at high G, we cannot ignore the other noie term Study the realitic cae that thermal noie dominate before and i negligible after amlification SNR SNR am noam n SNR imrovement aturate a G i increaed Imrovement can be very large 1 k 1/ G k Fiber Otical Communication Lecture 6, Slide 3 / G n In the thermal limit, amlification imrove the SNR k 1/ G k n

33 A hot noie-limited receiver, noie figure (7..3) Now intead aume that the otical ignal ha high ower hermal noie i negligible SNR SNR am noam n he SNR i decreaed by the amlification he noie figure i defined 1 k 1/ G k he SNR value are what you would obtain by utting an ideal receiver before and after an EDFA, reectively Ideal mean hot noie-limited, 100% quantum efficiency Our tudy above ha rovided u with the (invere) minimum value Fiber Otical Communication Lecture 6, Slide 33 / G n 1 1/ G EDFA amlification of a erfect ignal decreae the SNR by > n (> 3dB) NF F n F n (SNR) (SNR) n in out 1 n

34 For an EDFA, the noie figure i Noie figure In reality, N 1 and N change along the EDFA um ower and ignal ower are not contant he rate equation can be olved numerically Figure how Noie figure and amlifier gain a a function of......um ower and amlifier length A long amlifier Can rovide high gain Require high um ower e F n n N N n 1 e a N N N N 1 1 Fiber Otical Communication Lecture 6, Slide 34

35 he noie figure i increaed Noie figure If the oulation inverion i incomlete (omewhere in the amlifier) If there are couling loe into the amlifier uming i facilitated by uming at 980 nm No timulated emiion caued by um hoton (σ e 0) Correonding energy level i almot emty (hort-lived) Noie figure 3 db i oible, 3. db ha been meaured With 1480 nm uming σ e 0 Ground tate will alway be oulated by ome ion Some excited ion will be timulated by um hoton to relax Noie figure i larger for thi cae Couling into and out of an EDFA i efficient yical EDFA module have F n = 4 6 db Fiber Otical Communication Lecture 6, Slide 35

36 SNR/OSNR relation In general, there i no imle relation between the OSNR and the SNR OSNR i ro. to the otical ower, SNR i ro. to the electrical ower Electrical ower i roortional to the (otical ower) Not true in a coherent receiver When ignal ASE noie i dominating we have ( RdG ) G SNR 4R GS f 4 f f d For a ingle-olarization ignal, we can ue E f OSNR S S ASE OSNR E i the energy er ymbol, f i the ymbol rate (in baud) E /S ASE i often written E /N 0 i digital communication literature he relation between E /N 0 and the BER deend on the tye of receiver, modulation format and more ASE ASE 0.1 ASE 0.1 Fiber Otical Communication Lecture 6, Slide 36

37 Receiver enitivity and Q factor (7.6.1) When hot noie and thermal noie are negligible: he tatitic are not Gauian (cannot have negative current)......but Gauian tatitic are often ued anyway for imlicity 1 ig ig he receiver enitivity i then 0 1 rec h 0Fo f Q Q f Auming that rec = N hν 0 B and Δf = B/, we get 1 N 0 Fo Q Q f he number of hoton er bit deend on 0 he BER (via Q), the noie figure, and the receiver banda filter Low-noie amlification and narrow filtering i critical for high erformance 1 Fiber Otical Communication Lecture 6, Slide 37

38 Receiver enitivity of reamlified receiver Uing F o =, Q = 6, Δν 0 = B N = 43 hoton er bit on average he quantum limit i N = 10 hoton er bit on average BER = 10-9 N = 100 i realitic with a reaonable noie figure and filter bandwidth Fiber Otical Communication Lecture 6, Slide 38

39 Relation between Q and the OSNR When ASE noie dominate, we have Δν o = bandwidth of otical banda filter [nm] Δf = equivalent receiver electrical bandwidth [GHz] o 15 f 0.1 OSNR 0.1 4OSNR If we know the OSNR and the bandwidth, we can find Q and the BER Q o o 1 1 In figure, Δν o = 0.4 nm Reaonable value for a 10 Gbit/ ytem he neceary OSNR = 15 0 db at a bit rate of 10 Gbit/ Q (linear) BER = 10-1 f = 5GHz 10 GHz 0 GHz OSNR 0.1 nm Fiber Otical Communication Lecture 6, Slide 39