Lecture 11 Noie from optical amplifier EDFA noie Raman noie Optical SNR (OSNR), noie figure, (electrical) SNR Amplifier and receiver noie ASE and hot/thermal noie Preamplification for SNR improvement Fiber Optical Communication Lecture 11, Slide 1
All amplifier add noie Amplifier noie o amplify (make a larger copy), a phyical device mut oberve the ignal Cannot be done without perturbing the ignal Aured by the Heienberg uncertainty principle Lumped and ditributed amplification have different performance Noie come from pontaneouly emitted photon hee have random direction polarization frequency (within the band) phae Some of thee add to the ignal Caue intenity and phae noie Fiber Optical Communication Lecture 11, Slide
Optical ignal are often characterized by the optical SNR (OSNR) Eaily meaured with an optical pectrum analyzer (OSA) Make ignal monitoring in the lab eay i very popular he definition of the OSNR i Definition of the optical SNR OSNR P ignal, X P noie, X P P ignal, Y noie, Y {Foringle polarization ignal} P P ignal ASE he index X and Y denote the two polarization he OSNR i related to the SNR, Q, and BER OSNR i uually normalized to a.1 nm bandwidth Entire ignal power i included, noie i meaured over.1 nm Implie required OSNR (for given BER) i bit rate-dependent OSNR Fiber Optical Communication Lecture 11, Slide 3
EDFA noie (7..3) he noie i called amplified pontaneou emiion (ASE) I being amplified ince there i gain Will reach the receiver (remaining optical path i amplified) he ASE power at the output of the EDFA P ASE SASE o nph ( G 1) o Δν i the effective bandwidth of the optical filter ued to uppre noie S ASE i the (oneided) noie power pectral denity (PSD) hi i the power per polarization n p i the pontaneou-emiion factor alo known a the population-inverion factor For an EDFA n p e N e N N a 1 N N N 1 1 Fiber Optical Communication Lecture 11, Slide 4
OSNR due to EDFA noie (7.4.1) he OSNR i reduced each time a ignal i amplified Each EDFA add to the noie PSD due to the generation of more ASE After N A amplifier in a link with pan lo equal to the gain in each amplifier and with identical EDFA noie performance, we have OSNR In db and dbm at 155 nm and Δν =.1 nm, we have OSNR N db Pin P P in N n [dbm] N A Pin h ( G 1) [db] n p N n Pin h A ASE A p o o A p o. 1 [db] G[dB] 58dBm G P P 1 N A L EDFA A Fiber Optical Communication Lecture 11, Slide 5
OSNR due to EDFA noie, example What i the max. tranmiion ditance with 1 km or 5 km EDFA pacing? A 1 Gbit/ ytem with a OSNR requirement of db he lo i.5 db/km and n p = 5 db he launched power into each pan i 1 mw per WDM channel OSNR P [dbm] N [db] n [db] G[dB] 58dBm db in L A = 1 km N A = 8 db = 6.3 6 amp 7 km L A = 5 km N A =.5 db = 11. 11 amp 565 km he amplifier pacing play 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 performance echnique that enable cot reduction are deirable hi can, for example, be error correction or ditributed amplification Hint that ditributed amplification may perform better A p Fiber Optical Communication Lecture 11, Slide 6
OSNR due to EDFA noie, amplifier pacing We can expre the number of amplifier a L i the total ytem length hi give the OSNR Pin ln G OSNR nph.1l We ee that Figure how maximum ytem length = ytem reach OSNR = db α =. db/km n p =1.6 P Δν = 1 GHz ASE G 1 ln G ( G 1) N A L ln G Fiber Optical Communication Lecture 11, Slide 7
S Raman amplifier noie (7.3.4) Noie i generated by pontaneou Raman cattering he noie PSD per polarization after an amplified fiber i ASE n p h G( L) L g( z) dz G( z) Depend on the net power gain, G(L) Oberve: hi i net gain, for a tranparent ytem G(L) = 1 Depend on the ditribution of gain g (z) n p ha a different definition for Raman amplification h i Planck contant ν R i the Raman hift Maximum gain at 13. Hz k B i Boltzmann contant i the temperature, 93 K hi give n p = 1.13, n p 1 a G( z) exp z [ g ( ) d ] n p 1 1 exp( h g R ( z) / k B ) g R P a p p ( z) Fiber Optical Communication Lecture 11, Slide 8
Raman amplifier noie, example he pump experience lo gain i not contant Anyway, a an example, tudy an amplified tranparent fiber, g = α We then have... z z G( z) exp [ g ( ) ] d exp d 1...and the noie PSD become L g z L ( ) SASE nph G( L) dz nph dz nph L G( z) We compare thi with the cae where an EDFA i placed at the end S n h G 1) n h ( e L 1) ASE p ( p n p i imilar in both cae (omewhat better for Raman) he final term are very different, tudy exp(α L) = db L L 4.6,( e 1) 99 Ditributed amplification can be vatly uperior to lumped amplification Fiber Optical Communication Lecture 11, Slide 9
OSNR due to Raman noie (7.4.) Pump tation are et up paced by L A Gain i deigned to make P (z = nl A ) = P in he OSNR i given by OSNR S ASE mut be found uing the general expreion Depend on pumping; forward, backward, or both Figure how ASE PSD and OSNR, fiber i 1 km long Pumping i bidirectional to varying degree Sytem i tranparent at db net gain Forward pumping i better than backward pumping N Nonlinearitie are not conidered A P S in ASE.1 Fiber Optical Communication Lecture 11, Slide 1
Raman amplifier performance In general, it i preferable to amplify a trong ignal For a given gain (and added noie PSD), the (O)SNR decreae i maller Forward pumping i better than backward pumping Unfortunately, ignal power mut be limited due to nonlinearitie he Raman amplifier i affected by everal phenomena: Double Rayleigh cattering occur Light cattered back i cattered again Pump-noie tranfer decreae the SNR he gain change with the pump intenity fluctuation he amplifier i polarization dependent I counteracted uing polarization crambling Fiber Optical Communication Lecture 11, Slide 11
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 eparate from OSNR An EDFA can improve the enitivity of a thermally noie limited receiver A preamplified optical receiver he added optical noie can be much maller than the thermal noie he generated photocurrent in the receiver i E cp = ASE co-polarized with ignal E op = ASE orthogonal with ignal i = Shot noie i = hermal noie he ASE ha a broad pectrum, and can be written he magnitude quare i a multiplication new frequencie are generated beating I E P in R d G np GE E cp BPF E op i receiver i M 1/ cp ( SASE ) exp( im imt) m1 Fiber Optical Communication Lecture 11, Slide 1
Electrical ignal-to-noie ratio (SNR) he received electrical current i i ig-p = ignal-ase beat noie term I R i p-p = ASE-ASE beat noie term he variance of the noie term are d GP i igp i pp i i ig 4R p d GPS ASE f q R ( GP P ) f d ASE pp 4R d SASEf ( f (4k / R ) f B L / ) Δν i bandwidth of optical bandpa filter (reject out-of-band noie) he SNR i here defined a SNR I igp ( R d GP ) pp Fiber Optical Communication Lecture 11, Slide 13
Impact of ASE on SNR (7.5.) Let u compare the SNR without and with amplification by an EDFA Amplifier and bandpa filter i inerted before the receiver SNR noamp Notice that σ are different in the two cae (σ tay the ame) We neglect σ p-p and the noie current contribution to hot noie to get SNR amp ( RdGP ) (qrd P f ) SNR (4R GPS f ) (qr GPf ) ( R P ) noamp We ue the PSD and the ideal reponivity n h ( G 1) { G 1 n h G We get SNR ( R P ) d d ASE, SNR amp SASE p } p SNR amp noamp n p 1 k 1/ G k d pp Notice: k i ratio (thermal noie)/(hot noie) without amplification All quantitie in the denominator (qr d P Δf) are kept contant! Fiber Optical Communication Lecture 11, Slide 14 d / G igp ( R GP ) k R d q d /( h ) qr P f d
A thermal noie-limited receiver How i the SNR changed in the thermal limit? Firt aume that thermal noie dominate before and after amplification SNR amp 1 k k G SNR n 1/ G k / G k / G noamp here i a huge improvement in the SNR Signal power i increaed, noie power 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 amplification SNR SNR amp noamp n SNR improvement aturate a G i increaed Improvement can be very large p p 1 k 1/ G k Fiber Optical Communication Lecture 11, Slide 15 / G n In the thermal limit, amplification improve the SNR p k 1/ G k n p
A hot noie-limited receiver, noie figure (7..3) Now intead aume that the optical ignal ha high power hermal noie i negligible SNR SNR amp noamp n he SNR i decreaed by the amplification he noie figure i defined p 1 k 1/ G k he SNR value are what you would obtain by putting an ideal receiver before and after an EDFA, repectively Ideal mean hot noie-limited, 1% quantum efficiency Our tudy above ha provided u with the (invere) minimum value Fiber Optical Communication Lecture 11, Slide 16 / G n p 1 1/ G EDFA amplification of a perfect ignal decreae the SNR by > n p (> 3dB) NF F n F n (SNR) (SNR) n p in out 1 n p
For an EDFA, the noie figure i Noie figure In reality, N 1 and N change along the EDFA Pump power and ignal power are not contant he rate equation can be olved numerically Figure how Noie figure and amplifier gain a a function of......pump power and amplifier length A long amplifier Can provide high gain Require high pump power e F n n N N p np 1 e a N N N N 1 1 Fiber Optical Communication Lecture 11, Slide 17
he noie figure i increaed Noie figure If the population inverion i incomplete (omewhere in the amplifier) If there are coupling loe into the amplifier Pumping i facilitated by pumping at 98 nm No timulated emiion caued by pump photon (σ pe ) Correponding energy level i almot empty (hort-lived) Noie figure 3 db i poible, 3. db ha been meaured With 148 nm pumping σ pe Ground tate will alway be populated by ome ion Some excited ion will be timulated by pump photon to relax Noie figure i larger for thi cae Coupling into and out of an EDFA i efficient ypical EDFA module have F n = 4 6 db Fiber Optical Communication Lecture 11, Slide 18
SNR/OSNR relation In general, there i no imple relation between the OSNR and the SNR OSNR i prop. to the optical power, SNR i prop. to the electrical power Electrical power i proportional to the (optical power) Not true in a coherent receiver When ignal ASE noie i dominating we have ( RdGP ) GP.1. 1 SNR 4R GPS f 4P f f d For a ingle-polarization ignal, we can ue P E f OSNR S S ASE OSNR E i the energy per ymbol, f i the ymbol rate (in baud) E /S ASE i often written E /N i digital communication literature he relation between E /N and the BER depend on the type of receiver, modulation format and more ASE ASE.1 ASE.1 Fiber Optical Communication Lecture 11, Slide 19
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 implicity 1 igp pp igp pp he receiver enitivity i then 1 P rec h Fo f Q Q f Auming that P rec = N p hν B and Δf = B/, we get 1 N p Fo Q Q f he number of photon per bit depend on pp pp he BER (via Q), the noie figure, and the receiver bandpa filter Low-noie amplification and narrow filtering i critical for high performance 1 Fiber Optical Communication Lecture 11, Slide
Receiver enitivity of preamplified receiver Uing F o =, Q = 6, Δν = B N p = 43 photon per bit on average he quantum limit i N p = 1 photon per bit on average BER = 1-9 N p = 1 i realitic with a reaonable noie figure and filter bandwidth Fiber Optical Communication Lecture 11, Slide 1
Relation between Q and the OSNR When ASE noie dominate, we have Δν o = bandwidth of optical bandpa filter [nm] Δf = equivalent receiver electrical bandwidth [GHz] o 15 f.1 OSNR.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 =.4 nm Reaonable value for a 1 Gbit/ ytem he neceary OSNR = 15 db at a bit rate of 1 Gbit/ Q (linear) 16 14 1 1 8 6 4 BER = 1-1 f = 5GHz 1 GHz GHz 13 15 17 19 1 3 5 OSNR (db) @.1 nm Fiber Optical Communication Lecture 11, Slide
Optimum launched power (7.8.) Amplifier cancel the lo, but noie and nonlinearitie are accumulated High power potentially higher SNR but alo more nonlinear ditortion A power i increaed, BER firt drop, then increae again here i an optimal launch power that minimize the BER Fiber Optical Communication Lecture 11, Slide 3