Περιεχόμενα διάλεξης

9-10η Διάλεξη Οπτικοί ενισχυτές Γ. Έλληνας, Διάλεξη 9-10, σελ. 1 Περιεχόμενα διάλεξης Εισαγωγικές έννοιες Οπτικών Ενισχυτών Ανάλυση απολαβής και θορύβου Οπτικοί ενισχυτές με ίνα προσμίξεων ερβίου Οπτικοί ενισχυτές ημιαγωγού Γ. Έλληνας, Διάλεξη 9-10, σελ. 2 Page 1

Optical Amplifiers & WDM As an optical signal travels through fiber, it is degraded: p IN (t) p OUT (t) p IN (t - τ) fiber p (t) L = cτ/n g t o t τ Attenuation & dispersion Reduction in pulse energy Pulse spreading Γ. Έλληνας, Διάλεξη 9-10, σελ. 3 t Optical Signal Regeneration It is therefore necessary to re-amplify and reshape the pulses at regular intervals using regeneration: Optical source FIΒΕR R Photoreceiver fiber input Photoreceiver Electronics: Clock recovery, pulse reshaping Regenerator Laser transmitter Fiber output Γ. Έλληνας, Διάλεξη 9-10, σελ. 4 Page 2

Optical Signal Regeneration fiber input Photoreceiver Electronics: Clock recovery, pulse reshaping Regenerator Decision threshold Laser transmitter fiber output Decision times Γ. Έλληνας, Διάλεξη 9-10, σελ. 5 Optical Signal Regeneration Advantages: Clock recovery Pulse reshaping Disadvantages: O/E & E/O conversion needed Bit rate is locked in no upgrades Single wavelength only Γ. Έλληνας, Διάλεξη 9-10, σελ. 6 Page 3

Example of a fiber-optic regenerator (622 Mb/s) Transimpedance Laser driver PIN amplifier photodiode Limiting amplifier Laser diode Γ. Έλληνας, Διάλεξη 9-10, σελ. 7 Εισαγωγικές έννοιες Γ. Έλληνας, Διάλεξη 9-10, σελ. 8 Page 4

Basic Concepts Two types of optical amplifiers: SOAs and active fiber amplifiers Increase the power of incident light through stimulated emission Same mechanism to produce a population inversion as in laser diodes Lacks the feedback mechanism to produce lasing Device absorbs energy supplied by an external energy source called the pump. Electrons in active medium move to higher energy levels to produce population inversion Incoming signal photon triggers these excited electrons to drop to lower levels through a stimulated emission process Amplified signal is produced Γ. Έλληνας, Διάλεξη 9-10, σελ. 9 Basic Concepts SOAs use alloys of semiconductor elements (phosphorus, gallium, indium, arsenic) to make up the active medium SOAs work in 1300 and 1500 nm range Use external injection current as the pumping method Active-fiber amplifiers are created by doping a silica fiber core (10-30 meters) with rare earth elements (i.e., Erbium) EDFAs work in the 1500 nm range Optical pumping is used to excite the electrons (photons are used to directly raise electrons into excited states) Γ. Έλληνας, Διάλεξη 9-10, σελ. 10 Page 5

Οπτικός ενισχυτής Γ. Έλληνας, Διάλεξη 9-10, σελ. 11 Optical Amplifiers fiber input Optical gain medium fiber output Optical amplifier Pump laser Γ. Έλληνας, Διάλεξη 9-10, σελ. 12 Page 6

Optical Amplifiers Advantages: Optical input & output Photons in more photons out Transparent to both bit rate & modulation format Supports many wavelengths WDM: Wavelength division multiplexing Disadvantages: No pulse reshaping Needs dispersion compensation Adds noise to output signal Γ. Έλληνας, Διάλεξη 9-10, σελ. 13 Optical Amplifiers All-optical components (i.e. optical input/output) Have replaced regenerators, in which optical signals had to be photodetected, amplified electronically and then applied to laser. Have revolutionized optical communications used in wavelength division multiplexed (WDM) systems allow the use of soliton transmission at ultra high bit rates (1000s of Gb/s) over thousands of km Γ. Έλληνας, Διάλεξη 9-10, σελ. 14 Page 7

Optical Amplifiers In particular, an optical amplifier provides gain over a useful spectral range: fiber Attenuation (db/km) Optical amplifier gain (db) 1550 nm 40 nm λ λ Γ. Έλληνας, Διάλεξη 9-10, σελ. 15 Optical Amplifiers This broad spectral range enables a number of wavelengths to be multiplexed onto a fiber, thus increasing the bit rate that can be transmitted. Spectrum of 16 amplified WDM channels (using EDFA) Γ. Έλληνας, Διάλεξη 9-10, σελ. 16 Page 8

Optical Amplifiers Ideal amplifier: Output Input P OUT Gain Phase GAIN Gain P IN Flat gain response Linear phase response f P IN Γ. Έλληνας, Διάλεξη 9-10, σελ. 17 Optical Amplifiers Real amplifier: Output P OUT Input Gain Phase GAIN + NOISE Gain P IN f Gain saturation Nonlinearity P IN Γ. Έλληνας, Διάλεξη 9-10, σελ. 18 Page 9

Συνάρτηση μεταφοράς Ιδανικός ενισχυτής Πραγματικός ενισχυτής Γ. Έλληνας, Διάλεξη 9-10, σελ. 19 Oπτικοί ενισχυτές με ίνα προσμίξεων ερβίου Erbium-Doped Fiber Amplifiers (EDFAs) Γ. Έλληνας, Διάλεξη 9-10, σελ. 20 Page 10

Πλεονεκτήματα EDFAs Υψηλή απολαβή (high gain) Χαμηλός θόρυβος (low noise) Μικρές απώλειες σύζευξης (low coupling losses) Μεγάλο εύρος ζώνης Οπτική άντληση από laser ημιαγωγού Αναισθησία στην πόλωση Ασήμαντη διαφωνία μεταξύ οπτικών καναλιών (insignificant cross-talk between optical channels) Γ. Έλληνας, Διάλεξη 9-10, σελ. 21 Μειονεκτήματα EDFAs Διακυμάνσεις απολαβής συναρτήσει της συχνότητας Λειτουργία αποκλειστικά στα 1.55 μm Γ. Έλληνας, Διάλεξη 9-10, σελ. 22 Page 11

Μοντελοποίηση οπτικών ινών με προσμίξεις ερβίου Γ. Έλληνας, Διάλεξη 9-10, σελ. 23 Ενισχυτής laser τριών επιπέδων Γ. Έλληνας, Διάλεξη 9-10, σελ. 24 Page 12

Energy Levels in Er 3+ - Doped Silica fiber Note: Only main levels shown; there are more! E 3 Pump 980 nm E 2 Relaxation Metastable State Amplification at 1.55 μm E 1 Ground State Γ. Έλληνας, Διάλεξη 9-10, σελ. 25 Energy Levels in Er3+ - Doped Silica fiber Ground state absorption (GSA) corresponds to a photon exciting a carrier (electrons in erbium ion) from the ground state to a higher level. Excited state absorption (ESA) corresponds to photon exciting carrier from non-ground state to a higher level (e.g. E 2 to E 3 ) GSA is more likely than ESA, since there is a higher population in the ground state. Once a carrier is excited to E 3 by the pump photon, it rapidly decays to E 2. Once at E 2, it has a long lifetime (~10ms), so this level is metastable. This carrier then decays spontaneously or is stimulated by an incoming photon. Γ. Έλληνας, Διάλεξη 9-10, σελ. 26 Page 13

Energy Transitions in Er 3+ - Doped Silica fiber Γ. Έλληνας, Διάλεξη 9-10, σελ. 27 Ενεργός διατομή incident light Front view di I = ds S = (σ N σ N )Sdz e 2 a 1 S where I = Intensity = Power/Area σ a = Absorption cross section σ e = Emission cross section S = Area (1) Γ. Έλληνας, Διάλεξη 9-10, σελ. 28 Page 14

Συντελεστής απολαβής From (1) di dz = gi where g = gain coefficient= (σ e N 2 σ a N 1 ) Relative inversion D = N 2 N 1 ρ ρ = rare-earth element concentration Γ. Έλληνας, Διάλεξη 9-10, σελ. 29 Amplifier Gain From the principle of photon conservation, amplifier gain in EDFAs is defined as (assuming no spontaneous emission): G s, out = 1 P P s, in λp + λ s P P in p in s Amount of signal energy extracted from an EDFA cannot exceed the pump energy stored in the device (less than or equal sign corresponds to photons lost or pump energy lost due to spontaneous emission) For the pumping scheme to work we need λ p < λ s and to have an appropriate gain P s in << P p in Γ. Έλληνας, Διάλεξη 9-10, σελ. 30 Page 15

Amplifier Gain If the signal power is so large so that P s in >> (λ p /λ s ) P p in, then the maximum Gain is unity (device transparent to signal) Also, to achieve max Gain, the input power must not exceed P in s λ p ( / λ ) s P G 1 in p Γ. Έλληνας, Διάλεξη 9-10, σελ. 31 Amplifier Gain Gain is also dependent on the fiber length. The maximum gain in a three-level laser medium of length L is given by: [ ρσ ] G exp L e (assuming perfect population inversion) So, the maximum possible EDFA gain is λp P G min{exp( ρσ L),1+ e λ P s in p in s } Γ. Έλληνας, Διάλεξη 9-10, σελ. 32 Page 16

Amplifier Gain Since P P [ ρσ ] s, out G = = exp el s, in then, the maximum possible EDFA output power is given by: P out s min{ P in s λ in p exp( ρσ L), P e s + P λ s in p } Γ. Έλληνας, Διάλεξη 9-10, σελ. 33 Απολαβή συναρτήσει ισχύος άντλησης Γ. Έλληνας, Διάλεξη 9-10, σελ. 34 Page 17

Απολαβή συναρτήσει ισχύος εισόδου in P sat Γ. Έλληνας, Διάλεξη 9-10, σελ. 35 Απολαβή συναρτήσει ισχύος εξόδου out P sat Γ. Έλληνας, Διάλεξη 9-10, σελ. 36 Page 18

Βέλτιστο μήκος Γ. Έλληνας, Διάλεξη 9-10, σελ. 37 Gain profile of erbium-doped silica fiber Γ. Έλληνας, Διάλεξη 9-10, σελ. 38 Page 19

Erbium Doped fiber Amplifier (EDFA) Isolator Wavelength multiplexer Narrowband optical filter Weak input signal at 1.55μm Laser diode pump at 980 nm or 1480 nm Amplification section with erbium doped Silica fiber (Er 3+ ions) Amplified signal at 1.55μm Gain 20 to 30 db Γ. Έλληνας, Διάλεξη 9-10, σελ. 39 Packaged EDFA Γ. Έλληνας, Διάλεξη 9-10, σελ. 40 Scientific American / AT&T Page 20

EDFA output versus wavelength ASE = amplified spontaneous emission: noise Γ. Έλληνας, Διάλεξη 9-10, σελ. 41 Gain versus EDFA length Γ. Έλληνας, Διάλεξη 9-10, σελ. 42 Page 21

EDFA gain versus pump level Γ. Έλληνας, Διάλεξη 9-10, σελ. 43 Ανάλυση συστημάτων με οπτικούς ενισχυτές Γ. Έλληνας, Διάλεξη 9-10, σελ. 44 Page 22

Important figures of merit & considerations for an amplifier Gain Bandwidth Power source Nonlinearity & gain saturation Noise Noise figure given by: SNR = signal-to-noise ratio Note: F 1, i.e. F 0 db F = SNR SNR INPUT OUTPUT Γ. Έλληνας, Διάλεξη 9-10, σελ. 45 Properties of Ideal Optical Amplifiers Provide high gain (30 db or more) Have a wide spectral bandwidth to allow several wavelengths to be transmitted Provide uniform (i.e. flat) gain vs. λ to maintain relative strength of spectral components Allow bi-directional operation i.e. gain in both directions Have low insertion loss to maximize benefits of amplifier gain Γ. Έλληνας, Διάλεξη 9-10, σελ. 46 Page 23

Properties of Ideal Optical Amplifiers Have no crosstalk i.e. no interference between different spectral components Have wide dynamic range gain should not saturate with high input powers Use a compact pump source i.e. use laser diode for pump Have a good conversion efficiency pump power converted to amplifier gain Γ. Έλληνας, Διάλεξη 9-10, σελ. 47 Typical gain versus power profile for optical amplifier Γ. Έλληνας, Διάλεξη 9-10, σελ. 48 Page 24

Applications of optical amplifiers As in-line amplifiers in attenuation-limited links: Optical Source Optical Receiver Optical fiber Optical amplifier compensates for fiber loss Γ. Έλληνας, Διάλεξη 9-10, σελ. 49 Applications of optical amplifiers As post-amplifiers to increase source power: P S (dbm) G(dB) Optical Transmitter Output power (dbm) = P S + G Amplifier adds noise, but this is attenuated by the fiber Important that amplifier is not saturated by the transmitter Γ. Έλληνας, Διάλεξη 9-10, σελ. 50 Page 25

Applications of optical amplifiers As pre-amplifiers to improve receiver sensitivity: Optical input Optical Receiver High gain (e.g. 30 db) and low noise figure (e.g. 3 db) is important, because entire amplifier output is immediately detected. Γ. Έλληνας, Διάλεξη 9-10, σελ. 51 Applications of optical amplifiers As booster amplifiers in local area networks to compensate for losses in star coupler: Star coupler: splits into N fibers; has insertion and splitting loss Γ. Έλληνας, Διάλεξη 9-10, σελ. 52 Page 26

System performance of optical amplifiers gain G, noise figure F analogous to DC bias input signal gain + noise Γ. Έλληνας, Διάλεξη 9-10, σελ. 53 Optical Amplifier Gain Control Consider in-line amplifier application, as in long haul links: αl G αl G αl G Set amplifier gain to compensate for loss of inter-connecting fibers of length L, i.e.: G = αl So if the link consists of equal number of amplifiers and interconnecting fibers, overall link loss should be zero. Γ. Έλληνας, Διάλεξη 9-10, σελ. 54 Page 27

Optical Amplifier Gain Control αl G αl G αl G P x G + P x G + P x - αl = P x {If G = αl} Note! All powers expressed in dbm, all gains and losses expressed in db. Consider next example, with three in-line amplifiers, and length L chosen to be maximum for given source power and receiver sensitivity. Γ. Έλληνας, Διάλεξη 9-10, σελ. 55 Optical source P S Optical Amplifier Gain Control αl G αl G αl G αl Photoreceiver P R P s P S - αl : power entering first amplifier P s : source power (dbm) G + P S - αl = P S {If G = αl} : output power from first amplifier P R = receiver sensitivity P R = P S - αl Γ. Έλληνας, Διάλεξη 9-10, σελ. 56 Page 28

Now consider situation where power at some point in link drops suddenly (e.g. due to fault at laser): P S αl G αl G αl G αl P R P s - P x G + P S -P x - αl P S - P x - αl < P R P S - P x - αl P s - P x Bad news: drop in power means that the power incident on the photoreceiver is now less than the receiver sensitivity, which in a digital system means the BER specification is not met. Γ. Έλληνας, Διάλεξη 9-10, σελ. 57 One solution is passive gain control: relies on using the amplifier in its saturation region: If input power drops (rises), gain increases (decreases) to compensate for this. Similar effect to feedback (but it is not f/b!). Γ. Έλληνας, Διάλεξη 9-10, σελ. 58 Page 29

For example, consider an amplifier with a gain/input power slope of - 1 db/dbm in the saturation region: G(dB) P OUT = P nom - Δ + G nom + Δ = P nom + G nom P OUT = P nom + G nom G nom + Δ G nom G nom - Δ P OUT = P nom + Δ + G nom - Δ = P nom + G nom slope = -1 db/dbm P nom - Δ P nom P nom + Δ P IN (dbm) Γ. Έλληνας, Διάλεξη 9-10, σελ. 59 Optical Amplifier Gain Control This leads to a self-healing effect in systems where cascades of amplifiers are used (such as in-line). The disadvantage is that the gain is low, because the amplifiers operate in the saturation region. The slope in general is not -1 db/dbm, but even when it is not, self-healing will occur, but not immediately after the first amplifier. We will see this in the next example. Γ. Έλληνας, Διάλεξη 9-10, σελ. 60 Page 30

Optical Amplifier Gain Control - Example Consider a long-distance transmission system containing a cascaded chain of erbium-doped fiber amplifiers (EDFAs). Assume each EDFA is operated in saturation and that the slope of the gain-versus-input power curve is 0.5; for example, the gain changes by +/ 2 db for a -/+ 4 db variation in input power. The EDFAs in the link have the following operational parameters: Nominal gain: G nom = 7.3 db Nominal optical output power: P OUT = 3 dbm Nominal optical input power: P IN = -4.3 dbm Suppose there is a sudden 4 db drop in signal level at some point in the link. Find the output power levels after the degraded signal has passed through 1,2, and 3 succeeding EDFAs. Γ. Έλληνας, Διάλεξη 9-10, σελ. 61 Before power drop: G = 7.3 db αl G G αl = 7.3 db G Example cont d - 4.3 dbm 3 dbm - 4.3 dbm... After power drop: G(P IN1 ) G(P IN2 ) G(P IN3 ) αl αl αl - 4.3 dbm - 4 db = - 8.3 dbm Γ. Έλληνας, Διάλεξη 9-10, σελ. 62 Page 31

After power drop: Example cont d G(P IN1 ) G(P IN2 ) G(P IN3 ) αl = 7.3 db αl αl - 4.3 dbm - 4 db = - 8.3 dbm - 4 db drop for P IN1 (relative to the nominal value of -4.3 dbm) means that G for amp 1 goes up by 2 db from G nom, hence G(P IN1 ) = 7.3 + 2 = 9.3 db Γ. Έλληνας, Διάλεξη 9-10, σελ. 63 αl G(P IN1 ) = 9.3 db αl = 7.3 db αl Example cont d - 8.3 dbm - 8.3 dbm + 9.3 db = 1 dbm 1 dbm - 7.3 db = -6.3 dbm P IN2 is 2 db below the nominal value of - 4.3 dbm So G for amp 2 will be 1 db above the nominal value of 7.3 db, i.e. G(P IN2 ) = 8.3 db Γ. Έλληνας, Διάλεξη 9-10, σελ. 64 Page 32

αl αl G(P IN2 ) = 8.3 db αl = 7.3 db Example cont d - 6.3 dbm 2 dbm - 7.3 db = -5.3 dbm - 6.3 dbm + 8.3 db = 2 dbm P IN3 is 1 db below the nominal value of - 4.3 dbm So G for amp 2 will be 0.5 db above the nominal value of 7.3 db, i.e. G(P IN3 ) = 7.8 db Γ. Έλληνας, Διάλεξη 9-10, σελ. 65 Example cont d αl αl G(P IN3 ) = 7.8 db αl = 7.3 db - 5.3 dbm + 7.8 db = 2.5 dbm - 5.3 dbm 2.5 dbm - 7.3 db = -4.8 dbm P IN4 is 0.5 db below the nominal value of - 4.3 dbm Γ. Έλληνας, Διάλεξη 9-10, σελ. 66 Page 33

G 1 = 9.3 G(dB) 1 Example cont d self-healing G 2 = 8.3 G 3 = 7.8 2 3 nominal point G nom = 7.3 P IN1-8.3 P IN2-6.3 P IN2-5.3 P nom = -4.3 P IN (dbm) Γ. Έλληνας, Διάλεξη 9-10, σελ. 67 Exercise Hmwk no. 4 Problem no. 5 Continue this analysis for the next three amplifiers in the cascade (i.e. amplifiers 4 through 6). Can you deduce what the output power will be for the n-th amplifier? What impact does the slope of the saturation region have on the speed of self-healing? Γ. Έλληνας, Διάλεξη 9-10, σελ. 68 Page 34

Θόρυβος Γ. Έλληνας, Διάλεξη 9-10, σελ. 69 Simple SNR analysis 1 amp Γ. Έλληνας, Διάλεξη 9-10, σελ. 70 Page 35

Ισχύς θορύβου εξαναγκασμένης αυθόρμητης εκπομπής P = 2h ν n ( G 1) ASE Bo sp όπου n sp L n 2 n 2 n G N 2 ( z) = σ e dz G 1 G ( z) 0 1 Παράγων αυθόρμητης Εκπομπής n2 = excited state population n1 = ground-state population Γ. Έλληνας, Διάλεξη 9-10, σελ. 71 Ισχύς θορύβου εξαναγκασμένης αυθόρμητης εκπομπής P Bo s SNR = 2hν n ( G 1) sp In case of cascade amps, P ase grows linearly with the number of amps N a SNR N a Ps Bo 2hν n ( G 1) sp Γ. Έλληνας, Διάλεξη 9-10, σελ. 72 Page 36

Optical SNR P s SNR = 2 ( B / B )[2N hνn ( 1) B sp G ] e o a o Optical SNR 1. Signal Power into amps is critical 2. System NF doubles as Na doubles 3. Signal/spontaneous power ratio is critical At 2.5 Gbps, Bo = 0.1nm, approx. 14 db (ideal components), 17 db (real components) Γ. Έλληνας, Διάλεξη 9-10, σελ. 73 Ελάχιστος παράγων ενισχυμένης αυθόρμητης εκπομπής Γ. Έλληνας, Διάλεξη 9-10, σελ. 74 Page 37

Φάσματα θορύβου ΑSΕ Γ. Έλληνας, Διάλεξη 9-10, σελ. 75 Φάσματα εξόδου Γ. Έλληνας, Διάλεξη 9-10, σελ. 76 Page 38

SNR degradation Γ. Έλληνας, Διάλεξη 9-10, σελ. 77 Issues with Real Optical Amplifiers Inter-channel power spread (1 amp) Inter-channel SNR spread (1 amp) Power and SNR spread accumulates Dynamic cross-saturation Intolerance to loss variations Γ. Έλληνας, Διάλεξη 9-10, σελ. 78 Page 39

Γ. Έλληνας, Διάλεξη 9-10, σελ. 79 Γ. Έλληνας, Διάλεξη 9-10, σελ. 80 Page 40

Types of optical amplifier Semiconductor Optical amplifiers (SOAs) Fabry-Perot amplifiers: essentially laser diodes that are biased below lasing (oscillation) threshold; Fiber amplifiers stimulated Raman or Brillouin scattering rare earth doped fibers: most common type is erbium-doped (1.55μm central wavelength). Γ. Έλληνας, Διάλεξη 9-10, σελ. 85 Semiconductor Optical Amplifier Γ. Έλληνας, Διάλεξη 9-10, σελ. 86 Page 43

Κατασκευαστικές γεωμετρίες EDFAs Γ. Έλληνας, Διάλεξη 9-10, σελ. 87 EDFAs με μια βαθμίδα ενίσχυσης Γ. Έλληνας, Διάλεξη 9-10, σελ. 88 Page 44

Τύποι οπτικών ενισχυτών Οπτικοί ενισχυτές με ίνα προσμίξεων ερβίου Γ. Έλληνας, Διάλεξη 9-10, σελ. 89 EDFAs με δυο βαθμίδες ενίσχυσης EDF EDF 1 2 OI OI OI NF WSC WSC TAP 1 TAP 2 50:50 Pump 1 Pump 2 Γ. Έλληνας, Διάλεξη 9-10, σελ. 90 Page 45

Βιβλιογραφία E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Applications, Wiley, 1994. Γ. Έλληνας, Διάλεξη 9-10, σελ. 91 Ημιαγωγικοί οπτικοί ενισχυτές Semiconductor Optical Amplifiers (SOAs) Γ. Έλληνας, Διάλεξη 9-10, σελ. 92 Page 46

Τύποι οπτικών ενισχυτών Οπτικοί ενισχυτές ημιαγωγού Γ. Έλληνας, Διάλεξη 9-10, σελ. 93 Πλεονεκτήματα SOAs Ευαισθησία Απόδοση Μεγάλο εύρος ζώνης Μικρή εικόνα θορύβου Μικρό μέγεθος Αξιοπιστία Χαμηλό κόστος Γ. Έλληνας, Διάλεξη 9-10, σελ. 94 Page 47