semiconductor optical amplifier

PULSE AMPLIFICATION WITH TRAVELING-WAVE SEMICONDUCTOR OPTICAL

AMPLIFIER

Contents:

⇒⇒ basic properties of SOA gain saturation and gain recovery effects

⇒⇒ SOA for pulse compression

⇒⇒ SOA as wavelength converter

XGM and FWM

⇒⇒ SOA as in-line amplifiers

⇒⇒ conclusion

Description of traveling wave SOA

⇒ ⇒ smaller than 0.1 psintra-band processes: electron-electron scattering and electron

photon scattering the density-matrix approach

⇒ ⇒ larger than 0.1 psinter-band processes: radiative and non-radiative recombinations

the rate-equation approximationthe carrier - density rate equation the wave equation for the field in the SOA

Basic approximations :

⇒ the carrier - density rate equation

- neglect carrier diffusion

- neglect the amplified spontaneous emission noise and the shot noise

⇒ the wave equation for the field in the SOA

- linear dependence between the carrier induced susceptibility and the carrier density

- the amplifier supports a single wave-guide mode

- linearly polarized light and conservation of polarization

- neglect the group-velocity dispersion

- neglect the amplified spontaneous emission noise

Basic quantities and relations :

The material gain coefficient gm (t) = σg (N(t) –NT), whereσg – the differential gain coefficient,N(t) – the carrier density,NT – the carrier density at transparency point.

The net gain coefficient g(t)= Γ gm (t)-αinn, whereΓ- the optical confinement factor,αinn – effective loss coefficient.

The gain for a traveling wave SOA G=exp (g(t)L), whereL is the length of the amplifier

where Ip is the pump current and the carrier lifetime τC-1 = A + BN+CN2

The output optical field Eout(t) = Ein(t)exp[(1+jbC)g(t) / 2]

( ) ( ) ( ) ( )∑⇒−Γ−−=

k k

tNkPtNPhV

LtNPTNtNg

C

NqV

pI

tdNd

νννσ

τ,,,,

NT the transparency valueΓ the confinement factorL length of SOAw width of SOAd thickness of SOA

V = Lwd the volume of SOAσd the gain cross section, the differential gainbc the line-width enhancement factorA the non-radiative coefficient due to the

recombination of defectsB the spontaneous radiative recombination

coefficientC the Auger coefficientEsat = hv σm / σd the saturation energyσm = w d / Γ the cross-section area of the wave-guide mode

⇒⇒ basic properties of SOA - gain saturation effect

Gaussian pulse

Calculation parameters:N= 512 points; Bit Rate B= 71.4 Gb/s ⇒ TB = 14 psPulse parameters:Gaussian pulse E0 ~ 0.73 pJ; T0 ~ 7.9 ps ⇒ P~ 50 mW

SOA parameters: The carrier lifetime τC ~ 1.4 ns, The saturation energy Esat ~ 3.7 pJ, G0 ~ 30 dB

Therefore: ⇒ T0 /τC ~ 0.006 ⇒ E0 / Esat ~0.2

initial pulse initial spectrum

Observed properties:

asymmetric pulse , leading part sharper multi-peak structurecompared with the trailing one increased TFWHM red shift of dominant peak ~ 120 GHz

pulse after SOA pulse spectrum after SOA

G.P. Agrawal and N.A. Olsson, “Self_phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers”, IEEE Journal of Quantum electronics, vol. 25, pp.2297-2306, 1989

the phase follows time evolution of negative value across the entire pulsegain, gain has no time to recover increases towards the trailing part

⇒⇒ basic properties of SOA - gain saturation effectGaussian pulse - comparison with experimental results

Parameters from the experiment:T0 = 9.3ps, τC ~ 0.200 ns ⇒ T0 /τC ~ 0.0465, E0 ~ 0.18 pJ, Esat ~ 6 pJ,⇒ E0 / Esat ~0.03 , G0 ~30 dB

Calculation parameters:Bit Rate B= 40 Gb/s ⇒ TB = 25 ps, duty cycle = 0.624 ⇒ TFWHM = 15.6 ps ⇒ T0 ~ 9.4

ps;SOA parameters:The carrier lifetime τC ~ 1.4 ns, The saturation energy Esat ~ 3.7 pJOptical confinement factor Γ ~ 0.3, G0 ~30 dB

Pulse parameters:Gaussian pulse E0 ~ 0.017 pJ; T0 ~ 9.4 ps ⇒ P~ 1 mWT0/τC ~ 0.007, E0 / Esat ~ 0.004

N.A. Olsson and G.P. Agrawal, “Spectral shift and distortion due to selp-phase modulation of picosecond pulses in 1.5 µm amplifiers”, Appl. Phys. Lett, vol. 55, pp.13-15, 1989

the peak output red shifted with 0.3 nmthe secondary peak approximately 0.4 nm below the main peakthe main peak considerably broadening

well expressed qualitative similarity with experimental observation


⇒⇒ basic properties of SOA - gain saturation effectchirped Gaussian pulse : linewidth enhancement factor 5

initial pulse and negative chirp initial spectrum

comparison with usual Gaussian pulse:

similar shape in time reduction of the red shiftvery different form of the spectra


G.P. Agrawal and N.A. Olsson, “Self_phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers”, IEEE Journal of Quantum electronics, vol. 25, pp.2297-2306, 1989

for initial positive chirp the red shift increases!

phase of amplified pulse chirp of amplified pulsethe deformation of the initially negative chirp

⇒⇒ basic properties of SOA- gain saturation effect

super Gaussian pulse : m = 3


Amplified super Gaussian pulse : m = 3

comparison with usual Gaussian pulse:

reduced TFWHM increased red shiftchanges in the multi-peak structure


⇒⇒ basic properties of SOA- gain recovery effect

Calculation parameters:Pulse 1 parametersTFWHM ~ TB ~ 2.5 ns ⇒ T0 ~ 1.42 ns, Pin ~ 0.29 mWT0 /τC ~ 1.8, E0 / Esat ~ 0.1 ⇒ P0 / Psat ~ 0.056

Pulse 2 parametersTFWHM ~ TB ~ 10 ns ⇒ T0 ~ 5.67 ns, Pin ~ 0.074 mWT0 /τC ~ 7, E0 / Esat ~ 0.1 ⇒ P0 / Psat ~ 0.014

SOA parameters: The carrier lifetime τC ~ 1.4 ns, The saturation energy Esat ~ 7.4 mW

Pulse 1


pulse and chirp after SOA pulse spectrum after SOA

Pulse 2



Changes with increase of the ratio T0 /τCThe shape of the amplified pulse red shift continuously reducesbecome more symmetrical

the amplified pulse become broaderthan the initial one

Gain saturation induced self-phase modulationcomparison of results for pulse 2 for P0 / Psat = 0.014 and 0.14

structure of spectra similar to this obtained after pulse propagation in medium with Kerr nonlinearity

⇒⇒ SOA for pulse compression

Basic idea: to propagate amplified with SOA pulse, possessing therefore the positive chirp in dispersive medium that creates a negative chirp. As such medium SMF for wavelengths longer than 1.3 µm is used.

Calculation parameters:Bit Rate B= 40 Gb/s ⇒ TB = TFWHM = 25 ps;

Pulse parameters:Gaussian pulse T0 ~ 15 ps , P~ 1.4 mW

SOA parameters: The carrier lifetime τC ~ 1.4 ns, the saturation energy Esat ~ 3.7 pJ

⇒ T0 /τC ~ 0.01 and E0 / Esat ~ 0.01, G0 ~ 30 dB Fibers parameters:

SMF D = 16 (ps/nm.km), Aeff ~72 µm2, n2 ~ 2.6 × 10-20( m2/ W), α = 0.2 ( dB/km),LD ~ 11 km.

LC / LD ~ 0.3 ⇒ LC ~ 3.3 km

observations:compression factor of about 7 timesbroad pedestal of the leading side of the pulse (negative chirp in the leading part of the

pulse)time shift towards later times- red shift in anomalous group velocity dispersion

G.P. Agrawal and N.A. Olsson, “Amplification and compression of weak picosecond optical pulses by using semiconductor-laser amplifiers”, Optics letters, vol. 14, pp.500-502 , 1989

pulse after compression pulse spectrum after compression

SOA as wavelength converter (FWM)

Four wave mixing (FWM) ωc = 2ωp - ωs = ωp + Ω , where ωp - frequency of the pump field,ωs - frequency of the signal field,Ω = ω p - ωc - frequency detuning

physical phenomena generating FWM in SOA:Ω ~ several gigaherz – carrier density pulsation induced by the signal – pump beatingΩ > teraherz – fast interband relaxation processes: spectral hole burning and carrier

heating

advantage of frequency conversion based on FWMindependence of the modulation format and the bit rateinversion of spectrum and reversal of the frequency chirp

disadvantagelow conversion efficiency

two CW signals with carrier frequencies 193 and 193.1 THz and powers 1 mW.

spectrum after WDM Mux spectrum after the first SOA

New frequencies at 192.9 and 193.2 THz can be clearly seen

spectrum after WDM Demux, spectrum after the second SOA, ν = 193.1 THz channel ν = 193.2 THz channel

[1] G.P. Agrawal, “Fiber Optic Communication Systems”, second edition , John Wiley @ Sons, Inc., 1997.[2] R.Sabella and P.Ludgi, “High speed optical communications”, Kluwer Academic Publishers, 1999.

SOA as wavelength converter (XGM)

Principle of the use of cross-gain modulation in SOA:

Intensity modulated signal modulates the gain of SOA via gain saturation effect.A continuous wave signal at the desired wavelength is modulated by the gain saturation. After SOA a continuous wave signal carriers the same information as the intensity

modulated signal.

Aim: to show possibility of conversion at 10 Gb/s.

Intensity modulation signal at λ1 = 1550 nm with power P1 = 0.316 mW and CW signal at λ2 =1540 nm and power P2 = 0.158 mW

shape of the initial intensity spectrum of the initial intensity modulated signal modulated signal

signal after multiplexer

after demultiplexer at λ = 1550 nm

shape of signal spectrum of the signal

shape of signal spectrum of the signal

[1] Terji Durhuus, Benny Mikkelsen, Carsten Joergensen, Soergen Danielsen, Kristian Stunkjaer, “All-optical wavelength conversion by semiconductor optical amplifier”, J. Lightwave Technology, vol.14, pp.942-954,1996.[2] G.P. Agrawal, “Fiber Optic Communication Systems”, second edition , John Wiley @ Sons, Inc., 1997.

after demultiplexer at λ = 1540 nm

SOA as in line amplifiers

One possibility to upgrade existing network from already installed standard optical fibers (λ0) ~ 1.3 µm.

Advantages of this approach:Low dispersion of SMF at 1.3 µmAttractive features of SOA

Major negative factors:gain saturation effects:

pattern effectchirp after amplification

aim: to demonstrate the pattern effect at 10 Gb/s transmission over a 500 km SMF optical link

10 Gb/s transmission over 500 km standard mode fiber with semiconductor optical amplifiers

Bit rate B= 10 Gb/s ⇒ TB = 100 ps. The sequence length is 16 bit. The carrier wavelength of the pulse is λ ~1300 nm. TFWHM = 20 ps ⇒ T0 = 0.567 TFWHM ~ 11.34 ps. P0 = 21.7 mW.

SMF: length 50 km and losses 0.4 dB/km. For k2 = (- λ2D)/(2π c) ~ -1.5 (ps2/km) ⇒ D = 1.67 (ps/nm.km)⇒ LD = T0

2/| k2| ~ 85 km. (The effects of group delay and third order of dispersion are not taken into account). The Kerr nonlinearity coefficient γ = n2 ω0 / c Aeff = 2 2 [1/km.W], where nonlinear refractive index n2 = 2.6 10-20 [m2/W], ω0 / c = 2 π / λ = 2 π /1.3 10-6 [m-1], Aeff = 62.8 [µm2].

SOA: inner losses are 2000[m-1] and the linewidth enhancement factor =5, Γ =0.25 ⇒ Esat ~ 5.2 pJ.

After each fiber the signal will be amplified with SOA, therefore LA ~ 50 km. Note that the condition LA < LD is satisfied.

initial pattern of pulses pattern after 200 km

pattern after 350 km pattern after 500 km

the pattern effect:

reduction in the gain of the pulses after the first one in the first group even the last pulse, which is at distance approximately 1 nm from the first one, there is

no enough time for the gain to recover completely (the carrier lifetime is approximately 1.4 ns)

[1] M. Settembre, F. Matera, V. Hagele, I. Gabitov, A. W. Mattheus, and S. Turitsyn, “Cascaded optical communication systems with in-line semiconductor optical amplifiers”, Journal of Lightwave Technology, vol.15, pp. 962-967, 1997.

[2] F. Matera and M. Settembre, “Study of 1.3 µm transmission systems on standard step-index fibers with semiconductor optical amplifiers”, Optics communications, vol. 133, pp.463-470, 1997.

conclusions

⇒ gain saturation and gain recovery characteristics of SOA have been demonstrated

⇒ pulse compression based on the gain saturation effect has been shown

⇒ wavelength conversion using XGM and FWM was presented

⇒ the pattern effect at 10 Gb/s transmission over 500 km SMF with periodical SOA amplification has been demonstrated

semiconductor optical amplifier

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