Modeling of Semiconductor Optical Amplifier RIN and Phase Noise ...

NUSOD 2011Modeling of Semiconductor OpticalAmplifier RIN and Phase Noise forOptical PSK SystemsM.J. Connelly 1 and C.L. Janer 21 Optical Communications Research Group, Dept. Electronic and Computer Engineering, University ofLimerick, Limerick, Ireland. E-mail: michael.connelly@ul.ie.2 Department of Electronic Engineering, Escuela Superior de Ingenieros, Universidad de Sevilla,Camino de los Descubrimientos s/n, Seville, Spain. Email: janer@zipi.us.esAbstract- Phase modulation schemes are attracting muchinterest for use in ultra-fast optical communication systemsbecause they are much less sensitive to fibre nonlinearitiescompared to conventional intensity modulation formats.Semiconductor optical amplifiers (SOAs) can be used to amplifyand process phase modulated signals, but with a consequentaddition of nonlinear phase noise (NLPN). Existing SOA NLPNmodels are simplistic. In this paper we show that a more accuratemodel can be used, which results in simple expressions for SOAnonlinear noise, in particular when used to amplify differentialphase shift keyed (DPSK) modulated data. The model is used tocalculate the optical signal to noise ratio introduced by a powerbooster SOA and the first inline amplifier of a 40 Gb/s NRZ-DQPSK single channel link.I. INTRODUCTION* Constant envelope modulation formats, in particular RZandNRZ-DPSK, are among the most promising candidates forSOA-based high bit rate systems because of their resilience tofiber non-linearities and pattern effects [1]. Gain saturation inSOAs introduces NLPN that can be detrimental in PSKsystems. The phase noise behaviour of saturated SOAs inDPSK systems has been analysed in several papers [2 and itsreferences]. The advantage of these NLPN models is that theyare analytical and easy to apply, however they have limitedaccuracy, in that they do not consider the internal noisegenerated by the SOA or properly account for scattering losses.In this paper we show that these assumptions are not alwayscorrect. We also show that an existing computationally simpleand more accurate noise model can be used that leads to simpleNLPN expressions at the SOA for constant envelopemodulation schemes [3].II.THEORYThe model equations in the spectral domain (ω) are [3]:2z gS() z ρS()z2S S S∂ δρ() δρ()z=− + N∂ z ρ () z 1 + ρ () z + iωτ ρ () z∂δφαg z z z= + N∂ z 1 + ρ ( z) + i ( z)2S( ) ρS( ) δρ( )2Sωτ ρSφ( ω,z)ρ( ω,z)* This research was supported by the Spanish Department of Education underthe Programa Nacional de Recursos Humanos del Plan Nacional de I+D+I2008-2011 and Science Foundation Ireland Investigator Grant 09/IN.1/I2641.(1)(2)where z is the distance from the SOA input, ρ S (z) is the signalfield amplitude (equal to the square root of the optical power tothe SOA saturation energy), δρ(z) the amplitude noise(induced by the Langevin force N ρ (ω,z)), δφ(z) the phase noise(induced by the Langevin force N φ (ω,z)), g S (z) the saturatedgain, τ is the carrier lifetime and α the linewidth enhancementfactor. The Langevin forces account for field fluctuations dueto spontaneous emission, carrier noise and a term arising fromtheir interaction. The terms ρ S (z) and g S (z) are the unperturbed,distributions along the SOA and can be obtained bynumerically solving [3],∂E( z) 1= gS( z) ( 1 − iα)− γSCE( z)∂ z 2(3)[ ]2= go −gS z τ − gSz E z τ(4)0 ( ) ( ) ( )[ φS]E( z) = ρ ( z)exp i ( z)Swhere φ s (z) is the optical field phase, g o is the unsaturated gain,and γ sc the waveguide scattering losses. Once the spatialdependency of g S (z) and ρ S (z) have been determined, they canbe inserted in (1-2), which are then numerically solved todetermine the SOA output RIN and phase noise, due to thenoise of the input signal, spontaneous emission noise, carriernoise and the cross-correlation between the carrier noise andspontaneous emission. The numerical solution of (1-2) is notdifficult as it mainly involves numerical integration.III.NUMERICAL ANALYSISThe geometrical and material parameters used in the modelwere determined for a 1 mm long tensile-strained SOA [4] witha 20 dB unsaturated gain, α = 2.5, saturation power of 1.9 mW,g 0 = 9500 m -1 and γ sc = 4500 m -1 . Simulation results for SOAoutput RIN and phase noise for an input signal powernormalised (to the saturation power) of 0.1, with no input RINis shown in Figs. 1-2. The phase noise spectrum can be used todetermine the phase noise variance σ φ 2 after optical reception.For example if we consider a 40 Gb/s NRZ-DQPSK receiver,its bandwidth is typically 20 GHz. σ φ 2 can be determined byobtaining the autocorrelation function R(τ) of the filtered phasenoise by taking its inverse Fourier transform and letting τ = 0.(5)978-1-61284-878-5/11/$26.00 ©2011 IEEE95

NUSOD 2011It is simple to carry out this numerically. In Fig. 3, σ φ is plottedversus the normalised input power. It can be seen that σ φ isquite sensitive to the degree of saturation. To our knowledgethe probability density function of NRZ-DQPSK random datain the presence of NLPN has not yet been determined and so itis not presently possible to obtain an analytical expression forthe bit-error-rate. However it is possible to determine theOptical Signal-to-Noise Ratio (OSNR) which is given byOSNR = π 8σ(6)2 2φIn Fig. 4, the OSNRs at the outputs of a power booster (with noinput noise) and a first in-line SOA in a 40 Gb/s DQPSK linkare shown as a function of the SOA carrier lifetime. Both SOAinput normalised powers are equal to 0.01. It can be seen thatthere is a serious degradation in the OSNR, particularly at thein-line SOA output, for small carrier lifetimes. Similarsimulations show a similar dependency for increases in thelinewidth enhancement factors and scattering losses.Fig. 2: SOA output total phase noise and components spectra (centred at theoptical frequency) for a normalised input power of 0.1.REFERENCES[1] A.H. Gnauck and P.J. Winzer, “Optical phase-shift-keyed transmissions,” J.Lightwave Techol., vol 23, pp. 115-130, 2005.[2] X. Wei and L. Zhang, “Analysis of the phase noise in saturated SOAs forDPSK applications,” IEEE J. Quantum Electron., vol. QE-41, pp. 554-561, 2005.[3] M. Shtaif, B. Tromborg and G. Eisenstein, “Noise spectra of semiconductoroptical amplifiers: relation between semiclassical and quantumdescriptions,” IEEE J. Quantum Electron., vol. 34, pp. 869-878, 1998.[4] M.J. Connelly, “Wide-band steady-state numerical model and parameterextraction of a tensile-strained bulk semiconductor optical amplifier,”IEEE J. Quantum Electron., vol. 43, pp. 47-56, 2007.Fig. 3: SOA output phase noise standard deviation for input powers rangingfrom 0.01 to 0.1. The receiver bandwidth is 20 GHz.Fig. 1: SOA output total RIN and components spectra (centred at the opticalfrequency) for a normalised input power of 0.1.Fig. 4: OSNR at the output of SOA power booster and the first in-line amplifieras a function of the carrier lifetime for a normalised input power = 0.01. Thereceiver bandwidth is 20 GHz.96