Time-domain simulation of semiconductor laser light with correlated amplitude and phase noise

Transcription

1 Time-domain simulation of semiconductor laser light with correlated amplitude and phase noise Daniel Lasaosa, Martín Vega-Leal, Carlos Fañanas Universidad Pública de Navarra, NUSOD Pamplona, 007 Delaware SPAIN

2 Outline Motivation Physical principle Simulation algorithm Time-domain results Noise spectra Applications Conclusions

3 Motivation Physical principle Simulation algorithm Time-domain results Noise spectra Applications Conclusions

4 Motivation Frequency domain analysis is sufficient for LTI systems X ( f ) H ( f ) H ( f ) X ( f ) Increasing number of applications combine LTI and non-lti subsystems CW PM Correct system evaluation needs time-domain noise characterization

5 Motivation Physical principle Simulation algorithm Time-domain results Noise spectra Applications Conclusions

6 Noise Origin in Semiconductor Lasers ηii qv Carrier reservoir AN + CN 3 All processes are the sum of individual uncorrelated events BN N R 1 β sp BN R 1 Photon reservoir αivn g p N p ln L ln L ( ) R1 vn g p ( R ) vn g p Noise is similar to white noise colored by the laser response The lasing frequency depends on N through reffractive index Photon output adds partition noise Spontaneously emitted photons add random phase

7 Rate Equations and Langevin Picture dn dt η I qv i 3 = AN CN BN R1 + R1 + Related!!! F N Output photon number dn dt p ( ) ln ( ) ln R R = Γ R 1 Γ R 1 +Γβ BN + vn + v N α v N + F L L 1 sp g p g p i g p P Langevin noise sources F N and F P represent randomness in the generation/loss processes (poissonian characteristics) Effect of noise sources is analogous to substitution of rates with Poisson-distributed variables

8 Motivation Physical principle Simulation algorithm Time-domain results Noise spectra Applications Conclusions

9 Computation of carrier and photon evolution Approximation of evolution by numerically solving density rate equations as difference equations η I + Δt qv ( + ) ( t) + t ( nr ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) i 3 N tn+δ tt Δ = tn= N t Δ xi t ANx+ CN t Δxsp t tbn xδ1 t tr1 + Δ xt1+ Rt 1 ln ( 1) ln ( R ) ( N) p( tn +Δ ( t) ) = ΓN pδ( t) Γ +Γx1 Δ t( t+ ) Γ Γ xbn 1 ( tδ) + t+ Γβ sp xsp ( t ) Δxo 1+ ( t) xo ( v t) Δxl ( t ) R N p t + Δ t = p t + R1 t R1 βs p vn g p t g Np t αivgnpδt L L Instantaneous output power may be calculated using P () t out = ( ) E x t V ph o1 p Δt Allows the computation of instantaneous carrier and photon densities Partition noise taken into account

10 Simulation Algorithm Self-consistent solution to rate equations provides equilibrium point for given output power (N 0,N p,0 ) N N p ( 0) ( 0) = N = N 0 p,0 Calculate random variations Update N(t+Δt) N p (t+δt) Instantaneous carrier density, photon density and output power No t+δt t t+δt =t final? Yes Save results Exit Phase noise due to spontaneous emission noise is added as random variable with gaussian probability distribution α Δ f () t = Γvga N () t N + x t 4π ( 0 ) φ ()

11 Motivation Physical principle Simulation algorithm Time-domain results Noise spectra Applications Conclusions

12 Evolution of Output Power and Frequency Photon density fluctuations (10 8 cm -3 ) Simulated time evolution of carrier and photon density 0 0,5 1 1,5 Time (ns) Carrier density fluctuations (10 11 cm -3 ) Simulated time evolution of output power and lasing frequency Output power fluctuations (nw) ,5 1 1,5-30 Time (ns) Frequency variations (khz) Visible correlation between amplitude and phase noise Optical power variations trail frequency variations by about π/

13 Autocorrelations Output power fluctuations autocorrelation 1 Lasing frequency fluctuations autocorrelation 1 Autocorrelation (norm.) 0,8 0,6 0,4 0, 0-0, -0,4-0, Time (ns) 5 10 Autocorrelation (norm.) 0,5 0-0, Time (ns) 5 10 Partition noise makes the output power fluctuations autocorrelation noisier

14 Motivation Physical principle Simulation algorithm Time-domain results Noise spectra Applications Conclusions

15 RIN Spectra RIN spectrum (db/hz) μW per facet 00mW per facet 1mW per facet 5mW per facet RIN spectrum (db/hz) RIN spectrum (db/hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) RIN spectrum (db/hz) Good agreement between computed results and previously exising theoretical results

16 Frequency Noise Spectra μW per facet μW per facet mW per facet mW per facet FM spectrum (Hz) FM spectrum (Hz) FM spectrum (Hz) FM spectrum (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) Good agreement between computed results and previously exising theoretical results

17 Motivation Physical principle Simulation algorithm Time-domain results Noise spectra Applications Conclusions

18 RIN Reduction Input RIN output RIN (normalized) mW per facet Frequency (normalized) Input RIN output RIN (normalized) mW per facet Frequency (normalized) Future work: check with existing theory (Vahala & Newkirk)

19 Noise in Short Pulses Instantaneous power (norm.) Pulses generated by FM modulation and dispersion 4 3,5 3,5 1,5 1 0, ,1 0, 0,3 0,4 0,5 Time (ns) Due to phase noise (norm.) Due to amplitude noise (norm.) Noise in short pulses generated by FM and dispersion 1 0,5 0-0, ,1 0, 0,3 0,4 0,5 Time (ns) Future work: Evaluate critical parameters and reduce noise

20 Motivation Physical principle Simulation algorithm Time-domain results Noise spectra Applications Conclusions

21 Conclusions Time-domain algorithm that computes laser noise based on physical principle of operation Correlation ensured by use of coupled density-rate equations Natural introduction of partition noise artificial introduction of spontaneous emission effect on phase noise Results match predictions from existing frequency-domain models Possible application to systems combining both LTI and non-lti components