2. Injection Locked Oscillators Optoelectronic Applications E. Shumakher, J. Lasri, B. Sheinman, G. Eisenstein, D. Ritter Electrical Engineering Dept. TECHNION Haifa ISRAEL Q 1, ω 1 Q 2, ω 2

3. General Concept Single oscillator Interlocked oscillators

4. Fundamental Locking First formulated by R. Adler (1946) First formulated by R. Adler (1946) Principal locking criteria Given a master oscillator, coupled uni- directionally to a slave oscillator with Locking takes place within the locking range

5. Harmonic Locking  Two possible configurations  Sub-harmonic injection locking :  Super-harmonic injection locking :  Consequences Injected signal does not satisfy Injected signal does not satisfy Lifetime is very short inside the oscillating loop Lifetime is very short inside the oscillating loop Dynamics of the loop can not be altered Dynamics of the loop can not be altered

6. Locking requires mediation by a non-linearity  Harmonics generation –  Mixing with harmonics and creates a component at which locks the slave oscillator creates a component at which locks the slave oscillator Harmonic Locking

7. Unidirectional Locking  Improved signal quality Improved signal quality Superharmonic IL – further improvement Superharmonic IL – further improvement  or Synchronization – Timing extraction Synchronization – Timing extraction Harmonic IL – Multirate timing extraction Harmonic IL – Multirate timing extraction

8. 3 rd Harmonic Unidirectional Locking  Coupled oscillators :  1 st harmonic of Q 2 exhibits a lower noise than the 1 st harmonic of the higher quality injected signal by higher quality injected signal by  Explainable through correlated noise considerations 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 1 st Q 2 free 3 rd Q 2 free 1 st Q 2 locked 3 rd Q 2 locked 1 st Q 1 Offset Frequency Hz Phase Noise dBc Hz

9. 3 rd Harmonic Unidirectional Locking Initially uncorrelated signalsSignals turn into correlated Correlated signals 1 st harmonics of Q 1 at 1 st – 4 th harmonics of Q 2 at ω 2

10. Unidirectional Coupling Experiment  Injected frequency is followed by the corresponding harmonics 1 st Q 2 free 1 st Q 1 injected 1 st Q 2 locked 3 rd Q 2 locked Offset Frequency Hz Phase Noise dBc Hz 3 rd harmonics IL : 1 st harmonics IL :

11. Unidirectional Coupling Multi Rate Timing Extraction

12. Multi Rate Timing Extraction Frequency GHz RZ signal or optically processed NRZ signal Extracted electrical clock Lasri et. al 2002

13. Modulated RZ signal toward the photo – HBT based oscillator Transmitter Schematic 10 Gb/s – 40 Gb/s Multiplexer Mod. Data Out Phase shifter DBR ~ Pulse compression BER Transmitter (2 31 -1 @ 10 Gb/s) 40 Gbit/s 10 Gbit/s 10 GHz 10 Gb/s and 40 Gb/s modulated RZ signals Lasri et. al 2002

14. Recovered Clock Clock recovery of RZ data by direct optical IL of Photo-HBT based oscillator Lasri et. al 2002

15. Detected Power dBm 9.999810.000410.0012 -70 -60 -40 -20 0 injected signal 10.000210.000610.001 Free running signal Injection locked signal -70 -60 -40 -20 0 4 th harmonic signal injected signal Injection locked signal -70 -60 -50 -40 -70 -60 -50 -40 10 kHz/div 40 10 GHz Locking Frequency GHz Clock Recovery Results 40 GHz Locking Frequency GHz Detected Power dBm 10 kHz/div Lasri et. al 2002

16. -26-25-24-23-22-21-20-19-18 -9 -7 -5 -3 Optical Power dBm Log ( BER ) Direct Clock Recovered Clock BER performance for 10 GHz Locking Lasri et. al 2002

17. 3 rd Harmonic Bidirectional Locking  Coupled oscillators :  Injections strength is inversely relative to the quality factor Generalized Van der Pol

18. 3 rd Harmonic Bidirectional Locking 0.1110100 -95 -90 -85 -80 -75 -70 -65 Injection Ratio P 2 / P 1 Phase Noise dBc Hz 1 st Q 2 free 1 st Q 1 free 25:1 10:1 7:1 5:1 2:1 1.5:1 1:1 1:1.5 1:2 1:5 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 1 st Q 1 free 3 rd Q 1 free 1 st Q 2 free 3 rd Q 2 free free 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 1 st Q 1 lock 3 rd Q 1 lock 1 st Q 2 lock 3 rd Q 2 lock 1:51:2 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 1:1.5 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 1:11.5:1 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 2:1 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 5:1 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 7:1 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 10:1 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 25:1 Offset Frequency Hz Phase noise at offset Power Spectral Density

19. Bidirectional Coupling Experimental Setup

20. Bidirectional Coupling Experimental Results 1 st Q 2 free 1 st Q 1 free 1 st Q 1 locked 3 rd Q 2 locked 1 st Q 2 locked 1 st Q 2 free 1 st Q 1 free 1 st Q 1 locked 3 rd Q 2 locked 1 st Q 2 locked Offset Frequency Hz Phase Noise dBc Hz Offset Frequency Hz 3 rd harmonics IL : 1 st harmonics IL :

21. Ultra Low Jitter Pulse Sources  Active mode-locking of fiber/diode lasers : Clark et al. ( NRL Labs ) : Clark et al. ( NRL Labs ) : Ng et al. ( HRL Labs ) : Ng et al. ( HRL Labs ) : Jiang et al. ( MIT ) : Jiang et al. ( MIT ) :  In all cases, ultra low phase-noise microwave source employed  Self starting approach – Coupled OEO’s ( Yao and Maleki ) :

22. Lasri et. al 2002 Self-Starting Ultra Low Jitter Optical Pulse Source 10 GHz RF signal 10 GHz optical pulse-train AAAActively mode-locked diode laser PPPPhoto-HBT based oscillator EEEExtended cavity optoelectronic oscillator

23. Bidirectional Coupling Pulse Source Experimental Setup

24. Bidirectional Coupling Pulsed Source Experimental Results  Pulsed Source Mode locked diode laser Mode locked diode laser Modulated at it’s 6 th harmonics ( ) Modulated at it’s 6 th harmonics ( ) Driven by 3 rd harmonics of the EO ( ) Driven by 3 rd harmonics of the EO ( ) Repetition rate Repetition rate Resulting locked signal has better phase noise then the free running OEO Resulting locked signal has better phase noise then the free running OEO -140 10 2 3 4 5 6 -120 -100 -80 -60 -40 1 st Q 2 free 1 st Q 1 free 1 st Q 2 locked 3 rd Q 2 locked Offset Frequency Hz Phase Noise dBc Hz Electrical Signal

25. 10 GHz 5 kHz/div Power dBm -85 -75 -65 -55 -45 -35 -25 -15 -5 Closed loop Open loop 0.05 0.15 0.25 0.35 1542.515431543.51544 1544.5 0.05 0.15 0.25 0.35 Wavelength nm Open Loop Closed Loop 1543.51542.5154315441544.5 Power mW Phase noise at 10 kHz offset: Open loop: -98 dBc/Hz Close loop: -108 dBc/Hz Electrical 10 GHz signal  0.47 Power mW Wavelength nm Optical Spectrum Self-Starting Ultra Low Jitter Optical Pulse Source

26. Harmonic spectral analysis (van der Linde technique): 0 1 23 4 5 Harmonic number Power spectrum Amplitude noise contribution Jitter contribution -80 -60 -40 -20 0 10-50 GHz 5 kHz/div Power dBm 1 5 Harmonic number Open loop Power dBm -80 -60 -40 -20 0 10-50 GHz 5 kHz/div Closed loop 1 5 Harmonic number Lasri et. al 2002 Jitter Measurements

27. 10 2345 6 -120 -100 -80 -60 1 4 Harmonic number Closed Loop 01234 5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Harmonic Number RMS Noise mW 100 Hz – 1 MHz 500 Hz – 1 MHz 500 Hz – 15 kHz Curve fit to Frequency range Amplitude noise RMS Jitter 500 Hz – 15 kHz500 Hz –1 MHz100 Hz –1 MHz 0.1 % 0.15 %0.2 % 40 fS 43 fS 57 fS Note that the 40 fs jitter (with a power of – 6 dBm and 10 km fiber) could not be improved with higher powers or longer fibers. Phase Noise dBc Hz Offset Frequency Hz Lasri et. al 2002 Jitter Measurements

28. Conclusion  Photo HBT based oscillator – versatile multi functional system  Accurate numerical model  Fundamental and Harmonic injection locking  Uni and bi-directional locking  Improved noise performance due to correlated noise interaction in Harmonically locked oscillators  Multi rate timing extraction  Bi-directional locking – characteristics determined by mutual locking efficiency and relevant Q factors by mutual locking efficiency and relevant Q factors  Self starting low jitter mode locked diode laser

29. The locking mechanism Injected signal x 1 (t) saturates the gain Injected signal x 1 (t) saturates the gain Loop lifetime is long Loop lifetime is long Free running dynamics are overwritten by Free running dynamics are overwritten by x 1 (t) for x 1 (t) for Fundamental Locking

30. 1 st Q 1 lock 3 rd Q 1 lock 1 st Q 2 lock 3 rd Q 2 lock 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 1:1 1 st Q 1 lock 3 rd Q 1 lock 1 st Q 2 lock 3 rd Q 2 lock 1:2 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 1 st Q 1 lock 3 rd Q 1 lock 1 st Q 2 lock 3 rd Q 2 lock 2:1 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 1 st Q 1 free 3 rd Q 1 free 1 st Q 2 free 3 rd Q 2 free free

31. 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 1 st Q 1 lock 3 rd Q 1 lock 1 st Q 2 lock 3 rd Q 2 lock 5:1 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 1 st Q 1 lock 3 rd Q 1 lock 1 st Q 2 lock 3 rd Q 2 lock 7:1 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 1 st Q 1 lock 3 rd Q 1 lock 1 st Q 2 lock 3 rd Q 2 lock 10:1 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 1 st Q 1 lock 3 rd Q 1 lock 1 st Q 2 lock 3 rd Q 2 lock 1:5

32. 1 st Q 1 lock 3 rd Q 1 lock 1 st Q 2 lock 3 rd Q 2 lock 1.5:1 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 1 st Q 1 lock 3 rd Q 1 lock 1 st Q 2 lock 3 rd Q 2 lock 1:1.5 10 2 3 4 5 6 7 -120 -100 -80 -60 -40 -20 1 st Q 1 lock 3 rd Q 1 lock 1 st Q 2 lock 3 rd Q 2 lock 25:1

33. Feedback Model  Phenomenological model Self starting from noise Self starting from noise Easy injection modeling Easy injection modeling Polynomial Non-Linear Gain function Polynomial Non-Linear Gain function BPF implemented as IIR filter BPF implemented as IIR filter  Time domain simulation Transmission line – like propagation Transmission line – like propagation Decimation in time incorporating long FIR filter Decimation in time incorporating long FIR filter Ensemble averaged PSD Ensemble averaged PSD

34. Numerical Results – Single Oscillator  Noise parameter c derived for  Resulting PSDs agree perfectly  PSD has a single pole functional form Indicates Gaussian statistics Indicates Gaussian statistics CAN NOT be predicted by small signal analysis CAN NOT be predicted by small signal analysis 10 2 3 4 5 6 -100 -90 -80 -70 -60 -50 -40 -30 -20 1 st harmonics 2 nd harmonics 3 rd harmonics 4 th harmonics Linear fit 020406080 0 1 2 3 4 5 6 7 8Simulated Offset Frequency Hz Phase Noise dBc Hz Time μS Period Time Variance s 2 Analytical Simulated