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

General Concept Single oscillator Interlocked oscillators General Concept Single oscillator Interlocked oscillators

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

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

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

Unidirectional Locking Ø l l Improved signal quality Superharmonic IL – further improvement or Unidirectional Locking Ø l l Improved signal quality Superharmonic IL – further improvement or Ø l l Synchronization – Timing extraction Harmonic IL – Multirate timing extraction

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

3 rd Harmonic Unidirectional Locking 1 st harmonics of Q 1 at Correlated signals 3 rd Harmonic Unidirectional Locking 1 st harmonics of Q 1 at Correlated signals Initially uncorrelated signals Signals turn into correlated 1 st – 4 th harmonics of Q 2 at ω2

Unidirectional Coupling Experiment 3 rd harmonics IL : 1 st Q 2 free 1 Unidirectional Coupling Experiment 3 rd harmonics IL : 1 st Q 2 free 1 st Q 1 injected 1 st Q 2 locked 3 rd Q 2 locked -40 Phase Noise d. Bc Hz -60 -80 -100 -120 -140 2 10 3 10 4 10 Offset Frequency Hz Ø 5 10 Injected frequency is followed by the corresponding harmonics 6 10

Unidirectional Coupling Multi Rate Timing Extraction Unidirectional Coupling Multi Rate Timing Extraction

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

10 Gb/s and 40 Gb/s modulated RZ signals Transmitter Schematic 10 Gb/s – 40 10 Gb/s and 40 Gb/s modulated RZ signals Transmitter Schematic 10 Gb/s – 40 Gb/s Multiplexer Pulse compression DBR ~ 10 GHz Phase shifter Mod. 40 Gbit/s 10 Gbit/s BER Transmitter (231 -1 @ 10 Gb/s) Lasri et. al 2002 Data Out Modulated RZ signal toward the photo – HBT based oscillator

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

Clock Recovery Results 10 GHz Locking 0 -20 40 GHz Locking -40 injected signal Clock Recovery Results 10 GHz Locking 0 -20 40 GHz Locking -40 injected signal Free running signal -50 -40 -60 -70 9. 9998 10. 0004 0 10. 0012 Injection locked signal -20 -40 Detected Power d. Bm 4 th harmonic signal -70 10 k. Hz/div 40 -40 Injection locked signal -50 -60 -70 10 k. Hz/div -70 10. 0002 10. 0006 Frequency GHz 10. 001 40 Frequency GHz Lasri et. al 2002

BER performance for 10 GHz Locking Direct Clock -1 Recovered Clock Log ( BER BER performance for 10 GHz Locking Direct Clock -1 Recovered Clock Log ( BER ) -3 -5 -7 -9 -26 -25 -24 -23 -22 -21 -20 -19 -18 Optical Power d. Bm Lasri et. al 2002

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

3 rd Harmonic Bidirectional Locking Phase noise at -65 offset -20 Phase Noise d. 3 rd Harmonic Bidirectional Locking Phase noise at -65 offset -20 Phase Noise d. Bc Hz -70 -75 Power Spectral Density 1 st Q 1 lock free 3 rd Q 1 lock free st Q lock 1 2 free 3 rd Q 2 lock 3 rd Q 2 free -40 1 st Q 2 free 10: 1 -80 2: 1 5: 1 -60 25: 1 7: 1 1 st Q 1 free -85 1: 5 -90 1. 5: 1 1: 1. 5 -80 1: 1. 5 25: 1 10: 1 7: 1 5: 1 1: 5 free 2: 1 1: 2 -100 1: 1 1: 2 -95 0. 1 1 10 Injection Ratio P 2 / P 1 100 -120 2 10 10 3 10 4 10 5 Offset Frequency Hz 10 6 10 7

Bidirectional Coupling Experimental Setup Bidirectional Coupling Experimental Setup

Bidirectional Coupling Experimental Results 1 st harmonics IL : -20 1 st Q 2 Bidirectional Coupling Experimental Results 1 st harmonics IL : -20 1 st Q 2 free 1 st Q 1 free 1 st Q 2 locked 3 rd Q 2 locked 1 st Q 1 locked d. Bc Hz -40 -60 Phase Noise 3 rd harmonics IL : 1 st Q 2 free 1 st Q 1 free 1 st Q 2 locked 3 rd Q 2 locked 1 st Q 1 locked -80 -100 -120 -140 2 10 103 104 105 Offset Frequency Hz 106 102 103 104 105 Offset Frequency Hz 106

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

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

Bidirectional Coupling Pulse Source Experimental Setup Bidirectional Coupling Pulse Source Experimental Setup

Bidirectional Coupling Pulsed Source Experimental Results Pulsed Source l l Mode locked diode laser Bidirectional Coupling Pulsed Source Experimental Results Pulsed Source l l Mode locked diode laser Modulated at it’s 6 th harmonics ( ) Driven by 3 rd harmonics of the EO ( ) Repetition rate Resulting locked signal has better phase noise then the free running OEO -40 1 st Q 2 free 1 st Q 1 free 1 st Q 2 locked 3 rd Q 2 locked -60 d. Bc Hz l Electrical Signal -80 Phase Noise Ø -100 -120 -140 102 3 10 4 10 5 10 Offset Frequency Hz 6 10

Self-Starting Ultra Low Jitter Optical Pulse Source Electrical 10 GHz signal Optical Spectrum -5 Self-Starting Ultra Low Jitter Optical Pulse Source Electrical 10 GHz signal Optical Spectrum -5 -35 Open loop -45 Open Loop 0. 25 0. 15 0. 05 -55 Closed loop -65 1542. 5 1543. 5 1544. 5 Wavelength nm -75 0. 35 -85 5 k. Hz/div 10 GHz Phase noise at 10 k. Hz offset: Open loop: -98 d. Bc/Hz Close loop: -108 d. Bc/Hz Power m. W Power d. Bm -25 Power m. W 0. 35 -15 0. 25 Dt. Dn ~ 0. 47 Closed Loop 0. 15 0. 05 1542. 5 1543. 5 1544 Wavelength nm 1544. 5

Lasri et. al 2002 Jitter Measurements Power spectrum Harmonic spectral analysis (van der Linde Lasri et. al 2002 Jitter Measurements Power spectrum Harmonic spectral analysis (van der Linde technique): Amplitude noise contribution 0 1 2 3 4 5 Harmonic number 0 Open loop -20 Harmonic number -40 5 -60 1 -80 5 k. Hz/div 10 -50 GHz Power d. Bm 0 Jitter contribution Closed loop -20 Harmonic number -40 -60 5 -80 1 5 k. Hz/div 10 -50 GHz

Lasri et. al 2002 Jitter Measurements Closed Loop -60 100 Hz – 1 MHz Lasri et. al 2002 Jitter Measurements Closed Loop -60 100 Hz – 1 MHz 500 Hz – 15 k. Hz 0. 35 -80 Harmonic number -100 4 -120 10 1 2 10 3 10 4 10 5 10 6 RMS Noise m. W Phase Noise d. Bc Hz 0. 3 Curve fit to 0. 25 0. 2 0. 15 0. 1 0. 05 0 0 1 2 3 4 Harmonic Number Offset Frequency Hz Frequency range 500 Hz – 15 k. Hz 500 Hz – 1 MHz 100 Hz – 1 MHz Amplitude noise 0. 1 % 0. 15 % 0. 2 % RMS Jitter 40 f. S 43 f. S 57 f. S Note that the 40 fs jitter (with a power of – 6 d. Bm and 10 km fiber) could not be improved with higher powers or longer fibers. 5

Conclusion Ø Ø Ø Ø Photo HBT based oscillator – versatile multi functional system Conclusion Ø Ø Ø Ø 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 Self starting low jitter mode locked diode laser

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

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

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

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

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

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