Optoelectronic Applications. Injection Locked Oscillators. Injection Locked Oscillators. Q 2, ω 2. Q 1, ω 1

Transcription

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

2 V inj General Concept V ns Non-Linear Gain V r V sat V i V ns V r V sat Non-Linear Gain V i Delay Line ω Q BPF x () t Delay Line ω 0 BPF Q x () t α nω ω Non-Linear Gain BPF ω Q x () t V i V r V sat Delay Line α Single oscillator Interlocked oscillators V ns

3 Fundamental Locking Fundamental Locking First formulated by R. Adler (946) Principal locking criteria Given a master oscillator, coupled coupled uni- directionally to a slave oscillator with ω = ω ω ω,q ω,q Locking takes place within the locking range ω V ω l > V Q ω ω l

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

5 Harmonic Locking Locking requires mediation by a non-linearity Harmonics generation ω n ω Mixing with harmonics and Mixing with harmonics ( n ) ω ( ) n + ω creates a component at ω which locks the slave oscillator

6 Unidirectional Locking Unidirectional Locking Q Q >> Improved signal quality Superharmonic IL further improvement Q or Q >> Q << Q Synchronization Timing extraction Harmonic IL Multirate timing extraction

7 Harmonic Unidirectional Locking V ns Non-Linear Gain x () t V r BPF ω V sat Q V i Delay Line Non-Linear Gain Delay Line ω BPF Q Coupled oscillators : V i V r V sat x () t α V ns st harmonic of Q exhibits a lower noise than the st harmonic of the db ω =.5 GHz, Q 50 ω =.5 GHz, Q 5 4 = = st Q free st rd Q free ed Q locked st st Q Phase Noise dbc Hz Offset Frequency Hz higher quality injected signal by 0 log 0 3 9dB Explainable through correlated noise considerations

8 Harmonic Unidirectional Locking st harmonics of Q at ω = 3ω ω ω = Initially Signals Correlated uncorrelated turn into signals correlated signals ω 4ω st 4 th harmonics of Q at ω

9 Unidirectional Coupling Experiment Unidirectional Coupling Experiment rd st harmonics IL : ω = 3ω ω 3 rd st st Q free Agilent Spec. Anal. E4446A BPF st Q injected ω Bias-T ed st st st ed V B Photo-HBT Directional Low Noise Coupler Amplifier LNA Anritsu Synth C -00 Bias-T V C -0 Phase Noise dbc Hz EDFA Optical Filter 3 ω Mach-Zender Mudulator CW Laser Optical Isolator Polarization Controller Offset Frequency Hz Injected frequency is followed by the corresponding harmonics

10 Unidirectional Coupling Multi Rate Unidirectional Coupling Multi Rate Timing Extraction Transmitter Reciever Detector and Amplifier Clock Recovery Re-Timing Decision Re-Shaping Output

11 Multi Rate Timing Extraction Multi Rate Timing Extraction Extracted electrical clock BPF ω 0 Bias-T V B Directional Coupler Photo-HBT Frequency GHz Bias-T V C RZ signal or optically processed NRZ signal = 0 GHz ω 0 Lasri et. al 00

12 0 Gb/s and 40 Gb/s modulated RZ signals Transmitter Schematic DBR Pulse compression Mod. 0 Gb/s 40 Gb/s Multiplexer 40 Gbit/s ~ 0 GHz Phase shifter BER Transmitter ( 3 0 Gb/s) Data Out 0 Gbit/s Modulated RZ signal toward the photo HBT based oscillator Lasri et. al 00

13 Clock recovery of RZ data by direct optical IL of Photo-HBT based oscillator Incoming RZ stream Agilent PSA E4446A BER Receiver Data In Receiver Variable Attenuator Coupler Clock In Directional Coupler V C Bias-T Recovered Clock Directional Coupler Photo-HBT V B BPF Bias-T ω 0 = 0 GHz or 4 ω 0 = 40 GHz ω 0 Lasri et. al 00

14 Clock Recovery Results 0 GHz Locking 0 Free running injected signal -0 signal -50 injected signal 40 GHz Locking 4 th harmonic signal Injection locked signal Frequency GHz khz/div Frequency GHz Injection locked signal Detected Power dbm Detected Power dbm 0 khz/div Lasri et. al 00

15 BER performance for 0 GHz Locking - Direct Clock Recovered Clock Log ( BER ) Optical Power dbm Lasri et. al 00

16 Harmonic Bidirectional Locking V ns V r V sat Non-Linear Gain α nω ω Non-Linear Gain BPF V i Delay Line x () t V i ω Q V r V sat BPF Delay Line x & = ( F ( x )) x + y + α x x () t Q Q Q α V ns ω y & = ω x & Q x ω ω ω = x Q Q Q y & = ω Generalized Van der Pol Q x ω ω ( F ( x )) x + y + α ω Q Coupled oscillators : ω =.5 GHz, Q 50 ω =.5 GHz, Q 5 4 = = Injections strength is inversely relative to the quality factor

17 Harmonic Bidirectional Locking Phase noise at 00 khz offset Power Spectral Density st Q free : 5: 7: 0: 5: st Q free -0 :.5 free :5 :.5: : 7: 0: 5: st st st Q free lock rd Q free lock st Q free lock rd Q free lock :5 : :.5 :.5: Injection Ratio P / P Offset Frequency Hz Phase Noise dbc Hz

18 Bidirectional Coupling Bidirectional Coupling Experimental Setup Agilent PSA E4446A BPF ω Power Amplifier Bias-T EDFA Bias-T V B V C Loop BPF Directional Coupler Directional Coupler ω Loop Mach-Zender Modulator L fiber 3 km Photo-HBT Optical Filter CW Laser Optical Isolator Polarization Controller

19 Bidirectional Coupling Bidirectional Coupling Experimental Results st harmonics IL : ω = ω st st st st st Q free st Q free ed ed ed harmonics IL : ω = 3ω st st st st st Q free st Q free ed ed ed Phase Noise dbc Hz Offset Frequency Hz Offset Frequency Hz

20 Ultra Low Jitter Pulse Sources Ultra Low Jitter Pulse Sources Active mode-locking of fiber/diode lasers : Clark et al. ( NRL Labs ) : Ng et al. ( HRL Labs ) : Jiang et al. ( MIT ) : ( 00 Hz MHz ) at GHz ( 00 Hz 00 khz ) at GHz ( 0 Hz 0 MHz ) at GHz 9 f S 0 6 f S 0 47 f S 9 In all cases, ultra low phase-noise microwave source employed Self starting approach Coupled OEO s ( Yao and Maleki ) : RFSignal PD RF Amplifier RF BPF ω 0 Directional Coupler CW Laser Polarization Controller Coupler SOA Optical Pulses

21 Self-Starting Starting Ultra Low Jitter Optical Pulse Source Agilent PSA E4446A BPF I DC 0 GHz RF signal ω 0 Bias-T V B Bias-T Directional Coupler Directional Coupler Power Amplifier Photo-HBT Bias-T 0 GHz optical pulse-train V C Laser Diode FBG EDFA Optical Filter AR L fiber 0 km L laser Actively mode-locked diode laser Photo-HBT based oscillator Extended cavity optoelectronic oscillator Lasri et. al 00

22 Bidirectional Coupling Pulse Source Bidirectional Coupling Pulse Source Experimental Setup I DC Agilent PSA E4446A BPF Bias-T ω Loop V B Bias-T BPF Directional Coupler Directional Coupler Power Amplifier Photo-HBT ω Loop Bias-T V C Laser Diode FBG EDFA Optical Filter AR L fiber 0 km L laser

23 Bidirectional Coupling Pulsed Source Bidirectional Coupling Pulsed Source Experimental Results Pulsed Source Mode locked diode laser Modulated at it s s 6 th harmonics ( ω 3 = 773 MHz ) Driven by harmonics of the EO ( ω =.55 GHz ) Repetition rate 4.64 GHz Resulting locked signal has better phase noise then the free running OEO st Q free st Q free Electrical Signal Offset Frequency Hz st ed ed Phase Noise dbc Hz

24 Self-Starting Starting Ultra Low Jitter Optical Pulse Source khz/div Electrical 0 GHz signal Open loop 0 GHz Closed loop Wavelength nm Open Loop Closed Loop Power dbm Power mw Power mw Phase noise at 0 khz offset: Open loop: -98 dbc/hz Close loop: -08 dbc/hz Optical Spectrum τ ν 0.47 Wavelength nm

25 Harmonic spectral analysis (van der Linde technique): σ ( ) n n = σ A + σ J ω 0 Amplitude noise contribution Jitter contribution Harmonic number σ f f high x, n = S x ( f nf 0 ) df low Power spectrum 0-0 Jitter Measurements Lasri et. al 00 Open loop Harmonic number Closed loop Harmonic number 5 5 khz/div 0-50 GHz 5 khz/div Power dbm Power dbm 0-50 GHz

26 Jitter Measurements Lasri et. al Closed Loop Harmonic number Hz MHz 500 Hz MHz 500 Hz 5 khz Curve fit to σ = a n 0 + a n RMS Noise mw Offset Frequency Hz Harmonic Number Frequency range 500 Hz 5 khz 500 Hz MHz 00 Hz MHz Amplitude noise 0. % 0.5 % 0. % RMS Jitter 40 fs 43 fs 57 fs Note that the 40 fs jitter (with a power of 6 dbm and 0 km fiber) could not be improved with higher powers or longer fibers. Phase Noise dbc Hz

27 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 Self starting low jitter mode locked diode laser

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

29 -0 st st st Q free rd Q free st Q free rd Q free free st st : st st : st st :

30 -0 st st 5: st st 7: st st : st st 0:

31 -0 st st.5: st st 5: st st :

32 Feedback Model Feedback Model Phenomenological model Self starting from noise Easy injection modeling Polynomial Non-Linear Gain function BPF implemented as IIR filter Time domain simulation V inj V ns Non-Linear Gain V r V sat V i Delay Line Transmission line like propagation Decimation in time incorporating long FIR filter Ensemble averaged PSD ω 0 BPF Q x () t

33 Numerical Results Single Oscillator c s Hz Simulated Linear fit Simulated Analytical st harmonics nd 4 th nd harmonics rd harmonics th harmonics Phase Noise dbc Hz Time µs -00 Noise parameter c derived for ω.5 Resulting PSDs agree perfectly PSD has a single pole functional form Indicates Gaussian statistics CAN NOT be predicted by small signal analysis = GHz, Q = Offset Frequency Hz 5 Period Time Variance s