NOISE IN OPTICAL SYSTEMS

1. F. X. Kärtner High-Frequency and Quantum Electronics Laboratory NOISE IN OPTICAL SYSTEMS University of Karlsruhe

2. Outline I. Introduction: High-Speed A/D-Conversion II. Quantum and Classical Noise in Optical Systems III. Dynamics of Mode-Locked Lasers IV. Noise Processes in Mode-Locked Lasers V. Semiconductor Versus Solid-State-Lasers VI. Conclusions

3. V T V T V T o o o o o o DV DV High-Speed A/D-Conversion(100 GHz) Voltage Voltage Time Dt o o DV Modulator Time : 10 bit Dt Timing-Jitter Dt: = 2p => Dt ~ 1 fs 1 =100 GHz

4. 4+ Mode-Locked Cr : YAG Microchip-Laser Output Saturable Coupler Semiconductor Absorber Output @ 1350 - 1550 nm Nd:YAG Laser or Diode Laser Dichroic Beam Splitter 4+ Cr :YAG - Crystal 8mm long, 10 GHz Repetitionrate • Compact: Saturable Absorber, Dispersion Compensating Mirrors • 10 GHz, 20 fs - 1 ps, @ 1350 - 1550 nm • Very Small Timing-Jitter < 1 fs • Cheap (< 10.000 $)

5. Classical and Quantum-Noise in Optical Systems (Modes of the EM-Field) Length L Thermal Equilibrium

6. States and Quadrature Fluctuations Area=p/4 Area=p/4 1 Squeezed States Coherent States (Minium Uncertainty States)

7. Balanced Homodyne-Detection Continuum of modes LO

8. Loss- and Amplifier-Noise Loss: Necessary noise for maintaining uncertainty circle Amplifier: Spontaneous emission noise Non-Ideal Amplifier:

9. cavity roundtrip time • A(T,t) Dynamics of Mode-Locked Lasers l:loss Sat. Loss Gain g, Wg SPM  GDD D g small changes per roundtrip • Energy Conserving • Dissipative

10. Steady-State Solution If pulses are solitonlike

11. The System with Noise Amplifier Noise: Gain Fluctuations: Cavity Length or Index Fluctuations:

12. Soliton-Perturbation Theory Energy Phase Center-frequency Timing and Continuum

13. Linearized and Adjoint System Linearized system is not hamiltonian, it is pumped by the steady-state pulse Scalar Product: Interpretation: Field g is homodyne detected by LO f Adjoint System L+: Biorthogonal Basis

14. Basic Noise Processes

15. Noise Sources

16. Amplitude- and Frequency Fluctuations Amplitude- and frequency fluctuations are damped and remain bounded Correlation Spectra Variances

17. Phase- and Timing Fluctuations Phase- and timing fluctuations are unbounded diffusion processes Gordon-Haus Jitter

18. Timing Fluctuations Quantum Noise Classical Noise

19. Long-Term Timing Fluctuations T >> tp, tL, tn, tg Quantum Noise Classical Noise

20. Semicondutor versus Solid-State Lasers tg tn t Wg g Wgt tp/TR Dn/n Dg/g W0/hn ns fs THz ns Semicon- ductor Laser 107 0.2 40 300 10 375 10-3 1 1 10-3 10 450 fs Solid- State Laser 1 75 0 0 10-3 1000 2 1 fs 1010 0.01 200 10 Other parameters are: T=TR=100 ps, Fo =1 Dominant sources for timing jitter: Semiconductor -Laser: Gordon-Haus-Jitter + Index-Fluctuations Solid-State Laser: Gain-Fluctuations

21. Conclusions • Classical and quantum noise in modes of the EM-Field • Spontaneous emission noise of amplifiers • Dynamics of modelocked lasers (solitonlike pulses) • Amplitude-, phase-, frequency- and timing-fluctuations • Solid-State Lasers: no index fluctuations; possibly small Gordon-Haus Jitter; very short pulses; superior timing jitter in comparison to semiconductor lasers

22. References: H. A. Haus and A. Mecozzi: „Noise of modelocked lasers,“ IEEE JQE-29, 983 (1993). J. P. Gordon and H. A. Haus: „Random walk of coherently amplified solitons in optical fiber transmission,“ Opt. Lett. 11, 665 (1986). H. A. Haus, M. Margalit, and C. X. Yu: „Quantum noise of a mode-locked laser,“ JOSA B17, 1240 (2000). D. E. Spence, et. al.: „Nearly quantum-limited timing jitter in a self-mode-locked Ti:sapphire laser,“ Opt. Lett. 19, 481 (1994).