1. NOISE IN OPTICAL SYSTEMS F. X. Kärtner High-Frequency and Quantum Electronics Laboratory 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. High-Speed A/D-Conversion (100 GHz) Voltage Time o o T o tt Voltage Modulator Timing-Jitter  t: = 2  tt T o V o VV VV V o VV V o : 10 bit =100 GHz 1 T o =>  t ~ 1 fs Time

4. Output @ 1350 - 1550 nm Output Coupler Saturable Semiconductor Absorber Cr :YAG - Crystal 8mm long, 10 GHz Repetitionrate 4+ Dichroic Beam Splitter Nd:YAG Laser or Diode Laser Mode-Locked Cr : YAG Microchip-Laser 4+ 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 1 Area=  /4 Coherent States (Minium Uncertainty States) Squeezed States Area=  /4

7. Balanced Homodyne-Detection LO Continuum of modes

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

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

10. Steady-State Solution If pulses are solitonlike

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

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 Adjoint System L + : Biorthogonal Basis Scalar Product: Interpretation: Field g is homodyne detected by LO f

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 >>  p,  L,  n,  g Quantum Noise Classical Noise

20. Semicondutor versus Solid-State Lasers Semicon- ductor Laser Solid- State Laser W 0 /h g gg  gg p /T R  g/g  n/n nn gg 10 7 10 0.2 0.01 40 THz fs 200 300 10 1 375 75 10 -3 0 ns 1 0 10 -3 ns 1 1000 10 2 450 fs 1 fs Semiconductor -Laser: Gordon-Haus-Jitter + Index-Fluctuations Solid-State Laser: Gain-Fluctuations Dominant sources for timing jitter: Other parameters are: T=T R =100 ps,  o =1

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).