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Noise Analysis in High-Frequency Optical Systems at the University of Karlsruhe

This document outlines key topics explored in the Kärtner High-Frequency and Quantum Electronics Laboratory at the University of Karlsruhe, focusing on noise in optical systems. It covers high-speed A/D conversion (up to 100 GHz), the dynamics of mode-locked lasers, and the differences in noise characteristics between semiconductor and solid-state lasers. The analysis includes quantum and classical noise sources, timing jitter, and fluctuations in amplitude, phase, frequency, and timing. Insights are drawn from various research studies on modelocked lasers and noise processes.

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Noise Analysis in High-Frequency Optical Systems at the University of Karlsruhe

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  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).

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