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F. X. Kärtner

High-Frequency and Quantum Electronics Laboratory

NOISE IN OPTICAL SYSTEMS

University of Karlsruhe

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

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

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 $)

States and Quadrature Fluctuations

Area=p/4

Area=p/4

1

Squeezed States

Coherent States

(Minium Uncertainty States)

Loss:

Necessary noise for maintaining

uncertainty circle

Amplifier:

Spontaneous emission noise

Non-Ideal Amplifier:

- 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

If pulses are solitonlike

Energy Phase Center-frequency Timing and Continuum

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

Amplitude- and Frequency Fluctuations

Amplitude- and frequency fluctuations are

damped and remain bounded

Correlation Spectra Variances

Phase- and Timing Fluctuations

Phase- and timing fluctuations are unbounded

diffusion processes

Gordon-Haus Jitter

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

- 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

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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