PMD and PDL in optical fiber systems - TU · PDF file===!"§1 PMD and PDL in optical fiber...

PMD and PDLin optical fiber systems

A. Steinkamp, E. VogesUniversity of Dortmund

S. Vorbeck, W. WeiershausenT-Systems

1===!"§

PMD and PDL in optical fiber systems

PDL: Definitions

PMD + PDL: Theory

Simulations

The system

Wavelength-dependencies

Monte Carlo simulations

Impact of PMD and PDL on a pulse

Outline

2===!"§


PDL-Element

Tmax

Tmin

Magnitude of PDL

PDL: Definitions

Direction of PDL

( )1 2 3ˆ , ,e e e e=

SOP with Tmax

3===!"§


PDL: Definitions

PMD + PDL: TheoryStandard PMD theory

Theory of combined PMD and PDL

Simulations

The system




Outline

4===!"§

PMD and PDL in optical fiber systemsStandard PMD theory

Eigenvalue equation:

p pτ σ τ± ±⋅ ⋅ = ±∆ ⋅r r

PSPs (orthogonal: )0p p+ − =

1 00 10 11 00

0i

i

σ

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎜ ⎟⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

⎜ ⎟⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

−

≡

−

rVector of Pauli matrices

12 Ti T τ σω

−∂⎡ ⎤⋅ ⋅ ≡ ⋅⎢ ⎥∂⎣ ⎦r r

Definition of the PMD vector:

Definition of the PMD vector (real)- Trace = 0

- Hermitian

Transmission matrixof the system

with PMDunitary

DGD (real)

5===!"§


PDL: Definitions

PMD + PDL: Theory

Standard PMD theory


Simulations

The system




Outline

6===!"§


1 00 10 11 00

0i

i

σ

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎜ ⎟⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

⎜ ⎟⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

−

≡

−

rVector of Pauli matrices

p pτ σ τ± ±⋅ ⋅ = ±∆ ⋅r r

12 Ti T τ σω

−∂⎡ ⎤⋅ ⋅ ≡ ⋅⎢ ⎥∂⎣ ⎦r r


Eigenvalue equation:

Transmission matrixof the system

with PMD and PDLNot unitary

PSPs (not orthogonal: )

DGD (complex)

Definition of the PMD vector:

- 0p p+ ≠

- Trace = 0

- Not Hermitian

Definition of thePMD vector (complex)

7===!"§


PDL: Definitions

PMD + PDL: Theory

SimulationsThe system




Outline

8===!"§

PMD and PDL in optical fiber systemsThe system of the simulation

9===!"§

PMD and PDL in optical fiber systemsOutline

PDL: Definitions

PMD + PDL: Theory

Simulations

The system


Complex DGD

Angle between the PSPs

Global PDL



10===!"§

PMD and PDL in optical fiber systemsWavelength-dependencies: Complex DGD

PDL

0.04 dB

PMD

ps0.15km

11===!"§


PMD

ps0.15km

0.1 dB

PDL

12===!"§


PMD

ps0.15km0.2 dB

PDL

13===!"§


PMD

ps0.15km

0.4 dB

PDL

14===!"§


PMD

ps0.15km

1 dB

PDL

15===!"§


0.2 dB

PDL PMD

ps0.02km

16===!"§


0.2 dB

PDL PMD

ps0.05km

17===!"§


0.2 dB

PDL PMD

ps0.15km

18===!"§


0.2 dB

PDL PMD

ps0.45km

19===!"§


0.2 dB

PDL PMD

ps1km

20===!"§


PDL: Definitions

PMD + PDL: Theory

Simulations

The system


Complex DGD


Global PDL



21===!"§

PMD and PDL in optical fiber systemsWavelength-dependencies: Angle between the PSPs

PMD

ps0.15km

PDL

0.04 dB

22===!"§


PMD

ps0.15km

0.1 dB

PDL

23===!"§


PMD

ps0.15km0.2 dB

PDL

24===!"§


PMD

ps0.15km

0.4 dB

PDL

25===!"§


PMD

ps0.15km

1 dB

PDL

26===!"§


0.2 dB

PDL PMD

ps0.02km

27===!"§


0.2 dB

PDL PMD

ps0.05km

28===!"§


0.2 dB

PDL PMD

ps0.15km

29===!"§


0.2 dB

PDL PMD

ps0.45km

30===!"§


0.2 dB

PDL PMD

ps1km

31===!"§


const

PMD

ps1km

0.2 dB

PDL

32===!"§


PDL: Definitions

PMD + PDL: Theory

Simulations

The system


Complex DGD


Global PDL



33===!"§

PMD and PDL in optical fiber systemsWavelength-dependencies: Global PDL

PMD

ps0.15km

PDL

0.04 dB

34===!"§


PMD

ps0.15km

0.1 dB

PDL

35===!"§


PMD

ps0.15km0.2 dB

PDL

36===!"§


PMD

ps0.15km

0.4 dB

PDL

37===!"§


PMD

ps0.15km

1 dB

PDL

38===!"§


0.2 dB

PDL PMD

ps0.02km

39===!"§


0.2 dB

PDL PMD

ps0.05km

40===!"§


0.2 dB

PDL PMD

ps0.15km

41===!"§


0.2 dB

PDL PMD

ps0.45km

42===!"§


0.2 dB

PDL PMD

ps1km

43===!"§


0.2 dB

PDL PMD

ps1km

44===!"§


PDL: Definitions

PMD + PDL: Theory

Simulations

The system



Statistics of the complex DGD

Statistics of the global PDL

Statistics of the angle between the PSPs


45===!"§

PMD and PDL in optical fiber systemsMonte Carlo simulations: Statistics of the complex DGD

46===!"§


PDL: Definitions

PMD + PDL: Theory

Simulations

The system







47===!"§

PMD and PDL in optical fiber systemsMonte Carlo simulations: Statistics of the global PDL

48===!"§


PDL: Definitions

PMD + PDL: Theory

Simulations

The system







49===!"§

PMD and PDL in optical fiber systemsMonte Carlo simulations: Statistics of the angle between the PSPs

50===!"§


PDL: Definitions

PMD + PDL: Theory

Simulations

The system




51===!"§

PMD and PDL in optical fiber systemsThe Poincaré-sphere

52===!"§

PMD and PDL in optical fiber systemsImpact of PMD and PDL on a pulse: The system

TFWHM = 20 ps

53===!"§


PDL: Definitions

PMD + PDL: Theory

Simulations

The system




Very low PDL

High PDL (1556.31 nm)

54===!"§

PMD and PDL in optical fiber systemsImpact of PMD and PDL on a pulse: Very low PDL

55===!"§


PDL: Definitions

PMD + PDL: Theory

Simulations

The system




Very low PDL

High PDL

56===!"§

PMD and PDL in optical fiber systemsThe impact of PMD and PDL on a pulse: High PDL 1556.31 nm

57===!"§


58===!"§


Thank you

PMD and PDL in optical fiber systems - TU · PDF file===!"§1 PMD and PDL in optical fiber...

Documents

Transcript of PMD and PDL in optical fiber systems - TU · PDF file===!"§1 PMD and PDL in optical fiber...