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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===!"§
PMD and PDL in optical fiber systems
PDL-Element
Tmax
Tmin
Magnitude of PDL
PDL: Definitions
Direction of PDL
( )1 2 3ˆ , ,e e e e=
SOP with Tmax
3===!"§
PMD and PDL in optical fiber systems
PDL: Definitions
PMD + PDL: TheoryStandard PMD theory
Theory of combined PMD and PDL
Simulations
The system
Wavelength-dependencies
Monte Carlo simulations
Impact of PMD and PDL on a pulse
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===!"§
PMD and PDL in optical fiber systems
PDL: Definitions
PMD + PDL: Theory
Standard PMD theory
Theory of combined PMD and PDL
Simulations
The system
Wavelength-dependencies
Monte Carlo simulations
Impact of PMD and PDL on a pulse
Outline
6===!"§
PMD and PDL in optical fiber systems
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
Theory of combined PMD and PDL
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===!"§
PMD and PDL in optical fiber systems
PDL: Definitions
PMD + PDL: Theory
SimulationsThe system
Wavelength-dependencies
Monte Carlo simulations
Impact of PMD and PDL on a pulse
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
Wavelength-dependencies
Complex DGD
Angle between the PSPs
Global PDL
Monte Carlo simulations
Impact of PMD and PDL on a pulse
10===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Complex DGD
PDL
0.04 dB
PMD
ps0.15km
11===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Complex DGD
PMD
ps0.15km
0.1 dB
PDL
12===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Complex DGD
PMD
ps0.15km0.2 dB
PDL
13===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Complex DGD
PMD
ps0.15km
0.4 dB
PDL
14===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Complex DGD
PMD
ps0.15km
1 dB
PDL
15===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Complex DGD
0.2 dB
PDL PMD
ps0.02km
16===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Complex DGD
0.2 dB
PDL PMD
ps0.05km
17===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Complex DGD
0.2 dB
PDL PMD
ps0.15km
18===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Complex DGD
0.2 dB
PDL PMD
ps0.45km
19===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Complex DGD
0.2 dB
PDL PMD
ps1km
20===!"§
PMD and PDL in optical fiber systemsOutline
PDL: Definitions
PMD + PDL: Theory
Simulations
The system
Wavelength-dependencies
Complex DGD
Angle between the PSPs
Global PDL
Monte Carlo simulations
Impact of PMD and PDL on a pulse
21===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Angle between the PSPs
PMD
ps0.15km
PDL
0.04 dB
22===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Angle between the PSPs
PMD
ps0.15km
0.1 dB
PDL
23===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Angle between the PSPs
PMD
ps0.15km0.2 dB
PDL
24===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Angle between the PSPs
PMD
ps0.15km
0.4 dB
PDL
25===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Angle between the PSPs
PMD
ps0.15km
1 dB
PDL
26===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Angle between the PSPs
0.2 dB
PDL PMD
ps0.02km
27===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Angle between the PSPs
0.2 dB
PDL PMD
ps0.05km
28===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Angle between the PSPs
0.2 dB
PDL PMD
ps0.15km
29===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Angle between the PSPs
0.2 dB
PDL PMD
ps0.45km
30===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Angle between the PSPs
0.2 dB
PDL PMD
ps1km
31===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Angle between the PSPs
const
PMD
ps1km
0.2 dB
PDL
32===!"§
PMD and PDL in optical fiber systemsOutline
PDL: Definitions
PMD + PDL: Theory
Simulations
The system
Wavelength-dependencies
Complex DGD
Angle between the PSPs
Global PDL
Monte Carlo simulations
Impact of PMD and PDL on a pulse
33===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Global PDL
PMD
ps0.15km
PDL
0.04 dB
34===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Global PDL
PMD
ps0.15km
0.1 dB
PDL
35===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Global PDL
PMD
ps0.15km0.2 dB
PDL
36===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Global PDL
PMD
ps0.15km
0.4 dB
PDL
37===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Global PDL
PMD
ps0.15km
1 dB
PDL
38===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Global PDL
0.2 dB
PDL PMD
ps0.02km
39===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Global PDL
0.2 dB
PDL PMD
ps0.05km
40===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Global PDL
0.2 dB
PDL PMD
ps0.15km
41===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Global PDL
0.2 dB
PDL PMD
ps0.45km
42===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Global PDL
0.2 dB
PDL PMD
ps1km
43===!"§
PMD and PDL in optical fiber systemsWavelength-dependencies: Global PDL
0.2 dB
PDL PMD
ps1km
44===!"§
PMD and PDL in optical fiber systemsOutline
PDL: Definitions
PMD + PDL: Theory
Simulations
The system
Wavelength-dependencies
Monte Carlo simulations
Statistics of the complex DGD
Statistics of the global PDL
Statistics of the angle between the PSPs
Impact of PMD and PDL on a pulse
45===!"§
PMD and PDL in optical fiber systemsMonte Carlo simulations: Statistics of the complex DGD
46===!"§
PMD and PDL in optical fiber systemsOutline
PDL: Definitions
PMD + PDL: Theory
Simulations
The system
Wavelength-dependencies
Monte Carlo simulations
Statistics of the complex DGD
Statistics of the global PDL
Statistics of the angle between the PSPs
Impact of PMD and PDL on a pulse
47===!"§
PMD and PDL in optical fiber systemsMonte Carlo simulations: Statistics of the global PDL
48===!"§
PMD and PDL in optical fiber systemsOutline
PDL: Definitions
PMD + PDL: Theory
Simulations
The system
Wavelength-dependencies
Monte Carlo simulations
Statistics of the complex DGD
Statistics of the global PDL
Statistics of the angle between the PSPs
Impact of PMD and PDL on a pulse
49===!"§
PMD and PDL in optical fiber systemsMonte Carlo simulations: Statistics of the angle between the PSPs
50===!"§
PMD and PDL in optical fiber systemsOutline
PDL: Definitions
PMD + PDL: Theory
Simulations
The system
Wavelength-dependencies
Monte Carlo simulations
Impact of PMD and PDL on a pulse
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===!"§
PMD and PDL in optical fiber systemsOutline
PDL: Definitions
PMD + PDL: Theory
Simulations
The system
Wavelength-dependencies
Monte Carlo simulations
Impact of PMD and PDL on a pulse
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===!"§
PMD and PDL in optical fiber systemsOutline
PDL: Definitions
PMD + PDL: Theory
Simulations
The system
Wavelength-dependencies
Monte Carlo simulations
Impact of PMD and PDL on a pulse
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===!"§
PMD and PDL in optical fiber systemsThe impact of PMD and PDL on a pulse: High PDL 1556.31 nm
58===!"§
PMD and PDL in optical fiber systemsThe impact of PMD and PDL on a pulse: High PDL 1556.31 nm
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