Workshop ITG-Fachgruppe 5.3.1 Simulation and … · Multicore fiber: a fiber-cladding structure...
Transcript of Workshop ITG-Fachgruppe 5.3.1 Simulation and … · Multicore fiber: a fiber-cladding structure...
Chair for Communications
Kiel University
Christian-Albrechts Universität zu Kiel, Germany
Carlos Castro, Klaus Pulverer, Stefano Calabrò, Marc Bohn, and Werner Rosenkranz
Workshop ITG-Fachgruppe 5.3.1
Simulation and Experimental Verification of a Multicore Fiber System
February 2017
-2-Chair for Communications
Kiel University
C. Castro. 16-02-2017
[email protected]@tf.uni-kiel.de
Outline
1.Introduction
• Multicore fiber
2.Multicore fiber modelling
• Fiber structure
• Finite element method
• Mode-coupling coefficients
• Coupled-mode theory/Power-coupled theory
3.Simulation results
• FEM/PCT validation
• Comparison CMT/PCT
4.Experimental results
• Setup
• BER-distance measurements
5.Summary
-3-Chair for Communications
Kiel University
C. Castro. 16-02-2017
[email protected]@tf.uni-kiel.de
Introduction
Multicore fiber
Multicore fiber: a fiber-cladding structureencompassing more than one optical waveguide(core).
Lack of standardization diameter, distance
between cores, core layout.
Main challenge: Crosstalk
Disturbances induced on any given core by the remainingwaveguides.
Design-based strategies: pitch distance, refractive indices,cladding structures.
DSP-based strategies: MIMO-receiver complexity
Cladding
Cores
Trench
-4-Chair for Communications
Kiel University
C. Castro. 16-02-2017
[email protected]@tf.uni-kiel.de
Multicore fiber modelling
Fiber structure
Modelling structure of a multicore fiber (linear regime).
C11(f)
C12(f)
C13(f)
𝐶11 … 𝐶1𝑁⋮ ⋱ ⋮𝐶𝑁1 … 𝐶𝑁𝑁
Coupling matrix
-5-Chair for Communications
Kiel University
C. Castro. 16-02-2017
[email protected]@tf.uni-kiel.de
Multicore fiber modelling
Finite element method (FEM)
Finite Element Method solves complex differentialequations numerically Wave equation for a
cross-sectional plane.
Fiber is numerically analyzed by FEM using a meshof 3-pointed triangular elements mapped to thefiber characteristics.
FEM outputs two results: field distribution of themodes in the different waveguides and theeffective refractive indices of each of the N cores cores’ propagation constants (βc1,…,cN)
FEM Coupling coefficients.
References:
[1] R. Scarmozzino et al, JQE, V6, No1, 2000.
[2] A. Fallahkhair et al, JLT, V26, No11, 2008.
-6-Chair for Communications
Kiel University
C. Castro. 16-02-2017
[email protected]@tf.uni-kiel.de
Multicore fiber modelling
Mode coupling coefficients
Mode coupling coefficients are physical values thatexpress how one mode/core couples to another one(at the moment, not a function of distance z; justcoupling in the transverse plane).
In [3] a simplified expression to calculate thesecoupling coefficients has been derived, allowing tocalculate an approximate value based only on physicalcharacteristics of the fiber.
Coupling coefficients are mentioned in the literature tobe real, since phase is ‘irrelevant’ [4].
Overlapping field
x
y
κ𝑛𝑚 =ωε0 𝑛
2 − 𝑛𝑚2 𝒆𝑛∗ ∙ 𝒆𝑚 ⅆ𝑥 ⅆ𝑦
𝑧 ∙ 𝒆𝑛∗ × 𝒉𝑛 + 𝒆𝑛 × 𝒉𝑛
∗ ⅆ𝑥 ⅆ𝑦References:
[3] F. Ye et al, OE, V22, No19, 2014.
[4]. H. Haus, “Waves and fields in optoelectronics”, 1984.
-7-Chair for Communications
Kiel University
C. Castro. 16-02-2017
[email protected]@tf.uni-kiel.de
Multicore fiber modelling
Coupled Mode Theory (CMT)
CMT models the coupling between two or more opticalwaveguides over a certain distance by analyzing thebehavior of complex signals in different waveguidesdepending on coupling coefficients.
ⅆ𝐴𝑛ⅆ𝑧= −𝑖
𝑛≠𝑚
κ𝑛𝑚𝐴𝑚exp 𝑖 𝛽𝑛 − 𝛽𝑚 𝑧
The propagation constant difference in the CME is dictated by the FEM calculation, adeterministic part describing the twisting and bending effects, and a random part due torandom imperfections in the fiber structure.
Uniformly-distributed random phase offsets are applied in each fiber segment.
Solving the CMT outputs complex values (Cnm) to weight and add the signals in eachsegment to simulate crosstalk.
-8-Chair for Communications
Kiel University
C. Castro. 16-02-2017
[email protected]@tf.uni-kiel.de
Multicore fiber modelling
Power Coupled Theory (PCT)
PCT models the power transfer between two or moreoptical waveguides over a certain distance dependingon the values of power coupling coefficients How much interference one waveguide has at a
given point due to the neighboring waveguides.
ⅆ𝑃𝑛ⅆ𝑧=
𝑛≠𝑚
ℎ𝑛𝑚 𝑃𝑚 − 𝑃𝑛
The power coupling coefficients (hnm) are not the same as the mode coupling coefficient (κnm).
Power-coupling coefficients would need to be calculated for each fiber segment Average power-coupling coefficients.
Due to its nature, the PCT does not contemplate/allow to consider phase shifts/delaysbetween cores since it is a simplification of the CMT.
For a SISO DSP at the receiver, modelling XT by this method is sufficient, since it would be as if the whole interferenceprovoked by the coupling were external noise.
-9-Chair for Communications
Kiel University
C. Castro. 16-02-2017
[email protected]@tf.uni-kiel.de
Simulation results
FEM/PCT validation
Digital representation of the fiber’sproperties
Digital representation of the fiber is built fromphysical characteristics from the fiber(geometrical and structural).
Computation time depends on number ofelements and number of cores more
elements produce more accurate estimations.
Mesh of 44,402 elements for comparisons(150 divisions per axis).
-1 -0.5 0 0.5 1
x 10-4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1x 10
-4
X-axis [m]
Y-a
xis
[m
]
-10-Chair for Communications
Kiel University
C. Castro. 16-02-2017
[email protected]@tf.uni-kiel.de
Simulation results
FEM/PCT validation
Estimation of the propagationconstants for SAFARI’s 7-core fiber
At 150 divisions per axis (44,402 meshelements) seem to be a point where thepropagation constants begin to converge.
20 40 60 80 100 120 140 160 180 2005.89
5.892
5.894
5.896
5.898
5.9
5.902
5.904x 10
6
Divisions per axis
Pro
pagation c
onst
ants
(
c) [r
ad/m
]
Core 0
Core 1
Core 2
Core 3
Core 4
Core 5
Core 6
-11-Chair for Communications
Kiel University
C. Castro. 16-02-2017
[email protected]@tf.uni-kiel.de
Simulation results
FEM/PCT validation
FEM: Computation time with respectto the number of elements andwaveguides modelled
Computation time depends on number ofelements and number of cores more
elements produce more accurate estimations.
It is, in principle, valid to obtain the FEM’ssolution for every fiber piece in our mode, butit’s unpractical.
0 50 100 150 2000
20
40
60
80
100
120
140
Divisions per axis
Tim
e [
s]
2 cores
7 cores
12 cores
19 cores
32 cores
-12-Chair for Communications
Kiel University
C. Castro. 16-02-2017
[email protected]@tf.uni-kiel.de
Simulation results
FEM/PCT validation
XT estimation based on a simulatedMCF based on FEM and PCT
Mesh of 44,402 elements for comparisons.
Crosstalk was estimated using PCT due toits simplicity.
Values shown correspond to crosstalk seenby core-under-test (CUT).
References:
[5] Sakaguchi et al, JLT, V31, No4, 2013.
[6] Sakaguchi et al, OE, V22, No1, 2014.
[7] Matsuo et al, OL, V36, No23, 2011.
[8] Zhu et al, OE, V19, No17, 2011.
35 40 45 50-60
-50
-40
-30
-20
Pitch distance [m]
XT
CU
T [
dB]
Numerical simulation
XT measurements in [5]
Numerical simulation
XT measurements [6]
Numerical simulation
XT measurements in [7]
Numerical simulation
XT measurements in [8]
Numerical simulation
XT measurements 7c-MCF
10c - center core
no trench
7c - center core
no trench
19c- center core
trench
19c - center core
trench
7c - center core
trench
-13-Chair for Communications
Kiel University
C. Castro. 16-02-2017
[email protected]@tf.uni-kiel.de
Simulation results
Comparison CMT/PCT (60 km 7c-MCF)
CMT-PCT comparison usingSAFARI’s 7c-MCF
Power transfer behavior whencore 0 (middle core) is the onlyone active.
Steps when solving CMT’sdifferential equations are < 1 [m].Large steps, which speed upcomputation, produce results thatare not as similar as PCT.
0 1 2 3 4 5 6
x 104
-100
-80
-60
-40
-20
0
Transmitted distance [m]
Pow
er
in c
ore
s CM
T [
dB]
Core 0
Core 1
Core 2
Core 3
Core 4
Core 5
Core 6
0 1 2 3 4 5 6
x 104
-100
-80
-60
-40
-20
0
Transmitted distance [m]
Pow
er
in c
ore
s PCT [
dB]
-14-Chair for Communications
Kiel University
C. Castro. 16-02-2017
[email protected]@tf.uni-kiel.de
Simulation results
Comparison CMT/PCT (60 km 7c-MCF)
CMT-PCT comparison usingSAFARI’s 7c-MCF
Power transfer behavior whencore 1 (rightmost core) is the onlyone active.
Different XT levels close
neighbors and farther set ofneighbors.
0 1 2 3 4 5 6
x 104
-200
-150
-100
-50
0
Transmitted distance [m]
Pow
er
in c
ore
s CM
T [
dB]
Core 0
Core 1
Core 2
Core 3
Core 4
Core 5
Core 6
0 1 2 3 4 5 6
x 104
-200
-150
-100
-50
0
Transmitted distance [m]
Pow
er
in c
ore
s PCT [
dB]
-15-Chair for Communications
Kiel University
C. Castro. 16-02-2017
[email protected]@tf.uni-kiel.de
Experimental results
Setup
Experimental using a fully-spliced cladding-pumped multicore link
Has been modelled as close as possible using loss values provided by the manufactures and observing if the fibermodelling agrees to the information stated in the data sheet.
-16-Chair for Communications
Kiel University
C. Castro. 16-02-2017
[email protected]@tf.uni-kiel.de
Experimental results
BER-Distance measurements
MCF System simulation(linear regime)
Measurementscorresponding to core 0.
AVG BER from 15 WDMchannels w/ channelspacing of 50 GHz
Only consideringimpairments mentioned inSlide 4.
Conclusion: simulationcan be used to roughlymodel a MCF system inorder to set transmissionobjectives accordingly.0 500 1000 1500 2000 2500 3000
10-5
10-4
10-3
10-2
10-1
100
Distance [km]
BER
FEC20%
3.4E-2
4QAMEXP
4QAMCMT
4QAMPCT
8QAMEXP
8QAMCMT
8QAMPCT
16QAMEXP
16QAMCMT
16QAMPCT
-17-Chair for Communications
Kiel University
C. Castro. 16-02-2017
[email protected]@tf.uni-kiel.de
Multicore fiber modelling
Summary and acknowledgements
Implementation of a FEM+CMT/PCT multicore fiber model
MCF system analysis for arbitrary MCF (structural and geometrical characteristics of the fiber)
FEM: calculation of cross-sectional field distribution and propagation constants of the individual cores
CMT/PCT are used to estimate the amount of XT after a given length MCF coupling matrix: digitally
simulate XT
Simulation results have been theoretically analyzed
MCF simulation has been compared to own experimental results using a fully-spliced cladding-pumpedmulticore fiber link (SAFARI project)
Coriant R&D, SAFARI project members, and Christian-Albrechts Universität zuKiel.