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TwoTwo--dimensional FEM Analysis of Brillouin Gain dimensional FEM Analysis of Brillouin Gain Spectra in Acoustic Guiding and Antiguiding Spectra in Acoustic Guiding and Antiguiding
Single Mode Optical FibersSingle Mode Optical Fibers
Yolande Sikali1,Yves Jaouën2, Renaud Gabet2, Xavier Pheron3
Gautier Moreau1, Frédéric Taillade4
1EDF R&D,6 Quai Watier, 78401 Chatou, France2Telecom ParisTech, 46 rue Barrault, 75634 Paris, France
3ANDRA,1-7 Rue Jean Monnet, 92298 Chatenay-Malabry, France4LCPC, 58 Boulevard Lefebvre 75732 Paris, France
Contact: [email protected]
Presented at the COMSOL Conference 2010 Paris
Overview
Optical Fiber Sensors
Optical fiber properties
Distributed fiber sensors solutions
Brillouin Scattering in optical fibers
Brillouin Gain Spectrum computation using COMSOL Multiphysics Brillouin Gain Spectrum computation using COMSOL Multiphysics
2D-FEM modeling
Validation of the model : example of GeO2-doped core fiber
Analysis of acoustic anti-waveguides fibers Example : Fluorine-doped cladding fibers
Analysis of no-symmetrical geometry fibers
Example : Stress-induced polarization-maintaining fibers
2Y. Sikali Mamdem et. al., COMSOL conference, November 17-19, 2010
Optical fiber properties
Application fields
Optical fiber sensors
Analysis
Source
Interrogation unit
Quasi-distributedsensors Fully-distributed
sensors
Point like sensors
- Weakly intrusive- Electro-magnetic immunity
COATING
CLADDING
CORE
OPTICAL FIBER
Distance (km)
Po
we
r (u
.a.)
Distributed fiber sensors
3
OTDR Principle
11GHz
13THz
- Electro-magnetic immunity- Fast information transfer/ rate
Back-scattered spectrum at λ0 = 1550nm
Y. Sikali Mamdem et. al., COMSOL conference, November 17-19, 2010
1) Acoustic Wave
2) Propagating Bragg mirror
3) Backscattering wave
Photo-elasticity
Diffraction
νB= νS-ν0= ±2nVa/λ0
Brillouin Scattering
Pump wave
Stokes lightwave
Acoustic wave
4Y. Sikali Mamdem et. al., COMSOL conference, November 17-19, 2010
Frequency (GHz)
T↑ε↓
Dependences of the Brillouin shift νB
Brillouin Gain Spectrum is highly related to
• Doping composition:
Brillouin Scattering
Doping
Refractive index
variation
∆ n%/wt.%
Acoustic velocity
variation
∆ V l %/wt.%
GeO2 +0.056 -0.47
F -0.31 -3.6
P2O5 +0.020 -0.31
TiO +0.23 -0.59
• Geometry and doping profiles:
• Frozen-in stress profiles:
5
TiO2 +0.23 -0.59
Need of a precise tool to predict the Brillouin Gain Spectrum !
Y. Sikali Mamdem et. al., COMSOL conference, November 17-19, 2010
Optic
Monomode propagation : mode LP01
Acoustic
Solutions: L0m modes
Brillouin Scattering
L01
6
Brillouin Gain Spectrum
Y. Koyamada, ” Lightwave Technol., 22,631–639 (2004)
L. Tartara,Optics Com., 282, 2431-2436 (2009)Y. Sikali Mamdem et. al., COMSOL conference, November 17-19, 2010
Acousto-optic overlap
L03
VL(x,y) and n(x,y) vary on the cross-section with dopingcomposition, frozen-in stress and geometry
E(x, y) and neff are calculated with PDE solver
Simulation with COMSOL
Bragg condition gives um(x, y) and Ωm
The gain spectrum g(ν) is calculated taking into account overlap integrals of acoustic modes with the optical mode
7
Geometry Mesh Mode plot
Y. Sikali Mamdem et. al., COMSOL conference, November 17-19, 2010
A Ge02-doped core fiber acts as an acoustic waveguide
Measured Optical index profile
Doping
concentration5800
5900
6000
VL (
m/s
)
Calculated acoustic velocity profile
Validation : GeO2-doped core fiber
• Input data
1.446
1.448
1.45
Re
fra
ctive
in
de
x n
Core
Cla
dd
ing
Cla
dd
ing
Core
Cla
dd
ing
8
0 1 2 3 4 5 6 7 85700
Radius (µm)
-10 -5 0 5 10-0,5
0,0
0,5
1,0
Am
plit
ude (
a.u
.)
Radius µm)
Optical mode
L01
L02
L03
L04
Acoustic modes
• Modeling results
Y. Sikali Mamdem et. al., COMSOL conference, November 17-19, 2010
Brillouin spectrum
10.6 10.7 10.8 10.9 11 11.10
0.2
0.4
0.6
0.8
1
1.2
Frequency (GHz)
DS
P (
u.a
.)
Modelisation
MeasurementL
01
L02
L03 L
04
-10 -5 0 5 101.444
Radius (µm)
Re
fra
ctive
in
de
x n
Core
Applications
- Pure silica core (very low attenuation transmission fibers)
- High Stimulated Brillouin threshold (high power fiber lasers)
- High immunity to radiations (optical sensors)
Acoustic anti-guiding fiber
A Fluorine-doped cladding fiber
Optical index profile
-50 0 501.45
1.452
1.454
1.456
1.458
Refr
active index n
Co
re Cla
dd
ing
Cla
dd
ing
9
Overlap integrals ao
mI
Most efficient acoustic mode and optical mode profiles
Brillouin spectrum
Y. Sikali Mamdem et. al., COMSOL conference, November 17-19, 2010
-50 0 501.45
Radius (µm)
10.8 10.9 11 11.1 11.20
0.05
0.1
0.15
0.2
Frequency (GHz)
Overl
ap
inte
gra
l
10.8 10.9 11 11.1 11.20
0.2
0.4
0.6
0.8
1
Frequency (GHz)
DS
P (
u.a
.)
Measurement
Modelisation
-50 0 50-0.5
0
0.5
1
Radius (µm)
Am
plit
ud
e (
u.a
.)
Optical mode
Higher order acoustic mode
PANDA fiber : stress-induced birefringence
(a) (b)
Polarization-maintaining fiber
• Frozen-in stress distributions
10
Optical Birefringence profile
• Modeling results
Y. Sikali Mamdem et. al., COMSOL conference, November 17-19, 2010
-1 -0.5 0 0.5 1
x 10-4
0
2
4
6
8x 10
-4
x (m)
B =
nx-n
y
10.6 10.8 11 11.2 11.4
10-2
100
Frequency (GHz)
DS
P (
dB
)
No-stressed fiber
PMFx
PMFy
10.96 10.97 10.98 10.99 1110
-0.3
10-0.2
10-0.1
100
2 MHz
Brillouin spectra for polarization x and y compared to a no-stressed fiber
A 2D-FEM modal analysis to investigate the Brillouin spectrum insingle-mode optical fibers: no problems of convergence
Model to predict effectively the Brillouin spectrum in case ofacoustic anti-waveguides
Summary
Model adapted for more complicated geometries and stress-induced refractive index profiles and non-axis-symmetrical fibers
Useful tool to design and analyze optical fibers for opticalcommunications and Brillouin-based fiber sensors
11Y. Sikali Mamdem et. al., COMSOL conference, November 17-19, 2010
Thank you for your attention!Thank you for your attention!
12
Thank you for your attention!Thank you for your attention!
Y. Sikali Mamdem et. al., COMSOL conference, November 17-19, 2010
Stokeswave
EDFA
Polarizationcontroller
Tunableattenuator
Fiber under test
Polarizationscrambler
Balancedphotoreceiver
Spe
ctru
m
DFB
La
ser
15
60
nm
Circulator
Electricalamplifier
-
OL wave
Brillouin spectrum measurementSelf-heterodyne technique
13
scrambler
Spe
ctru
mA
na
lyse
r
Stokes OL
Optical domain
νo-νB νo
Electric domain
νB
OL wave
Y. Sikali Mamdem et. al., COMSOL conference, November 17-19, 2010