ttwowo-dimensional fem analysis of brillouin gain ... · ttwowo-dimensional fem analysis of...

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

http://www.comsol.com/conf_cd_2011_eu

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


Frequency (GHz)

T↑ε↓

Dependences of the Brillouin shift νB

Brillouin Gain Spectrum is highly related to

• Doping composition:


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 !


Optic

Monomode propagation : mode LP01

Acoustic

Solutions: L0m modes


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


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


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


-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


-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


Thank you for your attention!Thank you for your attention!

12

Thank you for your attention!Thank you for your attention!


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


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