Presented at the COMSOL Conference 2010 Paris Two-dimensional FEM Analysis of Brillouin Gain Spectra in Acoustic Guiding and Antiguiding Single Mode Optical Fibers Yolande Sikali 1,Yves Jaouën 2, Renaud Gabet 2, Xavier Pheron 3 Gautier Moreau 1, Frédéric Taillade 4 1 EDF R&D,6 Quai Watier, 78401 Chatou, France 2 Telecom ParisTech, 46 rue Barrault, 75634 Paris, France 3 ANDRA,1-7 Rue Jean Monnet, 92298 Chatenay-Malabry, France 4 LCPC, 58 Boulevard Lefebvre 75732 Paris, France Contact: yolande.sikali-mamdem@edf.fr
Overview Optical Fiber Sensors Optical fiber properties Distributed fiber sensors solutions Brillouin Scattering in optical fibers Brillouin Gain Spectrum computation using COMSOL Multiphysics 2D-FEM modeling Validation of the model : example of GeO 2 -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 2
Optical fiber sensors Optical fiber properties Interrogation unit OPTICAL FIBER COATING CORE Quasi-distributed sensors Fully-distributed sensors Source Analysis CLADDING Point like sensors Application fields - Weakly intrusive - Electro-magnetic immunity - Fast information transfer/ rate Distributed fiber sensors OTDR Principle Back-scattered spectrum at λ 0 = 1550nm Power (u.a.) 3 Distance (km) 11GHz 13THz
Brillouin Scattering 1) Acoustic Wave Photo-elasticity 2) Propagating Bragg mirror Diffraction 3) Backscattering wave Stokes lightwave Pump wave Acoustic wave ν B = ν S -ν 0 = ±2nV a /λ 0 Dependences of the Brillouin shift ν B T ε Frequency (GHz) 4
Brillouin Scattering Brillouin Gain Spectrum is highly related to Doping Refractive index variation n%/wt.% Acoustic velocity variation V l %/wt.% Doping composition: GeO 2 +0.056-0.47 F -0.31-3.6 P 2 O 5 +0.020-0.31 TiO 2 +0.23-0.59 Geometry and doping profiles: Frozen-in stress profiles: Need of a precise tool to predict the Brillouin Gain Spectrum! 5
Brillouin Scattering Optic Acoustic Monomode propagation : mode LP 01 Solutions: L 0m modes L 01 L 03 Acousto-optic overlap Brillouin Gain Spectrum 6 Y. Koyamada, Lightwave Technol., 22,631 639 (2004) L. Tartara,Optics Com., 282, 2431-2436 (2009)
Simulation with COMSOL V L (x,y) and n(x,y) vary on the cross-section with doping composition, frozen-in stress and geometry E(x, y) and n eff are calculated with PDE solver Geometry Mesh Mode plot Bragg condition gives u m (x, y) andω m The gain spectrum g(ν) is calculated taking into account overlap integrals of acoustic modes with the optical mode 7
Validation : GeO 2 -doped core fiber A Ge0 2 -doped core fiber acts as an acoustic waveguide Input data Measured Optical index profile 1.45 Calculated acoustic velocity profile 6000 8 Refractive index n 1.448 1.446 Cladding Core Cladding 1.444-10 -5 0 5 10 Radius (µm) Modeling results Amplitude (a.u.) 1,0 0,5 0,0 Acoustic modes Optical mode L 01 L 02 L 03 L 04-0,5-10 -5 0 5 10 Radius µm) Doping concentration DSP (u.a.) V L (m/s) 1.2 1 0.8 0.6 0.4 0.2 5900 5800 Cladding Core 5700 0 1 2 3 4 5 6 7 8 Radius (µm) Brillouin spectrum L 01 0 10.6 10.7 10.8 10.9 11 11.1 Frequency (GHz) Modelisation Measurement L 02 L 03 L 04
Acoustic anti-guiding fiber A Fluorine-doped cladding fiber Applications - Pure silica core (very low attenuation transmission fibers) - High Stimulated Brillouin threshold (high power fiber lasers) - High immunity to radiations (optical sensors) Refractive index n 1.458 1.456 1.454 1.452 Optical index profile Cladding Core Cladding 1.45-50 0 50 Radius (µm) Overlap integral 0.2 0.15 0.1 0.05 Overlap integrals I ao m Amplitude (u.a.) 1 0.5 0 Most efficient acoustic mode and optical mode profiles Optical mode Higher order acoustic mode DSP (u.a.) 1 0.8 0.6 0.4 0.2 Brillouin spectrum Measurement Modelisation 9 0 10.8 10.9 11 11.1 11.2 Frequency (GHz) -0.5-50 0 50 Radius (µm) 0 10.8 10.9 11 11.1 11.2 Frequency (GHz)
Polarization-maintaining fiber PANDA fiber : stress-induced birefringence Frozen-in stress distributions (a) (b) 10 Modeling results Optical Birefringence profile B = nx-ny 8 x 10-4 6 4 2 0-1 -0.5 0 0.5 1 x (m) x 10-4 Brillouin spectra for polarization x and y compared to a no-stressed fiber DSP (db) 10 0 10-2 No-stressed fiber PMF x PMF y 10 0 2 MHz 10-0.3 10.96 10.97 10.98 10.99 11 10.6 10.8 11 11.2 11.4 Frequency (GHz) 10-0.1 10-0.2
Summary A 2D-FEM modal analysis to investigate the Brillouin spectrum in single-mode optical fibers: no problems of convergence Model to predict effectively the Brillouin spectrum in case of acoustic anti-waveguides Model adapted for more complicated geometries and stressinduced refractive index profiles and non-axis-symmetrical fibers Useful tool to design and analyze optical fibers for optical communications and Brillouin-based fiber sensors 11
Thank you for your attention! 12
Brillouin spectrum measurement Self-heterodyne technique DFB Laser 1560nm Polarization controller EDFA Tunable attenuator Circulator Polarization scrambler Stokes wave OL wave Fiber under test Balanced photoreceiver - Electrical amplifier Spectrum Analyser Optical domain Stokes OL Electric domain ν o -ν B ν o ν B 13