Two-dimensional FEM Analysis of Brillouin Gain Spectra in Acoustic Guiding and Antiguiding Single Mode Optical Fibers

Transcription

1 Two-diensional FEM Analysis of Brillouin Gain Spectra in Acoustic Guiding and Antiguiding Single Mode Optical Fibers Yolande Sikali Made, Xavier Phéron, Frédéric Taillade, Yves Jüen, Renaud Gabet, Vincent Lanticq, Gautier Moreau, Aziz Boukenter, Y. Ouerdane, Sylvie Lesoille, et al. To cite this version: Yolande Sikali Made, Xavier Phéron, Frédéric Taillade, Yves Jüen, Renaud Gabet, et al.. Two-diensional FEM Analysis of Brillouin Gain Spectra in Acoustic Guiding and Antiguiding Single Mode Optical Fibers. COMSOL Conference, Nov, PARIS, France. <hal-68938> HAL Id: hal Subitted on 7 Mar HAL is a ulti-disciplinary open access archive for the deposit and disseination of scientific research docuents, whether they are published or not. The docuents ay coe fro teaching and research institutions in France or abroad, or fro public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de docuents scientifiques de niveau recherche, publiés ou non, éanant des établisseents d enseigneent et de recherche français ou étrangers, des laboratoires publics ou privés.

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3 Two-diensional FEM Analysis of Brillouin Gain Spectra in Acoustic Guiding and Antiguiding Single Mode Optical Fibers Y. Sikali Made *, X. Pheron, F.Taillade 3, Y. Juën 4, R. Gabet 4, V. Lanticq (+), G. Moreau, A. Boukenter 5, Y. Ouerdane 5, S. Lesoille, J. Bertrand EDF R&D, ANDRA, 3 LCPC, 4 Institut Teleco/Teleco ParisTech, 5 Laboratoire Hubert Curien (+) Now with CEMENTYS *Corresponding author: EDF R&D, 6 quai Watier 784 Chatou, France, Eail: yolande.sikali-ade@teleco-paristech.fr Abstract: The analysis of optical and acoustic properties of optical fibers is required for accurate Brillouin gain spectru (BGS) deterination. We present a full odal-analysis of the guided optical and acoustic odes based on a two-diensional finite-eleent ethod (D-FEM) for BGS calculation using COMSOL Multiphysics. We believe that this ethod will be helpful in analyzing and designing special fibers for applications, such as fiber aplifiers with significant SBS (Stiulated Brillouin Scattering) suppression or Brillouin-based fiber sensors. The odel is adapted for BGS evaluation of any single ode fiber (in ter of optical ode) based on its profile, naely its geoetry, and its doping coposition. Copared to standard ulti-layer ethods liited to axially-syetric fibers [], the D-FEM analysis enables the BGS coputation even for ore coplicated geoetries, such as PANDA polarization-aintaining fiber where the optical index and the aterial stress are aziuthally dependant. The results of nuerical odeling have shown good agreeent with easured Brillouin spectra for different types of silica fibers. Exaples are given for a standard GeO -doped core fiber (standard fiber for telecounication applications), Fluor-doped cladding fiber (acoustic anti-waveguide) and PANDA fiber. Keywords: Optical fibers, Stiulated Brillouin Scattering, acoustic waveguide, finite-eleent analysis.. Introduction Brillouin Scattering in optical fibers is a nonlinear process caused by interaction between optical wave and acoustic waves. It anifests through the generation of a backwardpropagating Stokes wave which the frequency is downshifted by ~GHz for a.55µ optical signal. The Brillouin scattering ect is a liitation for optical systes as fiber lasers [] or transission systes [3, 4] when sources are highly coherent. However, it can also be used in optical sensors for strain and teperature easureents [5] or optical signal processing systes [6]. The Brillouin gain spectru (BGS) properties are strongly related to interaction between the optical ode and the different acoustic odes guided in the core (acoustic waveguides) or guided in the cladding (acoustic anti-waveguides) [7]. As the Brillouin scattering properties are highly dependent of the doping coposition profile, a precise coputing tool to predict BGS is required. Multi-layers ethods are perfectly adapted for the BGS calculation of axially-syetric fibers [, 7]. It s well-known that software based on a finite-eleent ethod, such as COMSOL Multiphysics solve D electroagnetic probles. Thus it is an excellent tool to extend BGS coputation for any aziutal doping- and stress-dependant fibers such as polarization aintaining fibers [8, 9]. We present as an exaple the obtained BGS of a standard single fiber (GeO core doping). The very good agreeent with corresponding BGS easureents allows validation of the developed D-FEM coputation odel. The acoustic waves in a Fluor-doped cladding fiber act as anti-waveguides. Despite this difficulty, the BGS of a pure Fluor-doped cladding fiber based on its easured refractive index profile has been calculated and copared to BGS easureents. Finally, the calculated BGS of a polarizationaintaining fiber (PANDA type) is presented.. Theoretical background A BGS calculation requires a rigorous deterination of the acoustic-optical interaction, i.e. overlap between optical and acoustic odes.

4 In single-ode fiber only the fundaental optical LP ode is propagated. It results that the only excited acoustic odes are then the longitudinal acoustic odes L with no aziuthal dependence. The properties of the optical and longitudinal acoustic odes have been obtained by solving the D scalar-wave equations of the optical propagation () and the echanical equations () [7, 9]: te u t V l n n E acoust u () () where t is the transverse Laplacian operator in the (x,y) plane, E ( x, y) is the spatial distribution of the optical field, n is the ective index of the fundaental LP optical ode, acoust is the acoustic propagation constant, u ( x,y ) is the longitudinal displaceent field of the L acoustic ode and is the acoustic Brillouin resonance frequency (i.e. Brillouin frequency shift). Assuing that is uch saller than the optical frequency, the phase atching (i.e. Bragg condition) with the optical wave leads to the relation acoust opt where opt n is the propagation constant of the optical ode [3]. The refractive index n and the longitudinal acoustic velocity V l vary on the cross-section of the fiber according to the type and concentration of doping coponents. The fractional dependence for unit doping concentration on the optical and acoustical properties of pure silica is listed in Table for ost coonly used dopants. The acoustic velocity of pure silica is V silica =5944/s []. The odal field distributions of both the LP optical ode and the L acoustic odes deterine the iciency of the back-scattering wave. Fig. plots the typical field distribution for two different L acoustic odes. The acousto-optic coupling rate for the th acoustic ode can be expressed as []: I E u 4 E dxdy. u * dxdy dxdy (3) Because of exponential decrease of acoustic waves, the spontaneous Brillouin spectru of each acoustic ode has a Lorentzian shape. As each acoustic ode contribution adds up in an incoherent way, the BGS is then coputed by adding lorentzian curves centered at each ode Brillouin frequency shift, B with linewidth at half axiu and relative intensity I. Finally, the BGS S() can be expressed as: / S( ) (4) I / The Brillouin linewidth is assued to be 4MHz for every acoustic ode here. L L 5 B Table : Influence of doping concentrations on optical and acoustic properties of fibers paraeters [] Doping n%/wt.% V l %/wt.% GeO F P O TiO Al O B O Figure : Exaples of acoustic odes profiles for a Fluorine-doped cladding fiber 3. Siulation and use of COMSOL Multiphysics 3. D-FEM Modeling The optical paraeters E ( x,y ) and n, and the echanical paraeters u ( x, y) and are obtained separately by solving Eq. () and ()

5 Refractive index n Optical/acoustic odes V (/s) respectively using the PDE solver of COMSOL Multiphysics. The geoetry, the (ulti-)doping profile and eventually the stress distribution, are introduced in the PDEs. The nuber of eleents of the esh is varying between 4 and 6 depending of the coplexity of the fiber geoetry. The boundary condition is given by the perfectly atched layer for interior boundaries (i.e. Neuann boundary conditions: continuity of the fields and their derivative) and a restrictive trial space condition for the exterior boundaries (Dirichlet boundary condition: there is no field outside the fiber). First, we calculate the optical ode profile E ( x, y) and the corresponding ective index n. Note that the n paraeter is directly related to Brillouin frequency shift via the Bragg condition where V is the ective acoustic velocity of the th ode B n V. So, we can calculate the different longitudinal acoustic odes (in other words the different values of u and ) by introducing the value of n in Eq. () according to the phase-atching condition. Finally, the acousto-optic overlap paraeter I is calculated using E( x,y ) and u ( x,y ) (see Eq. 3), and the BGS S( ) can be easily deduced. 3. Validation: GeO -doped core fibers Our developed nuerical odel has been validated on the BGS deterination of a coonly used fiber at.55µ, the SMF8 fiber. The fiber consists of a GeO -doped core fiber with a radius of 4.µ and a doping concentration of 6% which corresponds to index variation of ( n n ).36%, and a pure silica Radius (µ) Figure : Measured refractive index profile of an SMF8 fiber cladding with radius 6.5µ. The index profile is given in Fig.. The phase velocity of the lower L o acoustic odes have been calculated nuerically and plotted in Fig. 3. The quasivertical line corresponds to the Bragg condition. It results that only four L o acoustic odes are propagated in the fiber. All acoustic odes excepted L ode have non-zero cutoff frequencies. The field distributions of the LP optical and L o acoustic odes are presented in Fig. 4. Figure 3: Calculated phase velocity of the lower acoustic odes L o propagating along the GeO - doped core fiber (SMF8). The quasi-vertical line corresponds to the Bragg condition. We have copared the calculated BGS with experiental results obtained on a ~k SMF8 fiber. The BGS easureent has been perfored using the well-known self-heterodyne technique [, 3] (cf. experiental set-up in Fig. 5). A 56n DFB laser is used as the input signal. The heterodyne detection of both the Brillouin frequency shift back-propagated Stokes V L clad = 5944/s V L core = 576/s L 5 5 Acoustic frequency (GHz) Optical ode L Radius (µ) Figure 4: Profiles of the LP optical ode and the different L o acoustic odes L L 3 L 4 L L 3 L 4

6 DSP (u.a.) Refractive index n Spectru Analyser DFB Laser 56n Polarization controller EDFA Tunable attenuator Polarization scrabler Circulator Fiber under test Balanced photoreceiver Electrical aplifier - Figure 5: Experiental set-up for the easureent of Brillouin spectru wave in the fiber under test and the injected input signal allows to direct easureent of the BGS. A polarization scrabler is used in order to polarization insensitive easureent during the experient. The laser linewidth is ~ MHZ, copared to ~35-4MHz for the acoustic odes, so the detected electrical spectru corresponds directly to the spontaneous BGS The calculated BGS is in very good agreeent copared with easureents as shown in Fig. 6. The BGS is coposed of 4 peaks, each one corresponding to the contribution of a L acoustic ode. The contribution of L acoustic ode is clearly doinant. The field distribution of the optical ode and fundaental L acoustic ode are siilar as shown in Fig. 5, so the corresponding acousto-optic coupling rate I is about. On the contrary, the field distributions of higher acoustic odes are coposed of out-of-phase contribution, resulting in strongly reduced acousto-optic coupling rates. These experiental results confir the accuracy of the D-FEM odeling L Modelisation Measureent L L 3 L Frequencies (GHz) Figure 6: Coparison easureent/siulation of the BGS of an SMF8 fiber (~k) 4. Fluorine-doped cladding fiber: case of acoustic anti-waveguides The lowest fiber attenuation of.484 db/k has been achieved using pure silica core, Fluorine-doped cladding resulting in a depressed optical index [4]. Moreover, this fiber structure is interesting because Fluorinedoped cladding allows design of ore sophisticated optical index profiles, for applications such as dispersion copensating fibers [5] or fibers with SBS (Stiulated Brillouin Scattering) itigating [6] (i.e. the overlap between the optical and acoustic ode field is reduced). Until recently they are only few studies of the BGS analysis of pure-fluorine doped cladding fibers [5, 9, 7]. The refractive index profile of the characterized Fluorine fiber is shown in Fig. 7. The fiber has a pure silica core of ~4.5µ radius and a Fluorine-doped cladding of ~43µ radius. The Fluorine doping in the cladding results in an acoustic velocity decrease. So, the acoustic waves are essentially confined in the cladding and not in the core. A Fluorine-doped cladding fiber acts as an acoustic anti-waveguide Radius (µ) Figure 7: Measured refractive index profile of the Fluorine-doped cladding fiber As we used the real profile with no approxiation for D-FEM coputation, it is necessary to have a highly thin esh because of the coposition of the fiber. COMSOL Multiphysics gives thousands of acoustic odes. As the optical ode distribution is no aziuthally dependent, only the acoustic odes with axially-syetric field distribution should be taken into account. We select the acoustic odes with a significant overlap with optical

7 DSP (u.a.) Overlap integral Mode aplitude (a.u.) power distribution. Fig. 8 shows the radial profile of the acoustic ode with the highest value of I. The contributions of the ost significant acoustic odes to BGS, as illustrated in Fig. 9,.5 Figure 8: Radial profiles of the optical ode and the ost icient acoustic ode in the Fluorine doped fiber Optical ode Higher order acoustic ode Radius (µ) show a predoinant influence of odes around.5ghz. Both easured and calculated BGS are plotted in Fig.. The lower-order acoustic odes are confined in the inner region of the cladding. At the opposite, the upper-order acoustic odes are confined in the outer region of the cladding, so their coupling with the optical ode are non-significant copared to the lowerorder odes around.5ghz. 5. Polarization-aintaining fibers Polarization-aintaining fibers (PMFs) are used in any applications such as optical fiber counications when polarization control is required, fiber-optics sensors, interferoeters, etc. PMFs have strong built-in birefringence. The ost popular PMF design, also called PANDA fiber, consists in two stress rods on both sides of the fiber core as shown in Fig.. As PANDA fiber are no axially-syetrical, D-FEM odeling is particularly adapted of the calculation of stress birefringence and BGS. The cross-section geoetry of the studied PANDA fiber is listed in [8]. Its structure consists in a GeO -doped core with radius a=4.5µ, a pure silica cladding with radius b=6.5µ and stress-applying eleents around the core (see Fig. ) Fréquencies (GHz) Figure 9: Values of the overlap integrals I of acoustic odes with significant contribution to BGS..8 Measureent Modelisation Figure : Cross-section of a PMF (PANDA fiber) Fréquencies (GHz) Figure : Measureent/siulation coparison of the BGS for a Fluorine-doped cladding fiber The finite eleent ethod and the odal resolution thanks to COMSOL Multiphysics allow us to calculate the theral stress distribution (Fig. a and b). The stress coponents x and y in the fiber deterine the spatial distribution of along x- and y-direction refractive indexes. The stress distributions could have been obtained using the Structural Mechanics Module of COMSOL. However for siplicity, we applied an analytical odel that is

8 B = nx-ny DSP (db) (a) (b) Figure : Stress distributions in the PANDA fiber cross-section: (a) x-axis, (b) y-axis. described in [8]. Having found the stress coponents x and y, the corresponding stress induced birefringence can be easily deduced (i.e. birefringence B=C ( x - y ) where C is the stressphotoelastic coicient of silica which is usually taken to be /kg). The birefringence distribution for the considered PANDA fiber is shown in Fig. 3. Moreover, the stress odifies the longitudinal acoustic velocity as follows: 8 x -4 V ' l Vl ( x y ) (5) E where V l is the acoustic velocity in the core region for the no-stressed fiber [9]. The Young s odulus E=783kg/² and the Poisson s ratio is. 86. The calculated BGS with incident light along the slow axis (PMF-x) and fast axis (PMF-y) are plotted in Fig. 4. The BGS of the no-stressed fiber (i.e. no-stress applying eleents) is shown for coparison. The BGS of the PMF on both x and y axis show a single-peak distribution, that can be explained by very close values of the Brillouin frequencies for the first four acoustic odes. The increase of the resonant frequencies fro the no-stressed fiber to the PMF is approxiately 53MHz, 7MHz corresponding to the stress induced dependence of n (fro.463 to.46), and 6MHz to the increase of V l (fro /s to 587.8/s). The difference of MHz between the PMF-x and PMF-y peaks is due to the birefringence induced by the n between the two light propagation axis x and y. - - No-stressed fiber PMF x PMF y MHz Frequencies (GHz) Figure 4: Stiulated BGS coputed in the PANDA along x polarization and y polarization copared with the BGS in the no-stressed fiber Note that our results are in good agreeent with the spectru easured experientally in [8, ]. In conclusion, we see that this approach is reliable even with non-syetric fiber s structure. 6. Conclusions x () x -4 Figure 3: Birefringence profile along the x-axis We have deonstrated a D-FEM odal analysis to investigate the BGS in optical fibers. This odel is particularly adapted for cladding

9 doped fibers that act as anti-waveguides and fibers with coplicated D geoetry and stressinduced refractive index profiles. We believe this ethod will be helpful designing and analyzing optical fibers for optical fiber counications and Brillouin-based fiber sensors. 7. References. V. Lanticq, R. Gabet, J.-L. Auguste, S. Délépine-Lesoille, S. Fortier and Y. Juën, Spontaneous Brillouin scattering odeling and easureent in various axis-syetric optical fibers, ECOC 7, Berlin (7). G. Kulscar, Y. Juën, et al., Multi-Stokes stiulated Brillouin scattering generated in pulsed high-power double cladding Er 3+ /Yb 3+ codoped fiber aplifiers Photon. Technol. Lett., vol. 5, pp (3) 3. G.P. Agrawal, Nonlinear Fiber Optics. Acadeic Press (6) 4. D.A Fishan and J.A. Nagel, Degradations due to stiulated Brillouin scattering in ultigigabit intensity-odulated fiber-optic systes, Lightwave Technol., vol., pp (99) 5. W. Zou, Z. He, M. Kishi, and K. Hotate, Stiulated Brillouin scattering and its dependences on teperature and strain in a high-delta optical fiber with F-doped depressed inner-cladding, Opt. Lett., 3, pp. 6 6, March 7. 6 K.Y. Song, M.G. Herraez and L. Thevenaz, Observation of pulse delaying and advanceent in optical fibers using stiulated Brillouin scattering, Opt. Express, 3, pp.8-88 (5) 7. Y. Koyaada, S. Sato, S. Nakaura, H. Sotobayashi, and W. Chujo, Siulating and designing Brillouin gain spectru in singleode fibers, Lightwave Technol., vol., pp (4) 8. W. Zou, Z. He and K. Hotate, Twodiensional finite-eleent odal analysis of Brillouin gain spectra in optical fibers Photon. Technol. Lett., vol.8, pp (6). 9. L. Tartara, C. Codeard, J.-N. Maran, R. Cherif and M. Zqhal, Full odal analysis of the Brillouin gain spectru of an optical fiber Optics Co., vol. 8, pp (9). C. K. Jen, A. Safaai-Jazi and G.W Farnell, Leaky odes in weakly guiding fiber acoustic waveguide IEEE Trans. Ultrason., Ferroelectr. Freq., Control., vol. 33, pp (986). A. Kobyakov, S. Kuar et al., Design concept for optical fibers with enhanced SBS threshold Opt. Express, 3, pp (5). A. Yeniay, J. M. Delavaux, and J. Toulouse. Spontaneous and stiulated Brillouin scattering gain spectra in optical fibers Lightwave. Technol., vol., pp () 3. V. Lanticq, S. Jiang, R. Gabet, T. Juën, et al. Self-referenced and single-ended ethod to easure Brillouin gain in onoode optical fibers Opt. Lett., 34, pp. 8- (9) 4. K. Nagayaa, M. KaKui, M. Matsui, T. Saiyoh and Y. Chigusa, Ultra-low-loss (.484 db/k) pure silica core fiber and extension of transission distance Electron. Lett., Vol. 38, pp () 5. T. Sasaki, K. Makihara, M. Hirano, et al., Novel dispersion copensation fiber with fluorine-doped cladding for siultaneous realization of high dispersion copensation iciency and low attenuation OFC 6, paper OThA (6) 6. M.-J. Li, X. Chen, J. Wang, et al, Fiber designs for reducing stiulated Brillouin scattering CLEO 6, paper OTuA4 (6) 7. Y. Koyaada, S. Sato, et al., Siulating and designing Brillouin gain spectru in singleode fibers Lightwave Technol., vol., pp (4) 8. P. L. Chu and R. A. Saut, Analytical ethod for calculation of stresses and aterial birefringence in polarization-aintaining optical fiber Lightwave Technol., vol., pp (984) 9. S. P. Tioshenko and J. N. Goodier, Theory of Elasticity, 3 rd ed. New York: McGraw-Hill (97). Q. Yu, X. B and L. Chen, Teperature dependence of Brillouin frequency, power, and bandwidth in panda, bow-tie, and tiger polarization-aintaining fibers Opt. Lett., 9, pp. 7-9 (4)