Abstract

Finite element method is a powerful technique for solving a wide range of engineering problems. However, the existence of the spurious solutions in full-vectorial finite element method has been a major problem for both acoustic and optic modal analyses. For emerging photonic devices exploiting light-sound interactions in high index contrast waveguides, this problem is a major limitation. A penalty function is introduced to remove these unwanted spurious modes in acoustic waveguides, which also identifies the acoustic modes more easily. Numerically simulated results also show considerably improved vector mode profiles. The proposed penalty method has been applied for the characterization of low index contrast single mode fiber and also for high index contrast silicon nanowire to demonstrate its effectiveness.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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2018 (1)

A. Gulistan, M. M. Rahman, S. Ghosh, and B. M. A. Rahman, “Tailoring light-sound interactions in a single mode fiber for the high-power transmission or sensing applications,” Proc. SPIE 10714, 1071403 (2018).

2017 (1)

R. Zhang, J. Sun, G. Chen, M. Cheng, and J. Jiang, “Demonstration of highly efficient forward stimulated Brillouin scattering in partly suspended silicon nanowire racetrack resonators,” Appl. Phys. Lett. 111(3), 031102 (2017).
[Crossref]

2015 (2)

C. Wolff, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Stimulated Brillouin scattering in integrated photonic waveguides: Forces, scattering mechanisms, and coupled-mode analysis,” Phys. Rev. A. 92(1), 013836 (2015).
[Crossref]

A. C. Bedoya, B. Morrison, M. Pagani, D. Marpaung, and B. J. Eggleton, “Tunable narrowband microwave photonic filter created by stimulated Brillouin scattering from a silicon nanowire,” Opt. Lett. 40(17), 4154–4157(2015).
[Crossref]

2014 (2)

2012 (3)

2011 (3)

2010 (1)

2009 (2)

S. Gray, D. T. Walton, X. Chen, J. Wang, M-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[Crossref]

M. A. Soto, G. Bolognini, and F. Di Pasquale, “Enhanced simultaneous distributed strain and temperature fiber sensor employing spontaneous Brillouin scattering and optical pulse coding,” IEEE Photonics Technol. Lett. 21(7), 450–452 (2009).
[Crossref]

2008 (3)

2007 (2)

M. D. Mermelstein, S. Ramachandran, J. M. Fini, and S. Ghalmi, “SBS gain efficiency measurements and modeling in a 1714 μm2 effective area LP08 higher-order mode optical fiber,” Opt. Express 15(24),15952–15963 (2007).
[Crossref] [PubMed]

J. Limpert, F. Roser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tunnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[Crossref]

2006 (4)

W. W. Zou, Z. Y. He, and K. Hotate, “Two-dimensional finite element modal analysis of Brillouin gain spectra in optical fibers,” IEEE Photon. Technol. Lett. 18(23), 2487–2489 (2006).
[Crossref]

P. Dainese, P. S. J. Russell, N. Joly, N. J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388 (2006).
[Crossref]

K. Y. Song, K. S. Abedin, K. Hotate, M. G. Herraez, and L. Thevenaz, “Highly efficient Brillouin slow and fast light using As2Se3 chalcogenide fiber,” Opt. Express 14(13), 5860–5865 (2006).
[Crossref] [PubMed]

I. C. M. Littler, L. B. Fu, E. C. Magi, D. Pudo, and B. J. Eggleton, “Widely tunable, acousto-optic resonances in chalcogenide As2Se3 fiber,” Opt. Express 14(18), 8088–8095 (2006).
[Crossref] [PubMed]

2002 (1)

2001 (1)

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33(4), 359–371 (2001).
[Crossref]

1998 (1)

L. Thevenaz, M. Nikles, A. Fellay, M. Facchini, and P. Robert, “Truly distributed strain and temperature sensing using embedded optical fibers,” Proc. SPIE 3330, 301–314 (1998).
[Crossref]

1995 (1)

D. Sun, J. Manges, X. Yuan, and Z. Cendes, “Spurious modes in finite-element methods,” IEEE Antennas Propag. Mag. 37(5), 12–24 (1995).
[Crossref]

1992 (1)

M. Koshiba and K. Inoue, “Simple and efficient finite–element analysis of microwave and optical waveguides,” IEEE Trans. Microw. Theory Tech. 40(2), 371–377 (1992).
[Crossref]

1984 (2)

B. M. A. Rahman and J. B. Davies, “Penalty function improvement of waveguide solution by finite elements,” IEEE Trans. Microw. Theory Tech. 32(8), 922–928 (1984).
[Crossref]

J. R. Winkler and J. B. Davies, “Elimination of spurious modes in finite element analysis,” J. Comput. Phys. 56(1), 1–14 (1984).
[Crossref]

1976 (1)

A. Konrad, “Vector variational formulation of electromagnetic fields in anisotropic media,” IEEE Trans. Microw. Theory Tech. 24(9), 55–559 (1976).
[Crossref]

1973 (1)

P. E. Lagasse, “Higher–order finite–element analysis of topographic guides supporting elastic surface waves,” J. Acoust. Soc. Am. 53(4), 1116–1122, (1973).
[Crossref]

Abedin, K. S.

Agrawal, A.

Auld, B. A.

B. A. Auld, Acoustic Fields and Waves in Solids, Vol. 2 (Ripol Classic, 1973).

Bahl, G.

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys. 8(3), 203–207 (2012).
[Crossref]

Bedoya, A. C.

Bolognini, G.

M. A. Soto, G. Bolognini, and F. Di Pasquale, “Enhanced simultaneous distributed strain and temperature fiber sensor employing spontaneous Brillouin scattering and optical pulse coding,” IEEE Photonics Technol. Lett. 21(7), 450–452 (2009).
[Crossref]

Bras, H. L.

H. L. Bras, M. Moignard, and B. Charbonnier, “Brillouin scattering in radio over fiber transmission,” in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2017), paper JWA86.

Burov, E.

Butsch, A.

M. S. Kang, A. Butsch, and P. St. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fiber,” Nat. Photonics 5(9), 549–553 (2011).
[Crossref]

Carmon, T.

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys. 8(3), 203–207 (2012).
[Crossref]

Cendes, Z.

D. Sun, J. Manges, X. Yuan, and Z. Cendes, “Spurious modes in finite-element methods,” IEEE Antennas Propag. Mag. 37(5), 12–24 (1995).
[Crossref]

Charbonnier, B.

H. L. Bras, M. Moignard, and B. Charbonnier, “Brillouin scattering in radio over fiber transmission,” in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2017), paper JWA86.

Chen, G.

R. Zhang, J. Sun, G. Chen, M. Cheng, and J. Jiang, “Demonstration of highly efficient forward stimulated Brillouin scattering in partly suspended silicon nanowire racetrack resonators,” Appl. Phys. Lett. 111(3), 031102 (2017).
[Crossref]

Chen, X.

S. Gray, D. T. Walton, X. Chen, J. Wang, M-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[Crossref]

M. J. Li, X. Chen, J. Wang, A. B. Ruffin, D. T. Walton, S. Li, D. A. Nolan, S. Gray, and L. A. Zenteno, “Fiber designs for reducing stimulated Brillouin scattering,” in Optical Fiber Communication Conference (Optical Society of America, 2006), p. 3.

Cheng, M.

R. Zhang, J. Sun, G. Chen, M. Cheng, and J. Jiang, “Demonstration of highly efficient forward stimulated Brillouin scattering in partly suspended silicon nanowire racetrack resonators,” Appl. Phys. Lett. 111(3), 031102 (2017).
[Crossref]

Choi, D. Y.

Cucinotta, A.

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33(4), 359–371 (2001).
[Crossref]

Dainese, P.

P. Dainese, P. S. J. Russell, N. Joly, N. J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388 (2006).
[Crossref]

Dasgupta, S.

Davies, B. L.

Davies, J. B.

B. M. A. Rahman and J. B. Davies, “Penalty function improvement of waveguide solution by finite elements,” IEEE Trans. Microw. Theory Tech. 32(8), 922–928 (1984).
[Crossref]

J. R. Winkler and J. B. Davies, “Elimination of spurious modes in finite element analysis,” J. Comput. Phys. 56(1), 1–14 (1984).
[Crossref]

de Montmorillon, L. A.

Delavaux, J. M.

Demeritt, J. A.

S. Gray, D. T. Walton, X. Chen, J. Wang, M-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[Crossref]

Eberhardt, R.

J. Limpert, F. Roser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tunnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[Crossref]

Eggleton, B. J.

Facchini, M.

L. Thevenaz, M. Nikles, A. Fellay, M. Facchini, and P. Robert, “Truly distributed strain and temperature sensing using embedded optical fibers,” Proc. SPIE 3330, 301–314 (1998).
[Crossref]

Fellay, A.

L. Thevenaz, M. Nikles, A. Fellay, M. Facchini, and P. Robert, “Truly distributed strain and temperature sensing using embedded optical fibers,” Proc. SPIE 3330, 301–314 (1998).
[Crossref]

Fini, J. M.

S. Ramachandran, J. M. Fini, M. Mermelstein, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Ultra large effective area, higher order mode fibers: a new strategy for high power lasers,” Laser Photonics Rev. 2(6),429–448 (2008).
[Crossref]

M. D. Mermelstein, S. Ramachandran, J. M. Fini, and S. Ghalmi, “SBS gain efficiency measurements and modeling in a 1714 μm2 effective area LP08 higher-order mode optical fiber,” Opt. Express 15(24),15952–15963 (2007).
[Crossref] [PubMed]

Fragnito, H. L.

P. Dainese, P. S. J. Russell, N. Joly, N. J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388 (2006).
[Crossref]

Fu, L. B.

Gabet, R.

Ghalmi, S.

S. Ramachandran, J. M. Fini, M. Mermelstein, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Ultra large effective area, higher order mode fibers: a new strategy for high power lasers,” Laser Photonics Rev. 2(6),429–448 (2008).
[Crossref]

M. D. Mermelstein, S. Ramachandran, J. M. Fini, and S. Ghalmi, “SBS gain efficiency measurements and modeling in a 1714 μm2 effective area LP08 higher-order mode optical fiber,” Opt. Express 15(24),15952–15963 (2007).
[Crossref] [PubMed]

Ghosh, S.

A. Gulistan, M. M. Rahman, S. Ghosh, and B. M. A. Rahman, “Tailoring light-sound interactions in a single mode fiber for the high-power transmission or sensing applications,” Proc. SPIE 10714, 1071403 (2018).

Godbout, N.

Grattan, K. T. V.

Gray, S.

S. Gray, D. T. Walton, X. Chen, J. Wang, M-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[Crossref]

M. J. Li, X. Chen, J. Wang, A. B. Ruffin, D. T. Walton, S. Li, D. A. Nolan, S. Gray, and L. A. Zenteno, “Fiber designs for reducing stimulated Brillouin scattering,” in Optical Fiber Communication Conference (Optical Society of America, 2006), p. 3.

Gruner-Nielsen, L.

Gulistan, A.

A. Gulistan, M. M. Rahman, S. Ghosh, and B. M. A. Rahman, “Tailoring light-sound interactions in a single mode fiber for the high-power transmission or sensing applications,” Proc. SPIE 10714, 1071403 (2018).

He, Z.

He, Z. Y.

W. W. Zou, Z. Y. He, and K. Hotate, “Two-dimensional finite element modal analysis of Brillouin gain spectra in optical fibers,” IEEE Photon. Technol. Lett. 18(23), 2487–2489 (2006).
[Crossref]

Herraez, M. G.

Herstrom, S.

Hile, S.

Hotate, K.

Inoue, K.

M. Koshiba and K. Inoue, “Simple and efficient finite–element analysis of microwave and optical waveguides,” IEEE Trans. Microw. Theory Tech. 40(2), 371–377 (1992).
[Crossref]

Jaouen, Y.

Jiang, J.

R. Zhang, J. Sun, G. Chen, M. Cheng, and J. Jiang, “Demonstration of highly efficient forward stimulated Brillouin scattering in partly suspended silicon nanowire racetrack resonators,” Appl. Phys. Lett. 111(3), 031102 (2017).
[Crossref]

Joly, N.

P. Dainese, P. S. J. Russell, N. Joly, N. J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388 (2006).
[Crossref]

Kang, M. S.

M. S. Kang, A. Butsch, and P. St. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fiber,” Nat. Photonics 5(9), 549–553 (2011).
[Crossref]

Kejalakshmy, N.

Khelif, A.

P. Dainese, P. S. J. Russell, N. Joly, N. J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388 (2006).
[Crossref]

Klingebiel, S.

J. Limpert, F. Roser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tunnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[Crossref]

Knight, N. J. C.

P. Dainese, P. S. J. Russell, N. Joly, N. J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388 (2006).
[Crossref]

Konrad, A.

A. Konrad, “Vector variational formulation of electromagnetic fields in anisotropic media,” IEEE Trans. Microw. Theory Tech. 24(9), 55–559 (1976).
[Crossref]

Koshiba, M.

M. Koshiba, “Optical waveguide theory by the finite element method,” IEICE Trans. Electronics 97(7), 625–635 (2014).
[Crossref]

M. Koshiba and K. Inoue, “Simple and efficient finite–element analysis of microwave and optical waveguides,” IEEE Trans. Microw. Theory Tech. 40(2), 371–377 (1992).
[Crossref]

Kumar, A.

Labonte, L.

Lacroix, S.

Lagasse, P. E.

P. E. Lagasse, “Higher–order finite–element analysis of topographic guides supporting elastic surface waves,” J. Acoust. Soc. Am. 53(4), 1116–1122, (1973).
[Crossref]

Laude, V.

P. Dainese, P. S. J. Russell, N. Joly, N. J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388 (2006).
[Crossref]

Leung, D. M. H.

Li, E.

Li, M. J.

M. J. Li, X. Chen, J. Wang, A. B. Ruffin, D. T. Walton, S. Li, D. A. Nolan, S. Gray, and L. A. Zenteno, “Fiber designs for reducing stimulated Brillouin scattering,” in Optical Fiber Communication Conference (Optical Society of America, 2006), p. 3.

Li, M-J.

S. Gray, D. T. Walton, X. Chen, J. Wang, M-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[Crossref]

Li, S.

M. J. Li, X. Chen, J. Wang, A. B. Ruffin, D. T. Walton, S. Li, D. A. Nolan, S. Gray, and L. A. Zenteno, “Fiber designs for reducing stimulated Brillouin scattering,” in Optical Fiber Communication Conference (Optical Society of America, 2006), p. 3.

Limpert, J.

J. Limpert, F. Roser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tunnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[Crossref]

Littler, I. C. M.

Liu, A.

S. Gray, D. T. Walton, X. Chen, J. Wang, M-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[Crossref]

Liu, S.

Madden, S. J.

Magi, E. C.

Mamdem, Y. S.

Manges, J.

D. Sun, J. Manges, X. Yuan, and Z. Cendes, “Spurious modes in finite-element methods,” IEEE Antennas Propag. Mag. 37(5), 12–24 (1995).
[Crossref]

Marpaung, D.

Marquardt, F.

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys. 8(3), 203–207 (2012).
[Crossref]

Mcfarlane, H.

Mermelstein, M.

S. Ramachandran, J. M. Fini, M. Mermelstein, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Ultra large effective area, higher order mode fibers: a new strategy for high power lasers,” Laser Photonics Rev. 2(6),429–448 (2008).
[Crossref]

Mermelstein, M. D.

Moignard, M.

H. L. Bras, M. Moignard, and B. Charbonnier, “Brillouin scattering in radio over fiber transmission,” in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2017), paper JWA86.

Moreau, G.

Morrison, B.

Nicholson, J. W.

S. Ramachandran, J. M. Fini, M. Mermelstein, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Ultra large effective area, higher order mode fibers: a new strategy for high power lasers,” Laser Photonics Rev. 2(6),429–448 (2008).
[Crossref]

Nikles, M.

L. Thevenaz, M. Nikles, A. Fellay, M. Facchini, and P. Robert, “Truly distributed strain and temperature sensing using embedded optical fibers,” Proc. SPIE 3330, 301–314 (1998).
[Crossref]

Nolan, D. A.

M. J. Li, X. Chen, J. Wang, A. B. Ruffin, D. T. Walton, S. Li, D. A. Nolan, S. Gray, and L. A. Zenteno, “Fiber designs for reducing stimulated Brillouin scattering,” in Optical Fiber Communication Conference (Optical Society of America, 2006), p. 3.

Pagani, M.

Pant, R.

Pasquale, F. Di

M. A. Soto, G. Bolognini, and F. Di Pasquale, “Enhanced simultaneous distributed strain and temperature fiber sensor employing spontaneous Brillouin scattering and optical pulse coding,” IEEE Photonics Technol. Lett. 21(7), 450–452 (2009).
[Crossref]

Peschel, T.

J. Limpert, F. Roser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tunnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[Crossref]

Petropoulos, P.

Poletti, F.

Poulton, C. G.

C. Wolff, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Stimulated Brillouin scattering in integrated photonic waveguides: Forces, scattering mechanisms, and coupled-mode analysis,” Phys. Rev. A. 92(1), 013836 (2015).
[Crossref]

R. Pant, C. G. Poulton, D. Y. Choi, H. Mcfarlane, S. Hile, E. Li, L. Thevenaz, B. L. Davies, S. J. Madden, and B. J. Eggleton, “On-chip stimulated Brillouin scattering,” Opt. Express 19(9), 8285–8290 (2011).
[Crossref] [PubMed]

Pudo, D.

Rahman, B. M. A.

A. Gulistan, M. M. Rahman, S. Ghosh, and B. M. A. Rahman, “Tailoring light-sound interactions in a single mode fiber for the high-power transmission or sensing applications,” Proc. SPIE 10714, 1071403 (2018).

S. Sriratanavaree, B. M. A. Rahman, D. M. H. Leung, N. Kejalakshmy, and K. T. V. Grattan, “Rigorous characterization of acoustic-optical interactions in silicon slot waveguides by full-vectorial finite element method,” Opt. Express 22(8), 9528–9537 (2014).
[Crossref] [PubMed]

A. Kumar, V. Rastogi, A. Agrawal, and B. M. A. Rahman, “Birefringence analysis of segmented cladding fiber,” Appl. Opt. 51(15), 3104–3108, (2012).
[Crossref] [PubMed]

B. M. A. Rahman and J. B. Davies, “Penalty function improvement of waveguide solution by finite elements,” IEEE Trans. Microw. Theory Tech. 32(8), 922–928 (1984).
[Crossref]

B. M. A. Rahman and A. Agrawal, Finite Element Modeling Methods for Photonics (Artech House, 2013).

Rahman, M. M.

A. Gulistan, M. M. Rahman, S. Ghosh, and B. M. A. Rahman, “Tailoring light-sound interactions in a single mode fiber for the high-power transmission or sensing applications,” Proc. SPIE 10714, 1071403 (2018).

Ramachandran, S.

S. Ramachandran, J. M. Fini, M. Mermelstein, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Ultra large effective area, higher order mode fibers: a new strategy for high power lasers,” Laser Photonics Rev. 2(6),429–448 (2008).
[Crossref]

M. D. Mermelstein, S. Ramachandran, J. M. Fini, and S. Ghalmi, “SBS gain efficiency measurements and modeling in a 1714 μm2 effective area LP08 higher-order mode optical fiber,” Opt. Express 15(24),15952–15963 (2007).
[Crossref] [PubMed]

Rastogi, V.

Richardson, D. J.

Robert, P.

L. Thevenaz, M. Nikles, A. Fellay, M. Facchini, and P. Robert, “Truly distributed strain and temperature sensing using embedded optical fibers,” Proc. SPIE 3330, 301–314 (1998).
[Crossref]

Roser, F.

J. Limpert, F. Roser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tunnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[Crossref]

Ruffin, A. B.

S. Gray, D. T. Walton, X. Chen, J. Wang, M-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[Crossref]

M. J. Li, X. Chen, J. Wang, A. B. Ruffin, D. T. Walton, S. Li, D. A. Nolan, S. Gray, and L. A. Zenteno, “Fiber designs for reducing stimulated Brillouin scattering,” in Optical Fiber Communication Conference (Optical Society of America, 2006), p. 3.

Russell, P. S. J.

P. Dainese, P. S. J. Russell, N. Joly, N. J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388 (2006).
[Crossref]

Russell, P. St. J.

M. S. Kang, A. Butsch, and P. St. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fiber,” Nat. Photonics 5(9), 549–553 (2011).
[Crossref]

Schneider, T.

Schreiber, T.

J. Limpert, F. Roser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tunnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[Crossref]

Selleri, S.

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33(4), 359–371 (2001).
[Crossref]

Song, K. Y.

Soto, M. A.

M. A. Soto, G. Bolognini, and F. Di Pasquale, “Enhanced simultaneous distributed strain and temperature fiber sensor employing spontaneous Brillouin scattering and optical pulse coding,” IEEE Photonics Technol. Lett. 21(7), 450–452 (2009).
[Crossref]

Sriratanavaree, S.

Steel, M. J.

C. Wolff, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Stimulated Brillouin scattering in integrated photonic waveguides: Forces, scattering mechanisms, and coupled-mode analysis,” Phys. Rev. A. 92(1), 013836 (2015).
[Crossref]

Sun, D.

D. Sun, J. Manges, X. Yuan, and Z. Cendes, “Spurious modes in finite-element methods,” IEEE Antennas Propag. Mag. 37(5), 12–24 (1995).
[Crossref]

Sun, J.

R. Zhang, J. Sun, G. Chen, M. Cheng, and J. Jiang, “Demonstration of highly efficient forward stimulated Brillouin scattering in partly suspended silicon nanowire racetrack resonators,” Appl. Phys. Lett. 111(3), 031102 (2017).
[Crossref]

Taillade, F.

Thevenaz, L.

Tomes, M.

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys. 8(3), 203–207 (2012).
[Crossref]

Toulouse, J.

Tunnermann, A.

J. Limpert, F. Roser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tunnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[Crossref]

Vincetti, L.

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33(4), 359–371 (2001).
[Crossref]

Virally, S.

Walton, D. T.

S. Gray, D. T. Walton, X. Chen, J. Wang, M-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[Crossref]

M. J. Li, X. Chen, J. Wang, A. B. Ruffin, D. T. Walton, S. Li, D. A. Nolan, S. Gray, and L. A. Zenteno, “Fiber designs for reducing stimulated Brillouin scattering,” in Optical Fiber Communication Conference (Optical Society of America, 2006), p. 3.

Wang, J.

S. Gray, D. T. Walton, X. Chen, J. Wang, M-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[Crossref]

M. J. Li, X. Chen, J. Wang, A. B. Ruffin, D. T. Walton, S. Li, D. A. Nolan, S. Gray, and L. A. Zenteno, “Fiber designs for reducing stimulated Brillouin scattering,” in Optical Fiber Communication Conference (Optical Society of America, 2006), p. 3.

Wiederhecker, G. S.

P. Dainese, P. S. J. Russell, N. Joly, N. J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388 (2006).
[Crossref]

Winkler, J. R.

J. R. Winkler and J. B. Davies, “Elimination of spurious modes in finite element analysis,” J. Comput. Phys. 56(1), 1–14 (1984).
[Crossref]

Wirth, C.

J. Limpert, F. Roser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tunnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[Crossref]

Wolff, C.

C. Wolff, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Stimulated Brillouin scattering in integrated photonic waveguides: Forces, scattering mechanisms, and coupled-mode analysis,” Phys. Rev. A. 92(1), 013836 (2015).
[Crossref]

Yan, M. F.

S. Ramachandran, J. M. Fini, M. Mermelstein, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Ultra large effective area, higher order mode fibers: a new strategy for high power lasers,” Laser Photonics Rev. 2(6),429–448 (2008).
[Crossref]

Yeniay, A.

Yuan, X.

D. Sun, J. Manges, X. Yuan, and Z. Cendes, “Spurious modes in finite-element methods,” IEEE Antennas Propag. Mag. 37(5), 12–24 (1995).
[Crossref]

Zenteno, L. A.

S. Gray, D. T. Walton, X. Chen, J. Wang, M-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[Crossref]

M. J. Li, X. Chen, J. Wang, A. B. Ruffin, D. T. Walton, S. Li, D. A. Nolan, S. Gray, and L. A. Zenteno, “Fiber designs for reducing stimulated Brillouin scattering,” in Optical Fiber Communication Conference (Optical Society of America, 2006), p. 3.

Zhang, R.

R. Zhang, J. Sun, G. Chen, M. Cheng, and J. Jiang, “Demonstration of highly efficient forward stimulated Brillouin scattering in partly suspended silicon nanowire racetrack resonators,” Appl. Phys. Lett. 111(3), 031102 (2017).
[Crossref]

Zoboli, M.

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33(4), 359–371 (2001).
[Crossref]

Zou, W.

Zou, W. W.

W. W. Zou, Z. Y. He, and K. Hotate, “Two-dimensional finite element modal analysis of Brillouin gain spectra in optical fibers,” IEEE Photon. Technol. Lett. 18(23), 2487–2489 (2006).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. Zhang, J. Sun, G. Chen, M. Cheng, and J. Jiang, “Demonstration of highly efficient forward stimulated Brillouin scattering in partly suspended silicon nanowire racetrack resonators,” Appl. Phys. Lett. 111(3), 031102 (2017).
[Crossref]

IEEE Antennas Propag. Mag. (1)

D. Sun, J. Manges, X. Yuan, and Z. Cendes, “Spurious modes in finite-element methods,” IEEE Antennas Propag. Mag. 37(5), 12–24 (1995).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

J. Limpert, F. Roser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tunnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007).
[Crossref]

S. Gray, D. T. Walton, X. Chen, J. Wang, M-J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in high-power, single-frequency sources,” IEEE J. Sel. Top. Quantum Electron. 15(1), 37–46 (2009).
[Crossref]

IEEE Photon. Technol. Lett. (1)

W. W. Zou, Z. Y. He, and K. Hotate, “Two-dimensional finite element modal analysis of Brillouin gain spectra in optical fibers,” IEEE Photon. Technol. Lett. 18(23), 2487–2489 (2006).
[Crossref]

IEEE Photonics Technol. Lett. (1)

M. A. Soto, G. Bolognini, and F. Di Pasquale, “Enhanced simultaneous distributed strain and temperature fiber sensor employing spontaneous Brillouin scattering and optical pulse coding,” IEEE Photonics Technol. Lett. 21(7), 450–452 (2009).
[Crossref]

IEEE Trans. Microw. Theory Tech. (3)

B. M. A. Rahman and J. B. Davies, “Penalty function improvement of waveguide solution by finite elements,” IEEE Trans. Microw. Theory Tech. 32(8), 922–928 (1984).
[Crossref]

A. Konrad, “Vector variational formulation of electromagnetic fields in anisotropic media,” IEEE Trans. Microw. Theory Tech. 24(9), 55–559 (1976).
[Crossref]

M. Koshiba and K. Inoue, “Simple and efficient finite–element analysis of microwave and optical waveguides,” IEEE Trans. Microw. Theory Tech. 40(2), 371–377 (1992).
[Crossref]

IEICE Trans. Electronics (1)

M. Koshiba, “Optical waveguide theory by the finite element method,” IEICE Trans. Electronics 97(7), 625–635 (2014).
[Crossref]

J. Acoust. Soc. Am. (1)

P. E. Lagasse, “Higher–order finite–element analysis of topographic guides supporting elastic surface waves,” J. Acoust. Soc. Am. 53(4), 1116–1122, (1973).
[Crossref]

J. Comput. Phys. (1)

J. R. Winkler and J. B. Davies, “Elimination of spurious modes in finite element analysis,” J. Comput. Phys. 56(1), 1–14 (1984).
[Crossref]

J. Lightwave Technol. (2)

Laser Photonics Rev. (1)

S. Ramachandran, J. M. Fini, M. Mermelstein, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Ultra large effective area, higher order mode fibers: a new strategy for high power lasers,” Laser Photonics Rev. 2(6),429–448 (2008).
[Crossref]

Nat. Photonics (1)

M. S. Kang, A. Butsch, and P. St. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fiber,” Nat. Photonics 5(9), 549–553 (2011).
[Crossref]

Nat. Phys. (2)

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys. 8(3), 203–207 (2012).
[Crossref]

P. Dainese, P. S. J. Russell, N. Joly, N. J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388 (2006).
[Crossref]

Opt. Express (8)

S. Sriratanavaree, B. M. A. Rahman, D. M. H. Leung, N. Kejalakshmy, and K. T. V. Grattan, “Rigorous characterization of acoustic-optical interactions in silicon slot waveguides by full-vectorial finite element method,” Opt. Express 22(8), 9528–9537 (2014).
[Crossref] [PubMed]

I. C. M. Littler, L. B. Fu, E. C. Magi, D. Pudo, and B. J. Eggleton, “Widely tunable, acousto-optic resonances in chalcogenide As2Se3 fiber,” Opt. Express 14(18), 8088–8095 (2006).
[Crossref] [PubMed]

S. Virally, N. Godbout, S. Lacroix, and L. Labonte, “Two-fold symmetric geometries for tailored phasematching in birefringent solid-core air-silica microstructured fibers,” Opt. Express 18(10), 10731–10741 (2010).
[Crossref] [PubMed]

R. Pant, C. G. Poulton, D. Y. Choi, H. Mcfarlane, S. Hile, E. Li, L. Thevenaz, B. L. Davies, S. J. Madden, and B. J. Eggleton, “On-chip stimulated Brillouin scattering,” Opt. Express 19(9), 8285–8290 (2011).
[Crossref] [PubMed]

K. Y. Song, K. S. Abedin, K. Hotate, M. G. Herraez, and L. Thevenaz, “Highly efficient Brillouin slow and fast light using As2Se3 chalcogenide fiber,” Opt. Express 14(13), 5860–5865 (2006).
[Crossref] [PubMed]

W. Zou, Z. He, and K. Hotate, “Acoustic modal analysis and control in W-shaped triple-layer optical fibers with highly-germanium-doped core and F-doped inner cladding,” Opt. Express 16(14), 10006–10017 (2008).
[Crossref] [PubMed]

Y. S. Mamdem, E. Burov, L. A. de Montmorillon, Y. Jaouen, G. Moreau, R. Gabet, and F. Taillade, “Importance of residual stresses in the Brillouin gain spectrum of single mode optical fibers,” Opt. Express 20(2), 1790–1797 (2012).
[Crossref] [PubMed]

M. D. Mermelstein, S. Ramachandran, J. M. Fini, and S. Ghalmi, “SBS gain efficiency measurements and modeling in a 1714 μm2 effective area LP08 higher-order mode optical fiber,” Opt. Express 15(24),15952–15963 (2007).
[Crossref] [PubMed]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33(4), 359–371 (2001).
[Crossref]

Phys. Rev. A. (1)

C. Wolff, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Stimulated Brillouin scattering in integrated photonic waveguides: Forces, scattering mechanisms, and coupled-mode analysis,” Phys. Rev. A. 92(1), 013836 (2015).
[Crossref]

Proc. SPIE (2)

A. Gulistan, M. M. Rahman, S. Ghosh, and B. M. A. Rahman, “Tailoring light-sound interactions in a single mode fiber for the high-power transmission or sensing applications,” Proc. SPIE 10714, 1071403 (2018).

L. Thevenaz, M. Nikles, A. Fellay, M. Facchini, and P. Robert, “Truly distributed strain and temperature sensing using embedded optical fibers,” Proc. SPIE 3330, 301–314 (1998).
[Crossref]

Other (4)

H. L. Bras, M. Moignard, and B. Charbonnier, “Brillouin scattering in radio over fiber transmission,” in National Fiber Optic Engineers Conference, OSA Technical Digest Series (Optical Society of America, 2017), paper JWA86.

M. J. Li, X. Chen, J. Wang, A. B. Ruffin, D. T. Walton, S. Li, D. A. Nolan, S. Gray, and L. A. Zenteno, “Fiber designs for reducing stimulated Brillouin scattering,” in Optical Fiber Communication Conference (Optical Society of America, 2006), p. 3.

B. M. A. Rahman and A. Agrawal, Finite Element Modeling Methods for Photonics (Artech House, 2013).

B. A. Auld, Acoustic Fields and Waves in Solids, Vol. 2 (Ripol Classic, 1973).

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Figures (8)

Fig. 1
Fig. 1 Reduction of spurious solutions with penalty (α) term for the Uz dominant LP01 acoustic mode in a SMF.
Fig. 2
Fig. 2 Dominant and non-dominant displacement vector profiles of the fundamental longitudinal LP01 acoustic mode for α = 0 where, (a) Ux, (b) Uy and (c) Uz contours, respectively.
Fig. 3
Fig. 3 Dominant and non-dominant displacement vector profiles of the fundamental longitudinal L P 01 acoustic mode for α = 105, where, (a) Ux, (b) Uy and (c) Uz contours, respectively.
Fig. 4
Fig. 4 Variation of frequency with respect to change in the value of penalty term (α) for the Uz dominant LP01 acoustic mode.
Fig. 5
Fig. 5 Dominant Uz displacement vector contours of higher order longitudinal acoustic modes for α = 0.
Fig. 6
Fig. 6 Dominant Uz displacement vector contours of higher order longitudinal acoustic modes for α = 105.
Fig. 7
Fig. 7 (a) The dominant Uz vector displacement of a highly hybrid mode and (b) is the variation along the x-axis, when α = 0.
Fig. 8
Fig. 8 (a) The non-dominant Ux vector displacement profile of a highly hybrid longitudinal mode (b) the variation of Ux displacement vector along the x-axis when α = 0, and (c) when α = 100.

Tables (1)

Tables Icon

Table 1 Effect of α on frequency shift and longitudinal velocities of the fundamental and higher order longitudinal acoustic modes.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

ω o 2 = [ ( × H ) * ε ^ 1 ( × H ) + α ( H ) * ( H ) ] d x d y H * μ ^ H d x d y
U i = u ( u x , u y , j u z ) e x p j ( ω a t k a z )
S = u
T = ρ 2 u t 2
u n ^ = 0 ;     n ^ is the unit vector
× u = 0
T i j = c i j k l S k l ; i , j , k , l = x , y , z
[ T ] = [ c ] [ S ]
ω a 2 = [ ( U ) * [ C ] ( U ) ] d x d y U * ρ U d x d y
[ A ] U ω a 2 [ B ] U = 0
ω a 2 = [ ( U ) * [ C ] ( U ) + α ( × U ) * ( × U ) ] d x d y U * ρ U d x d y
k a = 2 β o p t

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