Abstract

We report the observation of anti-crossings between hybrid-mode acoustic phonons in an axially-varying photonic crystal fiber. Our experimental results are analyzed using an electrostriction theory which reveals strong coupling between longitudinal and shear components of elastic wave. These anti-crossings are highly sensitive to the transverse fiber structure and thus could be potentially used for ultra-sensitive sensors and new opto-acoustic devices.

© 2015 Optical Society of America

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  1. L. Brillouin, “Diffusion de la lumière et des rayons X par un corps transparent homogène,” Ann. Phys. 17, 88–122 (1922).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  9. M. S. Kang, A. Butsch, and P. St. J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics 5(9), 549–553 (2011).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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  19. K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fibre by changing the core radius,” Electron. Lett. 31(8), 668–669 (1995).
    [Crossref]
  20. J. Yu, I.-B. Kwon, and K. Oh, “Analysis of Brillouin frequency shift and longitudinal acoustic wave in a silica optical fiber with a triple-layered structure,” J. Lightwave Technol. 21(8), 1779–1786 (2003).
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    [Crossref] [PubMed]

2013 (2)

V. Laude and J.-C. Beugnot, “Generation of phonons from electrostriction in small-core optical waveguides,” AIP Adv. 3(4), 042109 (2013).
[Crossref]

C. G. Poulton, R. Pant, and B. J. Eggleton, “Acoustic confinement and stimulated Brillouin scattering in integrated optical waveguides,” J. Opt. Soc. Am. B 30(10), 2657–2664 (2013).
[Crossref]

2012 (2)

J.-C. Beugnot and V. Laude, “Electrostriction and guidance of acoustic phonons in optical fibers,” Phys. Rev. B 86(22), 224304 (2012).
[Crossref]

B. Stiller, A. Kudlinski, M. W. Lee, G. Bouwmans, M. Delqué, J.-C. Beugnot, H. Maillotte, and T. Sylvestre, “SBS mitigation in a microstructured optical Fiber by periodically varying the core diameter,” IEEE Photonics Technol. Lett. 24(8), 667–669 (2012).
[Crossref]

2011 (2)

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

X. Bao and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors (Basel) 11(12), 4152–4187 (2011).
[Crossref] [PubMed]

2010 (3)

2009 (1)

M. S. Kang, A. Nazarkin, A. Brenn, and P. St. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators,” Nat. Phys. 5(4), 276–280 (2009).
[Crossref]

2008 (1)

S. Diaz, S. Foaleng Mafang, M. Lopez-Amo, and L. Thevenaz, “A high-performance optical time-domain Brillouin distributed fiber sensor,” IEEE Sens. J. 8(7), 1268–1272 (2008).
[Crossref]

2006 (3)

D. Elser, U. L. Andersen, A. Korn, O. Glöckl, S. Lorenz, Ch. Marquardt, and G. Leuchs, “Reduction of guided acoustic wave Brillouin scattering in photonic crystal fibers,” Phys. Rev. Lett. 97(13), 133901 (2006).
[Crossref] [PubMed]

P. Dainese, P. St. J. Russell, N. Joly, 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), 388–392 (2006).
[Crossref]

K. Furusawa, Z. Yusoff, F. Poletti, T. M. Monro, N. G. R. Broderick, and D. J. Richardson, “Brillouin characterization of holey optical fibers,” Opt. Lett. 31(17), 2541–2543 (2006).
[Crossref] [PubMed]

2004 (1)

2003 (3)

J. Yu, I.-B. Kwon, and K. Oh, “Analysis of Brillouin frequency shift and longitudinal acoustic wave in a silica optical fiber with a triple-layered structure,” J. Lightwave Technol. 21(8), 1779–1786 (2003).
[Crossref]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424(6949), 657–659 (2003).
[Crossref] [PubMed]

P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

1995 (1)

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fibre by changing the core radius,” Electron. Lett. 31(8), 668–669 (1995).
[Crossref]

1972 (2)

1922 (1)

L. Brillouin, “Diffusion de la lumière et des rayons X par un corps transparent homogène,” Ann. Phys. 17, 88–122 (1922).

Afshar V, S.

Allan, D. C.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424(6949), 657–659 (2003).
[Crossref] [PubMed]

Andersen, U. L.

D. Elser, U. L. Andersen, A. Korn, O. Glöckl, S. Lorenz, Ch. Marquardt, and G. Leuchs, “Reduction of guided acoustic wave Brillouin scattering in photonic crystal fibers,” Phys. Rev. Lett. 97(13), 133901 (2006).
[Crossref] [PubMed]

Bacquet, D.

Bao, X.

Beugnot, J.-C.

V. Laude and J.-C. Beugnot, “Generation of phonons from electrostriction in small-core optical waveguides,” AIP Adv. 3(4), 042109 (2013).
[Crossref]

B. Stiller, A. Kudlinski, M. W. Lee, G. Bouwmans, M. Delqué, J.-C. Beugnot, H. Maillotte, and T. Sylvestre, “SBS mitigation in a microstructured optical Fiber by periodically varying the core diameter,” IEEE Photonics Technol. Lett. 24(8), 667–669 (2012).
[Crossref]

J.-C. Beugnot and V. Laude, “Electrostriction and guidance of acoustic phonons in optical fibers,” Phys. Rev. B 86(22), 224304 (2012).
[Crossref]

B. Stiller, S. M. Foaleng, J.-C. Beugnot, M. W. Lee, M. Delqué, G. Bouwmans, A. Kudlinski, L. Thévenaz, H. Maillotte, and T. Sylvestre, “Photonic crystal fiber mapping using Brillouin echoes distributed sensing,” Opt. Express 18(19), 20136–20142 (2010).
[Crossref] [PubMed]

Borrelli, N. F.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424(6949), 657–659 (2003).
[Crossref] [PubMed]

Bouwmans, G.

B. Stiller, A. Kudlinski, M. W. Lee, G. Bouwmans, M. Delqué, J.-C. Beugnot, H. Maillotte, and T. Sylvestre, “SBS mitigation in a microstructured optical Fiber by periodically varying the core diameter,” IEEE Photonics Technol. Lett. 24(8), 667–669 (2012).
[Crossref]

B. Stiller, S. M. Foaleng, J.-C. Beugnot, M. W. Lee, M. Delqué, G. Bouwmans, A. Kudlinski, L. Thévenaz, H. Maillotte, and T. Sylvestre, “Photonic crystal fiber mapping using Brillouin echoes distributed sensing,” Opt. Express 18(19), 20136–20142 (2010).
[Crossref] [PubMed]

Brenn, A.

M. S. Kang, A. Nazarkin, A. Brenn, and P. St. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators,” Nat. Phys. 5(4), 276–280 (2009).
[Crossref]

Brillouin, L.

L. Brillouin, “Diffusion de la lumière et des rayons X par un corps transparent homogène,” Ann. Phys. 17, 88–122 (1922).

Broderick, N. G. R.

Butsch, A.

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

Chen, L.

Dainese, P.

P. Dainese, P. St. J. Russell, N. Joly, 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), 388–392 (2006).
[Crossref]

Delqué, M.

B. Stiller, A. Kudlinski, M. W. Lee, G. Bouwmans, M. Delqué, J.-C. Beugnot, H. Maillotte, and T. Sylvestre, “SBS mitigation in a microstructured optical Fiber by periodically varying the core diameter,” IEEE Photonics Technol. Lett. 24(8), 667–669 (2012).
[Crossref]

B. Stiller, S. M. Foaleng, J.-C. Beugnot, M. W. Lee, M. Delqué, G. Bouwmans, A. Kudlinski, L. Thévenaz, H. Maillotte, and T. Sylvestre, “Photonic crystal fiber mapping using Brillouin echoes distributed sensing,” Opt. Express 18(19), 20136–20142 (2010).
[Crossref] [PubMed]

Diaz, S.

S. Diaz, S. Foaleng Mafang, M. Lopez-Amo, and L. Thevenaz, “A high-performance optical time-domain Brillouin distributed fiber sensor,” IEEE Sens. J. 8(7), 1268–1272 (2008).
[Crossref]

Dossou, M.

Eggleton, B. J.

Elser, D.

D. Elser, U. L. Andersen, A. Korn, O. Glöckl, S. Lorenz, Ch. Marquardt, and G. Leuchs, “Reduction of guided acoustic wave Brillouin scattering in photonic crystal fibers,” Phys. Rev. Lett. 97(13), 133901 (2006).
[Crossref] [PubMed]

Foaleng, S. M.

Foaleng Mafang, S.

S. Diaz, S. Foaleng Mafang, M. Lopez-Amo, and L. Thevenaz, “A high-performance optical time-domain Brillouin distributed fiber sensor,” IEEE Sens. J. 8(7), 1268–1272 (2008).
[Crossref]

Fragnito, H. L.

P. Dainese, P. St. J. Russell, N. Joly, 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), 388–392 (2006).
[Crossref]

Furusawa, K.

Gallagher, M. T.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424(6949), 657–659 (2003).
[Crossref] [PubMed]

Glöckl, O.

D. Elser, U. L. Andersen, A. Korn, O. Glöckl, S. Lorenz, Ch. Marquardt, and G. Leuchs, “Reduction of guided acoustic wave Brillouin scattering in photonic crystal fibers,” Phys. Rev. Lett. 97(13), 133901 (2006).
[Crossref] [PubMed]

Ippen, E. P.

E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21(11), 539–541 (1972).
[Crossref]

Joly, N.

P. Dainese, P. St. J. Russell, N. Joly, 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), 388–392 (2006).
[Crossref]

Kang, M. S.

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

M. S. Kang, A. Nazarkin, A. Brenn, and P. St. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators,” Nat. Phys. 5(4), 276–280 (2009).
[Crossref]

Khelif, A.

P. Dainese, P. St. J. Russell, N. Joly, 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), 388–392 (2006).
[Crossref]

Knight, J. C.

P. Dainese, P. St. J. Russell, N. Joly, 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), 388–392 (2006).
[Crossref]

Koch, K. W.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424(6949), 657–659 (2003).
[Crossref] [PubMed]

Korn, A.

D. Elser, U. L. Andersen, A. Korn, O. Glöckl, S. Lorenz, Ch. Marquardt, and G. Leuchs, “Reduction of guided acoustic wave Brillouin scattering in photonic crystal fibers,” Phys. Rev. Lett. 97(13), 133901 (2006).
[Crossref] [PubMed]

Kudlinski, A.

B. Stiller, A. Kudlinski, M. W. Lee, G. Bouwmans, M. Delqué, J.-C. Beugnot, H. Maillotte, and T. Sylvestre, “SBS mitigation in a microstructured optical Fiber by periodically varying the core diameter,” IEEE Photonics Technol. Lett. 24(8), 667–669 (2012).
[Crossref]

B. Stiller, S. M. Foaleng, J.-C. Beugnot, M. W. Lee, M. Delqué, G. Bouwmans, A. Kudlinski, L. Thévenaz, H. Maillotte, and T. Sylvestre, “Photonic crystal fiber mapping using Brillouin echoes distributed sensing,” Opt. Express 18(19), 20136–20142 (2010).
[Crossref] [PubMed]

Kwon, I.-B.

Laude, V.

V. Laude and J.-C. Beugnot, “Generation of phonons from electrostriction in small-core optical waveguides,” AIP Adv. 3(4), 042109 (2013).
[Crossref]

J.-C. Beugnot and V. Laude, “Electrostriction and guidance of acoustic phonons in optical fibers,” Phys. Rev. B 86(22), 224304 (2012).
[Crossref]

P. Dainese, P. St. J. Russell, N. Joly, 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), 388–392 (2006).
[Crossref]

Lee, M. W.

B. Stiller, A. Kudlinski, M. W. Lee, G. Bouwmans, M. Delqué, J.-C. Beugnot, H. Maillotte, and T. Sylvestre, “SBS mitigation in a microstructured optical Fiber by periodically varying the core diameter,” IEEE Photonics Technol. Lett. 24(8), 667–669 (2012).
[Crossref]

B. Stiller, S. M. Foaleng, J.-C. Beugnot, M. W. Lee, M. Delqué, G. Bouwmans, A. Kudlinski, L. Thévenaz, H. Maillotte, and T. Sylvestre, “Photonic crystal fiber mapping using Brillouin echoes distributed sensing,” Opt. Express 18(19), 20136–20142 (2010).
[Crossref] [PubMed]

Leuchs, G.

D. Elser, U. L. Andersen, A. Korn, O. Glöckl, S. Lorenz, Ch. Marquardt, and G. Leuchs, “Reduction of guided acoustic wave Brillouin scattering in photonic crystal fibers,” Phys. Rev. Lett. 97(13), 133901 (2006).
[Crossref] [PubMed]

Lopez-Amo, M.

S. Diaz, S. Foaleng Mafang, M. Lopez-Amo, and L. Thevenaz, “A high-performance optical time-domain Brillouin distributed fiber sensor,” IEEE Sens. J. 8(7), 1268–1272 (2008).
[Crossref]

Lorenz, S.

D. Elser, U. L. Andersen, A. Korn, O. Glöckl, S. Lorenz, Ch. Marquardt, and G. Leuchs, “Reduction of guided acoustic wave Brillouin scattering in photonic crystal fibers,” Phys. Rev. Lett. 97(13), 133901 (2006).
[Crossref] [PubMed]

Maillotte, H.

B. Stiller, A. Kudlinski, M. W. Lee, G. Bouwmans, M. Delqué, J.-C. Beugnot, H. Maillotte, and T. Sylvestre, “SBS mitigation in a microstructured optical Fiber by periodically varying the core diameter,” IEEE Photonics Technol. Lett. 24(8), 667–669 (2012).
[Crossref]

B. Stiller, S. M. Foaleng, J.-C. Beugnot, M. W. Lee, M. Delqué, G. Bouwmans, A. Kudlinski, L. Thévenaz, H. Maillotte, and T. Sylvestre, “Photonic crystal fiber mapping using Brillouin echoes distributed sensing,” Opt. Express 18(19), 20136–20142 (2010).
[Crossref] [PubMed]

Marquardt, Ch.

D. Elser, U. L. Andersen, A. Korn, O. Glöckl, S. Lorenz, Ch. Marquardt, and G. Leuchs, “Reduction of guided acoustic wave Brillouin scattering in photonic crystal fibers,” Phys. Rev. Lett. 97(13), 133901 (2006).
[Crossref] [PubMed]

Mihélic, F.

Monro, T. M.

Müller, D.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424(6949), 657–659 (2003).
[Crossref] [PubMed]

Nazarkin, A.

M. S. Kang, A. Nazarkin, A. Brenn, and P. St. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators,” Nat. Phys. 5(4), 276–280 (2009).
[Crossref]

Oh, K.

Ohashi, M.

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fibre by changing the core radius,” Electron. Lett. 31(8), 668–669 (1995).
[Crossref]

Pant, R.

Poletti, F.

Poulton, C. G.

Richardson, D. J.

Russell, P.

P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

Russell, P. St. J.

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

M. S. Kang, A. Nazarkin, A. Brenn, and P. St. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators,” Nat. Phys. 5(4), 276–280 (2009).
[Crossref]

P. Dainese, P. St. J. Russell, N. Joly, 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), 388–392 (2006).
[Crossref]

Shiraki, K.

K. Shiraki, M. Ohashi, and M. Tateda, “Suppression of stimulated Brillouin scattering in a fibre by changing the core radius,” Electron. Lett. 31(8), 668–669 (1995).
[Crossref]

Smith, C. M.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424(6949), 657–659 (2003).
[Crossref] [PubMed]

Smith, R. G.

Stiller, B.

B. Stiller, A. Kudlinski, M. W. Lee, G. Bouwmans, M. Delqué, J.-C. Beugnot, H. Maillotte, and T. Sylvestre, “SBS mitigation in a microstructured optical Fiber by periodically varying the core diameter,” IEEE Photonics Technol. Lett. 24(8), 667–669 (2012).
[Crossref]

B. Stiller, S. M. Foaleng, J.-C. Beugnot, M. W. Lee, M. Delqué, G. Bouwmans, A. Kudlinski, L. Thévenaz, H. Maillotte, and T. Sylvestre, “Photonic crystal fiber mapping using Brillouin echoes distributed sensing,” Opt. Express 18(19), 20136–20142 (2010).
[Crossref] [PubMed]

Stolen, R. H.

E. P. Ippen and R. H. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21(11), 539–541 (1972).
[Crossref]

Sylvestre, T.

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Supplementary Material (1)

NameDescription
» Visualization 1: AVI (5651 KB)      Evolution as a function of decreasing pitch of the fundamental optical mode (left panel), the HM0 mode (middle panel) and the HM1 mode (right panel).

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Figures (5)

Fig. 1
Fig. 1 (a) and (c) SEM pictures of the PCF observed at its smallest (a) and its largest (c) section (shown with the same scale). (b) Evolution of the PCF outer diameter versus length as measured during drawing. (d) Density (left axis) and refractive index (right axis) across the germanium doped core. (e) “L” longitudinal (left axis) and “S” shear (right axis) acoustic velocities across the germanium doped core. In (d) and (e), black solid lines correspond to the small section and red dashed lines to the large one.
Fig. 2
Fig. 2 (a) and (c) Experimental relative intensity spectrogram (in dB) as a function of fiber distance. (b) and (d) Corresponding phase spectrograms (in radians). (a) and (b) are close-ups on the higher frequency (HM1) component experiencing anti-crossings. Top abscissa axis: pitch Λ (in µm) for the tapered section.
Fig. 3
Fig. 3 Measured relative frequency shift of HM0 and HM1 phonons (black and red lines respectively) as a function of distance along the PCF. Top axis: local pitch Λ in µm.
Fig. 4
Fig. 4 Numerical spectrogram versus equivalent distance (bottom axis) or pitch Λ in µm (top axis). In order to simulate a uniform section, identical data are replicated beyond a distance of 170 m. A closer view of the anti-crossing inside the red ellipse is reported Fig. 5(g) with higher numerical resolution.
Fig. 5
Fig. 5 (g) Close-up view at the anti-crossing appearing in Fig. 4 around a distance of 20 m. (a-f) Normalized acoustic kinetic energy distribution for different HM phonons selected along the two main branches of the anti-crossing. [Visualization 1] left to right: cross section of the fundamental optical mode (left), kinetic acoustic energy distribution of the HM0 mode (middle), and kinetic acoustic energy of the HM1 most intense mode, as a function of decreasing pitch (and thus fiber diameter).

Tables (1)

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Table 1 Geometrical frequency resolution of HM0 and the various HM1 acoustic phonons appearing along the fiber, as labelled in Fig. 3. Second line: resolution versus the effective index, neff. Third line: resolution versus the fiber pitch, Λ.

Equations (2)

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ν B = 2   n e f f V a λ P
m | n = m * ( x , y )   n ( x , y )   d x   d y  

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