Abstract

We examine the effect of acoustic mode confinement on stimulated Brillouin scattering (SBS) in optical waveguides that consist of a guiding core embedded in a solid substrate. We find that SBS can arise due to coupling to acoustic modes in three different regimes. First, the acoustic modes may be guided by total internal reflection; in this case, the SBS gain depends directly on the degree of confinement of the acoustic mode in the core, which is in turn determined by the acoustic V parameter. Second, the acoustic modes may be leaky but may nevertheless have a sufficiently long lifetime to have a large effect on the SBS gain; the lifetime of acoustic modes in this regime depends not only on the contrast in acoustic properties between the core and the cladding but is also highly dependent on the waveguide dimensions. Finally, SBS may occur due to coupling to free modes, which exist even in the absence of acoustic confinement; we find that the cumulative effect of coupling to these nonconfined modes results in significant SBS gain. We show how the different acoustic properties of core and cladding lead to these different regimes and discuss the feasibility of SBS experiments using different material systems.

© 2013 Optical Society of America

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  1. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2003).
  2. I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104, 083901 (2010).
    [CrossRef]
  3. G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403–408 (2011).
    [CrossRef]
  4. H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
    [CrossRef]
  5. R. Pant, C. G. Poulton, D.-Y. Choi, H. Mcfarlane, S. Hile, E. Li, L. Thevenaz, B. Luther-Davies, S. J. Madden, and B. J. Eggleton, “On-chip stimulated Brillouin scattering.” Opt. Express 19, 8285–8290 (2011).
    [CrossRef]
  6. P. Dainese, P. S. 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, 388–392 (2006).
    [CrossRef]
  7. S. Chin, L. Thévenaz, J. Sancho, S. Sales, J. Capmany, P. Berger, J. Bourderionnet, and D. Dolfi, “Broadband true time delay for microwave signal processing, using slow light based on stimulated Brillouin scattering in optical fibers,” Opt. Express 18, 22599–22613 (2010).
    [CrossRef]
  8. A. Byrnes, R. Pant, E. Li, D. Y. Choi, C. G. Poulton, S. Fan, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Photonic chip based tunable and reconfigurable narrowband microwave photonic filter using stimulated Brillouin scattering,” Opt. Express 20, 18836–18845 (2012).
    [CrossRef]
  9. S. Sternklar, M. Vart, A. Lifshitz, S. Bloch, and E. Granot, “Kilohertz laser frequency sensing with Brillouin mutually modulated cross-gain modulation,” Opt. Lett. 36, 4161–4163 (2011).
    [CrossRef]
  10. F. Gao, R. Pant, E. Li, C. G. Poulton, D.-Y. Choi, S. J. Madden, B. Luther-Davies, and B. J. Eggleton, “On-chip high sensitivity laser frequency sensing with Brillouin mutually-modulated cross-gain modulation,” Opt. Express 21, 8605–8613 (2013).
    [CrossRef]
  11. L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2, 474–481 (2008).
    [CrossRef]
  12. R. Pant, A. Byrnes, C. G. Poulton, E. Li, D.-Y. Choi, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based tunable slow and fast light via stimulated Brillouin scattering,” Opt. Lett. 37, 969–971 (2012).
    [CrossRef]
  13. X. Huang and S. Fan, “Complete all-optical silica fiber isolator via stimulated Brillouin scattering,” IEEE J. Lightwave Technol. 29, 2267–2275 (2011).
    [CrossRef]
  14. C. G. Poulton, R. Pant, A. Byrnes, S. Fan, M. J. Steel, and B. J. Eggleton, “Design for broadband on-chip isolator using stimulated Brillouin scattering in dispersion-engineered chalcogenide waveguides,” Opt. Express 20, 21235–21246 (2012).
    [CrossRef]
  15. A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
    [CrossRef]
  16. P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012).
    [CrossRef]
  17. H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
    [CrossRef]
  18. B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5, 141–148 (2011).
  19. A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photon. 59, 1–59 (2010).
    [CrossRef]
  20. B. A. Auld, Acoustic Fields and Waves in Solids, 1st ed. (Wiley, 1973), Vol. 2.
  21. A. Brenn, G. S. Wiederhecker, M. S. Kang, H. Hundertmark, N. Joly, and P. S. J. Russell, “Influence of air-filling fraction on forward Raman-like scattering by transversely trapped acoustic resonances in photonic crystal fibers,” J. Opt. Soc. Am. B 26, 1641–1648 (2009).
    [CrossRef]
  22. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).
  23. P. D. Dragic, “Estimating the effect of Ge doping on the acoustic damping coefficient via a highly Ge-doped MCVD silica fiber,” J. Opt. Soc. Am. B 26, 1614–1620 (2009).
    [CrossRef]
  24. B. Ward and J. Spring, “Finite element analysis of Brillouin gain in SBS-suppressing optical fibers with nonuniform acoustic velocity profiles,” Opt. Express 17, 15685–15699 (2009).
    [CrossRef]
  25. E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J 43, 1783–1809 (1964).
    [CrossRef]
  26. C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 1306–1321 (2006).
    [CrossRef]
  27. K. Ogusu, H. Li, and M. Kitao, “Brillouin-gain coefficients of chalcogenide glasses,” J. Opt. Soc. Am. B 21, 1302–1304 (2004).
    [CrossRef]
  28. W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7, 599–604 (1994).
    [CrossRef]

2013 (2)

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[CrossRef]

F. Gao, R. Pant, E. Li, C. G. Poulton, D.-Y. Choi, S. J. Madden, B. Luther-Davies, and B. J. Eggleton, “On-chip high sensitivity laser frequency sensing with Brillouin mutually-modulated cross-gain modulation,” Opt. Express 21, 8605–8613 (2013).
[CrossRef]

2012 (6)

R. Pant, A. Byrnes, C. G. Poulton, E. Li, D.-Y. Choi, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based tunable slow and fast light via stimulated Brillouin scattering,” Opt. Lett. 37, 969–971 (2012).
[CrossRef]

A. Byrnes, R. Pant, E. Li, D. Y. Choi, C. G. Poulton, S. Fan, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Photonic chip based tunable and reconfigurable narrowband microwave photonic filter using stimulated Brillouin scattering,” Opt. Express 20, 18836–18845 (2012).
[CrossRef]

C. G. Poulton, R. Pant, A. Byrnes, S. Fan, M. J. Steel, and B. J. Eggleton, “Design for broadband on-chip isolator using stimulated Brillouin scattering in dispersion-engineered chalcogenide waveguides,” Opt. Express 20, 21235–21246 (2012).
[CrossRef]

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[CrossRef]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[CrossRef]

P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012).
[CrossRef]

2011 (5)

X. Huang and S. Fan, “Complete all-optical silica fiber isolator via stimulated Brillouin scattering,” IEEE J. Lightwave Technol. 29, 2267–2275 (2011).
[CrossRef]

G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403–408 (2011).
[CrossRef]

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5, 141–148 (2011).

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

S. Sternklar, M. Vart, A. Lifshitz, S. Bloch, and E. Granot, “Kilohertz laser frequency sensing with Brillouin mutually modulated cross-gain modulation,” Opt. Lett. 36, 4161–4163 (2011).
[CrossRef]

2010 (3)

S. Chin, L. Thévenaz, J. Sancho, S. Sales, J. Capmany, P. Berger, J. Bourderionnet, and D. Dolfi, “Broadband true time delay for microwave signal processing, using slow light based on stimulated Brillouin scattering in optical fibers,” Opt. Express 18, 22599–22613 (2010).
[CrossRef]

A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photon. 59, 1–59 (2010).
[CrossRef]

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104, 083901 (2010).
[CrossRef]

2009 (3)

2008 (1)

L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2, 474–481 (2008).
[CrossRef]

2006 (2)

P. Dainese, P. S. 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, 388–392 (2006).
[CrossRef]

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 1306–1321 (2006).
[CrossRef]

2004 (1)

1994 (1)

W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7, 599–604 (1994).
[CrossRef]

1964 (1)

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J 43, 1783–1809 (1964).
[CrossRef]

Alegre, T. P. M.

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[CrossRef]

Auld, B. A.

B. A. Auld, Acoustic Fields and Waves in Solids, 1st ed. (Wiley, 1973), Vol. 2.

Bahl, G.

G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403–408 (2011).
[CrossRef]

Berger, P.

Bloch, S.

Bourderionnet, J.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2003).

Brenn, A.

Byrnes, A.

Camacho, R.

P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012).
[CrossRef]

Capmany, J.

Carmon, T.

G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403–408 (2011).
[CrossRef]

Chan, J.

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[CrossRef]

Chen, T.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[CrossRef]

Chew, W. C.

W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7, 599–604 (1994).
[CrossRef]

Chin, S.

Choi, D. Y.

Choi, D.-Y.

Chowdhury, D.

A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photon. 59, 1–59 (2010).
[CrossRef]

Cox, J. A.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[CrossRef]

Dainese, P.

P. Dainese, P. S. 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, 388–392 (2006).
[CrossRef]

Davids, P.

P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012).
[CrossRef]

Dolfi, D.

Dragic, P. D.

Eggleton, B. J.

Fan, S.

Fragnito, H. L.

P. Dainese, P. S. 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, 388–392 (2006).
[CrossRef]

Freude, W.

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 1306–1321 (2006).
[CrossRef]

Fujii, M.

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 1306–1321 (2006).
[CrossRef]

Gao, F.

Granot, E.

Grudinin, I. S.

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104, 083901 (2010).
[CrossRef]

Hile, S.

Hill, J. T.

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[CrossRef]

Huang, X.

X. Huang and S. Fan, “Complete all-optical silica fiber isolator via stimulated Brillouin scattering,” IEEE J. Lightwave Technol. 29, 2267–2275 (2011).
[CrossRef]

Hundertmark, H.

Jarecki, R.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[CrossRef]

Jeon, S.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[CrossRef]

Joly, N.

A. Brenn, G. S. Wiederhecker, M. S. Kang, H. Hundertmark, N. Joly, and P. S. J. Russell, “Influence of air-filling fraction on forward Raman-like scattering by transversely trapped acoustic resonances in photonic crystal fibers,” J. Opt. Soc. Am. B 26, 1641–1648 (2009).
[CrossRef]

P. Dainese, P. S. 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, 388–392 (2006).
[CrossRef]

Kang, M. S.

Khelif, A.

P. Dainese, P. S. 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, 388–392 (2006).
[CrossRef]

Kitao, M.

Knight, J. C.

P. Dainese, P. S. 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, 388–392 (2006).
[CrossRef]

Kobyakov, A.

A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photon. 59, 1–59 (2010).
[CrossRef]

Koos, C.

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 1306–1321 (2006).
[CrossRef]

Krause, A.

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[CrossRef]

Laude, V.

P. Dainese, P. S. 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, 388–392 (2006).
[CrossRef]

Lee, H.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[CrossRef]

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104, 083901 (2010).
[CrossRef]

Leuthold, J.

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 1306–1321 (2006).
[CrossRef]

Li, E.

Li, H.

Li, J.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[CrossRef]

Lifshitz, A.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).

Luther-Davies, B.

Madden, S.

Madden, S. J.

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J 43, 1783–1809 (1964).
[CrossRef]

Mcfarlane, H.

Ogusu, K.

Olsson, R. H.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[CrossRef]

Painter, O.

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[CrossRef]

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[CrossRef]

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104, 083901 (2010).
[CrossRef]

Pant, R.

Pfrang, A.

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 1306–1321 (2006).
[CrossRef]

Poulton, C. G.

F. Gao, R. Pant, E. Li, C. G. Poulton, D.-Y. Choi, S. J. Madden, B. Luther-Davies, and B. J. Eggleton, “On-chip high sensitivity laser frequency sensing with Brillouin mutually-modulated cross-gain modulation,” Opt. Express 21, 8605–8613 (2013).
[CrossRef]

A. Byrnes, R. Pant, E. Li, D. Y. Choi, C. G. Poulton, S. Fan, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Photonic chip based tunable and reconfigurable narrowband microwave photonic filter using stimulated Brillouin scattering,” Opt. Express 20, 18836–18845 (2012).
[CrossRef]

C. G. Poulton, R. Pant, A. Byrnes, S. Fan, M. J. Steel, and B. J. Eggleton, “Design for broadband on-chip isolator using stimulated Brillouin scattering in dispersion-engineered chalcogenide waveguides,” Opt. Express 20, 21235–21246 (2012).
[CrossRef]

R. Pant, A. Byrnes, C. G. Poulton, E. Li, D.-Y. Choi, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based tunable slow and fast light via stimulated Brillouin scattering,” Opt. Lett. 37, 969–971 (2012).
[CrossRef]

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

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 1306–1321 (2006).
[CrossRef]

Qiu, W.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[CrossRef]

Rakich, P.

P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012).
[CrossRef]

Rakich, P. T.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[CrossRef]

Reinke, C.

P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012).
[CrossRef]

Richardson, K.

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5, 141–148 (2011).

Russell, P. S. J.

A. Brenn, G. S. Wiederhecker, M. S. Kang, H. Hundertmark, N. Joly, and P. S. J. Russell, “Influence of air-filling fraction on forward Raman-like scattering by transversely trapped acoustic resonances in photonic crystal fibers,” J. Opt. Soc. Am. B 26, 1641–1648 (2009).
[CrossRef]

P. Dainese, P. S. 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, 388–392 (2006).
[CrossRef]

Safavi-Naeini, A. H.

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[CrossRef]

Sales, S.

Sancho, J.

Sauer, M.

A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photon. 59, 1–59 (2010).
[CrossRef]

Schimmel, T.

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 1306–1321 (2006).
[CrossRef]

Schmeltzer, R. A.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J 43, 1783–1809 (1964).
[CrossRef]

Shin, H.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[CrossRef]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).

Spring, J.

Starbuck, A.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[CrossRef]

Steel, M. J.

Sternklar, S.

Thevenaz, L.

Thévenaz, L.

Tomes, M.

G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403–408 (2011).
[CrossRef]

Vahala, K. J.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[CrossRef]

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104, 083901 (2010).
[CrossRef]

Vart, M.

Wang, Z.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[CrossRef]

P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012).
[CrossRef]

Ward, B.

Weedon, W. H.

W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7, 599–604 (1994).
[CrossRef]

Wiederhecker, G. S.

A. Brenn, G. S. Wiederhecker, M. S. Kang, H. Hundertmark, N. Joly, and P. S. J. Russell, “Influence of air-filling fraction on forward Raman-like scattering by transversely trapped acoustic resonances in photonic crystal fibers,” J. Opt. Soc. Am. B 26, 1641–1648 (2009).
[CrossRef]

P. Dainese, P. S. 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, 388–392 (2006).
[CrossRef]

Yang, K. Y.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[CrossRef]

Zehnpfennig, J.

G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403–408 (2011).
[CrossRef]

Adv. Opt. Photon. (1)

A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photon. 59, 1–59 (2010).
[CrossRef]

Bell Syst. Tech. J (1)

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J 43, 1783–1809 (1964).
[CrossRef]

IEEE J. Lightwave Technol. (1)

X. Huang and S. Fan, “Complete all-optical silica fiber isolator via stimulated Brillouin scattering,” IEEE J. Lightwave Technol. 29, 2267–2275 (2011).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 1306–1321 (2006).
[CrossRef]

J. Opt. Soc. Am. B (3)

Microw. Opt. Technol. Lett. (1)

W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7, 599–604 (1994).
[CrossRef]

Nat. Commun. (2)

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).
[CrossRef]

G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403–408 (2011).
[CrossRef]

Nat. Photonics (3)

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[CrossRef]

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5, 141–148 (2011).

L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2, 474–481 (2008).
[CrossRef]

Nat. Phys. (1)

P. Dainese, P. S. 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, 388–392 (2006).
[CrossRef]

Opt. Express (6)

S. Chin, L. Thévenaz, J. Sancho, S. Sales, J. Capmany, P. Berger, J. Bourderionnet, and D. Dolfi, “Broadband true time delay for microwave signal processing, using slow light based on stimulated Brillouin scattering in optical fibers,” Opt. Express 18, 22599–22613 (2010).
[CrossRef]

A. Byrnes, R. Pant, E. Li, D. Y. Choi, C. G. Poulton, S. Fan, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Photonic chip based tunable and reconfigurable narrowband microwave photonic filter using stimulated Brillouin scattering,” Opt. Express 20, 18836–18845 (2012).
[CrossRef]

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

C. G. Poulton, R. Pant, A. Byrnes, S. Fan, M. J. Steel, and B. J. Eggleton, “Design for broadband on-chip isolator using stimulated Brillouin scattering in dispersion-engineered chalcogenide waveguides,” Opt. Express 20, 21235–21246 (2012).
[CrossRef]

B. Ward and J. Spring, “Finite element analysis of Brillouin gain in SBS-suppressing optical fibers with nonuniform acoustic velocity profiles,” Opt. Express 17, 15685–15699 (2009).
[CrossRef]

F. Gao, R. Pant, E. Li, C. G. Poulton, D.-Y. Choi, S. J. Madden, B. Luther-Davies, and B. J. Eggleton, “On-chip high sensitivity laser frequency sensing with Brillouin mutually-modulated cross-gain modulation,” Opt. Express 21, 8605–8613 (2013).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (2)

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104, 083901 (2010).
[CrossRef]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[CrossRef]

Phys. Rev. X (1)

P. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012).
[CrossRef]

Other (3)

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2003).

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, 1983).

B. A. Auld, Acoustic Fields and Waves in Solids, 1st ed. (Wiley, 1973), Vol. 2.

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Figures (9)

Fig. 1.
Fig. 1.

Different waveguide geometries proposed for SBS experiments: (a) simple suspended nanowire, (b) suspended membrane, (c) suspended-core multistructured optical fiber, (d) buried waveguide, (e) optical nanowire, and (f) rib waveguide.

Fig. 2.
Fig. 2.

(a) Schematic of the SBS interaction between pump, signal, and acoustic wave in a waveguide. (b) Dispersion diagram illustrating the different regimes of acoustic modes.

Fig. 3.
Fig. 3.

(a) Waveguide cross section showing optical and acoustic properties. (b) Optoacoustic overlap for acoustically guiding modes (v1<v2) as a function of acoustic contrast, as represented by the acoustic V number in Eq. (6).

Fig. 4.
Fig. 4.

Optoacoustic overlap for leaky acoustic modes (v1>v2) as a function of acoustic contrast, as represented by the imaginary part of the acoustic V number.

Fig. 5.
Fig. 5.

Acoustic mode lifetimes for a cylindrical waveguide as a function of waveguide radius for four different core/cladding materials computed from Eq. (7). The horizontal line at 10 ns represents the phonon lifetime in chalcogenide glass.

Fig. 6.
Fig. 6.

(a) Dispersion diagram showing the phase matching for SBS coupling via acoustic radiation modes. (b) Illustration of coupling to an acoustic radiation mode, which is not bound to the core. The angle of emission depends on the frequency difference between the pump and the signal.

Fig. 7.
Fig. 7.

(a) Acoustic and optical properties for a perfectly acoustically matched waveguide in which the coupling will occur in the acoustic free modes. (b) Total SBS gain as a result of coupling to the continuum of nonguided acoustic modes. The SBS shift for the guided mode in an acoustically homogeneous “bulk” material is at 7.9 GHz.

Fig. 8.
Fig. 8.

(a) Waveguide cross section showing optical and acoustic properties. (b) Fundamental acoustic mode and SBS gain in the guided regime v1<v2. (c) Acoustic mode and SBS gain in the radiative regime v1v2. (d) Acoustic mode and SBS gain in the leaky regime v1>v2. The dotted curve shows the gain in the guided case and is included for comparison. The inset field profiles show the acoustic mode at the peak of the gain spectrum. The vertical dashed line shows the frequency of the SBS shift computed for this guided mode if the material were acoustically homogeneous.

Fig. 9.
Fig. 9.

SBS gain as a continuous function of the velocity ratio v2/v1. The inserts show the acoustic modes in the different regimes.

Equations (19)

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Gm=gmIIpL,
gmI=16π3n18p122cλp3ρ0ΩmΓm(Γm/2)2(ωωp+Ωm)2+(Γm/2)2ηm.
ηm=|E2ρ˜mdA|2E2dA|ρ˜m|2dA,
2ρ˜+(Ω2v1,22q2)ρ˜=0,
ρ˜|C=ρ˜|C+,μ1ρ˜n|C=μ2ρ˜n|C+,
R=Z2/(μ2ρ2)Z1/(μ1ρ1)Z2/(μ2ρ2)+Z1/(μ1ρ1),
Vac=Ωa1v121v22.
v1(r)=5944(10.78Δ%(r)),
τΩ2a3μ2v12j002μ11v221v12,
gI(Ω)=m=0dΩagmI(Ω,Ωa)
gmI(Ω,Ωa)=16π3n18p122cλp3ρ0ΩmΓm(Γm/2)2(ωωp+Ωm)2+(Γm/2)2×|E2ρ˜mrad(Ωa)dA|2E2dA.
ρ˜(r,θ)={AJm(k1r)eimθforr<aBHm(1)(k2r)eimθforra,
μ1k1aJm(k1a)Jm(k1a)=μ2k2aHm(1)(k2a)Hm(1)(k2a).
Hm(1)(k2a)Hm(1)(k2a)=i+O(1k2a).
J1(k1a)J0(k1a)iμ2k2μ1k1.
k1a=j0,0(1iμ1μ21k2a)+O(1(k2a)2),
Ω=v1q[1ij0,02μ1q2a21k2a+O(1(k2a)2)],
ReΩ=qv1,ImΩ=v1j0,02μ1μ2qk2a3.
τ1ImΩ=k2qa3μ2v1j0,02μ1=(ReΩ)2a3μ2v12j002μ11v221v12.

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