Abstract

We study slot waveguide geometries, comprising a combination of soft glasses and high-index guiding structures, for enhancing stimulated Brillouin scattering (SBS). We show that strong optical and acoustic mode confinement in these waveguides can lead to a substantial increase in SBS gain, comparable to or greater than recently proposed suspended silicon nanowire structures. We compute the optimal parameters of the structure and examine the physics of optical and acoustic confinement within slot waveguides. Finally, we compute the effects of linear and nonlinear loss mechanisms on optimum pump/Stokes powers and waveguide lengths.

© 2016 Optical Society of America

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References

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  1. R. Chiao, C. Townes, and B. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12, 592 (1964).
    [Crossref]
  2. R. Boyd, Nonlinear Optics, 3rd Edition (Academic, 2009).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  5. 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] [PubMed]
  6. J. Li, H. Lee, and K. J. Vahala, “Microwave synthesizer using an on-chip Brillouin oscillator,” Nat. Commun. 4, 2097 (2013).
    [PubMed]
  7. D. Culverhouse, F. Farahi, C. Pannell, and D. Jackson, “Potential of stimulated Brillouin scattering as sensing mechanism for distributed temperature sensors,” Electron. Lett. 25, 913–915 (1989).
    [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] [PubMed]
  9. P. Dainese, P. S. J. Russell, N. Joly, J. Knight, G. 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]
  10. M. Kang, A. Nazarkin, A. Brenn, P. St, and J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators,” Nat. Phys. 5, 276–280 (2009).
    [Crossref]
  11. K. S. Abedin, “Brillouin amplification and lasing in a single-mode As2Se3 chalcogenide fiber,” Opt. Lett. 31, 1615–1617 (2006).
    [Crossref] [PubMed]
  12. J. Li, H. Lee, T. Chen, and K. J. Vahala, “Characterization of a high coherence, Brillouin microcavity laser on silicon,” Opt. Express 20, 20170–20180 (2012).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  15. P. T. 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).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  22. B. J. Eggleton, C. G. Poulton, and R. Pant, “Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits,” Adv. Opt. Photon. 5, 536–587 (2013).
    [Crossref]
  23. 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, 013836 (2015).
    [Crossref]
  24. C. Wolff, P. Gutsche, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Impact of nonlinear loss on stimulated Brillouin scattering,” J. Opt. Soc. Am. B 32, 1968–1978 (2015).
    [Crossref]
  25. J. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices (Oxford University, 1985).
  26. P. T. Rakich, P. Davids, and Z. Wang, “Tailoring optical forces in waveguides through radiation pressure and electrostrictive forces,” Opt. Express 18, 14439–14453 (2010).
    [Crossref] [PubMed]
  27. B. A. Auld, Acoustic Fields and Waves in Solids (Wiley, 1973).
  28. 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] [PubMed]
  29. C. Wolff, M. J. Steel, and C. G. Poulton, “Formal selection rules for Brillouin scattering in integrated waveguides and structured fibers,” Opt. Express 22, 32489–32501 (2014).
    [Crossref]
  30. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15, 16604–16644 (2007).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  32. T. Han, S. Madden, D. Bulla, and B. Luther-Davies, “Low loss Chalcogenide glass waveguides by thermal nanoimprint lithography,” Opt. Express 18, 19286–19291 (2010).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2015 (5)

2014 (3)

2013 (5)

2012 (4)

2011 (1)

2010 (2)

2009 (1)

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

2008 (2)

2007 (1)

2006 (2)

K. S. Abedin, “Brillouin amplification and lasing in a single-mode As2Se3 chalcogenide fiber,” Opt. Lett. 31, 1615–1617 (2006).
[Crossref] [PubMed]

P. Dainese, P. S. J. Russell, N. Joly, J. Knight, G. 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]

2004 (1)

1989 (1)

D. Culverhouse, F. Farahi, C. Pannell, and D. Jackson, “Potential of stimulated Brillouin scattering as sensing mechanism for distributed temperature sensors,” Electron. Lett. 25, 913–915 (1989).
[Crossref]

1964 (1)

R. Chiao, C. Townes, and B. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12, 592 (1964).
[Crossref]

Abedin, K. S.

Agrawal, G. P.

Almeida, V. R.

Aryanfar, I.

Auld, B. A.

B. A. Auld, Acoustic Fields and Waves in Solids (Wiley, 1973).

Baets, R.

R. Van Laer, B. Kuyken, D. Van Thourhout, and R. Baets, “Interaction between light and highly confined hyper-sound in a silicon photonic nanowire,” Nat. Photonics 9, 199–203 (2015).
[Crossref]

R. Van Laer, B. Kuyken, D. Van Thourhout, and R. Baets, “Analysis of enhanced stimulated Brillouin scattering in silicon slot waveguides,” Opt. Lett. 39, 1242–1245 (2014).
[Crossref] [PubMed]

R. Van Laer, B. Kuyken, R. Baets, and D. Van Thourhout, “Unifying Brillouin scattering and cavity optomechanics,” arXiv preprinthttp://arxiv.org/abs/1503.03044 (2015).

Barrios, C. A.

Bauters, J. F.

Bohley, C.

P. W. Nolte, C. Bohley, and J. Schilling, “Degenerate four wave mixing in racetrack resonators formed by Chalcogenide infiltrated silicon slot waveguides,” in 2014 IEEE 11th International Conference on Group IV Photonics (GFP) (IEEE, 2014), pp. 118–119.

Bowers, J. E.

Boyd, R.

R. Boyd, Nonlinear Optics, 3rd Edition (Academic, 2009).

Brenn, A.

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

Bulla, D.

Byrnes, A.

Cabrera-Granado, E.

Calderón, O. G.

Camacho, R.

P. T. 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).

Casas-Bedoya, A.

Chen, A.

Chen, T.

Chiao, R.

R. Chiao, C. Townes, and B. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12, 592 (1964).
[Crossref]

Choi, D.-Y.

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] [PubMed]

Culverhouse, D.

D. Culverhouse, F. Farahi, C. Pannell, and D. Jackson, “Potential of stimulated Brillouin scattering as sensing mechanism for distributed temperature sensors,” Electron. Lett. 25, 913–915 (1989).
[Crossref]

Dainese, P.

P. Dainese, P. S. J. Russell, N. Joly, J. Knight, G. 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]

Davenport, M. L.

Davids, P.

P. T. 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).

P. T. Rakich, P. Davids, and Z. Wang, “Tailoring optical forces in waveguides through radiation pressure and electrostrictive forces,” Opt. Express 18, 14439–14453 (2010).
[Crossref] [PubMed]

Dong, H.

Doylend, J. K.

Eggleton, B. 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, 013836 (2015).
[Crossref]

C. Wolff, P. Gutsche, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Impact of nonlinear loss on stimulated Brillouin scattering,” J. Opt. Soc. Am. B 32, 1968–1978 (2015).
[Crossref]

A. Casas-Bedoya, B. Morrison, M. Pagani, D. Marpaung, and B. J. Eggleton, “Stimulated scattering, modulation, etc.; Nonlinear optics, integrated optics; Radio frequency photonics,” Opt. Lett. 40, 4154–4157 (2015).
[Crossref] [PubMed]

C. Wolff, P. Gutsche, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Power limits and a figure of merit for stimulated Brillouin scattering in the presence of third and fifth order loss,” Opt. Express 23, 26628–26638 (2015).
[Crossref] [PubMed]

I. Aryanfar, C. Wolff, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Mode conversion using stimulated Brillouin scattering in nanophotonic silicon waveguides,” Opt. Express 22, 29270–29282 (2014).
[Crossref] [PubMed]

B. J. Eggleton, C. G. Poulton, and R. Pant, “Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits,” Adv. Opt. Photon. 5, 536–587 (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] [PubMed]

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] [PubMed]

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] [PubMed]

Fan, S.

Fang, A. W.

Farahi, F.

D. Culverhouse, F. Farahi, C. Pannell, and D. Jackson, “Potential of stimulated Brillouin scattering as sensing mechanism for distributed temperature sensors,” Electron. Lett. 25, 913–915 (1989).
[Crossref]

Fragnito, H. L.

P. Dainese, P. S. J. Russell, N. Joly, J. Knight, G. 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]

Gauthier, D. J.

Gutsche, P.

Han, T.

Heck, M. J. R.

Hile, S.

Jackson, D.

D. Culverhouse, F. Farahi, C. Pannell, and D. Jackson, “Potential of stimulated Brillouin scattering as sensing mechanism for distributed temperature sensors,” Electron. Lett. 25, 913–915 (1989).
[Crossref]

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] [PubMed]

Joly, N.

P. Dainese, P. S. J. Russell, N. Joly, J. Knight, G. 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.

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

Khelif, A.

P. Dainese, P. S. J. Russell, N. Joly, J. Knight, G. 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]

Knight, J.

P. Dainese, P. S. J. Russell, N. Joly, J. Knight, G. 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]

Kuyken, B.

R. Van Laer, B. Kuyken, D. Van Thourhout, and R. Baets, “Interaction between light and highly confined hyper-sound in a silicon photonic nanowire,” Nat. Photonics 9, 199–203 (2015).
[Crossref]

R. Van Laer, B. Kuyken, D. Van Thourhout, and R. Baets, “Analysis of enhanced stimulated Brillouin scattering in silicon slot waveguides,” Opt. Lett. 39, 1242–1245 (2014).
[Crossref] [PubMed]

R. Van Laer, B. Kuyken, R. Baets, and D. Van Thourhout, “Unifying Brillouin scattering and cavity optomechanics,” arXiv preprinthttp://arxiv.org/abs/1503.03044 (2015).

Laude, V.

P. Dainese, P. S. J. Russell, N. Joly, J. Knight, G. 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.

J. Li, H. Lee, and K. J. Vahala, “Microwave synthesizer using an on-chip Brillouin oscillator,” Nat. Commun. 4, 2097 (2013).
[PubMed]

J. Li, H. Lee, T. Chen, and K. J. Vahala, “Characterization of a high coherence, Brillouin microcavity laser on silicon,” Opt. Express 20, 20170–20180 (2012).
[Crossref] [PubMed]

Lee, M.

Li, E.

Li, J.

J. Li, H. Lee, and K. J. Vahala, “Microwave synthesizer using an on-chip Brillouin oscillator,” Nat. Commun. 4, 2097 (2013).
[PubMed]

J. Li, H. Lee, T. Chen, and K. J. Vahala, “Characterization of a high coherence, Brillouin microcavity laser on silicon,” Opt. Express 20, 20170–20180 (2012).
[Crossref] [PubMed]

Lin, Q.

Lipson, M.

Luther-Davies, B.

Madden, S.

Madden, S. J.

Marpaung, D.

Mcfarlane, H.

Melle, S.

Morrison, B.

Nazarkin, A.

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

Neifeld, M. A.

Nolte, P. W.

P. W. Nolte, C. Bohley, and J. Schilling, “Degenerate four wave mixing in racetrack resonators formed by Chalcogenide infiltrated silicon slot waveguides,” in 2014 IEEE 11th International Conference on Group IV Photonics (GFP) (IEEE, 2014), pp. 118–119.

Nye, J.

J. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices (Oxford University, 1985).

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] [PubMed]

Pagani, M.

Painter, O. J.

Pannell, C.

D. Culverhouse, F. Farahi, C. Pannell, and D. Jackson, “Potential of stimulated Brillouin scattering as sensing mechanism for distributed temperature sensors,” Electron. Lett. 25, 913–915 (1989).
[Crossref]

Pant, R.

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, 013836 (2015).
[Crossref]

C. Wolff, P. Gutsche, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Impact of nonlinear loss on stimulated Brillouin scattering,” J. Opt. Soc. Am. B 32, 1968–1978 (2015).
[Crossref]

C. Wolff, P. Gutsche, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Power limits and a figure of merit for stimulated Brillouin scattering in the presence of third and fifth order loss,” Opt. Express 23, 26628–26638 (2015).
[Crossref] [PubMed]

C. Wolff, M. J. Steel, and C. G. Poulton, “Formal selection rules for Brillouin scattering in integrated waveguides and structured fibers,” Opt. Express 22, 32489–32501 (2014).
[Crossref]

I. Aryanfar, C. Wolff, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Mode conversion using stimulated Brillouin scattering in nanophotonic silicon waveguides,” Opt. Express 22, 29270–29282 (2014).
[Crossref] [PubMed]

B. J. Eggleton, C. G. Poulton, and R. Pant, “Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits,” Adv. Opt. Photon. 5, 536–587 (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] [PubMed]

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] [PubMed]

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] [PubMed]

Qiu, W.

W. Qiu, P. T. Rakich, H. Shin, H. Dong, M. Soljačić, and Z. Wang, “Stimulated Brillouin scattering in nanoscale silicon step-index waveguides: a general framework of selection rules and calculating SBS gain,” Opt. Express 21, 31402–31419 (2013).
[Crossref]

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] [PubMed]

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] [PubMed]

W. Qiu, P. T. Rakich, H. Shin, H. Dong, M. Soljačić, and Z. Wang, “Stimulated Brillouin scattering in nanoscale silicon step-index waveguides: a general framework of selection rules and calculating SBS gain,” Opt. Express 21, 31402–31419 (2013).
[Crossref]

P. T. 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).

P. T. Rakich, P. Davids, and Z. Wang, “Tailoring optical forces in waveguides through radiation pressure and electrostrictive forces,” Opt. Express 18, 14439–14453 (2010).
[Crossref] [PubMed]

Reinke, C.

P. T. 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).

Russell, J.

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

Russell, P. S. J.

P. Dainese, P. S. J. Russell, N. Joly, J. Knight, G. 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]

Schilling, J.

P. W. Nolte, C. Bohley, and J. Schilling, “Degenerate four wave mixing in racetrack resonators formed by Chalcogenide infiltrated silicon slot waveguides,” in 2014 IEEE 11th International Conference on Group IV Photonics (GFP) (IEEE, 2014), pp. 118–119.

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] [PubMed]

W. Qiu, P. T. Rakich, H. Shin, H. Dong, M. Soljačić, and Z. Wang, “Stimulated Brillouin scattering in nanoscale silicon step-index waveguides: a general framework of selection rules and calculating SBS gain,” Opt. Express 21, 31402–31419 (2013).
[Crossref]

Soljacic, M.

St, P.

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

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] [PubMed]

Steel, M. J.

Stoicheff, B.

R. Chiao, C. Townes, and B. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12, 592 (1964).
[Crossref]

Thevenaz, L.

Townes, C.

R. Chiao, C. Townes, and B. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12, 592 (1964).
[Crossref]

Vahala, K. J.

J. Li, H. Lee, and K. J. Vahala, “Microwave synthesizer using an on-chip Brillouin oscillator,” Nat. Commun. 4, 2097 (2013).
[PubMed]

J. Li, H. Lee, T. Chen, and K. J. Vahala, “Characterization of a high coherence, Brillouin microcavity laser on silicon,” Opt. Express 20, 20170–20180 (2012).
[Crossref] [PubMed]

Van Laer, R.

R. Van Laer, B. Kuyken, D. Van Thourhout, and R. Baets, “Interaction between light and highly confined hyper-sound in a silicon photonic nanowire,” Nat. Photonics 9, 199–203 (2015).
[Crossref]

R. Van Laer, B. Kuyken, D. Van Thourhout, and R. Baets, “Analysis of enhanced stimulated Brillouin scattering in silicon slot waveguides,” Opt. Lett. 39, 1242–1245 (2014).
[Crossref] [PubMed]

R. Van Laer, B. Kuyken, R. Baets, and D. Van Thourhout, “Unifying Brillouin scattering and cavity optomechanics,” arXiv preprinthttp://arxiv.org/abs/1503.03044 (2015).

Van Thourhout, D.

R. Van Laer, B. Kuyken, D. Van Thourhout, and R. Baets, “Interaction between light and highly confined hyper-sound in a silicon photonic nanowire,” Nat. Photonics 9, 199–203 (2015).
[Crossref]

R. Van Laer, B. Kuyken, D. Van Thourhout, and R. Baets, “Analysis of enhanced stimulated Brillouin scattering in silicon slot waveguides,” Opt. Lett. 39, 1242–1245 (2014).
[Crossref] [PubMed]

R. Van Laer, B. Kuyken, R. Baets, and D. Van Thourhout, “Unifying Brillouin scattering and cavity optomechanics,” arXiv preprinthttp://arxiv.org/abs/1503.03044 (2015).

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] [PubMed]

W. Qiu, P. T. Rakich, H. Shin, H. Dong, M. Soljačić, and Z. Wang, “Stimulated Brillouin scattering in nanoscale silicon step-index waveguides: a general framework of selection rules and calculating SBS gain,” Opt. Express 21, 31402–31419 (2013).
[Crossref]

P. T. 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).

P. T. Rakich, P. Davids, and Z. Wang, “Tailoring optical forces in waveguides through radiation pressure and electrostrictive forces,” Opt. Express 18, 14439–14453 (2010).
[Crossref] [PubMed]

Wiederhecker, G.

P. Dainese, P. S. J. Russell, N. Joly, J. Knight, G. 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]

Wolff, C.

Xu, Q.

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Electron. Lett. (1)

D. Culverhouse, F. Farahi, C. Pannell, and D. Jackson, “Potential of stimulated Brillouin scattering as sensing mechanism for distributed temperature sensors,” Electron. Lett. 25, 913–915 (1989).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Commun. (2)

J. Li, H. Lee, and K. J. Vahala, “Microwave synthesizer using an on-chip Brillouin oscillator,” Nat. Commun. 4, 2097 (2013).
[PubMed]

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] [PubMed]

Nat. Photonics (1)

R. Van Laer, B. Kuyken, D. Van Thourhout, and R. Baets, “Interaction between light and highly confined hyper-sound in a silicon photonic nanowire,” Nat. Photonics 9, 199–203 (2015).
[Crossref]

Nat. Phys. (2)

P. Dainese, P. S. J. Russell, N. Joly, J. Knight, G. 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]

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

Opt. Express (12)

I. Aryanfar, C. Wolff, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Mode conversion using stimulated Brillouin scattering in nanophotonic silicon waveguides,” Opt. Express 22, 29270–29282 (2014).
[Crossref] [PubMed]

C. Wolff, M. J. Steel, and C. G. Poulton, “Formal selection rules for Brillouin scattering in integrated waveguides and structured fibers,” Opt. Express 22, 32489–32501 (2014).
[Crossref]

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15, 16604–16644 (2007).
[Crossref] [PubMed]

E. Cabrera-Granado, O. G. Calderón, S. Melle, and D. J. Gauthier, “Observation of large 10-Gb/s SBS slow light delay with low distortion using an optimized gain profile,” Opt. Express 16, 16032–16042 (2008).
[Crossref] [PubMed]

P. T. Rakich, P. Davids, and Z. Wang, “Tailoring optical forces in waveguides through radiation pressure and electrostrictive forces,” Opt. Express 18, 14439–14453 (2010).
[Crossref] [PubMed]

T. Han, S. Madden, D. Bulla, and B. Luther-Davies, “Low loss Chalcogenide glass waveguides by thermal nanoimprint lithography,” Opt. Express 18, 19286–19291 (2010).
[Crossref] [PubMed]

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] [PubMed]

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] [PubMed]

J. Li, H. Lee, T. Chen, and K. J. Vahala, “Characterization of a high coherence, Brillouin microcavity laser on silicon,” Opt. Express 20, 20170–20180 (2012).
[Crossref] [PubMed]

J. F. Bauters, M. L. Davenport, M. J. R. Heck, J. K. Doylend, A. Chen, A. W. Fang, and J. E. Bowers, “Silicon on ultra-low-loss waveguide photonic integration platform,” Opt. Express 21, 544–555 (2013).
[Crossref] [PubMed]

W. Qiu, P. T. Rakich, H. Shin, H. Dong, M. Soljačić, and Z. Wang, “Stimulated Brillouin scattering in nanoscale silicon step-index waveguides: a general framework of selection rules and calculating SBS gain,” Opt. Express 21, 31402–31419 (2013).
[Crossref]

C. Wolff, P. Gutsche, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Power limits and a figure of merit for stimulated Brillouin scattering in the presence of third and fifth order loss,” Opt. Express 23, 26628–26638 (2015).
[Crossref] [PubMed]

Opt. Lett. (5)

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, 013836 (2015).
[Crossref]

Phys. Rev. Lett. (1)

R. Chiao, C. Townes, and B. Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,” Phys. Rev. Lett. 12, 592 (1964).
[Crossref]

Phys. Rev. X (1)

P. T. 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).

Other (5)

R. Van Laer, B. Kuyken, R. Baets, and D. Van Thourhout, “Unifying Brillouin scattering and cavity optomechanics,” arXiv preprinthttp://arxiv.org/abs/1503.03044 (2015).

R. Boyd, Nonlinear Optics, 3rd Edition (Academic, 2009).

J. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices (Oxford University, 1985).

B. A. Auld, Acoustic Fields and Waves in Solids (Wiley, 1973).

P. W. Nolte, C. Bohley, and J. Schilling, “Degenerate four wave mixing in racetrack resonators formed by Chalcogenide infiltrated silicon slot waveguides,” in 2014 IEEE 11th International Conference on Group IV Photonics (GFP) (IEEE, 2014), pp. 118–119.

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Figures (10)

Fig. 1
Fig. 1 Hybrid silicon chalcogenide slot waveguide on a silica substrate. Top panel: sketch of the geometry. Bottom panel: The transverse profile of the fundamental optical mode as well as the displacement field components and the acoustic frequency of three lowest order acoustic modes that can propagate in the waveguide. The waveguide dimensions are a = 250 nm, b = 190 nm and c = 150 nm.
Fig. 2
Fig. 2 BSBS gain of the acoustic modes described in Fig. 1. The gain is obtained by assuming the acoustic quality factor of 1000. The profile of acoustic power is shown for the three lowest modes.
Fig. 3
Fig. 3 (a) BSBS gain (red graph) in slot waveguide with a = 250 nm and b = 190 nm in a logarithmic scale. Gain is obtained only for the high gain acoustic mode. The green (blue) curve shows the gain when only radiation pressure (electrostriction) is considered in calculations. (b) Variation of acoustic frequency of the acoustic mode with slot gap width (blue curve) in Rayleigh surface waves. The red curve shows variations of the frequency as the slot gap varies from 240 nm to 85 nm assuming that a = 250 nm and b = 190 nm.
Fig. 4
Fig. 4 Interactions of radiation pressure and acoustic displacement fields in the slot waveguide. (a) The dominent contributions to the transverse boundary forces due to radiation pressure (i.e. Txx and Tyy). (b) Illustration of the radiation pressure forces F on waveguide walls, together with the acoustic mode displacements u. The product of F·u* is positive (negative) in vertical (horizontal) gap wall, regardless of the gap width.·As the gap width increases, ∫F·u*dy decreases on the vertical walls[see Fig. 4 (b right and left)]. However, the integral does not change on horizontal walls i.e reduction in the overlap integral is compensated as the gap width increases.
Fig. 5
Fig. 5 BSBS gain in [W−1m−1] for a slot waveguide with (a) c = 200 nm and (b) b = 220 nm.
Fig. 6
Fig. 6 Transverse profile of the electrostrictive force component Fz (left) and the acoustic displacement field uz for a slot waveguide and a slot with silica cover. It is clearly visible that the SiO2 cover shifts the maximum of uz down to the slot center.
Fig. 7
Fig. 7 (a) Comparison of the BSBS gain for silica cover layers with thicknesses 0 nm, 50 nm, 100 nm and 150 nm in a slot waveguide with a = 250 nm and b = 190 nm. The sketch of the geometry is shown on the right side. (b) Variation of BSBS gain in a slot with the cover thickness of c = 160 nm and similar silicon beam dimensions as in (a).
Fig. 8
Fig. 8 Nonlinear loss coefficients β and γ for two slot waveguides as a function of the gap size. The red curves in (a) and (b) shows the loss coefficients for slot with a = 220 nm and b = 220 nm, the blue curve shows the same for a waveguide with a silica cover with 150nm thickness.
Fig. 9
Fig. 9 (a) The Figure of merit for four slot waveguides, including two slots and two slots with silica cover (t = 150 nm). The silicon beams have fixed dimensions for all the structures (a = 220 nm and b = 220 nm). The linear loss of α = 2.3 m−1 and α = 11.5 m−1 are considered in finding the figures of merit. (b) The Stokes amplification corresponding to the waveguides described in (a). The waveguides have optimum lengths.
Fig. 10
Fig. 10 The Stokes amplification for four slot waveguides, two of them with a 150,nm thick silica cover. The waveguide length is considered to be shorter than the optimal value.

Tables (2)

Tables Icon

Table 1 Related permittivity, photo-elastic coefficients – in Voigt notation – and material symmetry of materials used in the proposed structures [16].

Tables Icon

Table 2 Material density and stiffness constants – in Voigt notation – for materials used in the proposed structures [27].

Equations (27)

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

Ω = ω p ω s ,
q = β p β s ,
P p z + ( α p + β P p + γ P p 2 ) P p = ( 2 β + 4 γ P p + γ P s + Γ ) P p P s ,
P s z + ( α s + β P s + γ P s 2 ) P s = ( 2 β + 4 γ P s + γ P p Γ ) P p P s ,
Γ = 2 Ω ω | Q c | 2 α a c P p P s P ac ,
Q c = F u * dA ,
F i = i j j σ i j ,
σ i j = 1 2 ε 0 ε r 2 k l p i j k l E k E l ,
E k = { a p ( z , t ) E ˜ k ( p ) ( x , y ) e ( i β p z i ω p t ) + a s ( z , t ) E ˜ k ( s ) ( x , y ) e ( i β s z i ω s t ) } + c . c . ,
F i = j ( T 2 i j T 1 i j ) n j ,
T i j = ε r ε 0 ( E i E j 1 2 δ i j | E | 2 ) + μ r μ 0 ( H i H j 1 2 δ i j | H | 2 ) ,
ρ 2 u i t 2 = ( j k l j ( C i j k l S k l + η i j k l S k l t ) ) + F i ,
α a c = Ω ac Q P ac ,
P p z = ( α + β P p + γ P p 2 ) P p ,
P s z = α P s + ( Γ + 2 β ) P p P s + γ P p 2 P s ,
γ P p 2 + ( Γ + 2 β ) P p + α < 0.
P p min = ( Γ + 2 β ) ( Γ + 2 β ) 2 4 γ α 2 γ ,
P p max = ( Γ + 2 β ) ( Γ + 2 β ) 2 4 γ α 2 γ ,
= Γ 2 β 2 α γ .
P opt = P p max = α γ ( + 2 1 ) .
L o p t = 1 2 α ln ( p p max p p min ) = 1 2 α ln ( + 2 1 2 1 ) ,
A ( L , P s ( 0 ) ) = 10 log 10 ( P s ( 0 ) / P s ( L ) ) ,
P s ( L ) = P opt × 10 ( 4 + 0.1 A ) ,
1 2 ln ( P p 2 α p + β P p + γ P p 2 ) β 4 α γ β 2 tan 1 ( 2 γ P p + β 4 α γ β 2 ) = α z + k 1 .
P p 2 α + β P p + γ P p 2 = k 2 e 2 α z ,
( P p max ) 2 α + β P p max + γ ( P p max ) 2 = k 2 ; ( P p min ) 2 α + β P p min + γ ( P p min ) 2 = k 2 e 2 α L opt .
( P p max ) 2 ( Γ + β ) P p max = k 2 ; ( P p min ) 2 ( Γ + β ) P p min = k 2 e 2 α L opt .

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