Abstract

Stimulated Brillouin scattering (SBS) processes have been enabling important technological breakthroughs in integrated photonics and nano-optomechanics by exploiting light-sound (photon-phonon) interactions at the nanoscale. These nonlinear processes are created by two main effects: radiation pressure and electrostriction; however, the former is the predominant one in high-index-contrast nanowaveguides. In this work, we derive a simple set of analytical expressions that can be used for optimizing the radiation pressure on the waveguide boundaries for any optical mode, polarization, and wavelength. We observe the very strong influence of waveguide geometric parameters on the optimal radiation pressure value. Furthermore, we explain how the existence of such optimal geometric dimensions is physically related to the minimization of the electromagnetic momentum flow in the propagation direction. This work provides a novel and robust yet simple method to optimize the radiation pressure in dielectric nanowaveguides, which may be of great relevance for designing integrated photonic-phononic devices.

© 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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    [Crossref]
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    [Crossref]

2018 (2)

N. T. Otterstrom, R. O. Behunin, E. A. Kittlaus, Z. Wang, and P. T. Rakich, “A silicon Brillouin laser,” Science 360(6393), 1113–1116 (2018).
[Crossref]

Y. Liu, A. Choudhary, D. Marpaung, and B. J. Eggleton, “Chip-based Brillouin Processing for Phase Control of RF Signals,” IEEE J. Quantum Electron. 54(3), 1–13 (2018).
[Crossref]

2017 (4)

E. A. Kittlaus, N. T. Otterstrom, and P. T. Rakich, “On-chip inter-modal Brillouin scattering,” Nat. Commun. 8, 15819 (2017).
[Crossref]

M. Merklein, B. Stiller, K. Vu, S. J. Madden, and B. J. Eggleton, “A chip-integrated coherent photonic-phononic memory,” Nat. Commun. 8(1), 574 (2017).
[Crossref]

B. Morrison, A. Casas-Bedoya, G. Ren, K. Vu, Y. Liu, A. Zarifi, T. G. Nguyen, D.-Y. Choi, D. Marpaung, S. J. Madden, A. Mitchell, and B. J. Eggleton, “Compact Brillouin devices through hybrid integration on Silicon,” Optica 4(8), 847–854 (2017).
[Crossref]

J. R. Rodrigues and V. R. Almeida, “Optical forces through the effective refractive index,” Opt. Lett. 42(21), 4371–4374 (2017).
[Crossref]

2016 (3)

E. A. Kittlaus, H. Shin, and P. T. Rakich, “Large Brillouin amplification in silicon,” Nat. Photonics 10(7), 463–467 (2016).
[Crossref]

M. Merklein, A. Casas-Bedoya, D. Marpaung, T. F. S. Buttner, M. Pagani, B. Morrison, I. V. Kabakova, and B. J. Eggleton, “Stimulated Brillouin Scattering in Photonic Integrated Circuits: Novel Applications and Devices,” IEEE J. Sel. Top. Quantum Electron. 22(2), 336–346 (2016).
[Crossref]

H. Zoubi and K. Hammerer, “Optomechanical multimode Hamiltonian for nanophotonic waveguides,” Phys. Rev. A 94(5), 053827 (2016).
[Crossref]

2015 (7)

R. V. Laer, B. Kuyken, D. V. Thourhout, and R. Baets, “Interaction between light and highly confined hypersound in a silicon photonic nanowire,” Nat. Photonics 9(3), 199–203 (2015).
[Crossref]

M. Merklein and et al., “Enhancing and inhibiting stimulated Brillouin scattering in photonic integrated circuits,” Nat. Commun. 6(1), 6396 (2015).
[Crossref]

R. V. Laer, A. Bazin, B. Kuyken, R. Baets, and D. V. Thourhout, “Net on-chip Brillouin gain based on suspended silicon nanowires,” New J. Phys. 17(11), 115005 (2015).
[Crossref]

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]

V. Laude and J. C. Beugnot, “Lagrangian description of Brillouin scattering and electrostriction in nanoscale optical waveguides,” New J. Phys. 17(12), 125003 (2015).
[Crossref]

L. Thévenaz, “Silicon nanophotonics: Good vibrations for light,” Nat. Photonics 9(3), 144–146 (2015).
[Crossref]

H. Shin, J. A. Cox, R. Jarecki, A. Starbuck, Z. Wang, and P. T. Rakich, “Control of coherent information via on-chip photonic-phononic emitter-receivers,” Nat. Commun. 6(1), 6427 (2015).
[Crossref]

2014 (1)

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[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(1), 2943 (2013).
[Crossref]

B. J. Eggleton, C. G. Poulton, and R. Pant, “Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits,” Adv. Opt. Photon. 5(4), 536–587 (2013).
[Crossref]

2012 (2)

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(1), 011008 (2012).
[Crossref]

Y. Okawachi and A. L. Gaeta, “Nonlinear photonics: Compressing light and sound,” Nat. Photonics 6(5), 274–276 (2012).
[Crossref]

2011 (2)

2010 (2)

2009 (2)

P. T. Rakich, M. A. Popović, and Z. Wang, “General treatment of optical forces and potentials in mechanically variable photonic systems,” Opt. Express 17(20), 18116–18135 (2009).
[Crossref]

P. Loh, A. F. Oskooi, M. Ibanescu, M. Skorobogatiy, and S. G. Johnson, “Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backward-wave structures,” Phys. Rev. E 79(6), 065601 (2009).
[Crossref]

2002 (1)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65(6), 066611 (2002).
[Crossref]

1976 (1)

1974 (1)

Almeida, V. R.

Baets, R.

R. V. Laer, B. Kuyken, D. V. Thourhout, and R. Baets, “Interaction between light and highly confined hypersound in a silicon photonic nanowire,” Nat. Photonics 9(3), 199–203 (2015).
[Crossref]

R. V. Laer, A. Bazin, B. Kuyken, R. Baets, and D. V. Thourhout, “Net on-chip Brillouin gain based on suspended silicon nanowires,” New J. Phys. 17(11), 115005 (2015).
[Crossref]

Bazin, A.

R. V. Laer, A. Bazin, B. Kuyken, R. Baets, and D. V. Thourhout, “Net on-chip Brillouin gain based on suspended silicon nanowires,” New J. Phys. 17(11), 115005 (2015).
[Crossref]

Behunin, R.

S. Gundavarapu, M. Puckett, T. Huffman, R. Behunin, T. Qiu, G. M. Brodnik, C. Pinho, D. Bose, P. T. Rakich, J. Nohava, K. D. Nelson, M. Salit, and D. J. Blumenthal, “Integrated Waveguide Brillouin Laser”, arXiv:1709.04512, 1–15 (2017).

Behunin, R. O.

N. T. Otterstrom, R. O. Behunin, E. A. Kittlaus, Z. Wang, and P. T. Rakich, “A silicon Brillouin laser,” Science 360(6393), 1113–1116 (2018).
[Crossref]

Beugnot, J. C.

V. Laude and J. C. Beugnot, “Lagrangian description of Brillouin scattering and electrostriction in nanoscale optical waveguides,” New J. Phys. 17(12), 125003 (2015).
[Crossref]

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

Blumenthal, D. J.

S. Gundavarapu, M. Puckett, T. Huffman, R. Behunin, T. Qiu, G. M. Brodnik, C. Pinho, D. Bose, P. T. Rakich, J. Nohava, K. D. Nelson, M. Salit, and D. J. Blumenthal, “Integrated Waveguide Brillouin Laser”, arXiv:1709.04512, 1–15 (2017).

Bose, D.

S. Gundavarapu, M. Puckett, T. Huffman, R. Behunin, T. Qiu, G. M. Brodnik, C. Pinho, D. Bose, P. T. Rakich, J. Nohava, K. D. Nelson, M. Salit, and D. J. Blumenthal, “Integrated Waveguide Brillouin Laser”, arXiv:1709.04512, 1–15 (2017).

Brodnik, G. M.

S. Gundavarapu, M. Puckett, T. Huffman, R. Behunin, T. Qiu, G. M. Brodnik, C. Pinho, D. Bose, P. T. Rakich, J. Nohava, K. D. Nelson, M. Salit, and D. J. Blumenthal, “Integrated Waveguide Brillouin Laser”, arXiv:1709.04512, 1–15 (2017).

Buttner, T. F. S.

M. Merklein, A. Casas-Bedoya, D. Marpaung, T. F. S. Buttner, M. Pagani, B. Morrison, I. V. Kabakova, and B. J. Eggleton, “Stimulated Brillouin Scattering in Photonic Integrated Circuits: Novel Applications and Devices,” IEEE J. Sel. Top. Quantum Electron. 22(2), 336–346 (2016).
[Crossref]

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(1), 011008 (2012).
[Crossref]

Casas-Bedoya, A.

B. Morrison, A. Casas-Bedoya, G. Ren, K. Vu, Y. Liu, A. Zarifi, T. G. Nguyen, D.-Y. Choi, D. Marpaung, S. J. Madden, A. Mitchell, and B. J. Eggleton, “Compact Brillouin devices through hybrid integration on Silicon,” Optica 4(8), 847–854 (2017).
[Crossref]

M. Merklein, A. Casas-Bedoya, D. Marpaung, T. F. S. Buttner, M. Pagani, B. Morrison, I. V. Kabakova, and B. J. Eggleton, “Stimulated Brillouin Scattering in Photonic Integrated Circuits: Novel Applications and Devices,” IEEE J. Sel. Top. Quantum Electron. 22(2), 336–346 (2016).
[Crossref]

Choi, D.

Choi, D.-Y.

Choudhary, A.

Y. Liu, A. Choudhary, D. Marpaung, and B. J. Eggleton, “Chip-based Brillouin Processing for Phase Control of RF Signals,” IEEE J. Quantum Electron. 54(3), 1–13 (2018).
[Crossref]

Chowdhury, D.

Cox, J. A.

H. Shin, J. A. Cox, R. Jarecki, A. Starbuck, Z. Wang, and P. T. Rakich, “Control of coherent information via on-chip photonic-phononic emitter-receivers,” Nat. Commun. 6(1), 6427 (2015).
[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(1), 2943 (2013).
[Crossref]

Davids, P.

Djafari-Rouhani, B.

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

Eggleton, B. J.

Y. Liu, A. Choudhary, D. Marpaung, and B. J. Eggleton, “Chip-based Brillouin Processing for Phase Control of RF Signals,” IEEE J. Quantum Electron. 54(3), 1–13 (2018).
[Crossref]

M. Merklein, B. Stiller, K. Vu, S. J. Madden, and B. J. Eggleton, “A chip-integrated coherent photonic-phononic memory,” Nat. Commun. 8(1), 574 (2017).
[Crossref]

B. Morrison, A. Casas-Bedoya, G. Ren, K. Vu, Y. Liu, A. Zarifi, T. G. Nguyen, D.-Y. Choi, D. Marpaung, S. J. Madden, A. Mitchell, and B. J. Eggleton, “Compact Brillouin devices through hybrid integration on Silicon,” Optica 4(8), 847–854 (2017).
[Crossref]

M. Merklein, A. Casas-Bedoya, D. Marpaung, T. F. S. Buttner, M. Pagani, B. Morrison, I. V. Kabakova, and B. J. Eggleton, “Stimulated Brillouin Scattering in Photonic Integrated Circuits: Novel Applications and Devices,” IEEE J. Sel. Top. Quantum Electron. 22(2), 336–346 (2016).
[Crossref]

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]

B. J. Eggleton, C. G. Poulton, and R. Pant, “Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits,” Adv. Opt. Photon. 5(4), 536–587 (2013).
[Crossref]

R. Pant, C. G. Poulton, D. 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(9), 8285–8290 (2011).
[Crossref]

El Jallal, S.

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

Escalante, J. M.

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

Fink, Y.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65(6), 066611 (2002).
[Crossref]

Gaeta, A. L.

Y. Okawachi and A. L. Gaeta, “Nonlinear photonics: Compressing light and sound,” Nat. Photonics 6(5), 274–276 (2012).
[Crossref]

Gundavarapu, S.

S. Gundavarapu, M. Puckett, T. Huffman, R. Behunin, T. Qiu, G. M. Brodnik, C. Pinho, D. Bose, P. T. Rakich, J. Nohava, K. D. Nelson, M. Salit, and D. J. Blumenthal, “Integrated Waveguide Brillouin Laser”, arXiv:1709.04512, 1–15 (2017).

Hammerer, K.

H. Zoubi and K. Hammerer, “Optomechanical multimode Hamiltonian for nanophotonic waveguides,” Phys. Rev. A 94(5), 053827 (2016).
[Crossref]

Haus, H. A.

Hile, S.

Huffman, T.

S. Gundavarapu, M. Puckett, T. Huffman, R. Behunin, T. Qiu, G. M. Brodnik, C. Pinho, D. Bose, P. T. Rakich, J. Nohava, K. D. Nelson, M. Salit, and D. J. Blumenthal, “Integrated Waveguide Brillouin Laser”, arXiv:1709.04512, 1–15 (2017).

Ibanescu, M.

P. Loh, A. F. Oskooi, M. Ibanescu, M. Skorobogatiy, and S. G. Johnson, “Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backward-wave structures,” Phys. Rev. E 79(6), 065601 (2009).
[Crossref]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65(6), 066611 (2002).
[Crossref]

Jarecki, R.

H. Shin, J. A. Cox, R. Jarecki, A. Starbuck, Z. Wang, and P. T. Rakich, “Control of coherent information via on-chip photonic-phononic emitter-receivers,” Nat. Commun. 6(1), 6427 (2015).
[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(1), 2943 (2013).
[Crossref]

Joannopoulos, J. D.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65(6), 066611 (2002).
[Crossref]

Johnson, S. G.

P. Loh, A. F. Oskooi, M. Ibanescu, M. Skorobogatiy, and S. G. Johnson, “Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backward-wave structures,” Phys. Rev. E 79(6), 065601 (2009).
[Crossref]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65(6), 066611 (2002).
[Crossref]

Kabakova, I. V.

M. Merklein, A. Casas-Bedoya, D. Marpaung, T. F. S. Buttner, M. Pagani, B. Morrison, I. V. Kabakova, and B. J. Eggleton, “Stimulated Brillouin Scattering in Photonic Integrated Circuits: Novel Applications and Devices,” IEEE J. Sel. Top. Quantum Electron. 22(2), 336–346 (2016).
[Crossref]

Kittlaus, E. A.

N. T. Otterstrom, R. O. Behunin, E. A. Kittlaus, Z. Wang, and P. T. Rakich, “A silicon Brillouin laser,” Science 360(6393), 1113–1116 (2018).
[Crossref]

E. A. Kittlaus, N. T. Otterstrom, and P. T. Rakich, “On-chip inter-modal Brillouin scattering,” Nat. Commun. 8, 15819 (2017).
[Crossref]

E. A. Kittlaus, H. Shin, and P. T. Rakich, “Large Brillouin amplification in silicon,” Nat. Photonics 10(7), 463–467 (2016).
[Crossref]

Kobyakov, A.

Kogelnik, H.

Kuyken, B.

R. V. Laer, A. Bazin, B. Kuyken, R. Baets, and D. V. Thourhout, “Net on-chip Brillouin gain based on suspended silicon nanowires,” New J. Phys. 17(11), 115005 (2015).
[Crossref]

R. V. Laer, B. Kuyken, D. V. Thourhout, and R. Baets, “Interaction between light and highly confined hypersound in a silicon photonic nanowire,” Nat. Photonics 9(3), 199–203 (2015).
[Crossref]

Laer, R. V.

R. V. Laer, B. Kuyken, D. V. Thourhout, and R. Baets, “Interaction between light and highly confined hypersound in a silicon photonic nanowire,” Nat. Photonics 9(3), 199–203 (2015).
[Crossref]

R. V. Laer, A. Bazin, B. Kuyken, R. Baets, and D. V. Thourhout, “Net on-chip Brillouin gain based on suspended silicon nanowires,” New J. Phys. 17(11), 115005 (2015).
[Crossref]

Laude, V.

V. Laude and J. C. Beugnot, “Lagrangian description of Brillouin scattering and electrostriction in nanoscale optical waveguides,” New J. Phys. 17(12), 125003 (2015).
[Crossref]

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

Li, E.

Liu, Y.

Loh, P.

P. Loh, A. F. Oskooi, M. Ibanescu, M. Skorobogatiy, and S. G. Johnson, “Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backward-wave structures,” Phys. Rev. E 79(6), 065601 (2009).
[Crossref]

Luther-davies, B.

Madden, S. J.

Marpaung, D.

Y. Liu, A. Choudhary, D. Marpaung, and B. J. Eggleton, “Chip-based Brillouin Processing for Phase Control of RF Signals,” IEEE J. Quantum Electron. 54(3), 1–13 (2018).
[Crossref]

B. Morrison, A. Casas-Bedoya, G. Ren, K. Vu, Y. Liu, A. Zarifi, T. G. Nguyen, D.-Y. Choi, D. Marpaung, S. J. Madden, A. Mitchell, and B. J. Eggleton, “Compact Brillouin devices through hybrid integration on Silicon,” Optica 4(8), 847–854 (2017).
[Crossref]

M. Merklein, A. Casas-Bedoya, D. Marpaung, T. F. S. Buttner, M. Pagani, B. Morrison, I. V. Kabakova, and B. J. Eggleton, “Stimulated Brillouin Scattering in Photonic Integrated Circuits: Novel Applications and Devices,” IEEE J. Sel. Top. Quantum Electron. 22(2), 336–346 (2016).
[Crossref]

Martínez, A.

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

Mcfarlane, H.

Merklein, M.

M. Merklein, B. Stiller, K. Vu, S. J. Madden, and B. J. Eggleton, “A chip-integrated coherent photonic-phononic memory,” Nat. Commun. 8(1), 574 (2017).
[Crossref]

M. Merklein, A. Casas-Bedoya, D. Marpaung, T. F. S. Buttner, M. Pagani, B. Morrison, I. V. Kabakova, and B. J. Eggleton, “Stimulated Brillouin Scattering in Photonic Integrated Circuits: Novel Applications and Devices,” IEEE J. Sel. Top. Quantum Electron. 22(2), 336–346 (2016).
[Crossref]

M. Merklein and et al., “Enhancing and inhibiting stimulated Brillouin scattering in photonic integrated circuits,” Nat. Commun. 6(1), 6396 (2015).
[Crossref]

Mitchell, A.

Morrison, B.

B. Morrison, A. Casas-Bedoya, G. Ren, K. Vu, Y. Liu, A. Zarifi, T. G. Nguyen, D.-Y. Choi, D. Marpaung, S. J. Madden, A. Mitchell, and B. J. Eggleton, “Compact Brillouin devices through hybrid integration on Silicon,” Optica 4(8), 847–854 (2017).
[Crossref]

M. Merklein, A. Casas-Bedoya, D. Marpaung, T. F. S. Buttner, M. Pagani, B. Morrison, I. V. Kabakova, and B. J. Eggleton, “Stimulated Brillouin Scattering in Photonic Integrated Circuits: Novel Applications and Devices,” IEEE J. Sel. Top. Quantum Electron. 22(2), 336–346 (2016).
[Crossref]

Nelson, K. D.

S. Gundavarapu, M. Puckett, T. Huffman, R. Behunin, T. Qiu, G. M. Brodnik, C. Pinho, D. Bose, P. T. Rakich, J. Nohava, K. D. Nelson, M. Salit, and D. J. Blumenthal, “Integrated Waveguide Brillouin Laser”, arXiv:1709.04512, 1–15 (2017).

Nguyen, T. G.

Nohava, J.

S. Gundavarapu, M. Puckett, T. Huffman, R. Behunin, T. Qiu, G. M. Brodnik, C. Pinho, D. Bose, P. T. Rakich, J. Nohava, K. D. Nelson, M. Salit, and D. J. Blumenthal, “Integrated Waveguide Brillouin Laser”, arXiv:1709.04512, 1–15 (2017).

Okawachi, Y.

Y. Okawachi and A. L. Gaeta, “Nonlinear photonics: Compressing light and sound,” Nat. Photonics 6(5), 274–276 (2012).
[Crossref]

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(1), 2943 (2013).
[Crossref]

Oskooi, A. F.

P. Loh, A. F. Oskooi, M. Ibanescu, M. Skorobogatiy, and S. G. Johnson, “Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backward-wave structures,” Phys. Rev. E 79(6), 065601 (2009).
[Crossref]

Otterstrom, N. T.

N. T. Otterstrom, R. O. Behunin, E. A. Kittlaus, Z. Wang, and P. T. Rakich, “A silicon Brillouin laser,” Science 360(6393), 1113–1116 (2018).
[Crossref]

E. A. Kittlaus, N. T. Otterstrom, and P. T. Rakich, “On-chip inter-modal Brillouin scattering,” Nat. Commun. 8, 15819 (2017).
[Crossref]

Oudich, M.

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

Pagani, M.

M. Merklein, A. Casas-Bedoya, D. Marpaung, T. F. S. Buttner, M. Pagani, B. Morrison, I. V. Kabakova, and B. J. Eggleton, “Stimulated Brillouin Scattering in Photonic Integrated Circuits: Novel Applications and Devices,” IEEE J. Sel. Top. Quantum Electron. 22(2), 336–346 (2016).
[Crossref]

Pant, R.

Papanikolaou, N.

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

Pennec, Y.

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

Pinho, C.

S. Gundavarapu, M. Puckett, T. Huffman, R. Behunin, T. Qiu, G. M. Brodnik, C. Pinho, D. Bose, P. T. Rakich, J. Nohava, K. D. Nelson, M. Salit, and D. J. Blumenthal, “Integrated Waveguide Brillouin Laser”, arXiv:1709.04512, 1–15 (2017).

Popovic, M. A.

Poulton, C. G.

Puckett, M.

S. Gundavarapu, M. Puckett, T. Huffman, R. Behunin, T. Qiu, G. M. Brodnik, C. Pinho, D. Bose, P. T. Rakich, J. Nohava, K. D. Nelson, M. Salit, and D. J. Blumenthal, “Integrated Waveguide Brillouin Laser”, arXiv:1709.04512, 1–15 (2017).

Qiu, T.

S. Gundavarapu, M. Puckett, T. Huffman, R. Behunin, T. Qiu, G. M. Brodnik, C. Pinho, D. Bose, P. T. Rakich, J. Nohava, K. D. Nelson, M. Salit, and D. J. Blumenthal, “Integrated Waveguide Brillouin Laser”, arXiv:1709.04512, 1–15 (2017).

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(1), 2943 (2013).
[Crossref]

Rakich, P. T.

N. T. Otterstrom, R. O. Behunin, E. A. Kittlaus, Z. Wang, and P. T. Rakich, “A silicon Brillouin laser,” Science 360(6393), 1113–1116 (2018).
[Crossref]

E. A. Kittlaus, N. T. Otterstrom, and P. T. Rakich, “On-chip inter-modal Brillouin scattering,” Nat. Commun. 8, 15819 (2017).
[Crossref]

E. A. Kittlaus, H. Shin, and P. T. Rakich, “Large Brillouin amplification in silicon,” Nat. Photonics 10(7), 463–467 (2016).
[Crossref]

H. Shin, J. A. Cox, R. Jarecki, A. Starbuck, Z. Wang, and P. T. Rakich, “Control of coherent information via on-chip photonic-phononic emitter-receivers,” Nat. Commun. 6(1), 6427 (2015).
[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(1), 2943 (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(1), 011008 (2012).
[Crossref]

P. T. Rakich, Z. Wang, and P. Davids, “Scaling of optical forces in dielectric waveguides: rigorous connection between radiation pressure and dispersion,” Opt. Lett. 36(2), 217 (2011).
[Crossref]

P. T. Rakich, P. Davids, and Z. Wang, “Tailoring optical forces in waveguides through radiation pressure and electrostrictive forces,” Opt. Express 18(14), 14439–14453 (2010).
[Crossref]

P. T. Rakich, M. A. Popović, and Z. Wang, “General treatment of optical forces and potentials in mechanically variable photonic systems,” Opt. Express 17(20), 18116–18135 (2009).
[Crossref]

S. Gundavarapu, M. Puckett, T. Huffman, R. Behunin, T. Qiu, G. M. Brodnik, C. Pinho, D. Bose, P. T. Rakich, J. Nohava, K. D. Nelson, M. Salit, and D. J. Blumenthal, “Integrated Waveguide Brillouin Laser”, arXiv:1709.04512, 1–15 (2017).

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(1), 011008 (2012).
[Crossref]

Ren, G.

Rodrigues, J. R.

Salit, M.

S. Gundavarapu, M. Puckett, T. Huffman, R. Behunin, T. Qiu, G. M. Brodnik, C. Pinho, D. Bose, P. T. Rakich, J. Nohava, K. D. Nelson, M. Salit, and D. J. Blumenthal, “Integrated Waveguide Brillouin Laser”, arXiv:1709.04512, 1–15 (2017).

Sauer, M.

Shin, H.

E. A. Kittlaus, H. Shin, and P. T. Rakich, “Large Brillouin amplification in silicon,” Nat. Photonics 10(7), 463–467 (2016).
[Crossref]

H. Shin, J. A. Cox, R. Jarecki, A. Starbuck, Z. Wang, and P. T. Rakich, “Control of coherent information via on-chip photonic-phononic emitter-receivers,” Nat. Commun. 6(1), 6427 (2015).
[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(1), 2943 (2013).
[Crossref]

Skorobogatiy, M.

P. Loh, A. F. Oskooi, M. Ibanescu, M. Skorobogatiy, and S. G. Johnson, “Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backward-wave structures,” Phys. Rev. E 79(6), 065601 (2009).
[Crossref]

Skorobogatiy, M. A.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65(6), 066611 (2002).
[Crossref]

Starbuck, A.

H. Shin, J. A. Cox, R. Jarecki, A. Starbuck, Z. Wang, and P. T. Rakich, “Control of coherent information via on-chip photonic-phononic emitter-receivers,” Nat. Commun. 6(1), 6427 (2015).
[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(1), 2943 (2013).
[Crossref]

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]

Stiller, B.

M. Merklein, B. Stiller, K. Vu, S. J. Madden, and B. J. Eggleton, “A chip-integrated coherent photonic-phononic memory,” Nat. Commun. 8(1), 574 (2017).
[Crossref]

Thevenaz, L.

Thévenaz, L.

L. Thévenaz, “Silicon nanophotonics: Good vibrations for light,” Nat. Photonics 9(3), 144–146 (2015).
[Crossref]

Thourhout, D. V.

R. V. Laer, A. Bazin, B. Kuyken, R. Baets, and D. V. Thourhout, “Net on-chip Brillouin gain based on suspended silicon nanowires,” New J. Phys. 17(11), 115005 (2015).
[Crossref]

R. V. Laer, B. Kuyken, D. V. Thourhout, and R. Baets, “Interaction between light and highly confined hypersound in a silicon photonic nanowire,” Nat. Photonics 9(3), 199–203 (2015).
[Crossref]

Vu, K.

Wang, Z.

N. T. Otterstrom, R. O. Behunin, E. A. Kittlaus, Z. Wang, and P. T. Rakich, “A silicon Brillouin laser,” Science 360(6393), 1113–1116 (2018).
[Crossref]

H. Shin, J. A. Cox, R. Jarecki, A. Starbuck, Z. Wang, and P. T. Rakich, “Control of coherent information via on-chip photonic-phononic emitter-receivers,” Nat. Commun. 6(1), 6427 (2015).
[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(1), 2943 (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(1), 011008 (2012).
[Crossref]

P. T. Rakich, Z. Wang, and P. Davids, “Scaling of optical forces in dielectric waveguides: rigorous connection between radiation pressure and dispersion,” Opt. Lett. 36(2), 217 (2011).
[Crossref]

P. T. Rakich, P. Davids, and Z. Wang, “Tailoring optical forces in waveguides through radiation pressure and electrostrictive forces,” Opt. Express 18(14), 14439–14453 (2010).
[Crossref]

P. T. Rakich, M. A. Popović, and Z. Wang, “General treatment of optical forces and potentials in mechanically variable photonic systems,” Opt. Express 17(20), 18116–18135 (2009).
[Crossref]

Weber, H. P.

Weisberg, O.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65(6), 066611 (2002).
[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]

Zarifi, A.

Zoubi, H.

H. Zoubi and K. Hammerer, “Optomechanical multimode Hamiltonian for nanophotonic waveguides,” Phys. Rev. A 94(5), 053827 (2016).
[Crossref]

Adv. Opt. Photon. (2)

IEEE J. Quantum Electron. (1)

Y. Liu, A. Choudhary, D. Marpaung, and B. J. Eggleton, “Chip-based Brillouin Processing for Phase Control of RF Signals,” IEEE J. Quantum Electron. 54(3), 1–13 (2018).
[Crossref]

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

M. Merklein, A. Casas-Bedoya, D. Marpaung, T. F. S. Buttner, M. Pagani, B. Morrison, I. V. Kabakova, and B. J. Eggleton, “Stimulated Brillouin Scattering in Photonic Integrated Circuits: Novel Applications and Devices,” IEEE J. Sel. Top. Quantum Electron. 22(2), 336–346 (2016).
[Crossref]

J. Opt. Soc. Am. (2)

Nanophotonics (1)

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics 3(6), 413–440 (2014).
[Crossref]

Nat. Commun. (5)

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(1), 2943 (2013).
[Crossref]

M. Merklein and et al., “Enhancing and inhibiting stimulated Brillouin scattering in photonic integrated circuits,” Nat. Commun. 6(1), 6396 (2015).
[Crossref]

E. A. Kittlaus, N. T. Otterstrom, and P. T. Rakich, “On-chip inter-modal Brillouin scattering,” Nat. Commun. 8, 15819 (2017).
[Crossref]

H. Shin, J. A. Cox, R. Jarecki, A. Starbuck, Z. Wang, and P. T. Rakich, “Control of coherent information via on-chip photonic-phononic emitter-receivers,” Nat. Commun. 6(1), 6427 (2015).
[Crossref]

M. Merklein, B. Stiller, K. Vu, S. J. Madden, and B. J. Eggleton, “A chip-integrated coherent photonic-phononic memory,” Nat. Commun. 8(1), 574 (2017).
[Crossref]

Nat. Photonics (4)

L. Thévenaz, “Silicon nanophotonics: Good vibrations for light,” Nat. Photonics 9(3), 144–146 (2015).
[Crossref]

E. A. Kittlaus, H. Shin, and P. T. Rakich, “Large Brillouin amplification in silicon,” Nat. Photonics 10(7), 463–467 (2016).
[Crossref]

R. V. Laer, B. Kuyken, D. V. Thourhout, and R. Baets, “Interaction between light and highly confined hypersound in a silicon photonic nanowire,” Nat. Photonics 9(3), 199–203 (2015).
[Crossref]

Y. Okawachi and A. L. Gaeta, “Nonlinear photonics: Compressing light and sound,” Nat. Photonics 6(5), 274–276 (2012).
[Crossref]

New J. Phys. (2)

R. V. Laer, A. Bazin, B. Kuyken, R. Baets, and D. V. Thourhout, “Net on-chip Brillouin gain based on suspended silicon nanowires,” New J. Phys. 17(11), 115005 (2015).
[Crossref]

V. Laude and J. C. Beugnot, “Lagrangian description of Brillouin scattering and electrostriction in nanoscale optical waveguides,” New J. Phys. 17(12), 125003 (2015).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Optica (1)

Phys. Rev. A (2)

H. Zoubi and K. Hammerer, “Optomechanical multimode Hamiltonian for nanophotonic waveguides,” Phys. Rev. A 94(5), 053827 (2016).
[Crossref]

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]

Phys. Rev. E (2)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65(6), 066611 (2002).
[Crossref]

P. Loh, A. F. Oskooi, M. Ibanescu, M. Skorobogatiy, and S. G. Johnson, “Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backward-wave structures,” Phys. Rev. E 79(6), 065601 (2009).
[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(1), 011008 (2012).
[Crossref]

Science (1)

N. T. Otterstrom, R. O. Behunin, E. A. Kittlaus, Z. Wang, and P. T. Rakich, “A silicon Brillouin laser,” Science 360(6393), 1113–1116 (2018).
[Crossref]

Other (1)

S. Gundavarapu, M. Puckett, T. Huffman, R. Behunin, T. Qiu, G. M. Brodnik, C. Pinho, D. Bose, P. T. Rakich, J. Nohava, K. D. Nelson, M. Salit, and D. J. Blumenthal, “Integrated Waveguide Brillouin Laser”, arXiv:1709.04512, 1–15 (2017).

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Figures (3)

Fig. 1.
Fig. 1. Schematic views of the dielectric waveguides and diagram of forces. (a) 3D view of the dielectric waveguide, with a rectangular cross-section and composed by a high-index material (${n_H}$) core surrounded by a low-index material (${n_L}$). (b) cross-section (2D) view of the rectangular waveguide with width w and height h. (c) planar (1D) approximation by considering the structure’s invariance also in the x-direction. (d) and (e) show the schematics of radiation-pressure induced optical forces on the surfaces of the rectangular (${F_x},{F_y}$) and the planar (${{{\cal F}}_y}$) waveguides.
Fig. 2.
Fig. 2. Optical forces distributions on the silicon waveguides in air and highlighted optimal height. (a) and (b) Optical forces on the horizontal boundaries (${{{\cal F}}_y}$) and their respective effective indexes for a silicon planar waveguide in air, for the fundamental TE and TM modes. (c) and (d) Intensity maps of y-component of optical forces (${F_y}$) on the horizontal boundaries of the silicon rectangular waveguide in air, as a function of its cross-section dimension, for the quasi-TE and the quasi-TM fundamental modes at ${\lambda _0} = 1550$ nm. The optimized heights are ${h^{TE}} = 52.04$ nm and ${h^{TM}} = 225.8$ nm
Fig. 3.
Fig. 3. Schematic of waveguides and their respective total optical forces for both polarizations at a wavelength of 1550 nm. (a) Silicon rib waveguide (${n_H} = 3.4764$) suspended in air (${n_L} = 1.0003$). (b) Chalcogenide strip waveguide (${n_H} = 2.405$) buried in silicon dioxide cladding (${n_L} = 1.4440$). (c) and (d) total optical forces on the silicon and the chalcogenide waveguides, respectively. The optimized heights for the silicon waveguide are ${h^{TE}} = 52.04$ nm (not shown) and ${h^{TM}} = 225.8$ nm and for the chalcogenide are ${h^{TE}} = 119.1$ nm and ${h^{TM}} = 308.7$ nm.

Equations (17)

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tan ( κ H h 2 ) = γ L κ H
tan ( κ H h 2 ) = n H 2 n L 2 γ L κ H
p ¯ x + p ¯ y = P c ( n g n e f f ) A w g
F q = P L c d n e f f d q
F y = P L c d n e f f d h
d n e f f d h = κ H 2 n e f f k 0 2 ( 1 h + 2 / κ H 2 n e f f k 0 2 γ L )
d n e f f d h = κ H 2 n e f f k 0 2 ( 1 h + 2 / κ H 2 n e f f k 0 2 γ L ( κ H 2 + γ L 2 ( n L / κ H 2 n e f f k 0 2 n H ) 2 κ H 2 + ( n H / κ H 2 n e f f k 0 2 n L ) 2 γ L 2 ) ) .
h T E = [ 2 γ L 2 2 k 0 2 n e f f 2 6 κ H 2 ] [ 1 k 0 2 n e f f 2 + 3 κ H 2 ] 1 γ L .
h T M = [ 4 X ( X n e f f 2 1 ) k 0 2 + 2 γ L 2 2 k 0 2 n e f f 2 6 κ H 2 ] [ 1 k 0 2 n e f f 2 + 3 κ H 2 ] ( X n e f f 2 1 ) 1 γ L
w g p r d l = P c ( n g n e f f )
n e f f = n g ( ( ε ( | E x | 2 + | E y | 2 | E z | 2 ) + μ ( | H x | 2 + | H y | 2 | H z | 2 ) ) d x d y ( ε ( | E x | 2 + | E y | 2 + | E z | 2 ) + μ ( | H x | 2 + | H y | 2 + | H z | 2 ) ) d x d y )
U x y E M = ( ε ( | E x | 2 + | E y | 2 ) + μ ( | H x | 2 + | H y | 2 ) ) d x d y
U z E M = ( ε | E z | 2 + μ | H z | 2 ) d x d y
n e f f = n g ( U x y E M U z E M U x y E M + U z E M )
w g p r d l = P n g c ( 2 U z E M U t o t a l E M ) .
U t o t a l E M = P n g c .
w g p r d l = 2 U z E M .

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