Abstract

We theoretically and numerically investigate Stimulated Brillouin Scattering generated mode conversion in high-contrast suspended silicon nanophotonic waveguides. We predict significantly enhanced mode conversion when the linked effects of radiation pressure and motion of the waveguide boundaries are taken into account. The mode conversion is more than 10 times larger than would be predicted if the effect of radiation pressure is not taken into account: we find a waveguide length of 740 μm is required for 20dB of mode conversion, assuming a total pump power of 1W. This is sufficient to bring the effect into the realm of chip-scale photonic waveguides. We explore the interaction between the different types of acoustic modes that can exist within these waveguides, and show how the presence of these modes leads to enhanced conversion between the different possible optical modes.

© 2014 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]

2014 (2)

T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, C. G. Poulton, A. C. Judge, and B. J. Eggleton, “Phase-locking and pulse generation in multi-frequency Brillouin oscillator via four wave mixing,” Sci. Rep. 4, 5032 (2014).
[Crossref] [PubMed]

B. J. H. Stadler and T. Mizumoto, “Integrated magneto-optical materials and isolators: a review,” IEEE Photonics Journal 6, 1–15 (2014).
[Crossref]

2013 (4)

B. J. Eggleton, C. G. Poulton, and R. Pant, “Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits,” Advances in Optics and Photonics 5, 536–587 (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,” Nature Commun. 4, 1944 (2013).

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[Crossref] [PubMed]

W. Qiu, P. T. Rakich, H. Shin, H. Dong, M. Soljacic, 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, 276–280 (2013).
[Crossref]

2012 (4)

2011 (5)

2010 (2)

P. T. Rakich, P. Davids, and Z. Wang, “Tailoring optical forces in waveguides through radiation pressure and electrostrictive forces,” Opt. Express 18, 14439–53 (2010).
[Crossref] [PubMed]

M. S. Kang, A. Brenn, and P. St J. Russell, “All-optical control of gigahertz acoustic resonances by forward stimulated interpolarization scattering in a photonic crystal fiber,” Phys. Rev. Lett. 105, 153901 (2010).
[Crossref]

2009 (4)

Z. Yu and S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94, 171116 (2009).
[Crossref]

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at x-band (11-GHz) rates,” Phys. Rev. Lett. 102, 113601 (2009).
[Crossref] [PubMed]

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

D. Braje, L. Hollberg, and S. Diddams, “Brillouin-enhanced hyperparametric generation of an optical frequency comb in a monolithic highly nonlinear fiber cavity pumped by a cw laser,” Phys. Rev. Lett. 102, 193902 (2009).
[Crossref] [PubMed]

2007 (2)

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318, 1748–1750 (2007).
[Crossref] [PubMed]

L. Yin and G. P. Agrawal, “Impact of two-photon absorption on self-phase modulation in silicon waveguides,” Opt. Lett. 32, 2031 (2007).
[Crossref] [PubMed]

2005 (2)

R. Jones, H. Rong, A. Liu, A. W. Fang, M. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 13, 519–525 (2005).
[Crossref] [PubMed]

Y. Okawachi, M. Bigelow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-Optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

2002 (1)

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80, 416 (2002).
[Crossref]

2000 (1)

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Waveguide optical isolator based on Mach-Zehnder interferometer,” Appl. Phys. Lett. 76, 2158 (2000).
[Crossref]

1996 (1)

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightw. Tech. 14, 58–65 (1996).
[Crossref]

1982 (1)

1974 (1)

K. David, “Photoelastic tensor of silicon and the volume dependence of the average gap,” Phys. Rev. Lett. 32, 1196–1199 (1974).
[Crossref]

Agrawal, G. P.

Asghari, M.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80, 416 (2002).
[Crossref]

Bhatia, V.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightw. Tech. 14, 58–65 (1996).
[Crossref]

Bigelow, M.

Y. Okawachi, M. Bigelow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-Optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

Bowers, J. E.

Boyd, R.

Y. Okawachi, M. Bigelow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-Optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

Boyd, R. W.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318, 1748–1750 (2007).
[Crossref] [PubMed]

R. W. Boyd, Nonlinear Optics3rd ed. (Academic Press, 2003).

Braje, D.

D. Braje, L. Hollberg, and S. Diddams, “Brillouin-enhanced hyperparametric generation of an optical frequency comb in a monolithic highly nonlinear fiber cavity pumped by a cw laser,” Phys. Rev. Lett. 102, 193902 (2009).
[Crossref] [PubMed]

Brenn, A.

M. S. Kang, A. Brenn, and P. St J. Russell, “All-optical control of gigahertz acoustic resonances by forward stimulated interpolarization scattering in a photonic crystal fiber,” Phys. Rev. Lett. 105, 153901 (2010).
[Crossref]

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

Butsch, A.

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

Büttner, T. F. S.

T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, C. G. Poulton, A. C. Judge, and B. J. Eggleton, “Phase-locking and pulse generation in multi-frequency Brillouin oscillator via four wave mixing,” Sci. Rep. 4, 5032 (2014).
[Crossref] [PubMed]

Byrnes, A.

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).

Carmon, T.

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at x-band (11-GHz) rates,” Phys. Rev. Lett. 102, 113601 (2009).
[Crossref] [PubMed]

Chodorow, M.

Choi, D.-Y.

Cohen, O.

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,” Nature Commun. 4, 1944 (2013).

David, K.

K. David, “Photoelastic tensor of silicon and the volume dependence of the average gap,” Phys. Rev. Lett. 32, 1196–1199 (1974).
[Crossref]

Davids, P.

Day, I. E.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80, 416 (2002).
[Crossref]

Diddams, S.

D. Braje, L. Hollberg, and S. Diddams, “Brillouin-enhanced hyperparametric generation of an optical frequency comb in a monolithic highly nonlinear fiber cavity pumped by a cw laser,” Phys. Rev. Lett. 102, 193902 (2009).
[Crossref] [PubMed]

Dong, H.

Dotsch, H.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Waveguide optical isolator based on Mach-Zehnder interferometer,” Appl. Phys. Lett. 76, 2158 (2000).
[Crossref]

Drake, J.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80, 416 (2002).
[Crossref]

Eggleton, B. J.

T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, C. G. Poulton, A. C. Judge, and B. J. Eggleton, “Phase-locking and pulse generation in multi-frequency Brillouin oscillator via four wave mixing,” Sci. Rep. 4, 5032 (2014).
[Crossref] [PubMed]

B. J. Eggleton, C. G. Poulton, and R. Pant, “Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits,” Advances in Optics and Photonics 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, 18836–45 (2012).
[Crossref] [PubMed]

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] [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]

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,” arXiv:1407.3521 pp. 1–17 (2014).

Erdogan, T.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightw. Tech. 14, 58–65 (1996).
[Crossref]

Evers, J.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[Crossref] [PubMed]

Fan, S.

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Phys. Rev. Lett. 109, 033901 (2012).
[Crossref] [PubMed]

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] [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, 18836–45 (2012).
[Crossref] [PubMed]

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

Z. Yu and S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94, 171116 (2009).
[Crossref]

Fang, A. W.

Fujita, J.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Waveguide optical isolator based on Mach-Zehnder interferometer,” Appl. Phys. Lett. 76, 2158 (2000).
[Crossref]

Gaeta, A.

Y. Okawachi, M. Bigelow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-Optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

Gauthier, D.

Y. Okawachi, M. Bigelow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-Optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

Gauthier, D. J.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318, 1748–1750 (2007).
[Crossref] [PubMed]

Guo, M.-J.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[Crossref] [PubMed]

Hak, D.

Harpin, A.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80, 416 (2002).
[Crossref]

Hile, S.

Hollberg, L.

D. Braje, L. Hollberg, and S. Diddams, “Brillouin-enhanced hyperparametric generation of an optical frequency comb in a monolithic highly nonlinear fiber cavity pumped by a cw laser,” Phys. Rev. Lett. 102, 193902 (2009).
[Crossref] [PubMed]

Huang, X.

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

Hudson, D. D.

T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, C. G. Poulton, A. C. Judge, and B. J. Eggleton, “Phase-locking and pulse generation in multi-frequency Brillouin oscillator via four wave mixing,” Sci. Rep. 4, 5032 (2014).
[Crossref] [PubMed]

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,” Nature Commun. 4, 1944 (2013).

Jones, R.

Judge, A. C.

T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, C. G. Poulton, A. C. Judge, and B. J. Eggleton, “Phase-locking and pulse generation in multi-frequency Brillouin oscillator via four wave mixing,” Sci. Rep. 4, 5032 (2014).
[Crossref] [PubMed]

Judkins, J. B.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightw. Tech. 14, 58–65 (1996).
[Crossref]

Kabakova, I. V.

T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, C. G. Poulton, A. C. Judge, and B. J. Eggleton, “Phase-locking and pulse generation in multi-frequency Brillouin oscillator via four wave mixing,” Sci. Rep. 4, 5032 (2014).
[Crossref] [PubMed]

Kang, M. S.

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

M. S. Kang, A. Brenn, and P. St J. Russell, “All-optical control of gigahertz acoustic resonances by forward stimulated interpolarization scattering in a photonic crystal fiber,” Phys. Rev. Lett. 105, 153901 (2010).
[Crossref]

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

Kromer, H.

Lemaire, P. J.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightw. Tech. 14, 58–65 (1996).
[Crossref]

Levy, M.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Waveguide optical isolator based on Mach-Zehnder interferometer,” Appl. Phys. Lett. 76, 2158 (2000).
[Crossref]

Li, E.

Liang, T. K.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80, 416 (2002).
[Crossref]

Lipson, M.

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Phys. Rev. Lett. 109, 033901 (2012).
[Crossref] [PubMed]

Lira, H.

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Phys. Rev. Lett. 109, 033901 (2012).
[Crossref] [PubMed]

Liu, A.

Luther-Davies, B.

Madden, S.

Madden, S. J.

Mcfarlane, H.

Mizumoto, T.

B. J. H. Stadler and T. Mizumoto, “Integrated magneto-optical materials and isolators: a review,” IEEE Photonics Journal 6, 1–15 (2014).
[Crossref]

M.-C. Tien, T. Mizumoto, P. Pintus, H. Kromer, and J. E. Bowers, “Silicon ring isolators with bonded nonreciprocal magneto-optic garnets,” Opt. Express 19, 11740–11745 (2011).
[Crossref] [PubMed]

Nazarkin, A.

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

Okawachi, Y.

Y. Okawachi, M. Bigelow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-Optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

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,” Nature Commun. 4, 1944 (2013).

Osgood, R. M.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Waveguide optical isolator based on Mach-Zehnder interferometer,” Appl. Phys. Lett. 76, 2158 (2000).
[Crossref]

Paniccia, M.

Pant, R.

Pintus, P.

Poulton, C. G.

T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, C. G. Poulton, A. C. Judge, and B. J. Eggleton, “Phase-locking and pulse generation in multi-frequency Brillouin oscillator via four wave mixing,” Sci. Rep. 4, 5032 (2014).
[Crossref] [PubMed]

B. J. Eggleton, C. G. Poulton, and R. Pant, “Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits,” Advances in Optics and Photonics 5, 536–587 (2013).
[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] [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, 18836–45 (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]

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,” arXiv:1407.3521 pp. 1–17 (2014).

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,” Nature Commun. 4, 1944 (2013).

W. Qiu, P. T. Rakich, H. Shin, H. Dong, M. Soljacic, 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, 276–280 (2013).
[Crossref]

Rakich, P. T.

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).

Roberts, S. W.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80, 416 (2002).
[Crossref]

Rong, H.

Russell, P. St J.

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

M. S. Kang, A. Brenn, and P. St J. Russell, “All-optical control of gigahertz acoustic resonances by forward stimulated interpolarization scattering in a photonic crystal fiber,” Phys. Rev. Lett. 105, 153901 (2010).
[Crossref]

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

Schweinsberg, A.

Y. Okawachi, M. Bigelow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-Optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

Sharping, J.

Y. Okawachi, M. Bigelow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-Optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

Shaw, H. J.

Shin, H.

W. Qiu, P. T. Rakich, H. Shin, H. Dong, M. Soljacic, 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, 276–280 (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,” Nature Commun. 4, 1944 (2013).

Sipe, J. E.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightw. Tech. 14, 58–65 (1996).
[Crossref]

Soljacic, M.

Stadler, B. J. H.

B. J. H. Stadler and T. Mizumoto, “Integrated magneto-optical materials and isolators: a review,” IEEE Photonics Journal 6, 1–15 (2014).
[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,” Nature Commun. 4, 1944 (2013).

Steel, M. J.

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] [PubMed]

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,” arXiv:1407.3521 pp. 1–17 (2014).

Stokes, L. F.

Thevenaz, L.

Tien, M.-C.

Tomes, M.

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at x-band (11-GHz) rates,” Phys. Rev. Lett. 102, 113601 (2009).
[Crossref] [PubMed]

Tsang, H. K.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80, 416 (2002).
[Crossref]

Vengsarkar, A. M.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightw. Tech. 14, 58–65 (1996).
[Crossref]

Wang, D.-W.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[Crossref] [PubMed]

Wang, Z.

Wilkens, L.

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Waveguide optical isolator based on Mach-Zehnder interferometer,” Appl. Phys. Lett. 76, 2158 (2000).
[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,” arXiv:1407.3521 pp. 1–17 (2014).

Wong, C. S.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80, 416 (2002).
[Crossref]

Yin, L.

Yu, Z.

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Phys. Rev. Lett. 109, 033901 (2012).
[Crossref] [PubMed]

Z. Yu and S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94, 171116 (2009).
[Crossref]

Zhang, J.-X.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[Crossref] [PubMed]

Zhou, H.-T.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[Crossref] [PubMed]

Zhu, S.-Y.

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[Crossref] [PubMed]

Zhu, Z.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318, 1748–1750 (2007).
[Crossref] [PubMed]

Y. Okawachi, M. Bigelow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-Optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

Advances in Optics and Photonics (1)

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

Appl. Phys. Lett. (3)

J. Fujita, M. Levy, R. M. Osgood, L. Wilkens, and H. Dotsch, “Waveguide optical isolator based on Mach-Zehnder interferometer,” Appl. Phys. Lett. 76, 2158 (2000).
[Crossref]

Z. Yu and S. Fan, “Optical isolation based on nonreciprocal phase shift induced by interband photonic transitions,” Appl. Phys. Lett. 94, 171116 (2009).
[Crossref]

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5μm wavelength,” Appl. Phys. Lett. 80, 416 (2002).
[Crossref]

IEEE Photonics Journal (1)

B. J. H. Stadler and T. Mizumoto, “Integrated magneto-optical materials and isolators: a review,” IEEE Photonics Journal 6, 1–15 (2014).
[Crossref]

J. Lightw. Tech. (2)

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

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightw. Tech. 14, 58–65 (1996).
[Crossref]

Nature Commun. (1)

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,” Nature Commun. 4, 1944 (2013).

Nature Photon. (1)

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

Nature Phys. (1)

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

Opt. Express (7)

R. Jones, H. Rong, A. Liu, A. W. Fang, M. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 13, 519–525 (2005).
[Crossref] [PubMed]

P. T. Rakich, P. Davids, and Z. Wang, “Tailoring optical forces in waveguides through radiation pressure and electrostrictive forces,” Opt. Express 18, 14439–53 (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]

M.-C. Tien, T. Mizumoto, P. Pintus, H. Kromer, and J. E. Bowers, “Silicon ring isolators with bonded nonreciprocal magneto-optic garnets,” Opt. Express 19, 11740–11745 (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, 18836–45 (2012).
[Crossref] [PubMed]

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] [PubMed]

W. Qiu, P. T. Rakich, H. Shin, H. Dong, M. Soljacic, 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, 276–280 (2013).
[Crossref]

Opt. Lett. (3)

Phys. Rev. Lett. (7)

K. David, “Photoelastic tensor of silicon and the volume dependence of the average gap,” Phys. Rev. Lett. 32, 1196–1199 (1974).
[Crossref]

Y. Okawachi, M. Bigelow, J. Sharping, Z. Zhu, A. Schweinsberg, D. Gauthier, R. Boyd, and A. Gaeta, “Tunable all-Optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[Crossref] [PubMed]

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at x-band (11-GHz) rates,” Phys. Rev. Lett. 102, 113601 (2009).
[Crossref] [PubMed]

M. S. Kang, A. Brenn, and P. St J. Russell, “All-optical control of gigahertz acoustic resonances by forward stimulated interpolarization scattering in a photonic crystal fiber,” Phys. Rev. Lett. 105, 153901 (2010).
[Crossref]

D. Braje, L. Hollberg, and S. Diddams, “Brillouin-enhanced hyperparametric generation of an optical frequency comb in a monolithic highly nonlinear fiber cavity pumped by a cw laser,” Phys. Rev. Lett. 102, 193902 (2009).
[Crossref] [PubMed]

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Phys. Rev. Lett. 109, 033901 (2012).
[Crossref] [PubMed]

D.-W. Wang, H.-T. Zhou, M.-J. Guo, J.-X. Zhang, J. Evers, and S.-Y. Zhu, “Optical diode made from a moving photonic crystal,” Phys. Rev. Lett. 110, 093901 (2013).
[Crossref] [PubMed]

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).

Sci. Rep. (1)

T. F. S. Büttner, I. V. Kabakova, D. D. Hudson, R. Pant, C. G. Poulton, A. C. Judge, and B. J. Eggleton, “Phase-locking and pulse generation in multi-frequency Brillouin oscillator via four wave mixing,” Sci. Rep. 4, 5032 (2014).
[Crossref] [PubMed]

Science (1)

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318, 1748–1750 (2007).
[Crossref] [PubMed]

Other (2)

R. W. Boyd, Nonlinear Optics3rd ed. (Academic Press, 2003).

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,” arXiv:1407.3521 pp. 1–17 (2014).

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Figures (9)

Fig. 1
Fig. 1 a) Schematic of mode conversion operation. Two differently polarized fundamental modes are pumped into a suspended high contrast waveguide to excite a guided acoustic mode. The acoustic mode creates a temporary traveling grating which drives conversion from the signal in the x-polarized fundamental mode at ω3 to a y-polarized fundamental mode at frequency ω4. b) A simplified dispersion diagram illustrating the photonic conversion process with respect to optical and acoustic modes. The black dot indicates the acoustic mode at frequency Ω = ω(2)ω(1) which is able to phase match between the two optical modes, so having propagation constant q = β(2)β(1). An optical signal which is traveling in counterpropagating direction does not satisfy the phase matching condition.
Fig. 2
Fig. 2 a) Waveguide geometry, silicon suspended in air with a rectangular cross-section of a = 350 nm by b = 300 nm. b) x-polarized mode 1 and c) y-polarized mode 2, as the two optical pumps.
Fig. 3
Fig. 3 a) Force distribution of radiation pressure (blue) and electrostriction body force (green) generated by applying two differently polarized optical modes, b) corresponding magnitude of the total displacement of the torsional acoustic mode excited by the forces. The strength of the acoustic oscillation is grossly exaggerated.
Fig. 4
Fig. 4 Calculated acoustic dispersion curves for the 350 × 300 nm suspended silicon waveguide. The red line corresponds to interaction between differently polarized optical pumps that excites quasi-torsional acoustic mode redwhich is phase-matched based on the beat between the two optical modes at the beat frequency Ω = ω(2)ω(1) with propagation constant q = β(2)β(1).
Fig. 5
Fig. 5 Evolution of pump powers in the waveguide and corresponding photonic conversion: a) by considering both electrostriction and radiation pressure and b) considering the electrostrictive body force only. The red and blue dashed lines show the evolution of the two optical pumps in the waveguide; the red and blue solid lines show conversion between the signals. The interaction of the two pumps excites an acoustic mode, shown here by the black straight line indicating the power in the acoustic field. The initial power in the pumps was 1 mW (pump 1) and 1 W (pump 2). Note that the horizontal scale is different between the two plots.
Fig. 6
Fig. 6 a) Computed κ as a function of waveguide width ranging from 250 nm to 1000 nm over the length of 2 mm waveguide. Height of the waveguide is fixed to b = 220 nm. In this computation radiation pressure and electrostriction are considered. b) Frequencies of excited acoustic mode as a function of waveguide width.
Fig. 7
Fig. 7 Coupling strength κmax, expressed as log10 [κ/m−1] resulting from coupling between two differently polarized fundamental modes: a) by considering both electrostriction and radiation pressure (together with the photoelastic effect and waveguide boundary motion) and b) considering the electrostrictive effect and photoelasticity only.
Fig. 8
Fig. 8 a) Fundamental and b) first order x-polarized optical modes in a 550 nm by 350 nm silicon waveguide. Because one mode is even and the other is odd, an asymmetric acoustic mode is excited. c) Force distribution of radiation pressure (blue) and electrostriction body force (green) generated by applying fundamental and first higher order optical modes. d) corresponding magnitude of the total displacement of the acoustic mode generated by the forces. The strength of the acoustic oscillation is grossly exaggerated.
Fig. 9
Fig. 9 Coupling strength κmax, expressed as log10 [κ/m−1] resulted from coupling between x-polarized fundamental and first higher order mode: a) by considering both electrostriction and radiation pressure (together with the photoelastic effect and waveguide boundary motion) and b) considering the electrostrictive effect and photoelasticity only.

Equations (16)

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

E ( i ) ( x , y , z , t ) = a ( i ) ( z , t ) e ˜ ( i ) ( x , y ) exp ( i β ( i ) z i ω ( i ) t ) + c . c . ,
e ˜ ( 3 ) = e ˜ ( 1 ) , e ˜ ( 4 ) = e ˜ ( 2 ) .
U ( x , y , z , t ) = b ( z , t ) u ˜ ( x , y ) exp ( i q z i Ω t ) + c . c . ,
𝒫 1 = 𝒫 3 = 2 d 2 r z ^ ( [ e ˜ ( 1 ) ] * × h ˜ ( 1 ) ) , 𝒫 2 = 𝒫 4 = 2 d 2 r z ^ ( [ e ˜ ( 2 ) ] * × h ˜ ( 2 ) ) ,
𝒫 b = 2 i Ω d 2 r i k l c z i k l u i * k u l ,
z a ( 1 ) = i ω ( 1 ) Q 1 𝒫 1 a ( 2 ) b * , z a ( 2 ) = i ω ( 2 ) Q 2 𝒫 2 a ( 1 ) b ,
z a ( 3 ) = i ω ( 3 ) Q 3 𝒫 3 a ( 4 ) b * , z a ( 4 ) = i ω ( 4 ) Q 4 𝒫 4 a ( 3 ) b .
b = i Ω Q b 𝒫 b α [ a ( 1 ) ] * a ( 2 ) ,
Q 1 = Q 2 * = Q 3 = Q 4 * = Q b = u ˜ * f ˜ d x d y ,
f ˜ i ( body ) = j j σ ˜ i j ( es )
[ σ ˜ x x ( es ) σ ˜ y y ( es ) σ ˜ z z ( es ) σ ˜ y z ( es ) σ ˜ x z ( es ) σ ˜ x y ( es ) ] = ε 0 ε r 2 [ p 11 p 12 p 13 0 0 0 p 21 p 22 p 23 0 0 0 p 31 p 32 p 33 0 0 0 0 0 0 p 44 0 0 0 0 0 0 p 55 0 0 0 0 0 0 p 66 ] [ [ e ˜ x ( 1 ) ] * e ˜ x ( 2 ) [ e ˜ y ( 1 ) ] * e ˜ y ( 2 ) [ e ˜ z ( 1 ) ] * e ˜ z ( 2 ) [ e ˜ y ( 1 ) ] * e ˜ z ( 2 ) + [ e ˜ z ( 1 ) ] * e ˜ y ( 2 ) [ e ˜ x ( 1 ) ] * e ˜ z ( 2 ) + [ e ˜ z ( 1 ) ] * e ˜ x ( 2 ) [ e ˜ x ( 1 ) ] * e ˜ y ( 2 ) + [ e ˜ y ( 1 ) ] * e ˜ x ( 2 ) ] .
σ ˜ i j ( rp ) = ε 0 ε r [ e ˜ i ( 1 ) ] * e ˜ j ( 2 ) + μ 0 [ h ˜ i ( 1 ) ] * h ˜ j ( 2 ) 1 2 δ i j ( ε 0 ε r [ e ˜ ( 1 ) ] * e ˜ ( 2 ) + μ 0 [ h ˜ ( 1 ) ] * h ˜ ( 2 ) ) ,
G ( SBS ) = 2 ω ( 1 ) Ω | Q 1 | 2 𝒫 1 𝒫 2 𝒫 b α .
I ( d B ) = 10 log 10 ( P 3 ( z = z max ) P 3 ( z = 0 ) ) ,
N c = τ β TPA 2 h f 0 ( P 0 A eff ) 2 ,
κ ( z ) = | b ( z ) Q 3 | ω ( 3 ) ω ( 4 ) 𝒫 3 𝒫 4 .

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