Abstract

We analyze the magnitude of the radiation pressure and electrostrictive stresses exerted by light confined inside GaAs semiconductor WGM optomechanical disk resonators, through analytical and numerical means, and find the electrostrictive stress to be of prime importance. We investigate the geometric and photoelastic optomechanical coupling resulting respectively from the deformation of the disk boundary and from the strain-induced refractive index changes in the material, for various mechanical modes of the disks. Photoelastic optomechanical coupling is shown to be a predominant coupling mechanism for certain disk dimensions and mechanical modes, leading to total coupling gom and g0 reaching respectively 3 THz/nm and 4 MHz. Finally, we point towards ways to maximize the photoelastic coupling in GaAs disk resonators, and we provide some upper bounds for its value in various geometries.

© 2014 Optical Society of America

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2014 (1)

J. Restrepo, C. Ciuti, and I. Favero, “Single-polariton optomechanics,” Phys. Rev. Lett. 112, 013601 (2014).
[Crossref] [PubMed]

2013 (3)

A. Fainstein, N. Lanzillotti-Kimura, B. Jusserand, and B. Perrin, “Strong optical-mechanical coupling in a vertical gaas/alas microcavity for subterahertz phonons and near-infrared light,” Phys. Rev. Lett. 110, 037403 (2013).
[Crossref] [PubMed]

Y. Liu, M. Davanço, V. Aksyuk, and K. Srinivasan, “Electromagnetically induced transparency and wideband wavelength conversion in silicon nitride microdisk optomechanical resonators,” Phys. Rev. Lett. 110, 223603 (2013).
[Crossref] [PubMed]

D. T. Nguyen, C. Baker, W. Hease, S. Sejil, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “Ultrahigh q-frequency product for optomechanical disk resonators with a mechanical shield,” Appl. Phys. Lett. 103, 241112 (2013).
[Crossref]

2012 (11)

X. Sun, X. Zhang, and H. X. Tang, “High-q silicon optomechanical microdisk resonators at gigahertz frequencies,” Appl. Phys. Lett. 100, 173116 (2012).
[Crossref]

W. C. Jiang, X. Lu, J. Zhang, and Q. Lin, “High-frequency silicon optomechanical oscillator with an ultralow threshold,” Opt. Express 20, 15991–15996 (2012).
[Crossref] [PubMed]

C. Xiong, W. H. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys. 14, 095014 (2012).
[Crossref]

K. Usami, A. Naesby, T. Bagci, B. M. Nielsen, J. Liu, S. Stobbe, P. Lodahl, and E. S. Polzik, “Optical cavity cooling of mechanical modes of a semiconductor nanomembrane,” Nat. Physics 8, 168–172 (2012).
[Crossref]

P. B. Deotare, I. Bulu, I. W. Frank, Q. Quan, Y. Zhang, R. Ilic, and M. Loncar, “All optical reconfiguration of optomechanical filters,” Nat. Commun. 3, 846 (2012).
[Crossref] [PubMed]

S. Forstner, S. Prams, J. Knittel, E. van Ooijen, J. Swaim, G. Harris, A. Szorkovszky, W. Bowen, and H. Rubinsztein-Dunlop, “Cavity optomechanical magnetometer,” Phys. Rev. Lett. 108, 120801 (2012).
[Crossref] [PubMed]

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).

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous brillouin cooling,” Nat. Physics 8, 203–207 (2012).
[Crossref]

I. Favero, “Optomechanics: The stress of light cools vibration,” Nat. Physics 8, 180–181 (2012).
[Crossref]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. Kastelik, G. Leveque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101, 061109 (2012).
[Crossref]

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101, 081115 (2012).
[Crossref]

2011 (6)

H. Okamoto, D. Ito, K. Onomitsu, H. Sanada, H. Gotoh, T. Sogawa, and H. Yamaguchi, “Vibration amplification, damping, and self-oscillations in micromechanical resonators induced by optomechanical coupling through carrier excitation,” Phys. Rev. Lett. 106, 036801 (2011).
[Crossref] [PubMed]

K. Y. Fong, W. H. Pernice, M. Li, and H. X. Tang, “Tunable optical coupler controlled by optical gradient forces,” Opt. Express 19, 15098–15108 (2011).
[Crossref] [PubMed]

J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Sirois, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

J. Chan, T. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref] [PubMed]

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “Wavelength-sized gaas optomechanical resonators with gigahertz frequency,” Appl. Phys. Lett. 98, 113108 (2011).
[Crossref]

C. Baker, C. Belacel, A. Andronico, P. Senellart, A. Lemaitre, E. Galopin, S. Ducci, G. Leo, and I. Favero, “Critical optical coupling between a gaas disk and a nanowaveguide suspended on the chip,” Appl. Phys. Lett. 99, 151117 (2011).
[Crossref]

2010 (4)

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4, 211–217 (2010).
[Crossref]

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency gaas nanooptomechanical disk resonator,” Phys. Rev. Lett. 105, 263903 (2010).
[Crossref]

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]

S. M. Barnett, “Resolution of the abraham-minkowski dilemma,” Phys. Rev. Lett. 104, 070401 (2010).
[Crossref] [PubMed]

2009 (2)

F. Marquardt and S. Girvin, “Optomechanics (a brief review),” Physics 2, 40 (2009).
[Crossref]

I. Favero and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics 3, 201–205 (2009).
[Crossref]

2008 (1)

2006 (1)

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97, 023903 (2006).
[Crossref]

2005 (1)

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. 95, 67401 (2005).
[Crossref]

2002 (1)

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

1995 (1)

J. E. Raynolds, Z. H. Levine, and J. W. Wilkins, “Strain-induced birefringence in gaas,” Phys. Rev. B 51, 10477 (1995).
[Crossref]

1975 (1)

A. Feldman, “Relations between electrostriction and the stress-optical effect,” Phys. Rev. B 11, 5112–5114 (1975).
[Crossref]

1974 (1)

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

1968 (1)

A. Feldman and D. Horowitz, “Dispersion of the piezobirefringence of gaas,” J. Appl. Phys. 39, 5597–5599 (1968).
[Crossref]

1956 (1)

M. Onoe, “Contour vibrations of isotropic circular plates,” J. Acoust. Soc. Am. 28, 1158 (1956).
[Crossref]

Aksyuk, V.

Y. Liu, M. Davanço, V. Aksyuk, and K. Srinivasan, “Electromagnetically induced transparency and wideband wavelength conversion in silicon nitride microdisk optomechanical resonators,” Phys. Rev. Lett. 110, 223603 (2013).
[Crossref] [PubMed]

Alegre, T. M.

J. Chan, T. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref] [PubMed]

Allman, M.

J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Sirois, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

Andronico, A.

C. Baker, C. Belacel, A. Andronico, P. Senellart, A. Lemaitre, E. Galopin, S. Ducci, G. Leo, and I. Favero, “Critical optical coupling between a gaas disk and a nanowaveguide suspended on the chip,” Appl. Phys. Lett. 99, 151117 (2011).
[Crossref]

A. Andronico, I. Favero, and G. Leo, “Difference frequency generation in gaas microdisks,” Opt. Lett. 33, 2026–2028 (2008).
[Crossref] [PubMed]

Aspelmeyer, M.

J. Chan, T. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref] [PubMed]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” arXiv preprint arXiv:1303.0733 (2013).

Bagci, T.

K. Usami, A. Naesby, T. Bagci, B. M. Nielsen, J. Liu, S. Stobbe, P. Lodahl, and E. S. Polzik, “Optical cavity cooling of mechanical modes of a semiconductor nanomembrane,” Nat. Physics 8, 168–172 (2012).
[Crossref]

Bahl, G.

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous brillouin cooling,” Nat. Physics 8, 203–207 (2012).
[Crossref]

Baker, C.

D. T. Nguyen, C. Baker, W. Hease, S. Sejil, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “Ultrahigh q-frequency product for optomechanical disk resonators with a mechanical shield,” Appl. Phys. Lett. 103, 241112 (2013).
[Crossref]

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “Wavelength-sized gaas optomechanical resonators with gigahertz frequency,” Appl. Phys. Lett. 98, 113108 (2011).
[Crossref]

C. Baker, C. Belacel, A. Andronico, P. Senellart, A. Lemaitre, E. Galopin, S. Ducci, G. Leo, and I. Favero, “Critical optical coupling between a gaas disk and a nanowaveguide suspended on the chip,” Appl. Phys. Lett. 99, 151117 (2011).
[Crossref]

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency gaas nanooptomechanical disk resonator,” Phys. Rev. Lett. 105, 263903 (2010).
[Crossref]

Barnett, S. M.

S. M. Barnett, “Resolution of the abraham-minkowski dilemma,” Phys. Rev. Lett. 104, 070401 (2010).
[Crossref] [PubMed]

Belacel, C.

C. Baker, C. Belacel, A. Andronico, P. Senellart, A. Lemaitre, E. Galopin, S. Ducci, G. Leo, and I. Favero, “Critical optical coupling between a gaas disk and a nanowaveguide suspended on the chip,” Appl. Phys. Lett. 99, 151117 (2011).
[Crossref]

Biegelsen, D. K.

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

Blasius, T. D.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics (2012).
[Crossref]

Bloch, J.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. 95, 67401 (2005).
[Crossref]

Bowen, W.

S. Forstner, S. Prams, J. Knittel, E. van Ooijen, J. Swaim, G. Harris, A. Szorkovszky, W. Bowen, and H. Rubinsztein-Dunlop, “Cavity optomechanical magnetometer,” Phys. Rev. Lett. 108, 120801 (2012).
[Crossref] [PubMed]

Bruno, T. J.

D. R. Lide and T. J. Bruno, CRC Handbook of Chemistry and Physics (CRC PressI Llc, 2012).

Bulu, I.

P. B. Deotare, I. Bulu, I. W. Frank, Q. Quan, Y. Zhang, R. Ilic, and M. Loncar, “All optical reconfiguration of optomechanical filters,” Nat. Commun. 3, 846 (2012).
[Crossref] [PubMed]

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.

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous brillouin cooling,” Nat. Physics 8, 203–207 (2012).
[Crossref]

Chan, J.

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101, 081115 (2012).
[Crossref]

J. Chan, T. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref] [PubMed]

Cicak, K.

J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Sirois, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

Ciuti, C.

J. Restrepo, C. Ciuti, and I. Favero, “Single-polariton optomechanics,” Phys. Rev. Lett. 112, 013601 (2014).
[Crossref] [PubMed]

Davanço, M.

Y. Liu, M. Davanço, V. Aksyuk, and K. Srinivasan, “Electromagnetically induced transparency and wideband wavelength conversion in silicon nitride microdisk optomechanical resonators,” Phys. Rev. Lett. 110, 223603 (2013).
[Crossref] [PubMed]

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]

Deotare, P. B.

P. B. Deotare, I. Bulu, I. W. Frank, Q. Quan, Y. Zhang, R. Ilic, and M. Loncar, “All optical reconfiguration of optomechanical filters,” Nat. Commun. 3, 846 (2012).
[Crossref] [PubMed]

Ding, L.

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “Wavelength-sized gaas optomechanical resonators with gigahertz frequency,” Appl. Phys. Lett. 98, 113108 (2011).
[Crossref]

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency gaas nanooptomechanical disk resonator,” Phys. Rev. Lett. 105, 263903 (2010).
[Crossref]

Djafari-Rouhani, B.

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. Kastelik, G. Leveque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101, 061109 (2012).
[Crossref]

Donner, T.

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Raynolds, J. E.

J. E. Raynolds, Z. H. Levine, and J. W. Wilkins, “Strain-induced birefringence in gaas,” Phys. Rev. B 51, 10477 (1995).
[Crossref]

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).

Restrepo, J.

J. Restrepo, C. Ciuti, and I. Favero, “Single-polariton optomechanics,” Phys. Rev. Lett. 112, 013601 (2014).
[Crossref] [PubMed]

Roels, J.

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4, 211–217 (2010).
[Crossref]

Rolland, Q.

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. Kastelik, G. Leveque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101, 061109 (2012).
[Crossref]

Rubinsztein-Dunlop, H.

S. Forstner, S. Prams, J. Knittel, E. van Ooijen, J. Swaim, G. Harris, A. Szorkovszky, W. Bowen, and H. Rubinsztein-Dunlop, “Cavity optomechanical magnetometer,” Phys. Rev. Lett. 108, 120801 (2012).
[Crossref] [PubMed]

Saada, A. S.

A. S. Saada, Elasticity: Theory and Applications (J. Ross Publishing, 2009).

Safavi-Naeini, A. H.

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101, 081115 (2012).
[Crossref]

J. Chan, T. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref] [PubMed]

Sanada, H.

H. Okamoto, D. Ito, K. Onomitsu, H. Sanada, H. Gotoh, T. Sogawa, and H. Yamaguchi, “Vibration amplification, damping, and self-oscillations in micromechanical resonators induced by optomechanical coupling through carrier excitation,” Phys. Rev. Lett. 106, 036801 (2011).
[Crossref] [PubMed]

Schuck, C.

C. Xiong, W. H. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys. 14, 095014 (2012).
[Crossref]

Sejil, S.

D. T. Nguyen, C. Baker, W. Hease, S. Sejil, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “Ultrahigh q-frequency product for optomechanical disk resonators with a mechanical shield,” Appl. Phys. Lett. 103, 241112 (2013).
[Crossref]

Senellart, P.

D. T. Nguyen, C. Baker, W. Hease, S. Sejil, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “Ultrahigh q-frequency product for optomechanical disk resonators with a mechanical shield,” Appl. Phys. Lett. 103, 241112 (2013).
[Crossref]

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “Wavelength-sized gaas optomechanical resonators with gigahertz frequency,” Appl. Phys. Lett. 98, 113108 (2011).
[Crossref]

C. Baker, C. Belacel, A. Andronico, P. Senellart, A. Lemaitre, E. Galopin, S. Ducci, G. Leo, and I. Favero, “Critical optical coupling between a gaas disk and a nanowaveguide suspended on the chip,” Appl. Phys. Lett. 99, 151117 (2011).
[Crossref]

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency gaas nanooptomechanical disk resonator,” Phys. Rev. Lett. 105, 263903 (2010).
[Crossref]

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. Gérard, and J. Bloch, “Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity,” Phys. Rev. Lett. 95, 67401 (2005).
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J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Sirois, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
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Sirois, A.

J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Sirois, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
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S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, J. Joannopoulos, and Y. Fink, “Perturbation theory for maxwells equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
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Sogawa, T.

H. Okamoto, D. Ito, K. Onomitsu, H. Sanada, H. Gotoh, T. Sogawa, and H. Yamaguchi, “Vibration amplification, damping, and self-oscillations in micromechanical resonators induced by optomechanical coupling through carrier excitation,” Phys. Rev. Lett. 106, 036801 (2011).
[Crossref] [PubMed]

Srinivasan, K.

Y. Liu, M. Davanço, V. Aksyuk, and K. Srinivasan, “Electromagnetically induced transparency and wideband wavelength conversion in silicon nitride microdisk optomechanical resonators,” Phys. Rev. Lett. 110, 223603 (2013).
[Crossref] [PubMed]

Stobbe, S.

K. Usami, A. Naesby, T. Bagci, B. M. Nielsen, J. Liu, S. Stobbe, P. Lodahl, and E. S. Polzik, “Optical cavity cooling of mechanical modes of a semiconductor nanomembrane,” Nat. Physics 8, 168–172 (2012).
[Crossref]

Sun, X.

C. Xiong, W. H. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys. 14, 095014 (2012).
[Crossref]

X. Sun, X. Zhang, and H. X. Tang, “High-q silicon optomechanical microdisk resonators at gigahertz frequencies,” Appl. Phys. Lett. 100, 173116 (2012).
[Crossref]

Swaim, J.

S. Forstner, S. Prams, J. Knittel, E. van Ooijen, J. Swaim, G. Harris, A. Szorkovszky, W. Bowen, and H. Rubinsztein-Dunlop, “Cavity optomechanical magnetometer,” Phys. Rev. Lett. 108, 120801 (2012).
[Crossref] [PubMed]

Szorkovszky, A.

S. Forstner, S. Prams, J. Knittel, E. van Ooijen, J. Swaim, G. Harris, A. Szorkovszky, W. Bowen, and H. Rubinsztein-Dunlop, “Cavity optomechanical magnetometer,” Phys. Rev. Lett. 108, 120801 (2012).
[Crossref] [PubMed]

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X. Sun, X. Zhang, and H. X. Tang, “High-q silicon optomechanical microdisk resonators at gigahertz frequencies,” Appl. Phys. Lett. 100, 173116 (2012).
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C. Xiong, W. H. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys. 14, 095014 (2012).
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J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Sirois, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

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G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous brillouin cooling,” Nat. Physics 8, 203–207 (2012).
[Crossref]

Usami, K.

K. Usami, A. Naesby, T. Bagci, B. M. Nielsen, J. Liu, S. Stobbe, P. Lodahl, and E. S. Polzik, “Optical cavity cooling of mechanical modes of a semiconductor nanomembrane,” Nat. Physics 8, 168–172 (2012).
[Crossref]

van Ooijen, E.

S. Forstner, S. Prams, J. Knittel, E. van Ooijen, J. Swaim, G. Harris, A. Szorkovszky, W. Bowen, and H. Rubinsztein-Dunlop, “Cavity optomechanical magnetometer,” Phys. Rev. Lett. 108, 120801 (2012).
[Crossref] [PubMed]

Van Thourhout, D.

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4, 211–217 (2010).
[Crossref]

Wang, Z.

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]

Weisberg, O.

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

Whittaker, J.

J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Sirois, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

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J. E. Raynolds, Z. H. Levine, and J. W. Wilkins, “Strain-induced birefringence in gaas,” Phys. Rev. B 51, 10477 (1995).
[Crossref]

Winger, M.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics (2012).
[Crossref]

Xiong, C.

C. Xiong, W. H. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys. 14, 095014 (2012).
[Crossref]

Yamaguchi, H.

H. Okamoto, D. Ito, K. Onomitsu, H. Sanada, H. Gotoh, T. Sogawa, and H. Yamaguchi, “Vibration amplification, damping, and self-oscillations in micromechanical resonators induced by optomechanical coupling through carrier excitation,” Phys. Rev. Lett. 106, 036801 (2011).
[Crossref] [PubMed]

Zhang, J.

Zhang, X.

X. Sun, X. Zhang, and H. X. Tang, “High-q silicon optomechanical microdisk resonators at gigahertz frequencies,” Appl. Phys. Lett. 100, 173116 (2012).
[Crossref]

Zhang, Y.

P. B. Deotare, I. Bulu, I. W. Frank, Q. Quan, Y. Zhang, R. Ilic, and M. Loncar, “All optical reconfiguration of optomechanical filters,” Nat. Commun. 3, 846 (2012).
[Crossref] [PubMed]

Appl. Phys. Lett. (6)

X. Sun, X. Zhang, and H. X. Tang, “High-q silicon optomechanical microdisk resonators at gigahertz frequencies,” Appl. Phys. Lett. 100, 173116 (2012).
[Crossref]

D. T. Nguyen, C. Baker, W. Hease, S. Sejil, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “Ultrahigh q-frequency product for optomechanical disk resonators with a mechanical shield,” Appl. Phys. Lett. 103, 241112 (2013).
[Crossref]

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “Wavelength-sized gaas optomechanical resonators with gigahertz frequency,” Appl. Phys. Lett. 98, 113108 (2011).
[Crossref]

C. Baker, C. Belacel, A. Andronico, P. Senellart, A. Lemaitre, E. Galopin, S. Ducci, G. Leo, and I. Favero, “Critical optical coupling between a gaas disk and a nanowaveguide suspended on the chip,” Appl. Phys. Lett. 99, 151117 (2011).
[Crossref]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. Kastelik, G. Leveque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101, 061109 (2012).
[Crossref]

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101, 081115 (2012).
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Nat. Commun. (1)

P. B. Deotare, I. Bulu, I. W. Frank, Q. Quan, Y. Zhang, R. Ilic, and M. Loncar, “All optical reconfiguration of optomechanical filters,” Nat. Commun. 3, 846 (2012).
[Crossref] [PubMed]

Nat. Photonics (2)

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4, 211–217 (2010).
[Crossref]

I. Favero and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics 3, 201–205 (2009).
[Crossref]

Nat. Physics (3)

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous brillouin cooling,” Nat. Physics 8, 203–207 (2012).
[Crossref]

I. Favero, “Optomechanics: The stress of light cools vibration,” Nat. Physics 8, 180–181 (2012).
[Crossref]

K. Usami, A. Naesby, T. Bagci, B. M. Nielsen, J. Liu, S. Stobbe, P. Lodahl, and E. S. Polzik, “Optical cavity cooling of mechanical modes of a semiconductor nanomembrane,” Nat. Physics 8, 168–172 (2012).
[Crossref]

Nature (2)

J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Sirois, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

J. Chan, T. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref] [PubMed]

New J. Phys. (1)

C. Xiong, W. H. Pernice, X. Sun, C. Schuck, K. Y. Fong, and H. X. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys. 14, 095014 (2012).
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Opt. Express (3)

Opt. Lett. (1)

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[Crossref]

Phys. Rev. E (1)

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, J. Joannopoulos, and Y. Fink, “Perturbation theory for maxwells equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
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A. Fainstein, N. Lanzillotti-Kimura, B. Jusserand, and B. Perrin, “Strong optical-mechanical coupling in a vertical gaas/alas microcavity for subterahertz phonons and near-infrared light,” Phys. Rev. Lett. 110, 037403 (2013).
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H. Okamoto, D. Ito, K. Onomitsu, H. Sanada, H. Gotoh, T. Sogawa, and H. Yamaguchi, “Vibration amplification, damping, and self-oscillations in micromechanical resonators induced by optomechanical coupling through carrier excitation,” Phys. Rev. Lett. 106, 036801 (2011).
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[Crossref]

J. Restrepo, C. Ciuti, and I. Favero, “Single-polariton optomechanics,” Phys. Rev. Lett. 112, 013601 (2014).
[Crossref] [PubMed]

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency gaas nanooptomechanical disk resonator,” Phys. Rev. Lett. 105, 263903 (2010).
[Crossref]

S. Forstner, S. Prams, J. Knittel, E. van Ooijen, J. Swaim, G. Harris, A. Szorkovszky, W. Bowen, and H. Rubinsztein-Dunlop, “Cavity optomechanical magnetometer,” Phys. Rev. Lett. 108, 120801 (2012).
[Crossref] [PubMed]

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97, 023903 (2006).
[Crossref]

Y. Liu, M. Davanço, V. Aksyuk, and K. Srinivasan, “Electromagnetically induced transparency and wideband wavelength conversion in silicon nitride microdisk optomechanical resonators,” Phys. Rev. Lett. 110, 223603 (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).

Physics (1)

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A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics (2012).
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Figures (7)

Fig. 1
Fig. 1

(a) Schematic side-view of a GaAs disk of thickness h (blue), positioned atop an AlGaAs pedestal (grey), along with the cylindrical coordinates used throughout this work. (b) Top view of a GaAs disk of radius R (blue). The dashed green and red lines represent the radial deformation of the disk by a mechanical mode. (c) Schematic view of an optical cavity composed of n=2, 4 or 6 mirrors, and the associated grazing angles.

Fig. 2
Fig. 2

2D axi-symmetric FEM modeling of the normal radial ‘radiation pressure’ stress σ rr rp in a 320 nm thick and 1 μm radius GaAs WGM disk resonator. The considered WGM is a (p=1, m=10). The solid lines show the boundary of the two computational domains: the GaAs disk and the surrounding air. 2D axi-symmetric cross sections are shown here, the whole disk is obtained by revolving around the z axial symmetry axis (dashed red line). The AlGaAs pedestal, being sufficiently remote from the optical field, is not included in the simulation. Images (a) through (e) show the computed electric and magnetic field cross-sections, normalized such that the total electromagnetic energy in the resonator is equal to the energy of one photon. (a) Er (b) Eθ (c) Ez (d) Hz (e) Hr. Since the simulated WGM is TE, the in-plane electric field and out-of-plane magnetic field components Er, Eθ and Hz are dominant. (f) Normal radial stress exerted by a confined photon σ rr rp. The optically induced stress is largest near the outer boundary of the disk resonator, where most of the electromagnetic energy is located.

Fig. 3
Fig. 3

(a) Illustration of the link between photoelasticity and electrostriction. A strain leads to change in refractive index (photoelasticity) which itself leads to a change in the stored electric energy. Electrostriction is the converse mechanism (red arrow), whereby electric fields (stored energy) induce strain in the material. (b) Schematic illustrating the direction of electrostrictive and radiation pressure forces acting on a GaAs disk resonator due to photons confined in a WGM (black arrows), and represented in the cross section plane over which the stress and volume force are plotted in Figs. 2 and 4.

Fig. 4
Fig. 4

2D axi-symmetric FEM modeling of the electrostrictive stress and volume force. (a) and (b) show respectively the rz cross-section of the radial σ rr es and axial σ zz es electrostrictive stress distributions. The azimuthal normal stress σ θ θ es (not shown here) is of comparable magnitude. (c) and (d) plot the associated radial and axial volume force distributions. Black arrows indicate the overall direction these forces point in.

Fig. 5
Fig. 5

(a) through (d): Displacement profile for the four mechanical eigenmodes listed in Table 3, with exaggerated deformation. The surface color code illustrates the total displacement, with red as maximum and blue as minimum.

Fig. 6
Fig. 6

Radial displacement and normal radial strain S1=Srr as a function of the radial coordinate, for the first RBM ((a) and (b)) and for the second RBM ((c) and (d)) of a 1μm radius and 320 nm thick GaAs disk resonator. The values are obtained through FEM modeling, using the approximation of an isotropic Young’s modulus for GaAs. The orange highlighted zone between r=0.6 μm and r=1μm and the black ring in the inset pictures mark the region of highest electromagnetic energy density for a p=1 WGM. (The displacements are normalized such that for both modes the mechanical energy is equal to kBT at 300 K).

Fig. 7
Fig. 7

Comparison between the geometric and photoelastic optomechanical coupling strength g0 for the TE (p=1) WGM of a GaAs disk of thickness 320 nm, as a function of radius, for the first RBM (a) and second RBM (b), in log scale. The vertical dashed red line represents the radius r=0.7μm, at which bending losses become limiting at the considered WGM wavelength of 1.3 μm. For the first RBM, the combined optomechanical coupling g 0 pe + g 0 geo reaches 4 MHz for the smallest disks. (The dashed blue lines represent the values given by Eq. (17) reduced by respectively 20% for the first RBM and 40% for the second RBM). For the second RBM, photoelasticity is the dominant optomechanical coupling mechanism, with g 0 pe reaching 2 MHz for R=1 μm.

Tables (4)

Tables Icon

Table 1 Radiation pressure values for a 1 μm radius, 320 nm thick GaAs disk resonator (such as the ones fabricated in [18]), and λ0=1.32 μm wavelength light.

Tables Icon

Table 2 Photoelastic material parameters for GaAs, and silicon (Si) for comparison. The photoelastic coefficients vary little for wavelengths with energies well below the material bandgap [34].

Tables Icon

Table 3 Comparison between the geometric and photoelastic optomechanical coupling strengths g om geo and g om pe, for four mechanical modes of a 320 nm thick, 1 μm radius GaAs disk, and a p=1 m=10, λ0 ≃ 1.3 μm WGM, obtained through FEM simulations. The mechanical deformation profiles are shown in Fig. 5.

Tables Icon

Table 4 First three values of the frequency parameter λP and effective mass ratios for GaAs disk RBMs, and GaAs material parameters used in the calculations. The effective mass ratio is defined as the effective mass associated to a reduction point on the disk boundary meff divided by the disk mass m.

Equations (18)

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

H ^ = ω 0 a ^ a ^ + Ω M b ^ b ^ g 0 a ^ a ^ ( b ^ + b ^ )
g om = d ω 0 ( R , ε ) d x = ω 0 R d R d x geometric g om geo ω 0 ε d ε d x photoelastic g om pe
E = N ph ω 0
F = Δ E Δ x = N ph Δ ω 0 Δ x = N ph g om
F rp = N ph g om geo and F es = N ph g om pe
2 k lim n n sin ( π / n ) = 2 π k
F = d P d t = 2 π k 2 π R n eff / c τ rt = k c n eff R
F rp = N ph k 0 c R = N ph g om geo
P rp = F rp / S = N ph × k 0 c 2 π R 2 h = N ph × c λ 0 R 2 h
T i j = ε 0 ε r ( r , z ) [ E i E j 1 2 δ i j | E | 2 ] + μ 0 μ r [ H i H j 1 2 δ i j | H | 2 ]
j rp = i σ i j rp = i T i j
ε i j 1 ( S k l ) = ε i j 1 + Δ ( ε i j 1 ) = ε i j 1 + p i j k l S k l
( σ rr es σ θ θ es σ zz es σ θ z es = σ z θ es σ r z es = σ z r es σ r θ es = σ θ r es ) = 1 2 ε 0 n 4 ( p 11 p 12 p 12 0 0 0 p 12 p 11 p 12 0 0 0 p 12 p 12 p 11 0 0 0 0 0 0 p 44 0 0 0 0 0 0 p 44 0 0 0 0 0 0 p 44 ) photoelastic tensor ( E r 2 E θ 2 E z 2 E θ E z E r E z E r E θ )
σ rr es = 1 2 ε 0 n 4 [ p 11 | E r | 2 + p 12 ( | E θ | 2 + | E z | 2 ) ] σ zz es = 1 2 ε 0 n 4 [ p 11 | E z | 2 + p 12 ( | E r | 2 + | E θ | 2 ) ]
g om geo = ω 0 4 disk ( q n ) [ Δ ε 12 | e | 2 Δ ( ε 12 1 ) | d | 2 ] d A
( ε 1 ε 2 ε 3 ) with { ε 1 = ( 1 / n 2 + p 11 S 1 + p 12 S 2 + p 12 S 3 ) 1 ε 2 = ( 1 / n 2 + p 12 S 1 + p 11 S 2 + p 12 S 3 ) 1 ε 3 = ( 1 / n 2 + p 12 S 1 + p 12 S 2 + p 11 S 3 ) 1
g 0 geo = g om geo x ZPF ω 0 R 2 m eff Ω M P with Ω M P = λ P R E ρ ( 1 ν 2 )
g om = 1 2 disk Σ σ i j S i k d V Δ x

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