Abstract

Chip-based cavity optomechanical systems are being considered for applications in sensing, metrology, and quantum information science. Critical to their development is an understanding of how the optical and mechanical modes interact, quantified by the coupling rate g0. Here, we develop GaAs optomechanical resonators and investigate the moving dielectric boundary and photoelastic contributions to g0. First, we consider coupling between the fundamental radial breathing mechanical mode and a 1550 nm band optical whispering gallery mode in microdisks. For decreasing disk radius from R=5 to 1 μm, simulations and measurements show that g0 changes from being dominated by the moving boundary contribution to having an equal photoelastic contribution. Next, we design and demonstrate nanobeam optomechanical crystals, in which a 2.5 GHz mechanical breathing mode couples to a 1550 nm optical mode, predominantly through the photoelastic effect. We show a significant (30%) dependence of g0 on the device’s in-plane orientation, resulting from the difference in GaAs photoelastic coefficients along different crystalline axes, with fabricated devices exhibiting g0/2π as high as 1.1 MHz, for orientation along the 110 axis. GaAs nanobeam optomechanical crystals are a promising system, which can combine the demonstrated large optomechanical coupling strength with additional functionality, such as piezoelectric actuation and incorporation of optical gain media.

© 2014 Optical Society of America

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2014 (5)

M. Wu, A. C. Hryciw, C. Healey, D. P. Lake, H. Jayakumar, M. R. Freeman, J. P. Davis, P. E. Barclay, “Dissipative and dispersive optomechanics in a nanocavity torque sensor,” Phys. Rev. X 4, 021052 (2014).
[Crossref]

I. Yeo, P.-L. de Assis, A. Gloppe, E. Dupont-Ferrier, P. Verlot, N. S. Malik, E. Dupuy, J. Claudon, J.-M. Gérard, A. Auffèves, G. Nogues, S. Seidelin, J.-P. Poizat, O. Arcizet, M. Richard, “Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system,” Nat. Nanotechnol. 9, 106–110 (2014).
[Crossref]

L. Kipfstuhl, F. Guldner, J. Riedrich-Möller, C. Becher, “Modeling of optomechanical coupling in a phoxonic crystal cavity in diamond,” Opt. Express 22, 12410–12423 (2014).
[Crossref]

M. Davanço, S. Ates, Y. Liu, K. Srinivasan, “Si3N4 optomechanical crystals in the resolved-sideband regime,” Appl. Phys. Lett. 104, 041101 (2014).
[Crossref]

C. Baker, W. Hease, D.-T. Nguyen, A. Andronico, S. Ducci, G. Leo, I. Favero, “Photoelastic coupling in gallium arsenide optomechanical disk resonators,” Opt. Express 22, 14072–14086 (2014).
[Crossref]

2013 (3)

J. Bochmann, A. Vainsencher, D. D. Awschalom, A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9, 712–716 (2013).
[Crossref]

L. Fan, X. Sun, C. Xiong, C. Schuck, H. X. Tang, “Aluminum nitride piezo-acousto-photonic crystal nanocavity with high quality factors,” Appl. Phys. Lett. 102, 153507 (2013).
[Crossref]

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

2012 (3)

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

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

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

2011 (3)

Q. Quan, M. Loncar, “Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities,” Opt. Express 19, 18529–18542 (2011).
[Crossref]

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

R. Ohta, Y. Ota, M. Nomura, N. Kumagai, S. Ishida, S. Iwamoto, Y. Arakawa, “Strong coupling between a photonic crystal nanobeam cavity and a single quantum dot,” Appl. Phys. Lett. 98, 173104 (2011).
[Crossref]

2010 (5)

2009 (3)

M. Li, W. H. P. Pernice, H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103, 223901 (2009).
[Crossref]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref]

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

2007 (3)

T. J. Kippenberg, K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15, 17172–17205 (2007).
[Crossref]

S. C. Masmanidis, R. B. Karabalin, I. De Vlaminck, G. Borghs, M. R. Freeman, M. L. Roukes, “Multifunctional nanomechanical systems via tunably coupled piezoelectric actuation,” Science 317, 780–783 (2007).
[Crossref]

D. M. Karabacak, V. Yakhot, K. L. Ekinci, “High-frequency nanofluidics: an experimental study using nanomechanical resonators,” Phys. Rev. Lett. 98, 254505 (2007).
[Crossref]

2005 (1)

K. Srinivasan, M. Borselli, T. J. Johnson, P. E. Barclay, O. Painter, A. Stintz, S. Krishna, “Optical loss and lasing characteristics of high-quality-factor AlGaAs microdisk resonators with embedded quantum dots,” Appl. Phys. Lett. 86, 151106 (2005).
[Crossref]

2004 (1)

I. Wilson-Rae, P. Zoller, A. Imamoglu, “Laser cooling of a nanomechanical resonator mode to its quantum ground state,” Phys. Rev. Lett. 92, 075507 (2004).
[Crossref]

1973 (1)

W. Brantley, “Calculated elastic constants for stress problems associated with semiconductor devices,” J. Appl. Phys. 44, 534–535 (1973).
[Crossref]

1967 (1)

R. W. Dixon, “Photoelastic properties of selected materials and their relevance for applications to acoustic light modulators and scanners,” J. Appl. Phys. 38, 5149–5153 (1967).
[Crossref]

Andronico, A.

Anetsberger, G.

Arakawa, Y.

R. Ohta, Y. Ota, M. Nomura, N. Kumagai, S. Ishida, S. Iwamoto, Y. Arakawa, “Strong coupling between a photonic crystal nanobeam cavity and a single quantum dot,” Appl. Phys. Lett. 98, 173104 (2011).
[Crossref]

Arcizet, O.

I. Yeo, P.-L. de Assis, A. Gloppe, E. Dupont-Ferrier, P. Verlot, N. S. Malik, E. Dupuy, J. Claudon, J.-M. Gérard, A. Auffèves, G. Nogues, S. Seidelin, J.-P. Poizat, O. Arcizet, M. Richard, “Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system,” Nat. Nanotechnol. 9, 106–110 (2014).
[Crossref]

Aspelmeyer, M.

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

Ates, S.

M. Davanço, S. Ates, Y. Liu, K. Srinivasan, “Si3N4 optomechanical crystals in the resolved-sideband regime,” Appl. Phys. Lett. 104, 041101 (2014).
[Crossref]

Auffèves, A.

I. Yeo, P.-L. de Assis, A. Gloppe, E. Dupont-Ferrier, P. Verlot, N. S. Malik, E. Dupuy, J. Claudon, J.-M. Gérard, A. Auffèves, G. Nogues, S. Seidelin, J.-P. Poizat, O. Arcizet, M. Richard, “Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system,” Nat. Nanotechnol. 9, 106–110 (2014).
[Crossref]

Awschalom, D. D.

J. Bochmann, A. Vainsencher, D. D. Awschalom, A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9, 712–716 (2013).
[Crossref]

Bahl, G.

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

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

Baker, C.

C. Baker, W. Hease, D.-T. Nguyen, A. Andronico, S. Ducci, G. Leo, I. Favero, “Photoelastic coupling in gallium arsenide optomechanical disk resonators,” Opt. Express 22, 14072–14086 (2014).
[Crossref]

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

Barclay, P. E.

M. Wu, A. C. Hryciw, C. Healey, D. P. Lake, H. Jayakumar, M. R. Freeman, J. P. Davis, P. E. Barclay, “Dissipative and dispersive optomechanics in a nanocavity torque sensor,” Phys. Rev. X 4, 021052 (2014).
[Crossref]

K. Srinivasan, M. Borselli, T. J. Johnson, P. E. Barclay, O. Painter, A. Stintz, S. Krishna, “Optical loss and lasing characteristics of high-quality-factor AlGaAs microdisk resonators with embedded quantum dots,” Appl. Phys. Lett. 86, 151106 (2005).
[Crossref]

Becher, C.

Bochmann, J.

J. Bochmann, A. Vainsencher, D. D. Awschalom, A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9, 712–716 (2013).
[Crossref]

Borghs, G.

S. C. Masmanidis, R. B. Karabalin, I. De Vlaminck, G. Borghs, M. R. Freeman, M. L. Roukes, “Multifunctional nanomechanical systems via tunably coupled piezoelectric actuation,” Science 317, 780–783 (2007).
[Crossref]

Borselli, M.

K. Srinivasan, M. Borselli, T. J. Johnson, P. E. Barclay, O. Painter, A. Stintz, S. Krishna, “Optical loss and lasing characteristics of high-quality-factor AlGaAs microdisk resonators with embedded quantum dots,” Appl. Phys. Lett. 86, 151106 (2005).
[Crossref]

Brantley, W.

W. Brantley, “Calculated elastic constants for stress problems associated with semiconductor devices,” J. Appl. Phys. 44, 534–535 (1973).
[Crossref]

Camacho, R. M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref]

Carmon, T.

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

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

Chan, J.

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

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref]

Claudon, J.

I. Yeo, P.-L. de Assis, A. Gloppe, E. Dupont-Ferrier, P. Verlot, N. S. Malik, E. Dupuy, J. Claudon, J.-M. Gérard, A. Auffèves, G. Nogues, S. Seidelin, J.-P. Poizat, O. Arcizet, M. Richard, “Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system,” Nat. Nanotechnol. 9, 106–110 (2014).
[Crossref]

Cleland, A. N.

J. Bochmann, A. Vainsencher, D. D. Awschalom, A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9, 712–716 (2013).
[Crossref]

Cox, J. A.

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

Davanço, M.

M. Davanço, S. Ates, Y. Liu, K. Srinivasan, “Si3N4 optomechanical crystals in the resolved-sideband regime,” Appl. Phys. Lett. 104, 041101 (2014).
[Crossref]

Davids, P.

Davis, J. P.

M. Wu, A. C. Hryciw, C. Healey, D. P. Lake, H. Jayakumar, M. R. Freeman, J. P. Davis, P. E. Barclay, “Dissipative and dispersive optomechanics in a nanocavity torque sensor,” Phys. Rev. X 4, 021052 (2014).
[Crossref]

de Assis, P.-L.

I. Yeo, P.-L. de Assis, A. Gloppe, E. Dupont-Ferrier, P. Verlot, N. S. Malik, E. Dupuy, J. Claudon, J.-M. Gérard, A. Auffèves, G. Nogues, S. Seidelin, J.-P. Poizat, O. Arcizet, M. Richard, “Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system,” Nat. Nanotechnol. 9, 106–110 (2014).
[Crossref]

De Vlaminck, I.

S. C. Masmanidis, R. B. Karabalin, I. De Vlaminck, G. Borghs, M. R. Freeman, M. L. Roukes, “Multifunctional nanomechanical systems via tunably coupled piezoelectric actuation,” Science 317, 780–783 (2007).
[Crossref]

Deleglise, S.

Ding, L.

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

Dixon, R. W.

R. W. Dixon, “Photoelastic properties of selected materials and their relevance for applications to acoustic light modulators and scanners,” J. Appl. Phys. 38, 5149–5153 (1967).
[Crossref]

Djafari-Rouhani, B.

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

Ducci, S.

C. Baker, W. Hease, D.-T. Nguyen, A. Andronico, S. Ducci, G. Leo, I. Favero, “Photoelastic coupling in gallium arsenide optomechanical disk resonators,” Opt. Express 22, 14072–14086 (2014).
[Crossref]

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

Dupont, S.

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

Dupont-Ferrier, E.

I. Yeo, P.-L. de Assis, A. Gloppe, E. Dupont-Ferrier, P. Verlot, N. S. Malik, E. Dupuy, J. Claudon, J.-M. Gérard, A. Auffèves, G. Nogues, S. Seidelin, J.-P. Poizat, O. Arcizet, M. Richard, “Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system,” Nat. Nanotechnol. 9, 106–110 (2014).
[Crossref]

Dupuy, E.

I. Yeo, P.-L. de Assis, A. Gloppe, E. Dupont-Ferrier, P. Verlot, N. S. Malik, E. Dupuy, J. Claudon, J.-M. Gérard, A. Auffèves, G. Nogues, S. Seidelin, J.-P. Poizat, O. Arcizet, M. Richard, “Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system,” Nat. Nanotechnol. 9, 106–110 (2014).
[Crossref]

Eichenfield, M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[Crossref]

Ekinci, K. L.

D. M. Karabacak, V. Yakhot, K. L. Ekinci, “High-frequency nanofluidics: an experimental study using nanomechanical resonators,” Phys. Rev. Lett. 98, 254505 (2007).
[Crossref]

El-Jallal, S.

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

Ellis, B.

Fan, L.

L. Fan, X. Sun, C. Xiong, C. Schuck, H. X. Tang, “Aluminum nitride piezo-acousto-photonic crystal nanocavity with high quality factors,” Appl. Phys. Lett. 102, 153507 (2013).
[Crossref]

Favero, I.

C. Baker, W. Hease, D.-T. Nguyen, A. Andronico, S. Ducci, G. Leo, I. Favero, “Photoelastic coupling in gallium arsenide optomechanical disk resonators,” Opt. Express 22, 14072–14086 (2014).
[Crossref]

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

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

Freeman, M. R.

M. Wu, A. C. Hryciw, C. Healey, D. P. Lake, H. Jayakumar, M. R. Freeman, J. P. Davis, P. E. Barclay, “Dissipative and dispersive optomechanics in a nanocavity torque sensor,” Phys. Rev. X 4, 021052 (2014).
[Crossref]

S. C. Masmanidis, R. B. Karabalin, I. De Vlaminck, G. Borghs, M. R. Freeman, M. L. Roukes, “Multifunctional nanomechanical systems via tunably coupled piezoelectric actuation,” Science 317, 780–783 (2007).
[Crossref]

Gazalet, J.

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J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101, 081115 (2012).
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J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101, 081115 (2012).
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H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013).

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K. Srinivasan, M. Borselli, T. J. Johnson, P. E. Barclay, O. Painter, A. Stintz, S. Krishna, “Optical loss and lasing characteristics of high-quality-factor AlGaAs microdisk resonators with embedded quantum dots,” Appl. Phys. Lett. 86, 151106 (2005).
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L. Fan, X. Sun, C. Xiong, C. Schuck, H. X. Tang, “Aluminum nitride piezo-acousto-photonic crystal nanocavity with high quality factors,” Appl. Phys. Lett. 102, 153507 (2013).
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G. Bahl, J. Zehnpfennig, M. Tomes, T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403 (2011).
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Phys. Rev. Lett. (4)

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Supplementary Material (1)

» Supplement 1: PDF (1688 KB)     

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Figures (6)

Fig. 1.
Fig. 1. GaAs microdisk optomechanical resonators; (a) scanning electron microscope image of a fabricated device, and finite-element method simulations of the optical ( TE 1 , 7 ) and mechanical mode (1.4 GHz radial breathing mode), in a R = 1 μm microdisk; (b) experimental setup for measuring the optomechanical coupling; APD, avalanche photodiode; EOPM, electrooptic phase modulator; (c) optical transmission spectrum for the TE 1 , 25 mode, in a R = 2.85 μm radius device; (d) thermal noise spectrum for the 490 MHz radial breathing mode, shown together with the Lorentzian fit (red), and the phase modulator calibration peak.
Fig. 2.
Fig. 2. Optomechanical coupling rate g 0 , as a function of radius R , for coupling between the TE 1 , m optical modes and fundamental radial breathing mechanical modes. Red, blue, and green curves are the calculated total coupling rate ( MB + PE ), MB contribution, and PE contribution, respectively. Dashed black line is a rough estimate g 0 = ( ω o / R ) x zpf , where ω o is the optical frequency, and x zpf is the zero-point motion amplitude. Black circles are experimental values, where the error bars are dominated by uncertainty in the modulator V π , and are 1 standard deviation values. Inset gives the measured mechanical frequency and Q m .
Fig. 3.
Fig. 3. GaAs nanobeam optomechanical crystal designs, with (a)–(d) showing results for a circular hole geometry and (e)–(h) showing results for an elliptical hole geometry. (a) Circular hole geometry design; (b) circular hole geometry variation in design parameters as a function of hole number; (c) circular hole geometry normalized electric field amplitude; (d) circular hole geometry normalized mechanical displacement; (e) elliptical hole geometry design; (f) elliptical hole geometry variation in design parameters as a function of hole number; (g) elliptical hole geometry normalized electric field amplitude; and (h) elliptical hole geometry normalized mechanical displacement.
Fig. 4.
Fig. 4. (a) Parameters for GaAs and Si nanobeam optomechanical crystal designs, including Young’s modulus along [100], mechanical mode frequency, optical wavelength, g 0 , MB , g 0 , PE (nanobeam long axis oriented along the [100] direction), zero-point motional amplitude, and effective motional mass; (b) dependence of g 0 , PE for the GaAs and Si elliptical designs on in-plane rotational angle; (c) breakdown of g 0 , PE , into p 11 + p 44 (top) and p 12 (bottom) terms.
Fig. 5.
Fig. 5. GaAs nanobeam optomechanical crystal measurements; (a) scanning electron microscope image of an array of fabricated devices, where the orientation of the nanobeam long axis is varied between [110] and [100]. Right image is zoomed-in on a single nanobeam cavity, aligned along the [110] axis; (b) thermal noise spectrum (blue curve) and Lorentzian fit (red curve), for a nanobeam breathing mode, when the device is aligned along the [110] axis. The phase modulator calibration approach is used to extract the optomechanical coupling rate g 0 / 2 π = 1.12 MHz ± 0.06 MHz . Inset shows the transmission spectrum (blue) and fit (red) for the nanobeam optical mode; (c) thermal noise spectrum (blue curve) and Lorentzian fit (red curve), for a nanobeam breathing mode, when the device is aligned along the [100] axis. The phase modulator calibration approach is used to extract the optomechanical coupling rate g 0 / 2 π = 870 kHz ± 45 kHz . Inset shows the transmission spectrum (blue) and fit (red) for the nanobeam optical mode. Uncertainty values in g 0 are dominated by uncertainty in the modulator V π , and are 1 standard deviation values.
Fig. 6.
Fig. 6. (a) Mechanical mode spectra, as a function of increasing optical power injected into a GaAs nanobeam optomechanical crystal, aligned along the [100] axis, showing a pronounced linewidth narrowing and peak height increase; (b) mechanical mode peak amplitude as a function of injected optical power, showing a clear threshold behavior, indicative of the system being driven into regenerative mechanical oscillation. Uncertainty in the peak amplitude is less than the data point size.

Equations (3)

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g 0 , MB = ω 0 2 A d A ( Q · n ^ ) ( Δ ϵ | E | | | 2 Δ ϵ 1 | D | 2 ) d V ϵ | E | 2 ,
g 0 , PE = ω 0 ϵ 0 n 4 2 d V ( | E | 2 ( p 11 S x x + p 12 ( S y y + S z z ) ) d V ϵ | E | 2 ω 0 ϵ 0 n 4 2 d V ( | E | 2 4 Re ( E x * E y ) p 44 S x y ) d V ϵ | E | 2 ,
g 0 2 = Ω m 2 k B T Ω m 2 β pm 2 S cav ( Ω m ) S pm ( Ω mod ) ,

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