Abstract

Gallium phosphide offers an attractive combination of a high refractive index (n>3 for vacuum wavelengths up to 4 μm) and a wide electronic bandgap (2.26 eV), enabling optical cavities with small mode volumes and low two-photon absorption at telecommunication wavelengths. Heating due to strongly confined light fields is therefore greatly reduced. Here, we investigate the benefits of these properties for cavity optomechanics. Utilizing a recently developed fabrication scheme based on direct wafer bonding, we realize integrated one-dimensional photonic crystal cavities made of gallium phosphide with optical quality factors as high as 1.1×105. We optimize their design to couple the optical eigenmode at 200THz via radiation pressure to a co-localized mechanical mode with a frequency of 3 GHz, yielding sideband-resolved devices. The high vacuum optomechanical coupling rate (g0=2π×400kHz) permits amplification of the mechanical mode into the so-called mechanical lasing regime with input power as low as 20μW. The observation of mechanical lasing implies a multiphoton cooperativity of C>1, an important threshold for the realization of quantum state transfer protocols. Because of the reduced thermo-optic resonance shift, optomechanically induced transparency can be detected at room temperature even in non-sideband-resolved devices in addition to the normally observed optomechanically induced absorption. Considering that GaP is also piezoelectric, these results establish GaP as an attractive material for future electro–opto-mechanical systems.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (4)

L. Midolo, A. Schliesser, and A. Fiore, “Nano-opto-electro-mechanical systems,” Nat. Nanotechnol. 13, 11–18 (2018).
[Crossref]

K. Schneider, P. Welter, Y. Baumgartner, H. Hahn, L. Czornomaz, and P. Seidler, “Gallium phosphide-on-silicon dioxide photonic devices,” J. Lightwave Technol. 36, 2994–3002 (2018).
[Crossref]

S. Hönl, H. Hahn, Y. Baumgartner, L. Czornomaz, and P. Seidler, “Highly selective dry etching of GaP in the presence of AlxGa1-xP with a SiCl4/SF6 plasma,” J. Phys. D 51, 1–21 (2018).
[Crossref]

M. H. P. Pfeiffer, J. Liu, A. S. Raja, T. Morais, B. Ghadiani, and T. J. Kippenberg, “Ultra-smooth silicon nitride waveguides based on the Damascene reflow process: fabrication and loss origins,” Optica 5, 884–892 (2018).
[Crossref]

2017 (1)

K. Schneider, P. Welter, S. Hönl, H. Hahn, L. Czornomaz, Y. Baumgartner, and P. F. Seidler, “Optomechanics with one-dimensional gallium phosphide photonic crystal cavities,” Proc. SPIE 10359, 103590K (2017).
[Crossref]

2016 (3)

2015 (2)

2014 (6)

M. Mitchell, A. C. Hryciw, and P. E. Barclay, “Cavity optomechanics in gallium phosphide microdisks,” Appl. Phys. Lett. 104, 141104 (2014).
[Crossref]

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10, 321–326 (2014).
[Crossref]

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref]

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

K. C. Balram, M. Davanço, J. Y. Lim, J. D. Song, and K. Srinivasan, “Moving boundary and photoelastic coupling in GaAs optomechanical resonators,” Optica 1, 414–420 (2014).
[Crossref]

M. Aspelmeyer, F. Marquardt, and T. J. Kippenberg, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
[Crossref]

2013 (4)

P. Rath, S. Khasminskaya, C. Nebel, C. Wild, and W. H. P. Pernice, “Diamond-integrated optomechanical circuits,” Nat. Commun. 4, 1690–1699 (2013).
[Crossref]

P. Seidler, K. Lister, U. Drechsler, H. Rothuizen, J. Hofrichter, and T. Stöferle, “Photonic crystal nanobeam cavities with an ultrahigh quality factor-to-modal volume ratio,” Opt. Express 21, 32468–32483 (2013).
[Crossref]

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

S. Etaki, F. Konschelle, Y. M. Blanter, H. Yamaguchi, and H. S. J. Van Der Zant, “Self-sustained oscillations of a torsional SQUID resonator induced by Lorentz-force back-action,” Nat. Commun. 4, 1803–1805 (2013).
[Crossref]

2012 (2)

2011 (2)

A. H. Safavi-Naeinii, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
[Crossref]

T. P. M. Alegre, A. Safavi-Naeini, M. Winger, and O. Painter, “Quasi-two-dimensional optomechanical crystals with a complete phononic bandgap,” Opt. Express 19, 5658–5669 (2011).
[Crossref]

2010 (4)

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref]

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104, 083901 (2010).
[Crossref]

M. L. Gorodetksy, A. Schliesser, G. Anetsberger, S. Deleglise, and T. J. Kippenberg, “Determination of the vacuum optomechanical coupling rate using frequency noise calibration,” Opt. Express 18, 23236–23246 (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]

2009 (1)

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

2008 (1)

K. Rivoire, A. Faraon, and J. Vučković, “Gallium phosphide photonic crystal nanocavities in the visible,” Appl. Phys. Lett. 93, 063103 (2008).
[Crossref]

2007 (1)

2005 (4)

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95, 033901 (2005).
[Crossref]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[Crossref]

P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal micresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005).
[Crossref]

M. Borselli, T. J. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13, 1515–1530 (2005).
[Crossref]

2002 (1)

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

2001 (1)

V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, “Parametric oscillatory instability in Fabry-Perot (FP) interferometer,” Phys. Lett. A 287, 331–338 (2001).
[Crossref]

1979 (1)

H. Yamashita, K. Fukui, S. Misawa, and S. Yoshida, “Optical properties of AlN epitaxial thin films in the vacuum ultraviolet region,” J. Appl. Phys. 50, 896–898 (1979).
[Crossref]

1965 (1)

W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
[Crossref]

1964 (1)

H. R. Philip and E. A. Taft, “Kramers-Kronig analysis of reflectance data for diamond,” Phys. Rev. 136, A1445–A1448 (1964).
[Crossref]

Alegre, T. P. M.

Aleksandrova, A.

Anderson, M.

D. J. Wilson, K. Schneider, S. Hoenl, M. Anderson, T. J. Kippenberg, and P. Seidler, “Gallium phosphide nonlinear photonics,” arXiv:1808.03554 (2018).

Andrews, R. W.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10, 321–326 (2014).
[Crossref]

Anetsberger, G.

Appel, J.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref]

Arcizet, O.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref]

Aspelmeyer, M.

M. Aspelmeyer, F. Marquardt, and T. J. Kippenberg, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
[Crossref]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity Optomechanics (Springer, 2014).

Ates, S.

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

Atikian, H. A.

Awschalom, D. D.

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

Bagci, T.

T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Usami, A. Schliesser, and E. S. Polzik, “Optical detection of radio waves through a nanomechanical transducer,” Nature 507, 81–85 (2014).
[Crossref]

Balram, K. C.

K. C. Balram, M. I. Davanço, J. D. Song, and K. Srinivasan, “Coherent coupling between radiofrequency, optical and acoustic waves in piezo- optomechanical circuits,” Nat. Photonics 10, 346–352 (2016).
[Crossref]

K. C. Balram, M. Davanço, J. Y. Lim, J. D. Song, and K. Srinivasan, “Moving boundary and photoelastic coupling in GaAs optomechanical resonators,” Optica 1, 414–420 (2014).
[Crossref]

Barclay, P. E.

Baumgartner, Y.

S. Hönl, H. Hahn, Y. Baumgartner, L. Czornomaz, and P. Seidler, “Highly selective dry etching of GaP in the presence of AlxGa1-xP with a SiCl4/SF6 plasma,” J. Phys. D 51, 1–21 (2018).
[Crossref]

K. Schneider, P. Welter, Y. Baumgartner, H. Hahn, L. Czornomaz, and P. Seidler, “Gallium phosphide-on-silicon dioxide photonic devices,” J. Lightwave Technol. 36, 2994–3002 (2018).
[Crossref]

K. Schneider, P. Welter, S. Hönl, H. Hahn, L. Czornomaz, Y. Baumgartner, and P. F. Seidler, “Optomechanics with one-dimensional gallium phosphide photonic crystal cavities,” Proc. SPIE 10359, 103590K (2017).
[Crossref]

Blanter, Y. M.

S. Etaki, F. Konschelle, Y. M. Blanter, H. Yamaguchi, and H. S. J. Van Der Zant, “Self-sustained oscillations of a torsional SQUID resonator induced by Lorentz-force back-action,” Nat. Commun. 4, 1803–1805 (2013).
[Crossref]

Bochmann, J.

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

Bond, W. L.

W. L. Bond, “Measurement of the refractive indices of several crystals,” J. Appl. Phys. 36, 1674–1677 (1965).
[Crossref]

Borselli, M.

Braginsky, V. B.

V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, “Parametric oscillatory instability in Fabry-Perot (FP) interferometer,” Phys. Lett. A 287, 331–338 (2001).
[Crossref]

Burek, M. J.

Camacho, R. M.

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

Carmon, T.

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95, 033901 (2005).
[Crossref]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[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]

A. H. Safavi-Naeinii, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
[Crossref]

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

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Chang, D. E.

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J. Phys. D (1)

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Nat. Commun. (2)

P. Rath, S. Khasminskaya, C. Nebel, C. Wild, and W. H. P. Pernice, “Diamond-integrated optomechanical circuits,” Nat. Commun. 4, 1690–1699 (2013).
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Nature (3)

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[Crossref]

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

A. H. Safavi-Naeinii, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
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P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal micresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005).
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[Crossref]

K. Schneider and P. Seidler, “Strong optomechanical coupling in a slotted photonic crystal nanobeam cavity with an ultrahigh quality factor-to-mode volume ratio,” Opt. Express 24, 13850–13865 (2016).
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Phys. Lett. A (1)

V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, “Parametric oscillatory instability in Fabry-Perot (FP) interferometer,” Phys. Lett. A 287, 331–338 (2001).
[Crossref]

Phys. Rev. (1)

H. R. Philip and E. A. Taft, “Kramers-Kronig analysis of reflectance data for diamond,” Phys. Rev. 136, A1445–A1448 (1964).
[Crossref]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (3)

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104, 083901 (2010).
[Crossref]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95, 033901 (2005).
[Crossref]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94, 223902 (2005).
[Crossref]

Proc. SPIE (1)

K. Schneider, P. Welter, S. Hönl, H. Hahn, L. Czornomaz, Y. Baumgartner, and P. F. Seidler, “Optomechanics with one-dimensional gallium phosphide photonic crystal cavities,” Proc. SPIE 10359, 103590K (2017).
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Science (1)

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
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D. J. Wilson, K. Schneider, S. Hoenl, M. Anderson, T. J. Kippenberg, and P. Seidler, “Gallium phosphide nonlinear photonics,” arXiv:1808.03554 (2018).

J. Chan, Laser Cooling of an Optomechanical Crystal Resonator to its Quantum Ground State of Motion (California Institute of Technology, 2012).

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Supplementary Material (1)

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Figures (8)

Fig. 1.
Fig. 1. Optimized device design obtained from finite-element simulations. (a) Dimensions of elliptical holes and unit cell. (b) Electric field y-component. The overlaid outline of the device structure is labeled with the dimensions optimized in the finite-element simulations. (c) Displacement profile of the mechanical breathing mode at 2.84 GHz. (d) Principal strain for the breathing mode. (e) Magnitude of the electric field. (b)–(e) are all for a plane passing through the middle of the PhCC, and the color scales are normalized.
Fig. 2.
Fig. 2. SEM images of a one-dimensional GaP PhCC. (a) Freestanding device with width and height of 542 nm and 300 nm, respectively. (b) Magnification of the central part of the PhCC showing smooth and straight sidewalls. (c) Device cross section before release, prepared by focused-ion-beam milling. False coloring indicates different materials.
Fig. 3.
Fig. 3. Schematic of the measurement apparatus. Dashed lines indicate optional equipment used for certain measurements. In the optical microscope image, the pink stripe is where 1.1μm of the underlying SiO2 layer has been removed by wet etching to release the PhCCs.
Fig. 4.
Fig. 4. Analysis of optical transmission measurements. (a) Spectrum of a PhCC with the highest measured optical quality factor Qo=(1.11±0.02)×105. (b) Dependence of Qo on the number of holes on each side of the PhCC. The green curve is a guide to the eye. (c) Transmission spectra of a device with 11 holes on each side for input powers ranging from 0.079 μW to 7.7 μW. (d) Increase of the optical quality factor with input power. (e) Dependence of the resonance frequency on dissipated power Pd. The red line is a linear fit to the data for dissipated power 0.55μW.
Fig. 5.
Fig. 5. Thermomechanical radio frequency spectrum of a device with 10 holes on each side. The two dominant modes are the accordion mode at 130 MHz and the breathing mode at 2.902 GHz. Simulated displacement profiles with a normalized color scale are shown for each mode. An expanded view of the breathing mode resonance is given in the inset.
Fig. 6.
Fig. 6. Power spectral density of the mechanical resonance near 2.9 GHz (left peak) and the calibration tone (right peak) used for determination of the vacuum optomechanical coupling rate g0.
Fig. 7.
Fig. 7. Measured VNA traces (blue dots) with fits to model (red curves). (a), (b) OMIA measurement with the laser control frequency blue-detuned from the optical resonance. (c), (d) OMIT measurement with the laser control frequency red-detuned from the optical resonance. The OMIA peak and OMIT dip in (b) and (d), respectively, are not evident in the broadband spectra (a) and (c) because of the limited number of data points.
Fig. 8.
Fig. 8. Dynamical radiation pressure backaction. (a), (b) Detuning-dependent optical stiffening and damping (blue dots are measured data; red curves are the prediction from the model, where the shaded area indicates uncertainty in g0 of ±2π×20kHz). (c), (d) Power-dependent optical stiffening and damping (blue dots are measured data; red lines are the prediction from the model). (e) Dramatic linewidth narrowing of the mechanical resonance with increasing input power, where the inset shows the peak power spectral density of the individual spectra. (f) Time-resolved transmission signal for 77 μW input power oscillating at a frequency of 2.91 GHz, i.e., mechanical resonance frequency. The non-sinusoidal shape is due to the optomechanical backaction becoming nonlinear. The signal is effectively low-pass filtered at this frequency by the 10 GHz bandwidth of the photodiode. (g) Radio frequency spectrum showing the fundamental mechanical resonance and its first harmonic.

Equations (2)

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δΩm=g02n¯cav(ΔocΩmκ2/4+(ΔocΩm)2+Δoc+Ωmκ2/4+(Δoc+Ωm)2),
Γopt=g02n¯cav(κκ2/4+(Δoc+Ωm)2κκ2/4+(ΔocΩm)2).