Abstract

Mechanical oscillators are at the heart of many sensor applications. Recently several groups have developed oscillators that are probed optically, fabricated from high-stress silicon nitride films. They exhibit outstanding force sensitivities of a few aN/Hz1/2 and can also be made highly reflective, for efficient detection. The optical read-out usually requires complex experimental setups, including positioning stages and bulky cavities, making them impractical for real applications. In this paper we propose a novel way of building fully integrated all-optical force sensors based on low-loss silicon nitride mechanical resonators with a photonic crystal reflector. We can circumvent previous limitations in stability and complexity by simulating a suspended focusing photonic crystal, purely made of silicon nitride. Our design allows for an all integrated sensor, built out of a single block that integrates a full Fabry-Pérot cavity, without the need for assembly or alignment. The presented simulations will allow for a radical simplification of sensors based on high-Q silicon nitride membranes. Our results comprise, to the best of our knowledge, the first simulations of a focusing mirror made from a mechanically suspended flat membrane with subwavelength thickness. Cavity lengths between a few hundred µm and mm should be directly realizable.

© 2017 Optical Society of America

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References

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2017 (1)

X. Chen, C. Chardin, K. Makles, C. Caër, S. Chua, R. Braive, I. Robert-Philip, T. Briant, P.-F. Cohadon, A. Heidmann, T. Jacqmin, and S. Deléglise, “High-finesse Fabry-Perot cavities with bidimensional Si3N4 photonic-crystal slabs,” Light Sci. Appl. 6, e16190 (2017).
[Crossref]

2016 (5)

R. A. Norte, J. P. Moura, and S. Gröblacher, “Mechanical resonators for quantum optomechanics experiments at room temperature,” Phys. Rev. Lett. 116, 147202 (2016).
[Crossref] [PubMed]

S. Bernard, C. Reinhardt, V. Dumont, Y.-A. Peter, and J. C. Sankey, “Precision resonance tuning and design of SiN photonic crystal reflectors,” Opt. Lett. 41, 5624–5627 (2016).
[Crossref] [PubMed]

S. M. Kamali, E. Arbabi, A. Arbabi, Y. Horie, and A. Faraon, “Highly tunable elastic dielectric metasurface lenses,” Laser Photonics Rev. 10, 1002–1008 (2016).
[Crossref]

A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photonics 3, 209–214 (2016).
[Crossref]

C. Reinhardt, T. Müller, A. Bourassa, and J. C. Sankey, “Ultralow-noise SiN trampoline MEMS for sensing and optomechanics,” Phys. Rev. X 6, 021001 (2016).

2015 (4)

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nature Commun. 6, 7069 (2015).
[Crossref]

Y. Wang, D. Stellinga, A. B. Klemm, C. P. Reardon, and T. F. Krauss, “Tunable optical filters based on silicon nitride high contrast gratings,” IEEE J. Sel. Top. Quantum Electron. 21, 2700706 (2015).

W. Wang, X. Gao, X. Fang, X. Li, H. Zhu, and Y. Wang, “Transmission properties of Fabry-Perot filter consisting of silicon-based high-contrast gratings,” IEEE Photon. J. 8, 6800614 (2015).

C. Stambaugh, H. Xu, U. Kemiktarak, J. Taylor, and J. Lawall, “From membrane-in-the-middle to mirror-in-the-middle with a high-reflectivity sub-wavelength grating,” Ann. Phys. 527, 81–88 (2015).
[Crossref]

2014 (2)

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

M. Metcalfe, “Applications of cavity optomechanics,” Appl. Phys. Rev. 1, 031105 (2014).
[Crossref]

2013 (1)

2012 (3)

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nature Photon. 6, 768–772 (2012).
[Crossref]

C. H. Bui, J. Zheng, S. W. Hoch, L. Y. T. Lee, J. G. E. Harris, and C. W. Wong, “High-reflectivity, high-Q micromechanical membranes via guided resonances for enhanced optomechanical coupling,” Appl. Phys. Lett. 100, 021110 (2012).
[Crossref]

A. Xuereb, C. Genes, and A. Dantan, “Strong Coupling and Long-Range Collective Interactions in Optomechanical Arrays,” Phys. Rev. Lett. 109, 223601 (2012).
[Crossref]

2011 (2)

J. Li, D. Fattal, M. Fiorentino, and R. G. Beausoleil, “Strong optical confinement between nonperiodic flat dielectric gratings,” Phys. Rev. Lett. 106, 193901 (2011).
[Crossref] [PubMed]

R. C. Rumpf, “Improved formulation of scattering matrices for semi-analytical methods that is consistent with convention,” Prog. Electromagn. Res. B 35, 241–261 (2011).
[Crossref]

2010 (2)

2009 (1)

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nature Phys. 5, 485–488 (2009).
[Crossref]

2006 (4)

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[Crossref] [PubMed]

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–74 (2006).
[Crossref] [PubMed]

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
[Crossref]

S. Boutami, B. B. Bakir, J.-L. Leclercq, X. Letartre, P. Rojo-Romeo, M. Garrigues, P. Viktorovitch, I. Sagnes, L. Legratiet, and M. Strassner, “Highly selective and compact tunable MOEMS photonic crystal Fabry-Perot filter,” Opt. Express 14, 3129–3137 (2006).
[Crossref] [PubMed]

2005 (1)

S. Feng, Z.-Y. Li, Z.-F. Feng, K. Ren, B.-Y. Cheng, and D.-Z. Zhang, “Focusing properties of a rectangular-rod photonic-crystal slab,” J. Appl. Phys. 98, 063102 (2005).
[Crossref]

2004 (1)

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 µm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004).
[Crossref]

2003 (1)

1981 (1)

Arbabi, A.

S. M. Kamali, E. Arbabi, A. Arbabi, Y. Horie, and A. Faraon, “Highly tunable elastic dielectric metasurface lenses,” Laser Photonics Rev. 10, 1002–1008 (2016).
[Crossref]

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nature Commun. 6, 7069 (2015).
[Crossref]

Arbabi, E.

S. M. Kamali, E. Arbabi, A. Arbabi, Y. Horie, and A. Faraon, “Highly tunable elastic dielectric metasurface lenses,” Laser Photonics Rev. 10, 1002–1008 (2016).
[Crossref]

Arcizet, O.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–74 (2006).
[Crossref] [PubMed]

L. M. de Lépinay, B. Pigeau, B. Besga, P. Vincent, P. Poncharal, and O. Arcizet, “A universal and ultrasensitive vectorial nanomechanical sensor for imaging 2D force fields,” Nature Nanotechnol. p. AOP (2016).

Aspelmeyer, M.

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

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nature Phys. 5, 485–488 (2009).
[Crossref]

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[Crossref] [PubMed]

Bagheri, M.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nature Commun. 6, 7069 (2015).
[Crossref]

Bakir, B. B.

Ball, A. J.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nature Commun. 6, 7069 (2015).
[Crossref]

Bäuerle, D.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[Crossref] [PubMed]

Beausoleil, R. G.

J. Li, D. Fattal, M. Fiorentino, and R. G. Beausoleil, “Strong optical confinement between nonperiodic flat dielectric gratings,” Phys. Rev. Lett. 106, 193901 (2011).
[Crossref] [PubMed]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nature Photon. 4, 466–470 (2010).
[Crossref]

Bernard, S.

Besga, B.

L. M. de Lépinay, B. Pigeau, B. Besga, P. Vincent, P. Poncharal, and O. Arcizet, “A universal and ultrasensitive vectorial nanomechanical sensor for imaging 2D force fields,” Nature Nanotechnol. p. AOP (2016).

Blaser, F.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[Crossref] [PubMed]

Blasius, T. D.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nature Photon. 6, 768–772 (2012).
[Crossref]

Böhm, H. R.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[Crossref] [PubMed]

Bourassa, A.

C. Reinhardt, T. Müller, A. Bourassa, and J. C. Sankey, “Ultralow-noise SiN trampoline MEMS for sensing and optomechanics,” Phys. Rev. X 6, 021001 (2016).

Boutami, S.

Braive, R.

X. Chen, C. Chardin, K. Makles, C. Caër, S. Chua, R. Braive, I. Robert-Philip, T. Briant, P.-F. Cohadon, A. Heidmann, T. Jacqmin, and S. Deléglise, “High-finesse Fabry-Perot cavities with bidimensional Si3N4 photonic-crystal slabs,” Light Sci. Appl. 6, e16190 (2017).
[Crossref]

Briant, T.

X. Chen, C. Chardin, K. Makles, C. Caër, S. Chua, R. Braive, I. Robert-Philip, T. Briant, P.-F. Cohadon, A. Heidmann, T. Jacqmin, and S. Deléglise, “High-finesse Fabry-Perot cavities with bidimensional Si3N4 photonic-crystal slabs,” Light Sci. Appl. 6, e16190 (2017).
[Crossref]

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–74 (2006).
[Crossref] [PubMed]

Bui, C. H.

C. H. Bui, J. Zheng, S. W. Hoch, L. Y. T. Lee, J. G. E. Harris, and C. W. Wong, “High-reflectivity, high-Q micromechanical membranes via guided resonances for enhanced optomechanical coupling,” Appl. Phys. Lett. 100, 021110 (2012).
[Crossref]

Caër, C.

X. Chen, C. Chardin, K. Makles, C. Caër, S. Chua, R. Braive, I. Robert-Philip, T. Briant, P.-F. Cohadon, A. Heidmann, T. Jacqmin, and S. Deléglise, “High-finesse Fabry-Perot cavities with bidimensional Si3N4 photonic-crystal slabs,” Light Sci. Appl. 6, e16190 (2017).
[Crossref]

Chang-Hasnain, C. J.

F. Lu, F. G. Sedgwick, V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Planar high-numerical-aperture low-loss focusing reflectors and lenses using subwavelength high contrast gratings,” Opt. Express 18, 12606–12614 (2010).
[Crossref] [PubMed]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 µm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004).
[Crossref]

Chardin, C.

X. Chen, C. Chardin, K. Makles, C. Caër, S. Chua, R. Braive, I. Robert-Philip, T. Briant, P.-F. Cohadon, A. Heidmann, T. Jacqmin, and S. Deléglise, “High-finesse Fabry-Perot cavities with bidimensional Si3N4 photonic-crystal slabs,” Light Sci. Appl. 6, e16190 (2017).
[Crossref]

Chase, C.

Chen, L.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 µm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004).
[Crossref]

Chen, X.

X. Chen, C. Chardin, K. Makles, C. Caër, S. Chua, R. Braive, I. Robert-Philip, T. Briant, P.-F. Cohadon, A. Heidmann, T. Jacqmin, and S. Deléglise, “High-finesse Fabry-Perot cavities with bidimensional Si3N4 photonic-crystal slabs,” Light Sci. Appl. 6, e16190 (2017).
[Crossref]

Cheng, B.-Y.

S. Feng, Z.-Y. Li, Z.-F. Feng, K. Ren, B.-Y. Cheng, and D.-Z. Zhang, “Focusing properties of a rectangular-rod photonic-crystal slab,” J. Appl. Phys. 98, 063102 (2005).
[Crossref]

Chua, S.

X. Chen, C. Chardin, K. Makles, C. Caër, S. Chua, R. Braive, I. Robert-Philip, T. Briant, P.-F. Cohadon, A. Heidmann, T. Jacqmin, and S. Deléglise, “High-finesse Fabry-Perot cavities with bidimensional Si3N4 photonic-crystal slabs,” Light Sci. Appl. 6, e16190 (2017).
[Crossref]

Cohadon, P.-F.

X. Chen, C. Chardin, K. Makles, C. Caër, S. Chua, R. Braive, I. Robert-Philip, T. Briant, P.-F. Cohadon, A. Heidmann, T. Jacqmin, and S. Deléglise, “High-finesse Fabry-Perot cavities with bidimensional Si3N4 photonic-crystal slabs,” Light Sci. Appl. 6, e16190 (2017).
[Crossref]

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–74 (2006).
[Crossref] [PubMed]

Colburn, S.

A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photonics 3, 209–214 (2016).
[Crossref]

Crozier, K. B.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
[Crossref]

Dantan, A.

A. Xuereb, C. Genes, and A. Dantan, “Strong Coupling and Long-Range Collective Interactions in Optomechanical Arrays,” Phys. Rev. Lett. 109, 223601 (2012).
[Crossref]

de Lépinay, L. M.

L. M. de Lépinay, B. Pigeau, B. Besga, P. Vincent, P. Poncharal, and O. Arcizet, “A universal and ultrasensitive vectorial nanomechanical sensor for imaging 2D force fields,” Nature Nanotechnol. p. AOP (2016).

Deléglise, S.

X. Chen, C. Chardin, K. Makles, C. Caër, S. Chua, R. Braive, I. Robert-Philip, T. Briant, P.-F. Cohadon, A. Heidmann, T. Jacqmin, and S. Deléglise, “High-finesse Fabry-Perot cavities with bidimensional Si3N4 photonic-crystal slabs,” Light Sci. Appl. 6, e16190 (2017).
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Fan, S.

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D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nature Photon. 4, 466–470 (2010).
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A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photonics 3, 209–214 (2016).
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R. A. Norte, J. P. Moura, and S. Gröblacher, “Mechanical resonators for quantum optomechanics experiments at room temperature,” Phys. Rev. Lett. 116, 147202 (2016).
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S. Gröblacher, J. B. Hertzberg, M. R. Vanner, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nature Phys. 5, 485–488 (2009).
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S. M. Kamali, E. Arbabi, A. Arbabi, Y. Horie, and A. Faraon, “Highly tunable elastic dielectric metasurface lenses,” Laser Photonics Rev. 10, 1002–1008 (2016).
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A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nature Commun. 6, 7069 (2015).
[Crossref]

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C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 µm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004).
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Jacqmin, T.

X. Chen, C. Chardin, K. Makles, C. Caër, S. Chua, R. Braive, I. Robert-Philip, T. Briant, P.-F. Cohadon, A. Heidmann, T. Jacqmin, and S. Deléglise, “High-finesse Fabry-Perot cavities with bidimensional Si3N4 photonic-crystal slabs,” Light Sci. Appl. 6, e16190 (2017).
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J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Second Edition) (Princeton University, 2008).

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S. M. Kamali, E. Arbabi, A. Arbabi, Y. Horie, and A. Faraon, “Highly tunable elastic dielectric metasurface lenses,” Laser Photonics Rev. 10, 1002–1008 (2016).
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Kemiktarak, U.

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K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
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K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
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M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391 (2014). -
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Klemm, A. B.

Y. Wang, D. Stellinga, A. B. Klemm, C. P. Reardon, and T. F. Krauss, “Tunable optical filters based on silicon nitride high contrast gratings,” IEEE J. Sel. Top. Quantum Electron. 21, 2700706 (2015).

A. B. Klemm, D. Stellinga, E. R. Martins, L. Lewis, G. Huyet, L. O’Faolain, and T. F. Krauss, “Experimental high numerical aperture focusing with high contrast gratings,” Opt. Lett. 38, 3410 (2013).
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Krause, A. G.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nature Photon. 6, 768–772 (2012).
[Crossref]

Krauss, T. F.

Y. Wang, D. Stellinga, A. B. Klemm, C. P. Reardon, and T. F. Krauss, “Tunable optical filters based on silicon nitride high contrast gratings,” IEEE J. Sel. Top. Quantum Electron. 21, 2700706 (2015).

A. B. Klemm, D. Stellinga, E. R. Martins, L. Lewis, G. Huyet, L. O’Faolain, and T. F. Krauss, “Experimental high numerical aperture focusing with high contrast gratings,” Opt. Lett. 38, 3410 (2013).
[Crossref] [PubMed]

Langer, G.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[Crossref] [PubMed]

Lawall, J.

C. Stambaugh, H. Xu, U. Kemiktarak, J. Taylor, and J. Lawall, “From membrane-in-the-middle to mirror-in-the-middle with a high-reflectivity sub-wavelength grating,” Ann. Phys. 527, 81–88 (2015).
[Crossref]

Leclercq, J. L.

Leclercq, J.-L.

Lee, L. Y. T.

C. H. Bui, J. Zheng, S. W. Hoch, L. Y. T. Lee, J. G. E. Harris, and C. W. Wong, “High-reflectivity, high-Q micromechanical membranes via guided resonances for enhanced optomechanical coupling,” Appl. Phys. Lett. 100, 021110 (2012).
[Crossref]

Legratiet, L.

Letartre, X.

Lewis, L.

Li, J.

J. Li, D. Fattal, M. Fiorentino, and R. G. Beausoleil, “Strong optical confinement between nonperiodic flat dielectric gratings,” Phys. Rev. Lett. 106, 193901 (2011).
[Crossref] [PubMed]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nature Photon. 4, 466–470 (2010).
[Crossref]

Li, X.

W. Wang, X. Gao, X. Fang, X. Li, H. Zhu, and Y. Wang, “Transmission properties of Fabry-Perot filter consisting of silicon-based high-contrast gratings,” IEEE Photon. J. 8, 6800614 (2015).

Li, Z.-Y.

S. Feng, Z.-Y. Li, Z.-F. Feng, K. Ren, B.-Y. Cheng, and D.-Z. Zhang, “Focusing properties of a rectangular-rod photonic-crystal slab,” J. Appl. Phys. 98, 063102 (2005).
[Crossref]

Lin, Q.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nature Photon. 6, 768–772 (2012).
[Crossref]

Lousse, V.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
[Crossref]

Lu, F.

Majumdar, A.

A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photonics 3, 209–214 (2016).
[Crossref]

Makles, K.

X. Chen, C. Chardin, K. Makles, C. Caër, S. Chua, R. Braive, I. Robert-Philip, T. Briant, P.-F. Cohadon, A. Heidmann, T. Jacqmin, and S. Deléglise, “High-finesse Fabry-Perot cavities with bidimensional Si3N4 photonic-crystal slabs,” Light Sci. Appl. 6, e16190 (2017).
[Crossref]

Marquardt, F.

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

Martins, E. R.

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 µm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004).
[Crossref]

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J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Second Edition) (Princeton University, 2008).

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C. Reinhardt, T. Müller, A. Bourassa, and J. C. Sankey, “Ultralow-noise SiN trampoline MEMS for sensing and optomechanics,” Phys. Rev. X 6, 021001 (2016).

Norte, R. A.

R. A. Norte, J. P. Moura, and S. Gröblacher, “Mechanical resonators for quantum optomechanics experiments at room temperature,” Phys. Rev. Lett. 116, 147202 (2016).
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O’Faolain, L.

Painter, O.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nature Photon. 6, 768–772 (2012).
[Crossref]

Paternostro, M.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[Crossref] [PubMed]

Peng, Z.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nature Photon. 4, 466–470 (2010).
[Crossref]

Peter, Y.-A.

Pigeau, B.

L. M. de Lépinay, B. Pigeau, B. Besga, P. Vincent, P. Poncharal, and O. Arcizet, “A universal and ultrasensitive vectorial nanomechanical sensor for imaging 2D force fields,” Nature Nanotechnol. p. AOP (2016).

Pinard, M.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–74 (2006).
[Crossref] [PubMed]

Poncharal, P.

L. M. de Lépinay, B. Pigeau, B. Besga, P. Vincent, P. Poncharal, and O. Arcizet, “A universal and ultrasensitive vectorial nanomechanical sensor for imaging 2D force fields,” Nature Nanotechnol. p. AOP (2016).

Reardon, C. P.

Y. Wang, D. Stellinga, A. B. Klemm, C. P. Reardon, and T. F. Krauss, “Tunable optical filters based on silicon nitride high contrast gratings,” IEEE J. Sel. Top. Quantum Electron. 21, 2700706 (2015).

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C. Reinhardt, T. Müller, A. Bourassa, and J. C. Sankey, “Ultralow-noise SiN trampoline MEMS for sensing and optomechanics,” Phys. Rev. X 6, 021001 (2016).

S. Bernard, C. Reinhardt, V. Dumont, Y.-A. Peter, and J. C. Sankey, “Precision resonance tuning and design of SiN photonic crystal reflectors,” Opt. Lett. 41, 5624–5627 (2016).
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S. Feng, Z.-Y. Li, Z.-F. Feng, K. Ren, B.-Y. Cheng, and D.-Z. Zhang, “Focusing properties of a rectangular-rod photonic-crystal slab,” J. Appl. Phys. 98, 063102 (2005).
[Crossref]

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X. Chen, C. Chardin, K. Makles, C. Caër, S. Chua, R. Braive, I. Robert-Philip, T. Briant, P.-F. Cohadon, A. Heidmann, T. Jacqmin, and S. Deléglise, “High-finesse Fabry-Perot cavities with bidimensional Si3N4 photonic-crystal slabs,” Light Sci. Appl. 6, e16190 (2017).
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C. Reinhardt, T. Müller, A. Bourassa, and J. C. Sankey, “Ultralow-noise SiN trampoline MEMS for sensing and optomechanics,” Phys. Rev. X 6, 021001 (2016).

S. Bernard, C. Reinhardt, V. Dumont, Y.-A. Peter, and J. C. Sankey, “Precision resonance tuning and design of SiN photonic crystal reflectors,” Opt. Lett. 41, 5624–5627 (2016).
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S. Gröblacher, J. B. Hertzberg, M. R. Vanner, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nature Phys. 5, 485–488 (2009).
[Crossref]

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[Crossref] [PubMed]

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Sedgwick, F. G.

Solgaard, O.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
[Crossref]

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C. Stambaugh, H. Xu, U. Kemiktarak, J. Taylor, and J. Lawall, “From membrane-in-the-middle to mirror-in-the-middle with a high-reflectivity sub-wavelength grating,” Ann. Phys. 527, 81–88 (2015).
[Crossref]

Stellinga, D.

Y. Wang, D. Stellinga, A. B. Klemm, C. P. Reardon, and T. F. Krauss, “Tunable optical filters based on silicon nitride high contrast gratings,” IEEE J. Sel. Top. Quantum Electron. 21, 2700706 (2015).

A. B. Klemm, D. Stellinga, E. R. Martins, L. Lewis, G. Huyet, L. O’Faolain, and T. F. Krauss, “Experimental high numerical aperture focusing with high contrast gratings,” Opt. Lett. 38, 3410 (2013).
[Crossref] [PubMed]

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Suzuki, Y.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62 µm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004).
[Crossref]

Taylor, J.

C. Stambaugh, H. Xu, U. Kemiktarak, J. Taylor, and J. Lawall, “From membrane-in-the-middle to mirror-in-the-middle with a high-reflectivity sub-wavelength grating,” Ann. Phys. 527, 81–88 (2015).
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A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photonics 3, 209–214 (2016).
[Crossref]

Vanner, M. R.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nature Phys. 5, 485–488 (2009).
[Crossref]

Viktorovitch, P.

Vincent, P.

L. M. de Lépinay, B. Pigeau, B. Besga, P. Vincent, P. Poncharal, and O. Arcizet, “A universal and ultrasensitive vectorial nanomechanical sensor for imaging 2D force fields,” Nature Nanotechnol. p. AOP (2016).

Wang, W.

W. Wang, X. Gao, X. Fang, X. Li, H. Zhu, and Y. Wang, “Transmission properties of Fabry-Perot filter consisting of silicon-based high-contrast gratings,” IEEE Photon. J. 8, 6800614 (2015).

Wang, Y.

Y. Wang, D. Stellinga, A. B. Klemm, C. P. Reardon, and T. F. Krauss, “Tunable optical filters based on silicon nitride high contrast gratings,” IEEE J. Sel. Top. Quantum Electron. 21, 2700706 (2015).

W. Wang, X. Gao, X. Fang, X. Li, H. Zhu, and Y. Wang, “Transmission properties of Fabry-Perot filter consisting of silicon-based high-contrast gratings,” IEEE Photon. J. 8, 6800614 (2015).

Winger, M.

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nature Photon. 6, 768–772 (2012).
[Crossref]

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J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Second Edition) (Princeton University, 2008).

Wong, C. W.

C. H. Bui, J. Zheng, S. W. Hoch, L. Y. T. Lee, J. G. E. Harris, and C. W. Wong, “High-reflectivity, high-Q micromechanical membranes via guided resonances for enhanced optomechanical coupling,” Appl. Phys. Lett. 100, 021110 (2012).
[Crossref]

Xu, H.

C. Stambaugh, H. Xu, U. Kemiktarak, J. Taylor, and J. Lawall, “From membrane-in-the-middle to mirror-in-the-middle with a high-reflectivity sub-wavelength grating,” Ann. Phys. 527, 81–88 (2015).
[Crossref]

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A. Xuereb, C. Genes, and A. Dantan, “Strong Coupling and Long-Range Collective Interactions in Optomechanical Arrays,” Phys. Rev. Lett. 109, 223601 (2012).
[Crossref]

Zeilinger, A.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444, 67–70 (2006).
[Crossref] [PubMed]

Zhan, A.

A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photonics 3, 209–214 (2016).
[Crossref]

Zhang, D.-Z.

S. Feng, Z.-Y. Li, Z.-F. Feng, K. Ren, B.-Y. Cheng, and D.-Z. Zhang, “Focusing properties of a rectangular-rod photonic-crystal slab,” J. Appl. Phys. 98, 063102 (2005).
[Crossref]

Zheng, J.

C. H. Bui, J. Zheng, S. W. Hoch, L. Y. T. Lee, J. G. E. Harris, and C. W. Wong, “High-reflectivity, high-Q micromechanical membranes via guided resonances for enhanced optomechanical coupling,” Appl. Phys. Lett. 100, 021110 (2012).
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Figures (3)

Fig. 1
Fig. 1

(a) Photonic crystal reflector. Air holes are repeated in the direction of ê1 and ê2, forming a hexagonal lattice. (b) Reflectivity and phase simulated using RCWA. A phase shift of 0.7π is covered by an area with high reflectivity (reflectance >98%). In order to find the best design for our focusing PC, we chose the path highlighted with the white dashed line. The reflectivity in the deep blue area is not calculated, as it is <20%. (c) Final pattern constituting a focusing photonic crystal at 1064 nm.

Fig. 2
Fig. 2

(a) Electric field distribution of the reflected wave assuming an incoming Gaussian beam. The field is maximal between 400–500 µm distance. Electric field at different distance is shown in (b)–(e). Due to the finite size of the reflector, the reflected beam deviates from an ideal Gaussian distribution for large x. (f) Spot radius at different positions, extracted through Gaussian fitting. The minimum of the focused beam can be found around 475 µm, as expected from theory.

Fig. 3
Fig. 3

(a) Sketch of a cavity formed by a focusing photonic crystal membrane and a plane mirror. The membrane does not need to be precisely aligned to the center of the mirror, as is usually required for other types of optomechanical cavities. (b) Shown is the field intensity each time the intra-cavity field reaches the PC membrane, normalized to the energy of the initial input plane wave. The initial faster decay is due to higher order modes decaying quickly in the cavity, while the final slope represents the decay rate of the fundamental mode inside the cavity. (c) Calculated force noise spectrum at low frequency of an optomechanical cavity with a focusing PC membrane, assuming an ideal detector. Already for these very moderate input powers the sensitivity is expected to be well below the standard quantum limit. The bandwidth of such a sensor is limited by the mechanical oscillation frequency, in our case to 140 kHz.

Tables (1)

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Table 1 Performance of various focusing photonic crystal cavities assuming a fixed mirror with 99% reflectivity. All photonic crystal designs exhibit an average reflectivity of 96%, while the optical phase shift is around 0.8π.

Equations (5)

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ϕ tag ( x ) = 2 π λ ( f f 2 + | x | 2 ) + ϕ 0 ,
ϕ tag ( x n , m ) = ϕ ( x n , m ) = arg ( ( a n , m , ζ n , m ) ) ,
x n , m = x n , m 1 + a n 1 , m + a n , m 2 , y n , m = y n 1 , m + 3 2 a n , m 1 + a n , m 2 ,
z 0 = f 1 + ( f / z R ) 2 .
E ( x ) = 1 4 π reflector d S exp ( i k ( x x ) ) | x x | [ i k z E ( x ) + E ( x ) z ] ,

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