Abstract

Spatial light modulators (SLMs) are central to numerous applications ranging from high-speed displays to adaptive optics, structured illumination microscopy, and holography. After decades of advances, SLM arrays based on liquid crystals can now reach large pixel counts exceeding $10^6$ with phase-only modulation with a pixel pitch of less than 10 µm and reflectance around 75%. However, the rather slow modulation speed in such SLMs (below hundreds of Hz) presents limitations for many applications. Here we propose an SLM architecture that can achieve two-dimensional phase-only modulation at high speed in excess of GHz. The architecture consists of a tunable two-dimensional array of vertically oriented, one-sided microcavities that are tuned through an electro-optic material such as barium titanate (BTO). We calculate that the optimized microcavity design achieves a $\pi$ phase shift under an applied bias voltage below 10 V, while maintaining nearly constant reflection amplitude. As two model applications, we consider high-speed 2D beam steering as well as beam forming. The outlined design methodology could also benefit future design of spatial light modulators with other specifications (for example amplitude modulators). This high-speed SLM architecture promises a wide range of new applications ranging from fully tunable metasurfaces to optical computing accelerators, high-speed interconnects, true 2D phased array beam steering, and quantum computing with cold atom arrays.

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

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2019 (4)

R. Hamerly, L. Bernstein, A. Sludds, M. Soljačić, and D. Englund, “Large-scale optical neural networks based on photoelectric multiplication,” Phys. Rev. X 9(2), 021032 (2019).
[Crossref]

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[Crossref]

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

D. Pierangeli, G. Marcucci, and C. Conti, “Large-scale photonic ising machine by spatial light modulation,” Phys. Rev. Lett. 122(21), 213902 (2019).
[Crossref]

2018 (2)

Y. Horie, A. Arbabi, E. Arbabi, S. M. Kamali, and A. Faraon, “High-speed, phase-dominant spatial light modulation with silicon-based active resonant antennas,” ACS Photonics 5(5), 1711–1717 (2018).
[Crossref]

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[Crossref]

2017 (4)

S. Colburn, A. Zhan, and A. Majumdar, “Tunable metasurfaces via subwavelength phase shifters with uniform amplitude,” Sci. Rep. 7(1), 40174 (2017).
[Crossref]

K. J. Kormondy, Y. Popoff, M. Sousa, F. Eltes, D. Caimi, M. D. Rossell, M. Fiebig, P. Hoffmann, C. Marchiori, M. Reinke, M. Trassin, A. A. Demkov, J. Fompeyrine, and S. Abel, “Microstructure and ferroelectricity of batio3 thin films on si for integrated photonics,” Nanotechnology 28(7), 075706 (2017).
[Crossref]

J. M. Kahn and D. A. Miller, “Communications expands its space,” Nat. Photonics 11(1), 5–8 (2017).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

2016 (2)

Y.-W. Huang, H. W. H. Lee, R. Sokhoyan, R. A. Pala, K. Thyagarajan, S. Han, D. P. Tsai, and H. A. Atwater, “Gate-tunable conducting oxide metasurfaces,” Nano Lett. 16(9), 5319–5325 (2016).
[Crossref]

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
[Crossref]

2014 (3)

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2d arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).
[Crossref]

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (lcos) devices,” Light: Sci. Appl. 3(10), e213 (2014).
[Crossref]

2013 (1)

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4(1), 1671 (2013).
[Crossref]

2010 (2)

D. Vettese, “Microdisplays: Liquid crystal on silicon,” Nat. Photonics 4(11), 752–754 (2010).
[Crossref]

B. Schwarz, “Lidar: Mapping the world in 3d,” Nat. Photonics 4(7), 429–430 (2010).
[Crossref]

2006 (1)

2005 (1)

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. Miller, and J. S. Harris, “Strong quantum-confined stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
[Crossref]

2003 (1)

W. M. Van Spengen, “Mems reliability from a failure mechanisms perspective,” Microelectron. Reliab. 43(7), 1049–1060 (2003).
[Crossref]

2001 (1)

A. Petraru, M. Siegert, M. Schmid, J. Schubert, and C. Buchal, “Ferroelectic batio 3 thin film optical waveguide modulators,” MRS Online Proc. Libr. Arch. 688, C8 (2001).

1982 (1)

Abel, S.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

K. J. Kormondy, Y. Popoff, M. Sousa, F. Eltes, D. Caimi, M. D. Rossell, M. Fiebig, P. Hoffmann, C. Marchiori, M. Reinke, M. Trassin, A. A. Demkov, J. Fompeyrine, and S. Abel, “Microstructure and ferroelectricity of batio3 thin films on si for integrated photonics,” Nanotechnology 28(7), 075706 (2017).
[Crossref]

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4(1), 1671 (2013).
[Crossref]

Arbabi, A.

Y. Horie, A. Arbabi, E. Arbabi, S. M. Kamali, and A. Faraon, “High-speed, phase-dominant spatial light modulation with silicon-based active resonant antennas,” ACS Photonics 5(5), 1711–1717 (2018).
[Crossref]

Arbabi, E.

Y. Horie, A. Arbabi, E. Arbabi, S. M. Kamali, and A. Faraon, “High-speed, phase-dominant spatial light modulation with silicon-based active resonant antennas,” ACS Photonics 5(5), 1711–1717 (2018).
[Crossref]

Atwater, H. A.

Y.-W. Huang, H. W. H. Lee, R. Sokhoyan, R. A. Pala, K. Thyagarajan, S. Han, D. P. Tsai, and H. A. Atwater, “Gate-tunable conducting oxide metasurfaces,” Nano Lett. 16(9), 5319–5325 (2016).
[Crossref]

Baeuerle, B.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

Barredo, D.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2d arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).
[Crossref]

Béguin, L.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2d arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).
[Crossref]

Bernien, H.

D. Kim, A. Keesling, A. Omran, H. Levine, H. Bernien, M. Greiner, M. D. Lukin, and D. R. Englund, “Large-scale uniform optical focus array generation with a phase spatial light modulator,” Opt. Lett. 44(12), 3178–3181 (2019).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

Bernstein, L.

R. Hamerly, L. Bernstein, A. Sludds, M. Soljačić, and D. Englund, “Large-scale optical neural networks based on photoelectric multiplication,” Phys. Rev. X 9(2), 021032 (2019).
[Crossref]

Browaeys, A.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2d arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).
[Crossref]

Buchal, C.

A. Petraru, M. Siegert, M. Schmid, J. Schubert, and C. Buchal, “Ferroelectic batio 3 thin film optical waveguide modulators,” MRS Online Proc. Libr. Arch. 688, C8 (2001).

Caimi, D.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

K. J. Kormondy, Y. Popoff, M. Sousa, F. Eltes, D. Caimi, M. D. Rossell, M. Fiebig, P. Hoffmann, C. Marchiori, M. Reinke, M. Trassin, A. A. Demkov, J. Fompeyrine, and S. Abel, “Microstructure and ferroelectricity of batio3 thin films on si for integrated photonics,” Nanotechnology 28(7), 075706 (2017).
[Crossref]

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4(1), 1671 (2013).
[Crossref]

Castera, P.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

Chelnokov, A.

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4(1), 1671 (2013).
[Crossref]

Choi, S.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

Chu, D.

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (lcos) devices,” Light: Sci. Appl. 3(10), e213 (2014).
[Crossref]

Colburn, S.

S. Colburn, A. Zhan, and A. Majumdar, “Tunable metasurfaces via subwavelength phase shifters with uniform amplitude,” Sci. Rep. 7(1), 40174 (2017).
[Crossref]

Conti, C.

D. Pierangeli, G. Marcucci, and C. Conti, “Large-scale photonic ising machine by spatial light modulation,” Phys. Rev. Lett. 122(21), 213902 (2019).
[Crossref]

Czornomaz, L.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

Demkov, A. A.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

K. J. Kormondy, Y. Popoff, M. Sousa, F. Eltes, D. Caimi, M. D. Rossell, M. Fiebig, P. Hoffmann, C. Marchiori, M. Reinke, M. Trassin, A. A. Demkov, J. Fompeyrine, and S. Abel, “Microstructure and ferroelectricity of batio3 thin films on si for integrated photonics,” Nanotechnology 28(7), 075706 (2017).
[Crossref]

Dudley, A.

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
[Crossref]

Dudley, D.

D. Dudley, W. M. Duncan, and J. Slaughter, “Emerging digital micromirror device (dmd) applications,” in MOEMS display and imaging systems, (International Society for Optics and Photonics, 2003), pp.14–26.

Duncan, W. M.

D. Dudley, W. M. Duncan, and J. Slaughter, “Emerging digital micromirror device (dmd) applications,” in MOEMS display and imaging systems, (International Society for Optics and Photonics, 2003), pp.14–26.

Eltes, F.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

K. J. Kormondy, Y. Popoff, M. Sousa, F. Eltes, D. Caimi, M. D. Rossell, M. Fiebig, P. Hoffmann, C. Marchiori, M. Reinke, M. Trassin, A. A. Demkov, J. Fompeyrine, and S. Abel, “Microstructure and ferroelectricity of batio3 thin films on si for integrated photonics,” Nanotechnology 28(7), 075706 (2017).
[Crossref]

Endres, M.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

Englund, D.

R. Hamerly, L. Bernstein, A. Sludds, M. Soljačić, and D. Englund, “Large-scale optical neural networks based on photoelectric multiplication,” Phys. Rev. X 9(2), 021032 (2019).
[Crossref]

Englund, D. R.

Erni, R.

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4(1), 1671 (2013).
[Crossref]

Faraon, A.

Y. Horie, A. Arbabi, E. Arbabi, S. M. Kamali, and A. Faraon, “High-speed, phase-dominant spatial light modulation with silicon-based active resonant antennas,” ACS Photonics 5(5), 1711–1717 (2018).
[Crossref]

Fiebig, M.

K. J. Kormondy, Y. Popoff, M. Sousa, F. Eltes, D. Caimi, M. D. Rossell, M. Fiebig, P. Hoffmann, C. Marchiori, M. Reinke, M. Trassin, A. A. Demkov, J. Fompeyrine, and S. Abel, “Microstructure and ferroelectricity of batio3 thin films on si for integrated photonics,” Nanotechnology 28(7), 075706 (2017).
[Crossref]

Fienup, J. R.

Fompeyrine, J.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
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K. J. Kormondy, Y. Popoff, M. Sousa, F. Eltes, D. Caimi, M. D. Rossell, M. Fiebig, P. Hoffmann, C. Marchiori, M. Reinke, M. Trassin, A. A. Demkov, J. Fompeyrine, and S. Abel, “Microstructure and ferroelectricity of batio3 thin films on si for integrated photonics,” Nanotechnology 28(7), 075706 (2017).
[Crossref]

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4(1), 1671 (2013).
[Crossref]

Forbes, A.

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
[Crossref]

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Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. Miller, and J. S. Harris, “Strong quantum-confined stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
[Crossref]

Greiner, M.

D. Kim, A. Keesling, A. Omran, H. Levine, H. Bernien, M. Greiner, M. D. Lukin, and D. R. Englund, “Large-scale uniform optical focus array generation with a phase spatial light modulator,” Opt. Lett. 44(12), 3178–3181 (2019).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

Gutierrez, A. M.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

Haellstig, E.

E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” in Laser Systems Technology, (International Society for Optics and Photonics, 2003), pp.13–23.

Hamerly, R.

R. Hamerly, L. Bernstein, A. Sludds, M. Soljačić, and D. Englund, “Large-scale optical neural networks based on photoelectric multiplication,” Phys. Rev. X 9(2), 021032 (2019).
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Y.-W. Huang, H. W. H. Lee, R. Sokhoyan, R. A. Pala, K. Thyagarajan, S. Han, D. P. Tsai, and H. A. Atwater, “Gate-tunable conducting oxide metasurfaces,” Nano Lett. 16(9), 5319–5325 (2016).
[Crossref]

Harris, J. S.

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. Miller, and J. S. Harris, “Strong quantum-confined stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
[Crossref]

Henderson, C. J.

Heni, W.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

Hoffmann, P.

K. J. Kormondy, Y. Popoff, M. Sousa, F. Eltes, D. Caimi, M. D. Rossell, M. Fiebig, P. Hoffmann, C. Marchiori, M. Reinke, M. Trassin, A. A. Demkov, J. Fompeyrine, and S. Abel, “Microstructure and ferroelectricity of batio3 thin films on si for integrated photonics,” Nanotechnology 28(7), 075706 (2017).
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Horie, Y.

Y. Horie, A. Arbabi, E. Arbabi, S. M. Kamali, and A. Faraon, “High-speed, phase-dominant spatial light modulation with silicon-based active resonant antennas,” ACS Photonics 5(5), 1711–1717 (2018).
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Huang, Y.-W.

Y.-W. Huang, H. W. H. Lee, R. Sokhoyan, R. A. Pala, K. Thyagarajan, S. Han, D. P. Tsai, and H. A. Atwater, “Gate-tunable conducting oxide metasurfaces,” Nano Lett. 16(9), 5319–5325 (2016).
[Crossref]

Hunt, J.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Jarrahi, M.

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science 361(6406), 1004–1008 (2018).
[Crossref]

Josten, A.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

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J. M. Kahn and D. A. Miller, “Communications expands its space,” Nat. Photonics 11(1), 5–8 (2017).
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Y. Horie, A. Arbabi, E. Arbabi, S. M. Kamali, and A. Faraon, “High-speed, phase-dominant spatial light modulation with silicon-based active resonant antennas,” ACS Photonics 5(5), 1711–1717 (2018).
[Crossref]

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Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. Miller, and J. S. Harris, “Strong quantum-confined stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
[Crossref]

Keesling, A.

D. Kim, A. Keesling, A. Omran, H. Levine, H. Bernien, M. Greiner, M. D. Lukin, and D. R. Englund, “Large-scale uniform optical focus array generation with a phase spatial light modulator,” Opt. Lett. 44(12), 3178–3181 (2019).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

Kim, D.

Kormondy, K. J.

K. J. Kormondy, Y. Popoff, M. Sousa, F. Eltes, D. Caimi, M. D. Rossell, M. Fiebig, P. Hoffmann, C. Marchiori, M. Reinke, M. Trassin, A. A. Demkov, J. Fompeyrine, and S. Abel, “Microstructure and ferroelectricity of batio3 thin films on si for integrated photonics,” Nanotechnology 28(7), 075706 (2017).
[Crossref]

Krishna, S.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Kuo, Y.-H.

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. Miller, and J. S. Harris, “Strong quantum-confined stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
[Crossref]

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F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2d arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).
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Lahaye, T.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2d arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).
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Lee, H. W. H.

Y.-W. Huang, H. W. H. Lee, R. Sokhoyan, R. A. Pala, K. Thyagarajan, S. Han, D. P. Tsai, and H. A. Atwater, “Gate-tunable conducting oxide metasurfaces,” Nano Lett. 16(9), 5319–5325 (2016).
[Crossref]

Lee, Y. K.

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. Miller, and J. S. Harris, “Strong quantum-confined stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
[Crossref]

Leuthold, J.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

Levine, H.

D. Kim, A. Keesling, A. Omran, H. Levine, H. Bernien, M. Greiner, M. D. Lukin, and D. R. Englund, “Large-scale uniform optical focus array generation with a phase spatial light modulator,” Opt. Lett. 44(12), 3178–3181 (2019).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

Leyva, D. G.

Lin, X.

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science 361(6406), 1004–1008 (2018).
[Crossref]

Lindgren, M.

E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” in Laser Systems Technology, (International Society for Optics and Photonics, 2003), pp.13–23.

Lipworth, G.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Lukin, M. D.

D. Kim, A. Keesling, A. Omran, H. Levine, H. Bernien, M. Greiner, M. D. Lukin, and D. R. Englund, “Large-scale uniform optical focus array generation with a phase spatial light modulator,” Opt. Lett. 44(12), 3178–3181 (2019).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

Luo, Y.

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science 361(6406), 1004–1008 (2018).
[Crossref]

Ma, P.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
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S. Colburn, A. Zhan, and A. Majumdar, “Tunable metasurfaces via subwavelength phase shifters with uniform amplitude,” Sci. Rep. 7(1), 40174 (2017).
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K. J. Kormondy, Y. Popoff, M. Sousa, F. Eltes, D. Caimi, M. D. Rossell, M. Fiebig, P. Hoffmann, C. Marchiori, M. Reinke, M. Trassin, A. A. Demkov, J. Fompeyrine, and S. Abel, “Microstructure and ferroelectricity of batio3 thin films on si for integrated photonics,” Nanotechnology 28(7), 075706 (2017).
[Crossref]

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4(1), 1671 (2013).
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Marcucci, G.

D. Pierangeli, G. Marcucci, and C. Conti, “Large-scale photonic ising machine by spatial light modulation,” Phys. Rev. Lett. 122(21), 213902 (2019).
[Crossref]

McLaren, M.

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
[Crossref]

Messner, A.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

Miller, D. A.

J. M. Kahn and D. A. Miller, “Communications expands its space,” Nat. Photonics 11(1), 5–8 (2017).
[Crossref]

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. Miller, and J. S. Harris, “Strong quantum-confined stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
[Crossref]

Montoya, J.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Nogrette, F.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2d arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).
[Crossref]

Offrein, B. J.

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4(1), 1671 (2013).
[Crossref]

Omran, A.

D. Kim, A. Keesling, A. Omran, H. Levine, H. Bernien, M. Greiner, M. D. Lukin, and D. R. Englund, “Large-scale uniform optical focus array generation with a phase spatial light modulator,” Opt. Lett. 44(12), 3178–3181 (2019).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

Ortmann, J. E.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

Ozcan, A.

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science 361(6406), 1004–1008 (2018).
[Crossref]

Padilla, W. J.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Pala, R. A.

Y.-W. Huang, H. W. H. Lee, R. Sokhoyan, R. A. Pala, K. Thyagarajan, S. Han, D. P. Tsai, and H. A. Atwater, “Gate-tunable conducting oxide metasurfaces,” Nano Lett. 16(9), 5319–5325 (2016).
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Petraru, A.

A. Petraru, M. Siegert, M. Schmid, J. Schubert, and C. Buchal, “Ferroelectic batio 3 thin film optical waveguide modulators,” MRS Online Proc. Libr. Arch. 688, C8 (2001).

Pichler, H.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

Pierangeli, D.

D. Pierangeli, G. Marcucci, and C. Conti, “Large-scale photonic ising machine by spatial light modulation,” Phys. Rev. Lett. 122(21), 213902 (2019).
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M. N. Polyanskiy, “Refractive index database,” https://refractiveindex.info . Accessed on 2019-08-01.

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K. J. Kormondy, Y. Popoff, M. Sousa, F. Eltes, D. Caimi, M. D. Rossell, M. Fiebig, P. Hoffmann, C. Marchiori, M. Reinke, M. Trassin, A. A. Demkov, J. Fompeyrine, and S. Abel, “Microstructure and ferroelectricity of batio3 thin films on si for integrated photonics,” Nanotechnology 28(7), 075706 (2017).
[Crossref]

Ravets, S.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2d arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).
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Reinke, M.

K. J. Kormondy, Y. Popoff, M. Sousa, F. Eltes, D. Caimi, M. D. Rossell, M. Fiebig, P. Hoffmann, C. Marchiori, M. Reinke, M. Trassin, A. A. Demkov, J. Fompeyrine, and S. Abel, “Microstructure and ferroelectricity of batio3 thin films on si for integrated photonics,” Nanotechnology 28(7), 075706 (2017).
[Crossref]

Ren, S.

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. Miller, and J. S. Harris, “Strong quantum-confined stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
[Crossref]

Rivenson, Y.

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science 361(6406), 1004–1008 (2018).
[Crossref]

Rosa, A.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
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Rossel, C.

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4(1), 1671 (2013).
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Rossell, M. D.

K. J. Kormondy, Y. Popoff, M. Sousa, F. Eltes, D. Caimi, M. D. Rossell, M. Fiebig, P. Hoffmann, C. Marchiori, M. Reinke, M. Trassin, A. A. Demkov, J. Fompeyrine, and S. Abel, “Microstructure and ferroelectricity of batio3 thin films on si for integrated photonics,” Nanotechnology 28(7), 075706 (2017).
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S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4(1), 1671 (2013).
[Crossref]

Roth, J. E.

Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. Miller, and J. S. Harris, “Strong quantum-confined stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
[Crossref]

Sanchis, P.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

Schmid, M.

A. Petraru, M. Siegert, M. Schmid, J. Schubert, and C. Buchal, “Ferroelectic batio 3 thin film optical waveguide modulators,” MRS Online Proc. Libr. Arch. 688, C8 (2001).

Schubert, J.

A. Petraru, M. Siegert, M. Schmid, J. Schubert, and C. Buchal, “Ferroelectic batio 3 thin film optical waveguide modulators,” MRS Online Proc. Libr. Arch. 688, C8 (2001).

Schwartz, S.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
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B. Schwarz, “Lidar: Mapping the world in 3d,” Nat. Photonics 4(7), 429–430 (2010).
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V. Shrauger and C. Warde, “Development of a high-speed high-fill-factor phase-only spatial light modulator,” in Diffractive and Holographic Technologies for Integrated Photonic Systems, (International Society for Optics and Photonics, 2001), pp.101–109.

Shrekenhamer, D.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Siegert, M.

A. Petraru, M. Siegert, M. Schmid, J. Schubert, and C. Buchal, “Ferroelectic batio 3 thin film optical waveguide modulators,” MRS Online Proc. Libr. Arch. 688, C8 (2001).

Sjoqvist, L.

E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” in Laser Systems Technology, (International Society for Optics and Photonics, 2003), pp.13–23.

Slaughter, J.

D. Dudley, W. M. Duncan, and J. Slaughter, “Emerging digital micromirror device (dmd) applications,” in MOEMS display and imaging systems, (International Society for Optics and Photonics, 2003), pp.14–26.

Sleasman, T.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Sludds, A.

R. Hamerly, L. Bernstein, A. Sludds, M. Soljačić, and D. Englund, “Large-scale optical neural networks based on photoelectric multiplication,” Phys. Rev. X 9(2), 021032 (2019).
[Crossref]

Smith, D. R.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Sokhoyan, R.

Y.-W. Huang, H. W. H. Lee, R. Sokhoyan, R. A. Pala, K. Thyagarajan, S. Han, D. P. Tsai, and H. A. Atwater, “Gate-tunable conducting oxide metasurfaces,” Nano Lett. 16(9), 5319–5325 (2016).
[Crossref]

Soljacic, M.

R. Hamerly, L. Bernstein, A. Sludds, M. Soljačić, and D. Englund, “Large-scale optical neural networks based on photoelectric multiplication,” Phys. Rev. X 9(2), 021032 (2019).
[Crossref]

Soref, R. A.

R. A. Soref, “Silicon spatial light modulator,” (1992). US Patent 5,157,538.

Sousa, M.

K. J. Kormondy, Y. Popoff, M. Sousa, F. Eltes, D. Caimi, M. D. Rossell, M. Fiebig, P. Hoffmann, C. Marchiori, M. Reinke, M. Trassin, A. A. Demkov, J. Fompeyrine, and S. Abel, “Microstructure and ferroelectricity of batio3 thin films on si for integrated photonics,” Nanotechnology 28(7), 075706 (2017).
[Crossref]

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4(1), 1671 (2013).
[Crossref]

Stigwall, J.

E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” in Laser Systems Technology, (International Society for Optics and Photonics, 2003), pp.13–23.

Stöferle, T.

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4(1), 1671 (2013).
[Crossref]

Thyagarajan, K.

Y.-W. Huang, H. W. H. Lee, R. Sokhoyan, R. A. Pala, K. Thyagarajan, S. Han, D. P. Tsai, and H. A. Atwater, “Gate-tunable conducting oxide metasurfaces,” Nano Lett. 16(9), 5319–5325 (2016).
[Crossref]

Trassin, M.

K. J. Kormondy, Y. Popoff, M. Sousa, F. Eltes, D. Caimi, M. D. Rossell, M. Fiebig, P. Hoffmann, C. Marchiori, M. Reinke, M. Trassin, A. A. Demkov, J. Fompeyrine, and S. Abel, “Microstructure and ferroelectricity of batio3 thin films on si for integrated photonics,” Nanotechnology 28(7), 075706 (2017).
[Crossref]

Tsai, D. P.

Y.-W. Huang, H. W. H. Lee, R. Sokhoyan, R. A. Pala, K. Thyagarajan, S. Han, D. P. Tsai, and H. A. Atwater, “Gate-tunable conducting oxide metasurfaces,” Nano Lett. 16(9), 5319–5325 (2016).
[Crossref]

Tulli, D.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
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S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

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W. M. Van Spengen, “Mems reliability from a failure mechanisms perspective,” Microelectron. Reliab. 43(7), 1049–1060 (2003).
[Crossref]

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X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science 361(6406), 1004–1008 (2018).
[Crossref]

Vernier, A.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2d arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).
[Crossref]

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D. Vettese, “Microdisplays: Liquid crystal on silicon,” Nat. Photonics 4(11), 752–754 (2010).
[Crossref]

Vuletic, V.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

Wagner, T.

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

Warde, C.

V. Shrauger and C. Warde, “Development of a high-speed high-fill-factor phase-only spatial light modulator,” in Diffractive and Holographic Technologies for Integrated Photonic Systems, (International Society for Optics and Photonics, 2001), pp.101–109.

Watts, C. M.

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
[Crossref]

Wilkinson, T. D.

Yardimci, N. T.

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science 361(6406), 1004–1008 (2018).
[Crossref]

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Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (lcos) devices,” Light: Sci. Appl. 3(10), e213 (2014).
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S. Colburn, A. Zhan, and A. Majumdar, “Tunable metasurfaces via subwavelength phase shifters with uniform amplitude,” Sci. Rep. 7(1), 40174 (2017).
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Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (lcos) devices,” Light: Sci. Appl. 3(10), e213 (2014).
[Crossref]

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H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
[Crossref]

ACS Photonics (1)

Y. Horie, A. Arbabi, E. Arbabi, S. M. Kamali, and A. Faraon, “High-speed, phase-dominant spatial light modulation with silicon-based active resonant antennas,” ACS Photonics 5(5), 1711–1717 (2018).
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Adv. Opt. Photonics (1)

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8(2), 200–227 (2016).
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Appl. Opt. (1)

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Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (lcos) devices,” Light: Sci. Appl. 3(10), e213 (2014).
[Crossref]

Microelectron. Reliab. (1)

W. M. Van Spengen, “Mems reliability from a failure mechanisms perspective,” Microelectron. Reliab. 43(7), 1049–1060 (2003).
[Crossref]

MRS Online Proc. Libr. Arch. (1)

A. Petraru, M. Siegert, M. Schmid, J. Schubert, and C. Buchal, “Ferroelectic batio 3 thin film optical waveguide modulators,” MRS Online Proc. Libr. Arch. 688, C8 (2001).

Nano Lett. (1)

Y.-W. Huang, H. W. H. Lee, R. Sokhoyan, R. A. Pala, K. Thyagarajan, S. Han, D. P. Tsai, and H. A. Atwater, “Gate-tunable conducting oxide metasurfaces,” Nano Lett. 16(9), 5319–5325 (2016).
[Crossref]

Nanotechnology (1)

K. J. Kormondy, Y. Popoff, M. Sousa, F. Eltes, D. Caimi, M. D. Rossell, M. Fiebig, P. Hoffmann, C. Marchiori, M. Reinke, M. Trassin, A. A. Demkov, J. Fompeyrine, and S. Abel, “Microstructure and ferroelectricity of batio3 thin films on si for integrated photonics,” Nanotechnology 28(7), 075706 (2017).
[Crossref]

Nat. Commun. (1)

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4(1), 1671 (2013).
[Crossref]

Nat. Mater. (1)

S. Abel, F. Eltes, J. E. Ortmann, A. Messner, P. Castera, T. Wagner, D. Urbonas, A. Rosa, A. M. Gutierrez, D. Tulli, P. Ma, B. Baeuerle, A. Josten, W. Heni, D. Caimi, L. Czornomaz, A. A. Demkov, J. Leuthold, P. Sanchis, and J. Fompeyrine, “Large pockels effect in micro-and nanostructured barium titanate integrated on silicon,” Nat. Mater. 18(1), 42–47 (2019).
[Crossref]

Nat. Photonics (4)

D. Vettese, “Microdisplays: Liquid crystal on silicon,” Nat. Photonics 4(11), 752–754 (2010).
[Crossref]

C. M. Watts, D. Shrekenhamer, J. Montoya, G. Lipworth, J. Hunt, T. Sleasman, S. Krishna, D. R. Smith, and W. J. Padilla, “Terahertz compressive imaging with metamaterial spatial light modulators,” Nat. Photonics 8(8), 605–609 (2014).
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J. M. Kahn and D. A. Miller, “Communications expands its space,” Nat. Photonics 11(1), 5–8 (2017).
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Nature (2)

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551(7682), 579–584 (2017).
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Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. Miller, and J. S. Harris, “Strong quantum-confined stark effect in germanium quantum-well structures on silicon,” Nature 437(7063), 1334–1336 (2005).
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Phys. Rev. Lett. (1)

D. Pierangeli, G. Marcucci, and C. Conti, “Large-scale photonic ising machine by spatial light modulation,” Phys. Rev. Lett. 122(21), 213902 (2019).
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Phys. Rev. X (2)

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2d arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).
[Crossref]

R. Hamerly, L. Bernstein, A. Sludds, M. Soljačić, and D. Englund, “Large-scale optical neural networks based on photoelectric multiplication,” Phys. Rev. X 9(2), 021032 (2019).
[Crossref]

Sci. Rep. (1)

S. Colburn, A. Zhan, and A. Majumdar, “Tunable metasurfaces via subwavelength phase shifters with uniform amplitude,” Sci. Rep. 7(1), 40174 (2017).
[Crossref]

Science (1)

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science 361(6406), 1004–1008 (2018).
[Crossref]

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A. Holoeye Photonics, “Holoeye corporation,” URL http://www.holoeye.com .

D. Dudley, W. M. Duncan, and J. Slaughter, “Emerging digital micromirror device (dmd) applications,” in MOEMS display and imaging systems, (International Society for Optics and Photonics, 2003), pp.14–26.

V. Shrauger and C. Warde, “Development of a high-speed high-fill-factor phase-only spatial light modulator,” in Diffractive and Holographic Technologies for Integrated Photonic Systems, (International Society for Optics and Photonics, 2001), pp.101–109.

R. A. Soref, “Silicon spatial light modulator,” (1992). US Patent 5,157,538.

E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” in Laser Systems Technology, (International Society for Optics and Photonics, 2003), pp.13–23.

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Figures (7)

Fig. 1.
Fig. 1. Spatial light modulators with two-dimensional tunable microcavity arrays. (a) One phase shifter element composed of a vertical microcavity and the corresponding electrical control components. (b) An array of phase shifter elements capable of modulating the spatial profile of the reflected wavefront.
Fig. 2.
Fig. 2. Quality factor analysis of the microcavity resonators. (a) Maximum loaded Q for the reflectance to be greater than certain values. Inset: Schematic illustration for reflectance in different regimes of coupling between the resonator mode and the free-space mode. (b) Minimum loaded Q for $V_{\pi }$, the voltage required to achieve $\pi$ phase shift, to be less than certain values. (c) Simulation of cavity loaded Q for different micropost widths $D$ and number of TiO2/SiO2 quarter-wavelength pairs $N_{top}$. (d) For $D = 5$ µm and $N_{top} = 5$, the reflectance can be maintained above $R = 0.9$ and the voltage for $\pi$ phase shift is $< 15 V$.
Fig. 3.
Fig. 3. Optimized phase shifter element with design parameters $D = 5$ µm and $N_{top} = 5$. (a) The reflectance spectrum. (b) The modulation characteristics as a function of the refractive index change of the active layer BTO.
Fig. 4.
Fig. 4. Optimized phase shifter element with design parameters $D = 5$ µm and $N_{top} = 5$. (a) Near-field intensity and phase profiles of the top surface of the microcavity at $\lambda =$ 1547 nm. The dashed box represents the outline of the microcavity’s top surface. (b) Far-field intensity profile of the microcavity’s radiation at $\lambda =$ 1547 nm.
Fig. 5.
Fig. 5. Optimization of BTO’s crystalline orientation. (a) Illustration of the BTO cavity layer, its crystalline orientation, and direction of the applied E field. (b) The electro-optic coefficients $r_{z'z'}$ and $r_{y'z'}$ as a function of the angle $\theta$ between the applied E field and the BTO $c$-axis for a single-domain BTO thin film. (c) The electro-optic coefficients $r_{z'z'}$ and $r_{y'z'}$ as a function of the angle $\theta$ between the applied E field and the BTO $c$-axis for a multi-domain BTO thin film.
Fig. 6.
Fig. 6. Demonstration of dynamical continuous beam steering using a $20\times 20$ array of phase shifters. (a) Far-field reflection pattern for phase profile representing phase gradients ranging from $0.2\pi$ / pixel to $\pi$ / pixel. (b) Line-cuts from (a) corresponding to $\frac {d\phi }{dx} = 0.35\pi$ / pixel (blue) and $\frac {d\phi }{dx} = 0.85\pi$ / pixel (red).
Fig. 7.
Fig. 7. Demonstration of dynamical beam shaping (a varifocal metalens) using a $16\times 16$ array of phase shifters. Intensity profiles for focusing of light at focal lengths (a) $f_0 = 250$ µm, (b) $f_0 = 500$ µm, and (c) $f_0 = 750$ µm. $z$ is the direction of reflected light propagation.

Tables (1)

Tables Icon

Table 1. Parameters used in simulations throughout the article.

Equations (17)

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Δ ( 1 n 2 ) i = Σ j = 1 3 r i j E j
r ( ω ) = ( 1 τ e 1 τ 0 ) + j ( ω 0 ω ) ( 1 τ e + 1 τ 0 ) j ( ω 0 ω )
R 0 = R ( ω = ω 0 ) = ( 1 τ e 1 τ 0 1 τ e + 1 τ 0 ) 2 = ( 1 τ e + 1 τ 0 2 τ 0 1 τ e + 1 τ 0 ) 2 = ( 1 Q t o t 2 Q i n t 1 Q t o t ) 2
Q t o t 1 R 0 2 Q i n t
Δ ω = ω 0 2 d 3 r Δ ϵ ( r ) | E ( r ) | 2 d 3 r ϵ ( r ) | E ( r ) | 2 + O ( Δ ϵ 2 )
Δ ω = ω 0 2 d 3 r 2 ϵ ( r ) Δ n ( r ) / n ( r ) | E ( r ) | 2 d 3 r ϵ ( r ) | E ( r ) | 2 = ω 0 B T O d 3 r ϵ ( r ) Δ n ( r ) / n ( r ) | E ( r ) | 2 d 3 r ϵ ( r ) | E ( r ) | 2 = ω 0 Δ n n 0 B T O d 3 r ϵ ( r ) | E ( r ) | 2 d 3 r ϵ ( r ) | E ( r ) | 2 = ω 0 Δ n n 0 U B T O U t o t
Δ ω π = 2 ( 1 τ e 1 τ 0 ) = ω 0 Q t o t 2 ω 0 Q i n t
Δ n π = n 0 Δ ω π ω 0 U t o t U B T O = n 0 ( 1 Q t o t 2 Q i n t ) U t o t U B T O
Q t o t 1 Δ n n 0 U B T O U t o t + 2 Q i n t
( 1 n o 2 + r 13 E z ) x 2 + ( 1 n o 2 + r 13 E z ) y 2 + ( 1 n e 2 + r 33 E z ) z 2 + ( r 42 E y ) 2 y z + ( r 42 E x ) 2 z x = 1
( 1 n o 2 + r 13 E z ) ( x ) 2 + [ ( 1 n o 2 + r 13 E z ) cos 2 θ + ( 1 n e 2 + r 33 E z ) sin 2 θ r 42 E y 2 sin θ cos θ ] ( y ) 2 + [ ( 1 n o 2 + r 13 E z ) sin 2 θ + ( 1 n e 2 + r 33 E z ) cos 2 θ + r 42 E y 2 sin θ cos θ ] ( z ) 2 + [ ( 1 n o 2 + r 13 E z ) 2 sin θ cos θ ( 1 n e 2 + r 33 E z ) 2 sin θ cos θ + r 42 E y 2 ( cos 2 θ sin 2 θ ) ] y z = 1
n z = n o n e ( sin 2 θ n e 2 + cos 2 θ n o 2 )
1 n z 2 ( E = E z z ^ ) = sin 2 θ n o 2 + cos 2 θ n e 2 + [ ( r 13 + 2 r 42 ) cos θ sin 2 θ + r 33 cos 3 θ ] E z = 1 n z 2 ( E = 0 ) + [ ( r 13 + 2 r 42 ) cos θ sin 2 θ + r 33 cos 3 θ ] E z
r z z ( θ ) = ( r 13 + 2 r 42 ) cos θ sin 2 θ + r 33 cos 3 θ
U ( x , y , z ) = A ( f x , f y , 0 ) e j 2 π 1 λ 2 f x 2 f y 2 e j 2 π ( f x x + f y y ) d f x d f y = U 1 ( θ , ϕ , z ) F a ( θ , ϕ , z )
d ϕ d x = 2 π λ sin ( θ r )
ϕ ( x , y ) = ϕ ( 0 , 0 ) + 2 π λ ( f 0 x 2 + y 2 + f 0 2 )