Abstract

We report a high speed 8x8 optical phased array using tunable 1550 nm all-pass filters with ultrathin high contrast gratings (HCGs) as the microelectromechanical-actuated top reflectors. The all-pass filter design enables a highly efficient phase tuning (1.7 π) with a small actuation voltage (10 V) and actuation displacement of the HCG (50 nm). The microelectromechanical HCG structure facilitates a high phase tuning speed >0.5 MHz. Beam steering is experimentally demonstrated with the optical phased array.

© 2014 Optical Society of America

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  1. U. Krishnamoorthy, K. Li, K. Yu, D. Lee, J. P. Heritage, and O. Solgaard, “Dual-mode micromirrors for optical phased array applications,” Sensor Actuat. A-Phys. 97–98, 21–26 (2002).
  2. P. F. Van Kessel, L. J. Hornbeck, R. E. Meier, and M. R. Douglass, “A MEMS-based projection display,” Proc. IEEE 86(8), 1687–1704 (1998).
    [CrossRef]
  3. P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
    [CrossRef]
  4. B. Wang, G. Zhang, A. Glushchenko, J. L. West, P. J. Bos, and P. F. McManamon, “Stressed liquid-crystal optical phased array for fast tip-tilt wavefront correction,” Appl. Opt. 44(36), 7754–7759 (2005).
    [CrossRef] [PubMed]
  5. D. Engström, M. J. O’Callaghan, C. Walker, and M. A. Handschy, “Fast beam steering with a ferroelectric-liquid-crystal optical phased array,” Appl. Opt. 48(9), 1721–1726 (2009).
    [CrossRef] [PubMed]
  6. M. Jarrahi, R. F. W. Pease, D. A. B. Miller, and T. H. Lee, “Optical switching based on high-speed phased array optical beam steering,” Appl. Phys. Lett. 92(1), 014106 (2008).
    [CrossRef]
  7. J. K. Doylend, M. J. R. Heck, J. T. Bovington, J. D. Peters, L. A. Coldren, and J. E. Bowers, “Two-dimensional free-space beam steering with an optical phased array on silicon-on-insulator,” Opt. Express 19(22), 21595–21604 (2011).
    [CrossRef] [PubMed]
  8. J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
    [CrossRef] [PubMed]
  9. C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultra-broadband mirror using low index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
    [CrossRef]
  10. C. J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photon. 4(3), 379–440 (2012).
    [CrossRef]
  11. M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
    [CrossRef]
  12. X. Gu, A. Imamura, and F. Koyama, “Wavelength trimming of vertical-cavity surface-emitting lasers with high-contrast subwavelength grating,” Jpn. J. Appl. Phys. 50(10R), 100207 (2011).
    [CrossRef]
  13. C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J.-M. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
    [CrossRef]
  14. T. Ansbaek, I.-S. Chung, E. S. Semenova, and K. Yvind, “1060-nm tunable monolithic high index contrast subwavelength grating VCSEL,” IEEE Photon. Technol. Lett. 25(4), 365–367 (2013).
    [CrossRef]
  15. W. Yang, J. Ferrara, K. Grutter, A. Yeh, C. Chase, Y. Yue, A. E. Willner, M. Wu, and C. J. Chang-Hasnain, “Low loss hollow-core waveguide on a silicon substrate,” Nanophotonics 1(1), 23–29 (2012).
    [CrossRef]
  16. B.-W. Yoo, M. Megens, T. Chan, T. Sun, W. Yang, C. J. Chang-Hasnain, D. A. Horsley, and M. C. Wu, “Optical phased array using high contrast gratings for two dimensional beamforming and beamsteering,” Opt. Express 21(10), 12238–12248 (2013).
    [CrossRef] [PubMed]
  17. C. K. Madsen and G. Lenz, “Optical all-pass filters for phase response design with applications for dispersion compensation,” IEEE Photon. Technol. Lett. 10(7), 994–996 (1998).
    [CrossRef]
  18. G. Lenz and C. K. Madsen, “General optical all-pass filter structures for dispersion control in WDM systems,” J. Lightwave Technol. 17(7), 1248–1254 (1999).
    [CrossRef]
  19. C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, “A tunable dispersion compensating MEMS all-pass filter,” IEEE Photon. Technol. Lett. 12(6), 651–653 (2000).
    [CrossRef]
  20. N. C. Singer and W. P. Seering, “Preshaping command inputs to reduce system vibration,” ASME. J. Dyn. Syst. Meas. Control 112(1), 76–82 (1990).
    [CrossRef]
  21. J. Vaughan, A. Yano, and W. Singhose, “Robust negative input shapers for vibration suppression,” ASME. J. Dyn. Syst. Meas. Control 131(3), 031014 (2009).
    [CrossRef]
  22. T. K. Chan, M. Megens, B.-W. Yoo, J. Wyras, C. J. Chang-Hasnain, M. C. Wu, and D. A. Horsley, “Optical beamsteering using an 8 × 8 MEMS phased array with closed-loop interferometric phase control,” Opt. Express 21(3), 2807–2815 (2013).
    [CrossRef] [PubMed]
  23. S. Boutami, B. B. Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photon. Technol. Lett. 18(7), 835–837 (2006).
    [CrossRef]
  24. H. Yang, D. Zhao, J.-H. Seo, S. Chuwongin, S. Kim, J. A. Rogers, Z. Ma, and W. Zhou, “Broadband membrane reflectors on glass,” IEEE Photon. Technol. Lett. 24(6), 476–478 (2012).
    [CrossRef]

2013 (4)

2012 (4)

C. J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photon. 4(3), 379–440 (2012).
[CrossRef]

W. Yang, J. Ferrara, K. Grutter, A. Yeh, C. Chase, Y. Yue, A. E. Willner, M. Wu, and C. J. Chang-Hasnain, “Low loss hollow-core waveguide on a silicon substrate,” Nanophotonics 1(1), 23–29 (2012).
[CrossRef]

H. Yang, D. Zhao, J.-H. Seo, S. Chuwongin, S. Kim, J. A. Rogers, Z. Ma, and W. Zhou, “Broadband membrane reflectors on glass,” IEEE Photon. Technol. Lett. 24(6), 476–478 (2012).
[CrossRef]

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J.-M. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

2011 (2)

X. Gu, A. Imamura, and F. Koyama, “Wavelength trimming of vertical-cavity surface-emitting lasers with high-contrast subwavelength grating,” Jpn. J. Appl. Phys. 50(10R), 100207 (2011).
[CrossRef]

J. K. Doylend, M. J. R. Heck, J. T. Bovington, J. D. Peters, L. A. Coldren, and J. E. Bowers, “Two-dimensional free-space beam steering with an optical phased array on silicon-on-insulator,” Opt. Express 19(22), 21595–21604 (2011).
[CrossRef] [PubMed]

2009 (2)

D. Engström, M. J. O’Callaghan, C. Walker, and M. A. Handschy, “Fast beam steering with a ferroelectric-liquid-crystal optical phased array,” Appl. Opt. 48(9), 1721–1726 (2009).
[CrossRef] [PubMed]

J. Vaughan, A. Yano, and W. Singhose, “Robust negative input shapers for vibration suppression,” ASME. J. Dyn. Syst. Meas. Control 131(3), 031014 (2009).
[CrossRef]

2008 (1)

M. Jarrahi, R. F. W. Pease, D. A. B. Miller, and T. H. Lee, “Optical switching based on high-speed phased array optical beam steering,” Appl. Phys. Lett. 92(1), 014106 (2008).
[CrossRef]

2007 (1)

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[CrossRef]

2006 (1)

S. Boutami, B. B. Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photon. Technol. Lett. 18(7), 835–837 (2006).
[CrossRef]

2005 (1)

2004 (1)

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultra-broadband mirror using low index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

2002 (1)

U. Krishnamoorthy, K. Li, K. Yu, D. Lee, J. P. Heritage, and O. Solgaard, “Dual-mode micromirrors for optical phased array applications,” Sensor Actuat. A-Phys. 97–98, 21–26 (2002).

2000 (1)

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, “A tunable dispersion compensating MEMS all-pass filter,” IEEE Photon. Technol. Lett. 12(6), 651–653 (2000).
[CrossRef]

1999 (1)

1998 (2)

C. K. Madsen and G. Lenz, “Optical all-pass filters for phase response design with applications for dispersion compensation,” IEEE Photon. Technol. Lett. 10(7), 994–996 (1998).
[CrossRef]

P. F. Van Kessel, L. J. Hornbeck, R. E. Meier, and M. R. Douglass, “A MEMS-based projection display,” Proc. IEEE 86(8), 1687–1704 (1998).
[CrossRef]

1996 (1)

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

1990 (1)

N. C. Singer and W. P. Seering, “Preshaping command inputs to reduce system vibration,” ASME. J. Dyn. Syst. Meas. Control 112(1), 76–82 (1990).
[CrossRef]

Ansbaek, T.

T. Ansbaek, I.-S. Chung, E. S. Semenova, and K. Yvind, “1060-nm tunable monolithic high index contrast subwavelength grating VCSEL,” IEEE Photon. Technol. Lett. 25(4), 365–367 (2013).
[CrossRef]

Bakir, B. B.

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J.-M. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

S. Boutami, B. B. Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photon. Technol. Lett. 18(7), 835–837 (2006).
[CrossRef]

Bos, P. J.

Boutami, S.

S. Boutami, B. B. Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photon. Technol. Lett. 18(7), 835–837 (2006).
[CrossRef]

Bovington, J. T.

Bowers, J. E.

Chan, T.

Chan, T. K.

Chang-Hasnain, C. J.

T. K. Chan, M. Megens, B.-W. Yoo, J. Wyras, C. J. Chang-Hasnain, M. C. Wu, and D. A. Horsley, “Optical beamsteering using an 8 × 8 MEMS phased array with closed-loop interferometric phase control,” Opt. Express 21(3), 2807–2815 (2013).
[CrossRef] [PubMed]

B.-W. Yoo, M. Megens, T. Chan, T. Sun, W. Yang, C. J. Chang-Hasnain, D. A. Horsley, and M. C. Wu, “Optical phased array using high contrast gratings for two dimensional beamforming and beamsteering,” Opt. Express 21(10), 12238–12248 (2013).
[CrossRef] [PubMed]

C. J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photon. 4(3), 379–440 (2012).
[CrossRef]

W. Yang, J. Ferrara, K. Grutter, A. Yeh, C. Chase, Y. Yue, A. E. Willner, M. Wu, and C. J. Chang-Hasnain, “Low loss hollow-core waveguide on a silicon substrate,” Nanophotonics 1(1), 23–29 (2012).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultra-broadband mirror using low index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Chase, C.

W. Yang, J. Ferrara, K. Grutter, A. Yeh, C. Chase, Y. Yue, A. E. Willner, M. Wu, and C. J. Chang-Hasnain, “Low loss hollow-core waveguide on a silicon substrate,” Nanophotonics 1(1), 23–29 (2012).
[CrossRef]

Chung, I.-S.

T. Ansbaek, I.-S. Chung, E. S. Semenova, and K. Yvind, “1060-nm tunable monolithic high index contrast subwavelength grating VCSEL,” IEEE Photon. Technol. Lett. 25(4), 365–367 (2013).
[CrossRef]

Chuwongin, S.

H. Yang, D. Zhao, J.-H. Seo, S. Chuwongin, S. Kim, J. A. Rogers, Z. Ma, and W. Zhou, “Broadband membrane reflectors on glass,” IEEE Photon. Technol. Lett. 24(6), 476–478 (2012).
[CrossRef]

Coldren, L. A.

Corkum, D. L.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Deng, Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultra-broadband mirror using low index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Dorschner, T. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Douglass, M. R.

P. F. Van Kessel, L. J. Hornbeck, R. E. Meier, and M. R. Douglass, “A MEMS-based projection display,” Proc. IEEE 86(8), 1687–1704 (1998).
[CrossRef]

Doylend, J. K.

Engström, D.

Fedeli, J.-M.

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J.-M. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

Ferrara, J.

W. Yang, J. Ferrara, K. Grutter, A. Yeh, C. Chase, Y. Yue, A. E. Willner, M. Wu, and C. J. Chang-Hasnain, “Low loss hollow-core waveguide on a silicon substrate,” Nanophotonics 1(1), 23–29 (2012).
[CrossRef]

Ford, J. E.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, “A tunable dispersion compensating MEMS all-pass filter,” IEEE Photon. Technol. Lett. 12(6), 651–653 (2000).
[CrossRef]

Friedman, L. J.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Garrigues, M.

S. Boutami, B. B. Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photon. Technol. Lett. 18(7), 835–837 (2006).
[CrossRef]

Glushchenko, A.

Goossen, K. W.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, “A tunable dispersion compensating MEMS all-pass filter,” IEEE Photon. Technol. Lett. 12(6), 651–653 (2000).
[CrossRef]

Grutter, K.

W. Yang, J. Ferrara, K. Grutter, A. Yeh, C. Chase, Y. Yue, A. E. Willner, M. Wu, and C. J. Chang-Hasnain, “Low loss hollow-core waveguide on a silicon substrate,” Nanophotonics 1(1), 23–29 (2012).
[CrossRef]

Gu, X.

X. Gu, A. Imamura, and F. Koyama, “Wavelength trimming of vertical-cavity surface-emitting lasers with high-contrast subwavelength grating,” Jpn. J. Appl. Phys. 50(10R), 100207 (2011).
[CrossRef]

Handschy, M. A.

Harduin, J.

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J.-M. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

Hattori, H.

S. Boutami, B. B. Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photon. Technol. Lett. 18(7), 835–837 (2006).
[CrossRef]

Heck, M. J. R.

Heritage, J. P.

U. Krishnamoorthy, K. Li, K. Yu, D. Lee, J. P. Heritage, and O. Solgaard, “Dual-mode micromirrors for optical phased array applications,” Sensor Actuat. A-Phys. 97–98, 21–26 (2002).

Hobbs, D. S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Holz, M.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Hornbeck, L. J.

P. F. Van Kessel, L. J. Hornbeck, R. E. Meier, and M. R. Douglass, “A MEMS-based projection display,” Proc. IEEE 86(8), 1687–1704 (1998).
[CrossRef]

Horsley, D. A.

Hosseini, E. S.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[CrossRef] [PubMed]

Huang, M. C. Y.

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultra-broadband mirror using low index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Imamura, A.

X. Gu, A. Imamura, and F. Koyama, “Wavelength trimming of vertical-cavity surface-emitting lasers with high-contrast subwavelength grating,” Jpn. J. Appl. Phys. 50(10R), 100207 (2011).
[CrossRef]

Jarrahi, M.

M. Jarrahi, R. F. W. Pease, D. A. B. Miller, and T. H. Lee, “Optical switching based on high-speed phased array optical beam steering,” Appl. Phys. Lett. 92(1), 014106 (2008).
[CrossRef]

Kim, S.

H. Yang, D. Zhao, J.-H. Seo, S. Chuwongin, S. Kim, J. A. Rogers, Z. Ma, and W. Zhou, “Broadband membrane reflectors on glass,” IEEE Photon. Technol. Lett. 24(6), 476–478 (2012).
[CrossRef]

Koyama, F.

X. Gu, A. Imamura, and F. Koyama, “Wavelength trimming of vertical-cavity surface-emitting lasers with high-contrast subwavelength grating,” Jpn. J. Appl. Phys. 50(10R), 100207 (2011).
[CrossRef]

Krishnamoorthy, U.

U. Krishnamoorthy, K. Li, K. Yu, D. Lee, J. P. Heritage, and O. Solgaard, “Dual-mode micromirrors for optical phased array applications,” Sensor Actuat. A-Phys. 97–98, 21–26 (2002).

Leclercq, J.-L.

S. Boutami, B. B. Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photon. Technol. Lett. 18(7), 835–837 (2006).
[CrossRef]

Lee, D.

U. Krishnamoorthy, K. Li, K. Yu, D. Lee, J. P. Heritage, and O. Solgaard, “Dual-mode micromirrors for optical phased array applications,” Sensor Actuat. A-Phys. 97–98, 21–26 (2002).

Lee, T. H.

M. Jarrahi, R. F. W. Pease, D. A. B. Miller, and T. H. Lee, “Optical switching based on high-speed phased array optical beam steering,” Appl. Phys. Lett. 92(1), 014106 (2008).
[CrossRef]

Lenz, G.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, “A tunable dispersion compensating MEMS all-pass filter,” IEEE Photon. Technol. Lett. 12(6), 651–653 (2000).
[CrossRef]

G. Lenz and C. K. Madsen, “General optical all-pass filter structures for dispersion control in WDM systems,” J. Lightwave Technol. 17(7), 1248–1254 (1999).
[CrossRef]

C. K. Madsen and G. Lenz, “Optical all-pass filters for phase response design with applications for dispersion compensation,” IEEE Photon. Technol. Lett. 10(7), 994–996 (1998).
[CrossRef]

Letartre, X.

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J.-M. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

S. Boutami, B. B. Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photon. Technol. Lett. 18(7), 835–837 (2006).
[CrossRef]

Li, K.

U. Krishnamoorthy, K. Li, K. Yu, D. Lee, J. P. Heritage, and O. Solgaard, “Dual-mode micromirrors for optical phased array applications,” Sensor Actuat. A-Phys. 97–98, 21–26 (2002).

Liberman, S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Ma, Z.

H. Yang, D. Zhao, J.-H. Seo, S. Chuwongin, S. Kim, J. A. Rogers, Z. Ma, and W. Zhou, “Broadband membrane reflectors on glass,” IEEE Photon. Technol. Lett. 24(6), 476–478 (2012).
[CrossRef]

Madsen, C. K.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, “A tunable dispersion compensating MEMS all-pass filter,” IEEE Photon. Technol. Lett. 12(6), 651–653 (2000).
[CrossRef]

G. Lenz and C. K. Madsen, “General optical all-pass filter structures for dispersion control in WDM systems,” J. Lightwave Technol. 17(7), 1248–1254 (1999).
[CrossRef]

C. K. Madsen and G. Lenz, “Optical all-pass filters for phase response design with applications for dispersion compensation,” IEEE Photon. Technol. Lett. 10(7), 994–996 (1998).
[CrossRef]

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultra-broadband mirror using low index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

McManamon, P. F.

B. Wang, G. Zhang, A. Glushchenko, J. L. West, P. J. Bos, and P. F. McManamon, “Stressed liquid-crystal optical phased array for fast tip-tilt wavefront correction,” Appl. Opt. 44(36), 7754–7759 (2005).
[CrossRef] [PubMed]

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Megens, M.

Meier, R. E.

P. F. Van Kessel, L. J. Hornbeck, R. E. Meier, and M. R. Douglass, “A MEMS-based projection display,” Proc. IEEE 86(8), 1687–1704 (1998).
[CrossRef]

Miller, D. A. B.

M. Jarrahi, R. F. W. Pease, D. A. B. Miller, and T. H. Lee, “Optical switching based on high-speed phased array optical beam steering,” Appl. Phys. Lett. 92(1), 014106 (2008).
[CrossRef]

Neureuther, A. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultra-broadband mirror using low index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Nguyen, H. Q.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Nielsen, T. N.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, “A tunable dispersion compensating MEMS all-pass filter,” IEEE Photon. Technol. Lett. 12(6), 651–653 (2000).
[CrossRef]

O’Callaghan, M. J.

Olivier, N.

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J.-M. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

Pease, R. F. W.

M. Jarrahi, R. F. W. Pease, D. A. B. Miller, and T. H. Lee, “Optical switching based on high-speed phased array optical beam steering,” Appl. Phys. Lett. 92(1), 014106 (2008).
[CrossRef]

Peters, J. D.

Resler, D. P.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Rogers, J. A.

H. Yang, D. Zhao, J.-H. Seo, S. Chuwongin, S. Kim, J. A. Rogers, Z. Ma, and W. Zhou, “Broadband membrane reflectors on glass,” IEEE Photon. Technol. Lett. 24(6), 476–478 (2012).
[CrossRef]

Rojo-Romeo, P.

S. Boutami, B. B. Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photon. Technol. Lett. 18(7), 835–837 (2006).
[CrossRef]

Sciancalepore, C.

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J.-M. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

Seassal, C.

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J.-M. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

S. Boutami, B. B. Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photon. Technol. Lett. 18(7), 835–837 (2006).
[CrossRef]

Seering, W. P.

N. C. Singer and W. P. Seering, “Preshaping command inputs to reduce system vibration,” ASME. J. Dyn. Syst. Meas. Control 112(1), 76–82 (1990).
[CrossRef]

Semenova, E. S.

T. Ansbaek, I.-S. Chung, E. S. Semenova, and K. Yvind, “1060-nm tunable monolithic high index contrast subwavelength grating VCSEL,” IEEE Photon. Technol. Lett. 25(4), 365–367 (2013).
[CrossRef]

Seo, J.-H.

H. Yang, D. Zhao, J.-H. Seo, S. Chuwongin, S. Kim, J. A. Rogers, Z. Ma, and W. Zhou, “Broadband membrane reflectors on glass,” IEEE Photon. Technol. Lett. 24(6), 476–478 (2012).
[CrossRef]

Sharp, R. C.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Singer, N. C.

N. C. Singer and W. P. Seering, “Preshaping command inputs to reduce system vibration,” ASME. J. Dyn. Syst. Meas. Control 112(1), 76–82 (1990).
[CrossRef]

Singhose, W.

J. Vaughan, A. Yano, and W. Singhose, “Robust negative input shapers for vibration suppression,” ASME. J. Dyn. Syst. Meas. Control 131(3), 031014 (2009).
[CrossRef]

Solgaard, O.

U. Krishnamoorthy, K. Li, K. Yu, D. Lee, J. P. Heritage, and O. Solgaard, “Dual-mode micromirrors for optical phased array applications,” Sensor Actuat. A-Phys. 97–98, 21–26 (2002).

Sun, J.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[CrossRef] [PubMed]

Sun, T.

Timurdogan, E.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[CrossRef] [PubMed]

Van Kessel, P. F.

P. F. Van Kessel, L. J. Hornbeck, R. E. Meier, and M. R. Douglass, “A MEMS-based projection display,” Proc. IEEE 86(8), 1687–1704 (1998).
[CrossRef]

Vaughan, J.

J. Vaughan, A. Yano, and W. Singhose, “Robust negative input shapers for vibration suppression,” ASME. J. Dyn. Syst. Meas. Control 131(3), 031014 (2009).
[CrossRef]

Viktorovitch, P.

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J.-M. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

S. Boutami, B. B. Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photon. Technol. Lett. 18(7), 835–837 (2006).
[CrossRef]

Walker, C.

Walker, J. A.

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, “A tunable dispersion compensating MEMS all-pass filter,” IEEE Photon. Technol. Lett. 12(6), 651–653 (2000).
[CrossRef]

Wang, B.

Watson, E. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Watts, M. R.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[CrossRef] [PubMed]

West, J. L.

Willner, A. E.

W. Yang, J. Ferrara, K. Grutter, A. Yeh, C. Chase, Y. Yue, A. E. Willner, M. Wu, and C. J. Chang-Hasnain, “Low loss hollow-core waveguide on a silicon substrate,” Nanophotonics 1(1), 23–29 (2012).
[CrossRef]

Wu, M.

W. Yang, J. Ferrara, K. Grutter, A. Yeh, C. Chase, Y. Yue, A. E. Willner, M. Wu, and C. J. Chang-Hasnain, “Low loss hollow-core waveguide on a silicon substrate,” Nanophotonics 1(1), 23–29 (2012).
[CrossRef]

Wu, M. C.

Wyras, J.

Yaacobi, A.

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[CrossRef] [PubMed]

Yang, H.

H. Yang, D. Zhao, J.-H. Seo, S. Chuwongin, S. Kim, J. A. Rogers, Z. Ma, and W. Zhou, “Broadband membrane reflectors on glass,” IEEE Photon. Technol. Lett. 24(6), 476–478 (2012).
[CrossRef]

Yang, W.

Yano, A.

J. Vaughan, A. Yano, and W. Singhose, “Robust negative input shapers for vibration suppression,” ASME. J. Dyn. Syst. Meas. Control 131(3), 031014 (2009).
[CrossRef]

Yeh, A.

W. Yang, J. Ferrara, K. Grutter, A. Yeh, C. Chase, Y. Yue, A. E. Willner, M. Wu, and C. J. Chang-Hasnain, “Low loss hollow-core waveguide on a silicon substrate,” Nanophotonics 1(1), 23–29 (2012).
[CrossRef]

Yoo, B.-W.

Yu, K.

U. Krishnamoorthy, K. Li, K. Yu, D. Lee, J. P. Heritage, and O. Solgaard, “Dual-mode micromirrors for optical phased array applications,” Sensor Actuat. A-Phys. 97–98, 21–26 (2002).

Yue, Y.

W. Yang, J. Ferrara, K. Grutter, A. Yeh, C. Chase, Y. Yue, A. E. Willner, M. Wu, and C. J. Chang-Hasnain, “Low loss hollow-core waveguide on a silicon substrate,” Nanophotonics 1(1), 23–29 (2012).
[CrossRef]

Yvind, K.

T. Ansbaek, I.-S. Chung, E. S. Semenova, and K. Yvind, “1060-nm tunable monolithic high index contrast subwavelength grating VCSEL,” IEEE Photon. Technol. Lett. 25(4), 365–367 (2013).
[CrossRef]

Zhang, G.

Zhao, D.

H. Yang, D. Zhao, J.-H. Seo, S. Chuwongin, S. Kim, J. A. Rogers, Z. Ma, and W. Zhou, “Broadband membrane reflectors on glass,” IEEE Photon. Technol. Lett. 24(6), 476–478 (2012).
[CrossRef]

Zhou, W.

H. Yang, D. Zhao, J.-H. Seo, S. Chuwongin, S. Kim, J. A. Rogers, Z. Ma, and W. Zhou, “Broadband membrane reflectors on glass,” IEEE Photon. Technol. Lett. 24(6), 476–478 (2012).
[CrossRef]

Zhou, Y.

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Opt. (2)

Appl. Phys. Lett. (1)

M. Jarrahi, R. F. W. Pease, D. A. B. Miller, and T. H. Lee, “Optical switching based on high-speed phased array optical beam steering,” Appl. Phys. Lett. 92(1), 014106 (2008).
[CrossRef]

ASME. J. Dyn. Syst. Meas. Control (2)

N. C. Singer and W. P. Seering, “Preshaping command inputs to reduce system vibration,” ASME. J. Dyn. Syst. Meas. Control 112(1), 76–82 (1990).
[CrossRef]

J. Vaughan, A. Yano, and W. Singhose, “Robust negative input shapers for vibration suppression,” ASME. J. Dyn. Syst. Meas. Control 131(3), 031014 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (7)

C. K. Madsen and G. Lenz, “Optical all-pass filters for phase response design with applications for dispersion compensation,” IEEE Photon. Technol. Lett. 10(7), 994–996 (1998).
[CrossRef]

S. Boutami, B. B. Bakir, H. Hattori, X. Letartre, J.-L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2-D photonic crystal reflectors with controllable polarization dependence,” IEEE Photon. Technol. Lett. 18(7), 835–837 (2006).
[CrossRef]

H. Yang, D. Zhao, J.-H. Seo, S. Chuwongin, S. Kim, J. A. Rogers, Z. Ma, and W. Zhou, “Broadband membrane reflectors on glass,” IEEE Photon. Technol. Lett. 24(6), 476–478 (2012).
[CrossRef]

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J.-M. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55- μ m emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24(6), 455–457 (2012).
[CrossRef]

T. Ansbaek, I.-S. Chung, E. S. Semenova, and K. Yvind, “1060-nm tunable monolithic high index contrast subwavelength grating VCSEL,” IEEE Photon. Technol. Lett. 25(4), 365–367 (2013).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultra-broadband mirror using low index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

C. K. Madsen, J. A. Walker, J. E. Ford, K. W. Goossen, T. N. Nielsen, and G. Lenz, “A tunable dispersion compensating MEMS all-pass filter,” IEEE Photon. Technol. Lett. 12(6), 651–653 (2000).
[CrossRef]

J. Lightwave Technol. (1)

Jpn. J. Appl. Phys. (1)

X. Gu, A. Imamura, and F. Koyama, “Wavelength trimming of vertical-cavity surface-emitting lasers with high-contrast subwavelength grating,” Jpn. J. Appl. Phys. 50(10R), 100207 (2011).
[CrossRef]

Nanophotonics (1)

W. Yang, J. Ferrara, K. Grutter, A. Yeh, C. Chase, Y. Yue, A. E. Willner, M. Wu, and C. J. Chang-Hasnain, “Low loss hollow-core waveguide on a silicon substrate,” Nanophotonics 1(1), 23–29 (2012).
[CrossRef]

Nat. Photonics (1)

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[CrossRef]

Nature (1)

J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013).
[CrossRef] [PubMed]

Opt. Express (3)

Proc. IEEE (2)

P. F. Van Kessel, L. J. Hornbeck, R. E. Meier, and M. R. Douglass, “A MEMS-based projection display,” Proc. IEEE 86(8), 1687–1704 (1998).
[CrossRef]

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84(2), 268–298 (1996).
[CrossRef]

Sensor Actuat. A-Phys. (1)

U. Krishnamoorthy, K. Li, K. Yu, D. Lee, J. P. Heritage, and O. Solgaard, “Dual-mode micromirrors for optical phased array applications,” Sensor Actuat. A-Phys. 97–98, 21–26 (2002).

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Figures (7)

Fig. 1
Fig. 1

Schematic of an individual pixel of the optical phased array. The Al0.6Ga0.4As HCG and 22 pairs of GaAs/Al0.9Ga0.1As DBR serve as the top and bottom reflector of the Fabry-Perot etalon. The incident light is surface normal to the etalon, and polarized in parallel to the grating bar. Λ, HCG period; s, grating bar width; tg, HCG thickness; d, air gap between HCG and DBR. We design Λ = 1150 nm, s = 700 nm, tg = 450 nm, and d = 700 nm.

Fig. 2
Fig. 2

(a) SEM image of an 8x8 optical phased array. Each pixel is an HCG-APF, which can be individually electrically addressed by the fanned-out metal contacts. The pitch of the HCG mirror is ~33.5 μm. (b) Zoom-in view of the HCG mirror in a single pixel. The HCG mirror size (without the MEMS) is 20 μm by 20 μm.

Fig. 3
Fig. 3

(a) Reflection spectrum of an HCG-APF with different actuation voltages. As the reversed bias voltage increases, the cavity length decreases, resulting in a blue-shift of the resonance wavelength. (b) Reflection phase shift versus applied voltage on a single HCG-APF of the phased array. ~1.7 π phase shift is achieved within 10 V actuation voltage range at a wavelength of 1550 nm; this corresponds to a displacement of ~50 nm of the HCG. The measured results are curve fitted to extract the reflectivity of the DBR and HCG.

Fig. 4
Fig. 4

(a) Laser Doppler velocimetry measurement to characterize the mechanical resonance frequency of the HCG MEMS mirror. (b) Time resolved phase measurement of the HCG APF with a step voltage actuation signal. The blue dots are recorded in the experiment, and red traces are the simulated fitting curve from the second harmonic oscillator model.

Fig. 5
Fig. 5

Comparison of the ringing between a single step and two step voltage control. In the two step voltage control case, the time interval between the two different steps is 1 μs, corresponding to half of the ringing period. The individual ringing from these two separate steps would have destructive interference, leading to an overall reduced ringing.

Fig. 6
Fig. 6

Beam steering experiment. (a) Near-field phase pattern created by the HCG-APF optical phased array. (b) The corresponding far-field pattern calculated by Fourier optics. (c) Experimentally measured far-field pattern, in reasonably good agreement with the calculation. The strong zeroth order beam is due to the relatively low filling factor of the phased array (~36%). The light that does not hit on the HCG-APF gets reflected with a fixed phase shift, contributing strongly to the zeroth order beam. The field of view of the image windows is 13° x 13°. The box in dashed line in (c) indicates the TFOV of the phased array (9.14° x 9.14°).

Fig. 7
Fig. 7

(a) SEM image of the two-dimensional HCG mirror for HCG-AFP array. (b) Beam steering experiment of the optical phased array using two-dimensional HCG as the top mirrors of the APF. Top panel, near-field phase pattern created by the HCG-APF optical phased array. Middle panel, the corresponding far-field pattern calculated by Fourier optics. Bottom panel, experimentally measured far-field pattern, in good agreement with the calculation.

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