Abstract

We propose a pattern-search-like algorithm to design an aperiodic optical phased array for extensive applications in light detection and ranging and free-space communication. The designed phased array with 128 isotropic elements achieves a scan range, peak side-lobe level, minimum beam width, and mean pitch of ± 82°, –14.34 dB, 0.062°, and 9.75 μm, respectively. To our knowledge, it has the widest steering range, narrowest divergence, and largest mean pitch for the same waveguide number. The minimum pitch can be greater than 2.67λ to avoid cross-coupling. The calculated relationship between the machine error and side-lobe level indicates that the designed structure has a higher error tolerance than its uniformly spaced counterpart.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Sparse aperiodic arrays for optical beam forming and LIDAR

Tin Komljenovic, Roger Helkey, Larry Coldren, and John E. Bowers
Opt. Express 25(3) 2511-2528 (2017)

Fast and wide-range optical beam steering with ultralow side lobes by applying an optimized multi-circular optical phased array

Fangzheng Zhang, Daocheng Zhang, and Shilong Pan
Appl. Opt. 57(18) 4977-4984 (2018)

Electronically controlled optical beam-steering by an active phased array of metallic nanoantennas

C. T. DeRose, R. D. Kekatpure, D. C. Trotter, A. Starbuck, J. R. Wendt, A. Yaacobi, M. R. Watts, U. Chettiar, N. Engheta, and P. S. Davids
Opt. Express 21(4) 5198-5208 (2013)

References

  • View by:
  • |
  • |
  • |

  1. M. J. R. Heck, “Highly integrated optical phased arrays: photonic integrated circuits for optical beam shaping and beam steering,” Nanophotonics 6(1), 93–107 (2017).
    [Crossref]
  2. 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]
  3. P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
    [Crossref]
  4. Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018).
    [Crossref] [PubMed]
  5. W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
    [Crossref] [PubMed]
  6. Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
    [Crossref] [PubMed]
  7. Y. Arakawa, T. Nakamura, Y. Urino, and T. Fujita, “Silicon photonics for next generation system integration platform,” IEEE Commun. Mag. 51(3), 72–77 (2013).
    [Crossref]
  8. K. Van Acoleyen, W. Bogaerts, J. Jágerská, N. Le Thomas, R. Houdré, and R. Baets, “Off-chip beam steering with a one-dimensional optical phased array on silicon-on-insulator,” Opt. Lett. 34(9), 1477–1479 (2009).
    [Crossref] [PubMed]
  9. K. Van Acoleyen, H. Rogier, and R. Baets, “Two-dimensional optical phased array antenna on silicon-on-insulator,” Opt. Express 18(13), 13655–13660 (2010).
    [Crossref] [PubMed]
  10. K. V. Acoleyen, K. Komorowska, W. Bogaerts, and R. Baets, “One-dimensional off-chip beam steering and shaping using optical phased arrays on silicon-on-insulator,” J. Lightwave Technol. 29(23), 3500–3505 (2011).
    [Crossref]
  11. 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]
  12. K. V. Acoleyen, W. Bogaerts, and R. Baets, “Two-dimensional dispersive off-chip beam scanner fabricated on silicon-on-insulator,” IEEE Photonics Technol. Lett. 23(17), 1270–1272 (2011).
    [Crossref]
  13. J. K. Doylend, M. J. R. Heck, J. T. Bovington, J. D. Peters, M. L. Davenport, L. A. Coldren, and J. E. Bowers, “Hybrid III/V silicon photonic source with integrated 1D free-space beam steering,” Opt. Lett. 37(20), 4257–4259 (2012).
    [Crossref] [PubMed]
  14. 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]
  15. J. Sun, E. Hosseini, A. Yaacobi, D. B. Cole, G. Leake, D. Coolbaugh, and M. R. Watts, “Two-dimensional apodized silicon photonic phased arrays,” Opt. Lett. 39(2), 367–370 (2014).
    [Crossref] [PubMed]
  16. D. Kwong, A. Hosseini, J. Covey, Y. Zhang, X. Xu, H. Subbaraman, and R. T. Chen, “On-chip silicon optical phased array for two-dimensional beam steering,” Opt. Lett. 39(4), 941–944 (2014).
    [Crossref] [PubMed]
  17. H. Abediasl and H. Hashemi, “Monolithic optical phased-array transceiver in a standard SOI CMOS process,” Opt. Express 23(5), 6509–6519 (2015).
    [Crossref] [PubMed]
  18. B. Guan, C. Qin, R. P. Scott, B. Ercan, N. K. Fontaine, T. Su, and S. J. B. Yoo, “Hybrid 3D photonic integrated circuit for optical phased array beam steering,” Lasers Electro-Optics a115, 1–2 (2015).
  19. A. Khavasi, L. Chrostowski, Z. Lu, and R. Bojko, “Significant crosstalk reduction using all-dielectric CMOS-compatible metamaterials,” IEEE Photonics Technol. Lett. 28(24), 2787–2790 (2016).
    [Crossref]
  20. N. Yang, H. Yang, H. Hu, R. Zhu, S. Chen, H. Zhang, and W. Jiang, “Theory of high-density low-cross-talk waveguide superlattices,” Photon. Res. 4(6), 233–239 (2016).
    [Crossref]
  21. H. Unz, “Linear arrays with arbitrarily distributed elements,” IRE Trans. Antennas Propag. 8(2), 222–223 (1960).
    [Crossref]
  22. M. G. Bray, D. H. Werner, D. W. Boeringer, and D. W. Machuga, “Optimization of thinned aperiodic linear phased arrays using genetic algorithms to reduce grating lobes during scanning,” IEEE Trans. Antenn. Propag. 50(12), 1732–1742 (2002).
    [Crossref]
  23. D. King, R. Packard, and R. Thomas, “Unequally-spaced, broad-band antenna arrays,” IRE Trans. Antennas Propag. 8(4), 380–384 (1960).
    [Crossref]
  24. F. Soltankarimi, J. Nourinia, and C. Ghobadi, “Side lobe level optimization in phased array antennas using genetic algorithm,” in Proceedings of IEEE Eighth International Symposium on Spread Spectrum Techniques and Applications (IEEE, 2004), pp. 389–394.
    [Crossref]
  25. K.-K. Yan and Y. Lu, “Sidelobe reduction in array-pattern synthesis using genetic algorithm,” IEEE Trans. Antenn. Propag. 45(7), 1117–1122 (1997).
    [Crossref]
  26. D. Kwong, A. Hosseini, Y. Zhang, and R. T. Chen, “1 × 12 Unequally spaced waveguide array for actively tuned optical phased array on a silicon nanomembrane,” Appl. Phys. Lett. 99(5), 051104 (2011).
    [Crossref]
  27. J. C. Hulme, J. K. Doylend, M. J. R. Heck, J. D. Peters, M. L. Davenport, J. T. Bovington, L. A. Coldren, and J. E. Bowers, “Fully integrated hybrid silicon two dimensional beam scanner,” Opt. Express 23(5), 5861–5874 (2015).
    [Crossref] [PubMed]
  28. D. N. Hutchison, J. Sun, J. K. Doylend, R. Kumar, J. Heck, W. Kim, C. T. Phare, A. Feshali, and H. Rong, “High-resolution aliasing-free optical beam steering,” Optica 3(8), 887–890 (2016).
    [Crossref]
  29. T. Komljenovic, R. Helkey, L. Coldren, and J. E. Bowers, “Sparse aperiodic arrays for optical beam forming and LIDAR,” Opt. Express 25(3), 2511–2528 (2017).
    [Crossref] [PubMed]
  30. B. R. Mahafza and A. Z. Elsherbeni, Simulations for Radar Systems Design (CRC, 2004).
  31. S. Tata and J. M. Patel, “Estimating the selectivity of tf-idf based cosine similarity predicates,” SIGMOD Rec. 36(2), 7–12 (2007).
    [Crossref]
  32. H. V. Nguyen and L. Bai, “Cosine similarity metric learning for face verification,” in Proceedings of ACCV 2010 (Academic, 2010), pp. 709–720.
  33. A. Trastoy and F. Ares, “Phase-only control of antenna sum patterns - Abstract,” J. Electromagn. Waves Appl. 14(8), 1103–1104 (2000).
    [Crossref]
  34. P. Harikumar, V. V. B. Bikkani, G. K. Mahanti, and B. C. Mahato, “Phase-only side lobe level reduction of uniformly excited linear array antenna using iterative fast Fourier transform,” in Proceedings of 2011 Annual IEEE India Conference (IEEE, 2011), pp. 1–4.
    [Crossref]
  35. B. Shi and Q. Luo, “Genetic algorithm in suppression of quantization side-lobes of phased array antenna,” in Proceedings of 2011 4th IEEE International Symposium on Microwave, Antenna, Propagation, and EMC Technologies for Wireless Communications (IEEE, 2011), pp. 83–86.
    [Crossref]

2018 (2)

Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018).
[Crossref] [PubMed]

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

2017 (2)

M. J. R. Heck, “Highly integrated optical phased arrays: photonic integrated circuits for optical beam shaping and beam steering,” Nanophotonics 6(1), 93–107 (2017).
[Crossref]

T. Komljenovic, R. Helkey, L. Coldren, and J. E. Bowers, “Sparse aperiodic arrays for optical beam forming and LIDAR,” Opt. Express 25(3), 2511–2528 (2017).
[Crossref] [PubMed]

2016 (3)

2015 (4)

B. Guan, C. Qin, R. P. Scott, B. Ercan, N. K. Fontaine, T. Su, and S. J. B. Yoo, “Hybrid 3D photonic integrated circuit for optical phased array beam steering,” Lasers Electro-Optics a115, 1–2 (2015).

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

J. C. Hulme, J. K. Doylend, M. J. R. Heck, J. D. Peters, M. L. Davenport, J. T. Bovington, L. A. Coldren, and J. E. Bowers, “Fully integrated hybrid silicon two dimensional beam scanner,” Opt. Express 23(5), 5861–5874 (2015).
[Crossref] [PubMed]

H. Abediasl and H. Hashemi, “Monolithic optical phased-array transceiver in a standard SOI CMOS process,” Opt. Express 23(5), 6509–6519 (2015).
[Crossref] [PubMed]

2014 (2)

2013 (2)

Y. Arakawa, T. Nakamura, Y. Urino, and T. Fujita, “Silicon photonics for next generation system integration platform,” IEEE Commun. Mag. 51(3), 72–77 (2013).
[Crossref]

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]

2012 (1)

2011 (4)

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]

K. V. Acoleyen, K. Komorowska, W. Bogaerts, and R. Baets, “One-dimensional off-chip beam steering and shaping using optical phased arrays on silicon-on-insulator,” J. Lightwave Technol. 29(23), 3500–3505 (2011).
[Crossref]

K. V. Acoleyen, W. Bogaerts, and R. Baets, “Two-dimensional dispersive off-chip beam scanner fabricated on silicon-on-insulator,” IEEE Photonics Technol. Lett. 23(17), 1270–1272 (2011).
[Crossref]

D. Kwong, A. Hosseini, Y. Zhang, and R. T. Chen, “1 × 12 Unequally spaced waveguide array for actively tuned optical phased array on a silicon nanomembrane,” Appl. Phys. Lett. 99(5), 051104 (2011).
[Crossref]

2010 (1)

2009 (2)

K. Van Acoleyen, W. Bogaerts, J. Jágerská, N. Le Thomas, R. Houdré, and R. Baets, “Off-chip beam steering with a one-dimensional optical phased array on silicon-on-insulator,” Opt. Lett. 34(9), 1477–1479 (2009).
[Crossref] [PubMed]

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

2007 (1)

S. Tata and J. M. Patel, “Estimating the selectivity of tf-idf based cosine similarity predicates,” SIGMOD Rec. 36(2), 7–12 (2007).
[Crossref]

2002 (1)

M. G. Bray, D. H. Werner, D. W. Boeringer, and D. W. Machuga, “Optimization of thinned aperiodic linear phased arrays using genetic algorithms to reduce grating lobes during scanning,” IEEE Trans. Antenn. Propag. 50(12), 1732–1742 (2002).
[Crossref]

2000 (1)

A. Trastoy and F. Ares, “Phase-only control of antenna sum patterns - Abstract,” J. Electromagn. Waves Appl. 14(8), 1103–1104 (2000).
[Crossref]

1997 (1)

K.-K. Yan and Y. Lu, “Sidelobe reduction in array-pattern synthesis using genetic algorithm,” IEEE Trans. Antenn. Propag. 45(7), 1117–1122 (1997).
[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]

1960 (2)

D. King, R. Packard, and R. Thomas, “Unequally-spaced, broad-band antenna arrays,” IRE Trans. Antennas Propag. 8(4), 380–384 (1960).
[Crossref]

H. Unz, “Linear arrays with arbitrarily distributed elements,” IRE Trans. Antennas Propag. 8(2), 222–223 (1960).
[Crossref]

Abediasl, H.

Acoleyen, K. V.

K. V. Acoleyen, W. Bogaerts, and R. Baets, “Two-dimensional dispersive off-chip beam scanner fabricated on silicon-on-insulator,” IEEE Photonics Technol. Lett. 23(17), 1270–1272 (2011).
[Crossref]

K. V. Acoleyen, K. Komorowska, W. Bogaerts, and R. Baets, “One-dimensional off-chip beam steering and shaping using optical phased arrays on silicon-on-insulator,” J. Lightwave Technol. 29(23), 3500–3505 (2011).
[Crossref]

Arakawa, Y.

Y. Arakawa, T. Nakamura, Y. Urino, and T. Fujita, “Silicon photonics for next generation system integration platform,” IEEE Commun. Mag. 51(3), 72–77 (2013).
[Crossref]

Ares, F.

A. Trastoy and F. Ares, “Phase-only control of antenna sum patterns - Abstract,” J. Electromagn. Waves Appl. 14(8), 1103–1104 (2000).
[Crossref]

Baets, R.

Bai, L.

H. V. Nguyen and L. Bai, “Cosine similarity metric learning for face verification,” in Proceedings of ACCV 2010 (Academic, 2010), pp. 709–720.

Bikkani, V. V. B.

P. Harikumar, V. V. B. Bikkani, G. K. Mahanti, and B. C. Mahato, “Phase-only side lobe level reduction of uniformly excited linear array antenna using iterative fast Fourier transform,” in Proceedings of 2011 Annual IEEE India Conference (IEEE, 2011), pp. 1–4.
[Crossref]

Boeringer, D. W.

M. G. Bray, D. H. Werner, D. W. Boeringer, and D. W. Machuga, “Optimization of thinned aperiodic linear phased arrays using genetic algorithms to reduce grating lobes during scanning,” IEEE Trans. Antenn. Propag. 50(12), 1732–1742 (2002).
[Crossref]

Bogaerts, W.

Bojko, R.

A. Khavasi, L. Chrostowski, Z. Lu, and R. Bojko, “Significant crosstalk reduction using all-dielectric CMOS-compatible metamaterials,” IEEE Photonics Technol. Lett. 28(24), 2787–2790 (2016).
[Crossref]

Bos, P. J.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Bovington, J. T.

Bowers, J. E.

Bray, M. G.

M. G. Bray, D. H. Werner, D. W. Boeringer, and D. W. Machuga, “Optimization of thinned aperiodic linear phased arrays using genetic algorithms to reduce grating lobes during scanning,” IEEE Trans. Antenn. Propag. 50(12), 1732–1742 (2002).
[Crossref]

Cai, H.

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Chen, R. T.

D. Kwong, A. Hosseini, J. Covey, Y. Zhang, X. Xu, H. Subbaraman, and R. T. Chen, “On-chip silicon optical phased array for two-dimensional beam steering,” Opt. Lett. 39(4), 941–944 (2014).
[Crossref] [PubMed]

D. Kwong, A. Hosseini, Y. Zhang, and R. T. Chen, “1 × 12 Unequally spaced waveguide array for actively tuned optical phased array on a silicon nanomembrane,” Appl. Phys. Lett. 99(5), 051104 (2011).
[Crossref]

Chen, S.

Chen, T.

Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018).
[Crossref] [PubMed]

Chen, T. N.

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

Chen, Y.

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

Chin, L. K.

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018).
[Crossref] [PubMed]

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Chrostowski, L.

A. Khavasi, L. Chrostowski, Z. Lu, and R. Bojko, “Significant crosstalk reduction using all-dielectric CMOS-compatible metamaterials,” IEEE Photonics Technol. Lett. 28(24), 2787–2790 (2016).
[Crossref]

Coldren, L.

Coldren, L. A.

Cole, D. B.

Coolbaugh, D.

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]

Covey, J.

Davenport, M. L.

Deng, T. W.

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

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]

Doylend, J. K.

Ercan, B.

B. Guan, C. Qin, R. P. Scott, B. Ercan, N. K. Fontaine, T. Su, and S. J. B. Yoo, “Hybrid 3D photonic integrated circuit for optical phased array beam steering,” Lasers Electro-Optics a115, 1–2 (2015).

Escuti, M. J.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Feshali, A.

Fontaine, N. K.

B. Guan, C. Qin, R. P. Scott, B. Ercan, N. K. Fontaine, T. Su, and S. J. B. Yoo, “Hybrid 3D photonic integrated circuit for optical phased array beam steering,” Lasers Electro-Optics a115, 1–2 (2015).

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]

Fujita, T.

Y. Arakawa, T. Nakamura, Y. Urino, and T. Fujita, “Silicon photonics for next generation system integration platform,” IEEE Commun. Mag. 51(3), 72–77 (2013).
[Crossref]

Ghobadi, C.

F. Soltankarimi, J. Nourinia, and C. Ghobadi, “Side lobe level optimization in phased array antennas using genetic algorithm,” in Proceedings of IEEE Eighth International Symposium on Spread Spectrum Techniques and Applications (IEEE, 2004), pp. 389–394.
[Crossref]

Gu, Y.

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Guan, B.

B. Guan, C. Qin, R. P. Scott, B. Ercan, N. K. Fontaine, T. Su, and S. J. B. Yoo, “Hybrid 3D photonic integrated circuit for optical phased array beam steering,” Lasers Electro-Optics a115, 1–2 (2015).

Hao, Y.

Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018).
[Crossref] [PubMed]

Hao, Y. L.

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

Harikumar, P.

P. Harikumar, V. V. B. Bikkani, G. K. Mahanti, and B. C. Mahato, “Phase-only side lobe level reduction of uniformly excited linear array antenna using iterative fast Fourier transform,” in Proceedings of 2011 Annual IEEE India Conference (IEEE, 2011), pp. 1–4.
[Crossref]

Hashemi, H.

Heck, J.

Heck, M. J. R.

Heikenfeld, J.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Helkey, R.

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]

Hoi, L. S.

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

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]

Hosseini, A.

D. Kwong, A. Hosseini, J. Covey, Y. Zhang, X. Xu, H. Subbaraman, and R. T. Chen, “On-chip silicon optical phased array for two-dimensional beam steering,” Opt. Lett. 39(4), 941–944 (2014).
[Crossref] [PubMed]

D. Kwong, A. Hosseini, Y. Zhang, and R. T. Chen, “1 × 12 Unequally spaced waveguide array for actively tuned optical phased array on a silicon nanomembrane,” Appl. Phys. Lett. 99(5), 051104 (2011).
[Crossref]

Hosseini, E.

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]

Houdré, R.

Hu, H.

Huang, R.

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Hulme, J. C.

Hutchison, D. N.

Jágerská, J.

Jiang, W.

Khavasi, A.

A. Khavasi, L. Chrostowski, Z. Lu, and R. Bojko, “Significant crosstalk reduction using all-dielectric CMOS-compatible metamaterials,” IEEE Photonics Technol. Lett. 28(24), 2787–2790 (2016).
[Crossref]

Kim, W.

King, D.

D. King, R. Packard, and R. Thomas, “Unequally-spaced, broad-band antenna arrays,” IRE Trans. Antennas Propag. 8(4), 380–384 (1960).
[Crossref]

Komljenovic, T.

Komorowska, K.

Kumar, R.

Kwong, D.

D. Kwong, A. Hosseini, J. Covey, Y. Zhang, X. Xu, H. Subbaraman, and R. T. Chen, “On-chip silicon optical phased array for two-dimensional beam steering,” Opt. Lett. 39(4), 941–944 (2014).
[Crossref] [PubMed]

D. Kwong, A. Hosseini, Y. Zhang, and R. T. Chen, “1 × 12 Unequally spaced waveguide array for actively tuned optical phased array on a silicon nanomembrane,” Appl. Phys. Lett. 99(5), 051104 (2011).
[Crossref]

Kwong, D. L.

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Larson, A.

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

Le Thomas, N.

Leake, G.

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]

Liedberg, B.

Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018).
[Crossref] [PubMed]

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

Liu, A. Q.

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018).
[Crossref] [PubMed]

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Lo, G. Q.

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Lu, Y.

K.-K. Yan and Y. Lu, “Sidelobe reduction in array-pattern synthesis using genetic algorithm,” IEEE Trans. Antenn. Propag. 45(7), 1117–1122 (1997).
[Crossref]

Lu, Z.

A. Khavasi, L. Chrostowski, Z. Lu, and R. Bojko, “Significant crosstalk reduction using all-dielectric CMOS-compatible metamaterials,” IEEE Photonics Technol. Lett. 28(24), 2787–2790 (2016).
[Crossref]

Luo, Q.

B. Shi and Q. Luo, “Genetic algorithm in suppression of quantization side-lobes of phased array antenna,” in Proceedings of 2011 4th IEEE International Symposium on Microwave, Antenna, Propagation, and EMC Technologies for Wireless Communications (IEEE, 2011), pp. 83–86.
[Crossref]

Machuga, D. W.

M. G. Bray, D. H. Werner, D. W. Boeringer, and D. W. Machuga, “Optimization of thinned aperiodic linear phased arrays using genetic algorithms to reduce grating lobes during scanning,” IEEE Trans. Antenn. Propag. 50(12), 1732–1742 (2002).
[Crossref]

Mahanti, G. K.

P. Harikumar, V. V. B. Bikkani, G. K. Mahanti, and B. C. Mahato, “Phase-only side lobe level reduction of uniformly excited linear array antenna using iterative fast Fourier transform,” in Proceedings of 2011 Annual IEEE India Conference (IEEE, 2011), pp. 1–4.
[Crossref]

Mahato, B. C.

P. Harikumar, V. V. B. Bikkani, G. K. Mahanti, and B. C. Mahato, “Phase-only side lobe level reduction of uniformly excited linear array antenna using iterative fast Fourier transform,” in Proceedings of 2011 Annual IEEE India Conference (IEEE, 2011), pp. 1–4.
[Crossref]

McManamon, P. F.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[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]

Nakamura, T.

Y. Arakawa, T. Nakamura, Y. Urino, and T. Fujita, “Silicon photonics for next generation system integration platform,” IEEE Commun. Mag. 51(3), 72–77 (2013).
[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]

Nguyen, H. V.

H. V. Nguyen and L. Bai, “Cosine similarity metric learning for face verification,” in Proceedings of ACCV 2010 (Academic, 2010), pp. 709–720.

Nourinia, J.

F. Soltankarimi, J. Nourinia, and C. Ghobadi, “Side lobe level optimization in phased array antennas using genetic algorithm,” in Proceedings of IEEE Eighth International Symposium on Spread Spectrum Techniques and Applications (IEEE, 2004), pp. 389–394.
[Crossref]

Packard, R.

D. King, R. Packard, and R. Thomas, “Unequally-spaced, broad-band antenna arrays,” IRE Trans. Antennas Propag. 8(4), 380–384 (1960).
[Crossref]

Patel, J. M.

S. Tata and J. M. Patel, “Estimating the selectivity of tf-idf based cosine similarity predicates,” SIGMOD Rec. 36(2), 7–12 (2007).
[Crossref]

Peters, J. D.

Phare, C. T.

Qin, C.

B. Guan, C. Qin, R. P. Scott, B. Ercan, N. K. Fontaine, T. Su, and S. J. B. Yoo, “Hybrid 3D photonic integrated circuit for optical phased array beam steering,” Lasers Electro-Optics a115, 1–2 (2015).

Qiu, C. W.

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018).
[Crossref] [PubMed]

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]

Rogier, H.

Rong, H.

Scott, R. P.

B. Guan, C. Qin, R. P. Scott, B. Ercan, N. K. Fontaine, T. Su, and S. J. B. Yoo, “Hybrid 3D photonic integrated circuit for optical phased array beam steering,” Lasers Electro-Optics a115, 1–2 (2015).

Ser, W.

Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018).
[Crossref] [PubMed]

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

Serati, S.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[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]

Shen, Z. X.

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Shi, B.

B. Shi and Q. Luo, “Genetic algorithm in suppression of quantization side-lobes of phased array antenna,” in Proceedings of 2011 4th IEEE International Symposium on Microwave, Antenna, Propagation, and EMC Technologies for Wireless Communications (IEEE, 2011), pp. 83–86.
[Crossref]

Shi, Y.

Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018).
[Crossref] [PubMed]

Shi, Y. Z.

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

Soltankarimi, F.

F. Soltankarimi, J. Nourinia, and C. Ghobadi, “Side lobe level optimization in phased array antennas using genetic algorithm,” in Proceedings of IEEE Eighth International Symposium on Spread Spectrum Techniques and Applications (IEEE, 2004), pp. 389–394.
[Crossref]

Song, Q.

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Su, T.

B. Guan, C. Qin, R. P. Scott, B. Ercan, N. K. Fontaine, T. Su, and S. J. B. Yoo, “Hybrid 3D photonic integrated circuit for optical phased array beam steering,” Lasers Electro-Optics a115, 1–2 (2015).

Subbaraman, H.

Sun, J.

Tata, S.

S. Tata and J. M. Patel, “Estimating the selectivity of tf-idf based cosine similarity predicates,” SIGMOD Rec. 36(2), 7–12 (2007).
[Crossref]

Thomas, R.

D. King, R. Packard, and R. Thomas, “Unequally-spaced, broad-band antenna arrays,” IRE Trans. Antennas Propag. 8(4), 380–384 (1960).
[Crossref]

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]

Ting, S. K.

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Trastoy, A.

A. Trastoy and F. Ares, “Phase-only control of antenna sum patterns - Abstract,” J. Electromagn. Waves Appl. 14(8), 1103–1104 (2000).
[Crossref]

Tsai, D. P.

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018).
[Crossref] [PubMed]

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Unz, H.

H. Unz, “Linear arrays with arbitrarily distributed elements,” IRE Trans. Antennas Propag. 8(2), 222–223 (1960).
[Crossref]

Urino, Y.

Y. Arakawa, T. Nakamura, Y. Urino, and T. Fujita, “Silicon photonics for next generation system integration platform,” IEEE Commun. Mag. 51(3), 72–77 (2013).
[Crossref]

Van Acoleyen, K.

Watson, E. A.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[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]

Watts, M. R.

J. Sun, E. Hosseini, A. Yaacobi, D. B. Cole, G. Leake, D. Coolbaugh, and M. R. Watts, “Two-dimensional apodized silicon photonic phased arrays,” Opt. Lett. 39(2), 367–370 (2014).
[Crossref] [PubMed]

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]

Werner, D. H.

M. G. Bray, D. H. Werner, D. W. Boeringer, and D. W. Machuga, “Optimization of thinned aperiodic linear phased arrays using genetic algorithms to reduce grating lobes during scanning,” IEEE Trans. Antenn. Propag. 50(12), 1732–1742 (2002).
[Crossref]

Wu, J.

Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018).
[Crossref] [PubMed]

Wu, J. H.

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

Wu, P. C.

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Xie, H.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Xiong, S.

Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018).
[Crossref] [PubMed]

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

Xu, X.

Yaacobi, A.

J. Sun, E. Hosseini, A. Yaacobi, D. B. Cole, G. Leake, D. Coolbaugh, and M. R. Watts, “Two-dimensional apodized silicon photonic phased arrays,” Opt. Lett. 39(2), 367–370 (2014).
[Crossref] [PubMed]

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]

Yan, K.-K.

K.-K. Yan and Y. Lu, “Sidelobe reduction in array-pattern synthesis using genetic algorithm,” IEEE Trans. Antenn. Propag. 45(7), 1117–1122 (1997).
[Crossref]

Yan, L.

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Yang, H.

Yang, N.

Yang, Z.

Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018).
[Crossref] [PubMed]

Yang, Z. C.

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Yap, P. H.

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018).
[Crossref] [PubMed]

Yoo, S. J. B.

B. Guan, C. Qin, R. P. Scott, B. Ercan, N. K. Fontaine, T. Su, and S. J. B. Yoo, “Hybrid 3D photonic integrated circuit for optical phased array beam steering,” Lasers Electro-Optics a115, 1–2 (2015).

Zhang, H.

Zhang, J.

Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018).
[Crossref] [PubMed]

Zhang, J. B.

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

Zhang, T. H.

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

Zhang, W.

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Zhang, Y.

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

D. Kwong, A. Hosseini, J. Covey, Y. Zhang, X. Xu, H. Subbaraman, and R. T. Chen, “On-chip silicon optical phased array for two-dimensional beam steering,” Opt. Lett. 39(4), 941–944 (2014).
[Crossref] [PubMed]

D. Kwong, A. Hosseini, Y. Zhang, and R. T. Chen, “1 × 12 Unequally spaced waveguide array for actively tuned optical phased array on a silicon nanomembrane,” Appl. Phys. Lett. 99(5), 051104 (2011).
[Crossref]

Zheludev, N.

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Zhu, R.

Zhu, W.

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Adv. Mater. (1)

W. Zhu, Q. Song, L. Yan, W. Zhang, P. C. Wu, L. K. Chin, H. Cai, D. P. Tsai, Z. X. Shen, T. W. Deng, S. K. Ting, Y. Gu, G. Q. Lo, D. L. Kwong, Z. C. Yang, R. Huang, A. Q. Liu, and N. Zheludev, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial,” Adv. Mater. 27(32), 4739–4743 (2015).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

D. Kwong, A. Hosseini, Y. Zhang, and R. T. Chen, “1 × 12 Unequally spaced waveguide array for actively tuned optical phased array on a silicon nanomembrane,” Appl. Phys. Lett. 99(5), 051104 (2011).
[Crossref]

IEEE Commun. Mag. (1)

Y. Arakawa, T. Nakamura, Y. Urino, and T. Fujita, “Silicon photonics for next generation system integration platform,” IEEE Commun. Mag. 51(3), 72–77 (2013).
[Crossref]

IEEE Photonics Technol. Lett. (2)

K. V. Acoleyen, W. Bogaerts, and R. Baets, “Two-dimensional dispersive off-chip beam scanner fabricated on silicon-on-insulator,” IEEE Photonics Technol. Lett. 23(17), 1270–1272 (2011).
[Crossref]

A. Khavasi, L. Chrostowski, Z. Lu, and R. Bojko, “Significant crosstalk reduction using all-dielectric CMOS-compatible metamaterials,” IEEE Photonics Technol. Lett. 28(24), 2787–2790 (2016).
[Crossref]

IEEE Trans. Antenn. Propag. (2)

M. G. Bray, D. H. Werner, D. W. Boeringer, and D. W. Machuga, “Optimization of thinned aperiodic linear phased arrays using genetic algorithms to reduce grating lobes during scanning,” IEEE Trans. Antenn. Propag. 50(12), 1732–1742 (2002).
[Crossref]

K.-K. Yan and Y. Lu, “Sidelobe reduction in array-pattern synthesis using genetic algorithm,” IEEE Trans. Antenn. Propag. 45(7), 1117–1122 (1997).
[Crossref]

IRE Trans. Antennas Propag. (2)

D. King, R. Packard, and R. Thomas, “Unequally-spaced, broad-band antenna arrays,” IRE Trans. Antennas Propag. 8(4), 380–384 (1960).
[Crossref]

H. Unz, “Linear arrays with arbitrarily distributed elements,” IRE Trans. Antennas Propag. 8(2), 222–223 (1960).
[Crossref]

J. Electromagn. Waves Appl. (1)

A. Trastoy and F. Ares, “Phase-only control of antenna sum patterns - Abstract,” J. Electromagn. Waves Appl. 14(8), 1103–1104 (2000).
[Crossref]

J. Lightwave Technol. (1)

Lasers Electro-Optics (1)

B. Guan, C. Qin, R. P. Scott, B. Ercan, N. K. Fontaine, T. Su, and S. J. B. Yoo, “Hybrid 3D photonic integrated circuit for optical phased array beam steering,” Lasers Electro-Optics a115, 1–2 (2015).

Nanophotonics (1)

M. J. R. Heck, “Highly integrated optical phased arrays: photonic integrated circuits for optical beam shaping and beam steering,” Nanophotonics 6(1), 93–107 (2017).
[Crossref]

Nat. Commun. (1)

Y. Z. Shi, S. Xiong, Y. Zhang, L. K. Chin, Y. Chen, J. B. Zhang, T. H. Zhang, W. Ser, A. Larson, L. S. Hoi, J. H. Wu, T. N. Chen, Z. C. Yang, Y. L. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement,” Nat. Commun. 9(1), 815 (2018).
[Crossref] [PubMed]

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 (5)

Opt. Lett. (4)

Optica (1)

Photon. Res. (1)

Proc. IEEE (2)

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]

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Sci. Adv. (1)

Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018).
[Crossref] [PubMed]

SIGMOD Rec. (1)

S. Tata and J. M. Patel, “Estimating the selectivity of tf-idf based cosine similarity predicates,” SIGMOD Rec. 36(2), 7–12 (2007).
[Crossref]

Other (5)

H. V. Nguyen and L. Bai, “Cosine similarity metric learning for face verification,” in Proceedings of ACCV 2010 (Academic, 2010), pp. 709–720.

B. R. Mahafza and A. Z. Elsherbeni, Simulations for Radar Systems Design (CRC, 2004).

P. Harikumar, V. V. B. Bikkani, G. K. Mahanti, and B. C. Mahato, “Phase-only side lobe level reduction of uniformly excited linear array antenna using iterative fast Fourier transform,” in Proceedings of 2011 Annual IEEE India Conference (IEEE, 2011), pp. 1–4.
[Crossref]

B. Shi and Q. Luo, “Genetic algorithm in suppression of quantization side-lobes of phased array antenna,” in Proceedings of 2011 4th IEEE International Symposium on Microwave, Antenna, Propagation, and EMC Technologies for Wireless Communications (IEEE, 2011), pp. 83–86.
[Crossref]

F. Soltankarimi, J. Nourinia, and C. Ghobadi, “Side lobe level optimization in phased array antennas using genetic algorithm,” in Proceedings of IEEE Eighth International Symposium on Spread Spectrum Techniques and Applications (IEEE, 2004), pp. 389–394.
[Crossref]

Supplementary Material (2)

NameDescription
» Visualization 1       Details of the beam-forming process of the designed 128-element aperiodic OPA.
» Visualization 2       The scanning schematic of the uniformly spaced and aperiodic OPAs in polar coordinates.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1 (a) Layout of a uniformly spaced OPA. The main components usually include a laser, multi-mode interference, and phase shifter. (b) Far-field pattern of the uniformly spaced OPA.
Fig. 2
Fig. 2 Calculated properties of the far-field pattern of a uniformly spaced OPA when the element factor is not considered; the operating wavelength is set to 1.55 μm. For a fixed chip width, increasing the number of waveguides will decrease the pitch. (a) BW, (b) scan angle, (c) PSLL, and (d) power in the main lobe as functions of the number of waveguides for uniformly spaced OPAs with widths of 50, 100, and 150 μm.
Fig. 3
Fig. 3 (a) Cosine similarity between the delta function and actual far-field pattern as a function of the number of waveguides when the search area is equal to the minimum pitch requirement. The minimum pitch requirement is set to 2, 3, and 4 μm. (b) Cosine similarity between the delta function and actual far-field pattern as a function of the number of waveguides when the minimum pitch requirement is equal to 4 μm and the search area is set to one, two, and three times the minimum pitch requirement. (c) BW, (d) PSLL, and (e) power of the 128-element OPA designed by the proposed method as functions of the minimum pitch requirement when the search area is thrice the minimum pitch requirement.
Fig. 4
Fig. 4 Search results with a minimum pitch requirement of 4 μm and search scope of 12 μm. (a) Contrast of the placement method of aperiodic and uniform OPA. (b) Difference between the pitch of the designed aperiodic OPA and uniform OPA. Illustrative far-field pattern for (c) 16-element, (d) 32-element, and (e) 64-element aperiodic OPA. See Visualization 1 for a video showing the details of the beamforming process of the designed 128-element aperiodic OPA.
Fig. 5
Fig. 5 Beam scanning with a uniform and non-uniform phased array consisting of 128 waveguides with an operation wavelength of 1.55 μm without considering the width of the waveguide. Visualization 2 shows a schematic of the scanning of the uniformly spaced and aperiodic OPAs in polar coordinates for an intuitive comparison. (a) Far-field pattern along θ for uniform emitter pitches when θ0 = 0° and 5°. (b) Far-field pattern along θ for non-uniform emitter pitches when θ0 = –82°, –60°, –40°, 20°, 0°, 20°, 40°, 60°, and 82°. (c) BW, (d) PSLL, and (e) power in the main lobe as a function of scan angle for the non-uniformly spaced OPA.
Fig. 6
Fig. 6 Original beam and varied beam with different limits of phase errors of each waveguide. The inset shows the feature of the main lobe. (a) No-machine-error condition. The original beam has a BW of 0.062°, PSLL of –14.34 dB, and main-lobe power ratio of 0.054. (b) Far-field pattern when the range of phase errors is [–0.3π, 0.3π], (c) [–0.6π, 0.6π], and (d) [–π, π].
Fig. 7
Fig. 7 Theoretical upper and lower bounds of the PSLL and the simulation result for the designed aperiodic 128-element OPA when considering the phase error. The values of ξ are 3, 4, and 5, respectively, which implies that the probability of the actual PSLL being in the forecast range is greater than 88.89%, 93.75%, and 96%, respectively. The simulation for each scope is conducted one hundred times. Error bars are specified by the maximum, minimum, and mean value of the PSLL.
Fig. 8
Fig. 8 Estimated value of the PSLL of the 128-element OPA when the initial value of the PSLL is known and the phase errors are considered.
Fig. 9
Fig. 9 Theoretical upper and lower bounds of the PSLL and the simulation result for the designed aperiodic 128-element OPA when considering the amplitude error. The values of ξ are 3, 4, and 5, respectively. The simulation for each scope is conducted one hundred times. Error bars are specified by the maximum, minimum, and mean value of the PSLL.
Fig. 10
Fig. 10 Estimated value of the PSLL of the 128-element OPA when the initial value of the PSLL is known and the amplitude errors are considered.

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

U( P )=k( θ ) exp( j k 0 r 0 ) jλ r 0 Σ U( x 0 , y 0 )exp[ j k 0 ( x r 0 x 0 + y r 0 y 0 ) ] d x 0 d y 0 ,
U( x 0 )= i=0 N1 A i exp( φ i )δ( x 0 x i ) .
U( θ )=k( θ ) exp( j k 0 r 0 ) jλ r 0 i=0 N1 A i exp( j k 0 x i sinθ+ φ i ) .
U( θ )=k( θ ) exp( j k 0 r 0 ) jλ r 0 i=0 N1 A i exp[ j k 0 id( sin θ 0 sinθ ) ] = i=0 N1 A i exp[ j k 0 id( sin θ 0 sinθ ) ] .
Δ θ FWHM 0.886λ Ndcos θ 0 .
| sin θ 0 sinθ |= λm d .
cos( f( n ),g( n ) )= i=1 n ( f( i )g( i ) ) i=1 n f 2 ( i ) i=1 n g 2 ( i ) .
f( θ )= i=0 N1 A i exp{ j[ k 0 x i (sin θ 0 sinθ) ] },
U e ( θ )= i=0 N1 A i exp{ j[ k 0 x i (sin θ 0 sinθ)+Δφ ] }.
E{ U e ( θ ) }=E{ i=0 N1 A i exp{ j[ k 0 x i (sin θ 0 sinθ)+Δφ ] } } =E{ exp( jΔφ ) } i=0 N1 A i exp( jk x i (sin θ 0 sinθ) ) . =E{ exp( jΔφ ) }U( θ )
σ 2 { U e ( θ ) }=E{ | U e ( θ ) | 2 } | E{ U e ( θ ) } | 2 = i=0 N1 A i 2 i=0 N1 A i 2 | E{ exp( jΔφ ) } | 2 . =( 1 ( sinΔ φ max Δ φ max ) 2 ) i=0 N1 A i 2
P( | xμ |<ε )>1 σ 2 ε 2 ,
P( E{ p }ξσ{ p }<p<E{ p }+ξσ{ p } )>1 1 ξ 2
E{ p }= E{ exp( jΔφ ) }| U( θ= θ 1 ) | | E{ U e } | max
| E{ U e } | max =E{ exp( jΔφ ) } i=0 N1 A i
E{ p }= | U( θ= θ 1 ) | i=0 N1 A i
ξσ{ p }= ξσ{ U e ( θ ) } | E{ U e } | max = ξσ{ U e ( θ ) } E{ exp( jΔφ ) } i=0 N1 A i =ξ ( 1 Nη )( ( Δ φ max sinΔ φ max ) 2 1 )
η= ( i=0 N1 A i ) 2 N i=0 N1 A i 2 .
U a ( θ )= i=0 N1 ( 1-Δ A i ) A max exp{ j[ k 0 x i (sin θ 0 sinθ) ] } .
E{ U a ( θ ) }=E{ 1-Δ A i } i=0 N1 A max exp{ j[ k 0 x i (sin θ 0 sinθ) ] } =E{ 1-Δ A i }U( θ ) .
σ 2 { U a ( θ ) }=E{ | U a ( θ ) | 2 } | E{ U a ( θ ) } | 2 =( E{ ( 1-Δ A i ) 2 } | E{ ( 1-Δ A i ) } | 2 ) i=0 N1 A max 2 . = NΔ A i 2 A max 2 12
E{ p a }= | U( θ= θ 2 ) | N A max .
ξσ{ p a }= ξσ{ U a ( θ ) } | E{ U a } | max = ξσ{ U a ( θ ) } E{ ( 1-Δ A i ) }N A max = ξΔ A i 2 3N ( 1- 1 2 Δ A i ) .

Metrics