Abstract

We investigate the feasibility of generating a plateau envelope for beam-steering with optical phased arrays (OPAs). The design guidelines are summarized from numerical simulations and verified with a fabricated chip, which incorporates both a coupling-suppressed curved waveguide array with a pitch of 0.8 μm for light emission and a 1-μm-long silica cavity for envelope tailoring. This silicon-on-insulator (SOI) based device demonstrates aliasing-free beam-steering over the entire field-of-view available (−32°~32°) with a far-field addressability of 6.71°. The steered beam exhibits a plateau envelope, with a peak intensity fluctuation of less than 0.45 dB, from −30° to 30°. These results represent a significant step towards realizing integrated OPA for optical beam-forming with a large aliasing-free steering range and a uniform beam intensity.

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

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    [Crossref]

2018 (3)

S. Chung, H. Abediasl, and H. Hashemi, “A monolithically integrated large-scale optical phased array in silicon-on-insulator CMOS,” IEEE J. Solid-State Circuits 53(1), 275–296 (2018).
[Crossref]

M. R. Kossey, C. Rizk, and A. C. Foster, “End-fire silicon optical phased array with half-wavelength spacing,” APL Photonics 3(1), 011301 (2018).
[Crossref]

D. Zhuang, L. Zhagn, X. Han, Y. Li, Y. Li, X. Liu, F. Gao, and J. Song, “Omnidirectional beam steering using aperiodic optical phased array with high error margin,” Opt. Express 26(15), 19154–19170 (2018).
[Crossref] [PubMed]

2017 (1)

2016 (4)

2015 (6)

2014 (3)

2013 (2)

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]

W. Guo, P. R. A. Binetti, C. Althouse, M. L. Mašanović, H. P. Ambrosius, L. A. Johansson, and L. A. Coldren, “Two-dimensional optical beam steering with InP-based photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 19(4), 6100212 (2013).
[Crossref]

2012 (2)

Z. Sheng, Z. Q. Wang, C. Qiu, L. Li, A. Pang, A. M. Wu, X. Wang, S. C. Zou, and F. W. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

A. Biberman, M. J. Shaw, E. Timurdogan, J. B. Wright, and M. R. Watts, “Ultralow-loss silicon ring resonators,” Opt. Lett. 37(20), 4236–4238 (2012).
[Crossref] [PubMed]

2010 (1)

2009 (1)

2001 (1)

V. V. Nikulin, “Modeling of an acousto-optic laser beam steering system intended for satellite communication,” Opt. Eng. 40(10), 2208–2214 (2001).
[Crossref]

Abbaslou, S.

W. Song, R. Gatdula, S. Abbaslou, M. Lu, A. Stein, W. Y. C. Lai, J. Provine, R. F. W. Pease, D. N. Christodoulides, and W. Jiang, “High-density waveguide superlattices with low crosstalk,” Nat. Commun. 6(1), 7027 (2015).
[Crossref] [PubMed]

Abediasl, H.

S. Chung, H. Abediasl, and H. Hashemi, “A monolithically integrated large-scale optical phased array in silicon-on-insulator CMOS,” IEEE J. Solid-State Circuits 53(1), 275–296 (2018).
[Crossref]

Abiri, B.

Aflatouni, F.

Althouse, C.

W. Guo, P. R. A. Binetti, C. Althouse, M. L. Mašanović, H. P. Ambrosius, L. A. Johansson, and L. A. Coldren, “Two-dimensional optical beam steering with InP-based photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 19(4), 6100212 (2013).
[Crossref]

Ambrosius, H. P.

W. Guo, P. R. A. Binetti, C. Althouse, M. L. Mašanović, H. P. Ambrosius, L. A. Johansson, and L. A. Coldren, “Two-dimensional optical beam steering with InP-based photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 19(4), 6100212 (2013).
[Crossref]

Baets, R.

Biberman, A.

Binetti, P. R. A.

W. Guo, P. R. A. Binetti, C. Althouse, M. L. Mašanović, H. P. Ambrosius, L. A. Johansson, and L. A. Coldren, “Two-dimensional optical beam steering with InP-based photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 19(4), 6100212 (2013).
[Crossref]

Bogaerts, W.

Bovington, J. T.

Bowers, J. E.

Chakravarty, S.

D. Kwong, A. Hosseini, J. Covey, X. Xu, Y. Zhang, S. Chakravarty, and R. T. Chen, “Corrugated waveguide-based optical phased array with crosstalk suppression,” IEEE Photonics Technol. Lett. 26(10), 991–994 (2014).
[Crossref]

Chen, J.

W. Xu, L. Lu, L. Zhou, and J. Chen, “Reconfiguring the 16 × 16 silicon optical switch for optical beam steering application,” in Proceedings of International Topical Meeting on Microwave Photonics (IEEE, 2017, pp. 1–4).
[Crossref]

Chen, K.

Chen, R. T.

D. Kwong, A. Hosseini, J. Covey, X. Xu, Y. Zhang, S. Chakravarty, and R. T. Chen, “Corrugated waveguide-based optical phased array with crosstalk suppression,” IEEE Photonics Technol. Lett. 26(10), 991–994 (2014).
[Crossref]

Chen, S.

Christodoulides, D. N.

W. Song, R. Gatdula, S. Abbaslou, M. Lu, A. Stein, W. Y. C. Lai, J. Provine, R. F. W. Pease, D. N. Christodoulides, and W. Jiang, “High-density waveguide superlattices with low crosstalk,” Nat. Commun. 6(1), 7027 (2015).
[Crossref] [PubMed]

Chrostowski, L.

Chung, S.

S. Chung, H. Abediasl, and H. Hashemi, “A monolithically integrated large-scale optical phased array in silicon-on-insulator CMOS,” IEEE J. Solid-State Circuits 53(1), 275–296 (2018).
[Crossref]

Coldren, L.

Coldren, L. A.

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]

W. Guo, P. R. A. Binetti, C. Althouse, M. L. Mašanović, H. P. Ambrosius, L. A. Johansson, and L. A. Coldren, “Two-dimensional optical beam steering with InP-based photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 19(4), 6100212 (2013).
[Crossref]

Covey, J.

D. Kwong, A. Hosseini, J. Covey, X. Xu, Y. Zhang, S. Chakravarty, and R. T. Chen, “Corrugated waveguide-based optical phased array with crosstalk suppression,” IEEE Photonics Technol. Lett. 26(10), 991–994 (2014).
[Crossref]

Dai, D.

Davenport, M. L.

Ding, Y.

Doylend, J. K.

Feshali, A.

Foster, A. C.

M. R. Kossey, C. Rizk, and A. C. Foster, “End-fire silicon optical phased array with half-wavelength spacing,” APL Photonics 3(1), 011301 (2018).
[Crossref]

Gan, F. W.

Z. Sheng, Z. Q. Wang, C. Qiu, L. Li, A. Pang, A. M. Wu, X. Wang, S. C. Zou, and F. W. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

Gao, F.

Gatdula, R.

W. Song, R. Gatdula, S. Abbaslou, M. Lu, A. Stein, W. Y. C. Lai, J. Provine, R. F. W. Pease, D. N. Christodoulides, and W. Jiang, “High-density waveguide superlattices with low crosstalk,” Nat. Commun. 6(1), 7027 (2015).
[Crossref] [PubMed]

Guo, W.

W. Guo, P. R. A. Binetti, C. Althouse, M. L. Mašanović, H. P. Ambrosius, L. A. Johansson, and L. A. Coldren, “Two-dimensional optical beam steering with InP-based photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 19(4), 6100212 (2013).
[Crossref]

Hajimiri, A.

Han, X.

Hashemi, H.

S. Chung, H. Abediasl, and H. Hashemi, “A monolithically integrated large-scale optical phased array in silicon-on-insulator CMOS,” IEEE J. Solid-State Circuits 53(1), 275–296 (2018).
[Crossref]

Heck, J.

Heck, M. J. R.

Helkey, R.

Horikawa, T.

T. Horikawa, D. Shimura, and T. Mogami, “Low-loss silicon wire waveguides for optical integrated circuits,” MRS Commun. 6(01), 9–15 (2016).
[Crossref]

Hosseini, A.

D. Kwong, A. Hosseini, J. Covey, X. Xu, Y. Zhang, S. Chakravarty, and R. T. Chen, “Corrugated waveguide-based optical phased array with crosstalk suppression,” IEEE Photonics Technol. Lett. 26(10), 991–994 (2014).
[Crossref]

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.

Hulme, J. C.

Hutchison, D. N.

Jacob, Z.

Jágerská, J.

Jahani, S.

Jiang, W.

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]

W. Song, R. Gatdula, S. Abbaslou, M. Lu, A. Stein, W. Y. C. Lai, J. Provine, R. F. W. Pease, D. N. Christodoulides, and W. Jiang, “High-density waveguide superlattices with low crosstalk,” Nat. Commun. 6(1), 7027 (2015).
[Crossref] [PubMed]

Johansson, L. A.

W. Guo, P. R. A. Binetti, C. Althouse, M. L. Mašanović, H. P. Ambrosius, L. A. Johansson, and L. A. Coldren, “Two-dimensional optical beam steering with InP-based photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 19(4), 6100212 (2013).
[Crossref]

Kim, W.

Komljenovic, T.

Kossey, M. R.

M. R. Kossey, C. Rizk, and A. C. Foster, “End-fire silicon optical phased array with half-wavelength spacing,” APL Photonics 3(1), 011301 (2018).
[Crossref]

Kumar, R.

Kwong, D.

D. Kwong, A. Hosseini, J. Covey, X. Xu, Y. Zhang, S. Chakravarty, and R. T. Chen, “Corrugated waveguide-based optical phased array with crosstalk suppression,” IEEE Photonics Technol. Lett. 26(10), 991–994 (2014).
[Crossref]

Lai, W. Y. C.

W. Song, R. Gatdula, S. Abbaslou, M. Lu, A. Stein, W. Y. C. Lai, J. Provine, R. F. W. Pease, D. N. Christodoulides, and W. Jiang, “High-density waveguide superlattices with low crosstalk,” Nat. Commun. 6(1), 7027 (2015).
[Crossref] [PubMed]

Le Thomas, N.

Li, L.

Z. Sheng, Z. Q. Wang, C. Qiu, L. Li, A. Pang, A. M. Wu, X. Wang, S. C. Zou, and F. W. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

Li, Y.

Liu, L.

Liu, X.

Lu, L.

W. Xu, L. Lu, L. Zhou, and J. Chen, “Reconfiguring the 16 × 16 silicon optical switch for optical beam steering application,” in Proceedings of International Topical Meeting on Microwave Photonics (IEEE, 2017, pp. 1–4).
[Crossref]

Lu, M.

W. Song, R. Gatdula, S. Abbaslou, M. Lu, A. Stein, W. Y. C. Lai, J. Provine, R. F. W. Pease, D. N. Christodoulides, and W. Jiang, “High-density waveguide superlattices with low crosstalk,” Nat. Commun. 6(1), 7027 (2015).
[Crossref] [PubMed]

Mašanovic, M. L.

W. Guo, P. R. A. Binetti, C. Althouse, M. L. Mašanović, H. P. Ambrosius, L. A. Johansson, and L. A. Coldren, “Two-dimensional optical beam steering with InP-based photonic integrated circuits,” IEEE J. Sel. Top. Quantum Electron. 19(4), 6100212 (2013).
[Crossref]

Mogami, T.

T. Horikawa, D. Shimura, and T. Mogami, “Low-loss silicon wire waveguides for optical integrated circuits,” MRS Commun. 6(01), 9–15 (2016).
[Crossref]

Mulugeta, T.

Nikulin, V. V.

V. V. Nikulin, “Modeling of an acousto-optic laser beam steering system intended for satellite communication,” Opt. Eng. 40(10), 2208–2214 (2001).
[Crossref]

Ou, H.

Pang, A.

Z. Sheng, Z. Q. Wang, C. Qiu, L. Li, A. Pang, A. M. Wu, X. Wang, S. C. Zou, and F. W. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

Pease, R. F. W.

W. Song, R. Gatdula, S. Abbaslou, M. Lu, A. Stein, W. Y. C. Lai, J. Provine, R. F. W. Pease, D. N. Christodoulides, and W. Jiang, “High-density waveguide superlattices with low crosstalk,” Nat. Commun. 6(1), 7027 (2015).
[Crossref] [PubMed]

Peters, J. D.

Peucheret, C.

Phare, C. T.

Provine, J.

W. Song, R. Gatdula, S. Abbaslou, M. Lu, A. Stein, W. Y. C. Lai, J. Provine, R. F. W. Pease, D. N. Christodoulides, and W. Jiang, “High-density waveguide superlattices with low crosstalk,” Nat. Commun. 6(1), 7027 (2015).
[Crossref] [PubMed]

Qiu, C.

Z. Sheng, Z. Q. Wang, C. Qiu, L. Li, A. Pang, A. M. Wu, X. Wang, S. C. Zou, and F. W. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

Rasras, M.

Rekhi, A.

Rizk, C.

M. R. Kossey, C. Rizk, and A. C. Foster, “End-fire silicon optical phased array with half-wavelength spacing,” APL Photonics 3(1), 011301 (2018).
[Crossref]

Rong, H.

Rouger, N.

Shaw, M. J.

Sheng, Z.

Z. Sheng, Z. Q. Wang, C. Qiu, L. Li, A. Pang, A. M. Wu, X. Wang, S. C. Zou, and F. W. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

Shi, Y.

Shimura, D.

T. Horikawa, D. Shimura, and T. Mogami, “Low-loss silicon wire waveguides for optical integrated circuits,” MRS Commun. 6(01), 9–15 (2016).
[Crossref]

Song, J.

Song, W.

W. Song, R. Gatdula, S. Abbaslou, M. Lu, A. Stein, W. Y. C. Lai, J. Provine, R. F. W. Pease, D. N. Christodoulides, and W. Jiang, “High-density waveguide superlattices with low crosstalk,” Nat. Commun. 6(1), 7027 (2015).
[Crossref] [PubMed]

Stein, A.

W. Song, R. Gatdula, S. Abbaslou, M. Lu, A. Stein, W. Y. C. Lai, J. Provine, R. F. W. Pease, D. N. Christodoulides, and W. Jiang, “High-density waveguide superlattices with low crosstalk,” Nat. Commun. 6(1), 7027 (2015).
[Crossref] [PubMed]

Sun, J.

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]

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]

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]

A. Biberman, M. J. Shaw, E. Timurdogan, J. B. Wright, and M. R. Watts, “Ultralow-loss silicon ring resonators,” Opt. Lett. 37(20), 4236–4238 (2012).
[Crossref] [PubMed]

Vafaei, R.

Van Acoleyen, K.

Wang, S.

Wang, X.

Z. Sheng, Z. Q. Wang, C. Qiu, L. Li, A. Pang, A. M. Wu, X. Wang, S. C. Zou, and F. W. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[Crossref]

Wang, Z. Q.

Z. Sheng, Z. Q. Wang, C. Qiu, L. Li, A. Pang, A. M. Wu, X. Wang, S. C. Zou, and F. W. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
[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]

A. Biberman, M. J. Shaw, E. Timurdogan, J. B. Wright, and M. R. Watts, “Ultralow-loss silicon ring resonators,” Opt. Lett. 37(20), 4236–4238 (2012).
[Crossref] [PubMed]

Wright, J. B.

Wu, A. M.

Z. Sheng, Z. Q. Wang, C. Qiu, L. Li, A. Pang, A. M. Wu, X. Wang, S. C. Zou, and F. W. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
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W. Xu, L. Lu, L. Zhou, and J. Chen, “Reconfiguring the 16 × 16 silicon optical switch for optical beam steering application,” in Proceedings of International Topical Meeting on Microwave Photonics (IEEE, 2017, pp. 1–4).
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Xu, X.

D. Kwong, A. Hosseini, J. Covey, X. Xu, Y. Zhang, S. Chakravarty, and R. T. Chen, “Corrugated waveguide-based optical phased array with crosstalk suppression,” IEEE Photonics Technol. Lett. 26(10), 991–994 (2014).
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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).
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D. Kwong, A. Hosseini, J. Covey, X. Xu, Y. Zhang, S. Chakravarty, and R. T. Chen, “Corrugated waveguide-based optical phased array with crosstalk suppression,” IEEE Photonics Technol. Lett. 26(10), 991–994 (2014).
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Zhou, L.

W. Xu, L. Lu, L. Zhou, and J. Chen, “Reconfiguring the 16 × 16 silicon optical switch for optical beam steering application,” in Proceedings of International Topical Meeting on Microwave Photonics (IEEE, 2017, pp. 1–4).
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Z. Sheng, Z. Q. Wang, C. Qiu, L. Li, A. Pang, A. M. Wu, X. Wang, S. C. Zou, and F. W. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
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S. Chung, H. Abediasl, and H. Hashemi, “A monolithically integrated large-scale optical phased array in silicon-on-insulator CMOS,” IEEE J. Solid-State Circuits 53(1), 275–296 (2018).
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IEEE Photonics J. (1)

Z. Sheng, Z. Q. Wang, C. Qiu, L. Li, A. Pang, A. M. Wu, X. Wang, S. C. Zou, and F. W. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photonics J. 4(6), 2272–2277 (2012).
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IEEE Photonics Technol. Lett. (1)

D. Kwong, A. Hosseini, J. Covey, X. Xu, Y. Zhang, S. Chakravarty, and R. T. Chen, “Corrugated waveguide-based optical phased array with crosstalk suppression,” IEEE Photonics Technol. Lett. 26(10), 991–994 (2014).
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W. Xu, L. Lu, L. Zhou, and J. Chen, “Reconfiguring the 16 × 16 silicon optical switch for optical beam steering application,” in Proceedings of International Topical Meeting on Microwave Photonics (IEEE, 2017, pp. 1–4).
[Crossref]

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[Crossref]

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Figures (12)

Fig. 1
Fig. 1 Schematic of a typical implementation of one-dimensional OPA, consisting of a common laser input, a block of beam splitters, as well as an array of phase shifters followed by their corresponding antennas for light emission.
Fig. 2
Fig. 2 Six incidences recorded in a simulated beam-steering process of a uniform array with an emitter size of 0.5 μm and a pitch of 1.8 μm. In each incidence, the steering envelope is indicated by the orange dashed curve, and the intensity distribution is depicted by the blue curve. The main lobe highlighted with the red dashed line is steered from 0° to 60°, overtaken by the side lobe highlighted with the green dashed line from (d), causing aliasing and limiting the steering range.
Fig. 3
Fig. 3 (a, b) Schematics of the SOI-based 16-channel OPA, the underlying silicon substrates are omitted to highlight the silica cavity. (c, d) Normalized angular optical intensity distributions of the far-field diffraction pattern of the central emitter, captured on a hemisphere with a radius of 1 m. (e, f) Corresponding parallel (orange curve) and perpendicular (blue curve) axial optical intensity distributions, together with their corresponding angular plateau size indicated by the red/blue dashed lines. Left column: OPA with 1-um-long silica cavity; right column: OPA without silica cavity. (g) Comparison of the parallel-axis intensity distributions of the OPA with (red curve) and without (black curve) the silica cavity, together with their corresponding angular plateau size indicated by the red/black dashed lines.
Fig. 4
Fig. 4 (a) Two-dimensional electric-field diffraction pattern of the configuration where a cavity with a variable length is attached to a single silicon waveguide, revealing the effect of the silica cavity at the waveguide end. (b) Angular plateau size and transmittance as a function of silica cavity size. The far-field pattern adheres to the Gaussian shape, resulting in a little variation in the angular plateau size. Meanwhile, the transmittance exhibits an F-P resonance fringe characteristic.
Fig. 5
Fig. 5 (a) Two-dimensional electric-field diffraction pattern of the configuration where a fixed-length cavity is attached to an array of variable size, revealing the contribution of the array. (b) Angular plateau size and transmittance as a function of waveguide number. The out-coupling transmittance is generally stabilized at 0.86. The far-field diffraction pattern converges to the plateau shape after the waveguide number in the array exceeds 19.
Fig. 6
Fig. 6 (a) Two-dimensional electric-field diffraction pattern of the configuration where a length-varying cavity is attached to a fixed array, revealing the contribution of the cavity. (b) Angular plateau size and transmittance as a function of silica cavity length. The out-coupling transmittance still exhibits an F-P modulation effect. The far-field diffraction pattern varies considerably in terms of the light intensity angular distribution.
Fig. 7
Fig. 7 (a) Contour map of the transmittance with brighter colors for larger values. The out-coupling always exhibits pseudo-periodic intensity variation w.r.t the cavity length. (b) Contour map of the angular plateau size. The local maxima are indicated with the gray dashed lines.
Fig. 8
Fig. 8 (a) Two-dimensional electric-field diffraction pattern of the configuration where a 1-μm-long cavity is attached to a fixed-size array. Light is launched from a waveguide away from the center. (b) Extracted plateau angular size and transmittance from the simulation. The out-coupling approaches 0.73 with a weak dependence on the position of the launching waveguide. The plateau envelop is maximized when the light is launched into the central waveguides.
Fig. 9
Fig. 9 (a) Simulated beam-steering process of the waveguide. The two magenta lobes on both sides belong to the same incidence, causing aliasing. Blue dashed curve: plateau envelope averaged from diffraction patterns of all waveguides; red dashed curve: Gaussian-shape envelope. (b) Main lobe peak intensity (orange squares) and sidelobe suppression ratio (blue triangles) as a function of beam steering angle. The dashed lines of the same colors indicate the median values.
Fig. 10
Fig. 10 (a) Mask layout of the entire OPA chip. (b) Zoom-in of the curved waveguide array together with its transition sections that reduce the pitch from 50.5 μm to 0.8 μm. (c) Concentrically curved waveguides in the emission section with its critical design parameters labeled accordingly. (d) Microscope image of the fabricated chip. The footprint of the chip is 1.4 mm by 1.7 mm.
Fig. 11
Fig. 11 (a) Schematic of the reference curved waveguide array with the same design parameters as those in Fig. 10. (b) Measured inter-channel crosstalk (blue stars) and insertion loss (orange circles) for each channel. Median values representing the typical performances are indicated by dashed lines with the same color.
Fig. 12
Fig. 12 (a) Measured far-field intensity pattern of the aligned phased array (red line) together with the theoretical prediction via numerical simulation (black dashed line). The nearest local minimums of the experimental data, i.e. the 1st-order destructive inference points, are marked by blue dots. (b) Corresponding far-field image captured by the near-infrared camera when the beam is formed at the center of the FOV. the characterization region, also the region where incidences are cropped, is indicated by the orange dashed box. (c) The steered beams quantized by the averaged intensity distribution from the same characterization region with different incidences colored individually. (d) 14 slices cropped from the corresponding far-field patterns recorded by the near-infrared imaging system during the beam-steering process. (e) Normalized peak intensity (orange squares) and noise suppression w.r.t. the largest side lobe (blue triangles) for each incidence. The dashed lines indicate the median values.

Equations (3)

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I(θ)= I 0 ( sinα α ) 2 [ sin N 2 (δφ) sin 1 2 (δφ) ] 2 α= 1 2 kasinθ δ=kdsinθ
max{ G[(δφ)] }= lim (δφ)2mπ G[(δφ)]= N 2
sin[ N 2 (δφ)]=0 & δφ2mπ

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