Abstract

Sub-aperture coherence (SAC) algorithm, which is based on the classical phase modulation method called variable period grating (VPG), was usually used to control liquid crystal optical phased arrays (LCOPA) to achieve agile beam steering with high precision. However, the beam steering angle of SAC is severely affected by the beam aperture, which limits the generality of the algorithm distinctly. In this article, two kinds of new phase modulation method have been proposed to solve this problem, which were named as radial sub-aperture coherence (RSAC) and symmetrical radial sub-aperture coherence (SRSAC). By using RSAC, the holistic drift of steering angle, which is caused by the variation of beam aperture, can be effectively avoided. In addition, a series of equidistant steering points with ultra-high precision can be obtained. Upon this basis, SRSAC greatly enhances the steering angle’s stability in the presence of system alignment error and relative vibration. Thus, the practicability of LCOPA for beam steering can be improved effectively.

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

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    [Crossref]
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2018 (1)

X. Wang, L. Wu, X. He, X. Huang, and Q. Tan, “Theoretical analysis on power stability and switch time of the non-mechanical beam steering using liquid crystal optical phased array,” Liq. Cryst. 45(10), 1477–1486 (2018).
[Crossref]

2017 (1)

X. He, X. Wang, L. Wu, Q. Tan, M. Li, J. Shang, S. Wu, and Z. Huang, “Theoretical modeling on the laser induced effect of liquid crystal optical phased beam steering,” Opt. Commun. 382, 437–443 (2017).
[Crossref]

2016 (1)

Y. Wang and M. C. Wu, “An optical phased array for LIDAR,” J. Phys. Conf. Ser. 772(1), 012004 (2016).
[Crossref]

2015 (1)

Z. Tang, X. Wang, Z. Huang, Q. Tan, Y. Duan, G. Suo, J. Du, and Q. Qiu, “Sub-aperture coherence method to realize ultra-high resolution laser beam deflection,” Opt. Commun. 335, 1–6 (2015).
[Crossref]

2014 (1)

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

2013 (1)

2012 (1)

2011 (1)

Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivnenko, J. Moore, B. Crossland, D. P. Chu, and B. Milne, “High quality assembly of phase-only Liquid Crystal on Silicon (LCOS) devices,” J. Disp. Technol. 7(3), 120–126 (2011).
[Crossref]

2010 (2)

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 eystems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

2008 (2)

D. Engström, J. Bengtsson, E. Eriksson, and M. Goksör, “Improved beam steering accuracy of a single beam with a 1D phase-only spatial light modulator,” Opt. Express 16(22), 18275–18287 (2008).
[Crossref] [PubMed]

D. Engström, J. Bengtsson, E. Eriksson, and M. Goksör, “Steering accuracy of a spatial light modulator-based single beam steerer: guidelines and limitations,” Proc. SPIE 7038, 703829 (2008).
[Crossref]

2006 (2)

A. Linnenberger, S. Serati, and J. Stockley, “Advances in optical phased array technology,” Proc. SPIE 6304(2), 268–298 (2006).

N. L. Seldomridge, J. A. Shaw, and K. S. Repasky, “Dual-polarization lidar using a liquid crystal variable retarder,” Opt. Eng. 45(10), 106202 (2006).
[Crossref]

2005 (2)

A. Choubey, F. Andros, and B. Sammakia, “Study of assembly processes for liquid crystal on silicon (LCoS) microdisplays,” IEEE Trans. Compon. Packag. Tech. 28(2), 303–310 (2005).
[Crossref]

Y. Lin, M. Mahajan, D. Taber, B. Wen, and B. Winker, “Compact 4 cm aperture transmissive liquid crystal optical phased array for free-space optical communications,” Proc. SPIE 5892(3077), 58920C (2005).
[Crossref]

2003 (1)

E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” Proc. SPIE 5087(10), 13 (2003).
[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)

E. Santamato, G. Abbate, P. Maddalena, L. Marrucci, and Y. R. Shen, “Laser-induced nonlinear dynamics in a nematic liquid-crystal film,” Phys. Rev. Lett. 64(12), 1377–1380 (1990).
[Crossref] [PubMed]

1980 (1)

I. C. Khoo and S. L. Zhuang, “Nonlinear optical amplification in a nematic liquid crystal above the Frederiks transition,” Appl. Phys. Lett. 37(1), 3–4 (1980).
[Crossref]

Abbate, G.

E. Santamato, G. Abbate, P. Maddalena, L. Marrucci, and Y. R. Shen, “Laser-induced nonlinear dynamics in a nematic liquid-crystal film,” Phys. Rev. Lett. 64(12), 1377–1380 (1990).
[Crossref] [PubMed]

Andros, F.

A. Choubey, F. Andros, and B. Sammakia, “Study of assembly processes for liquid crystal on silicon (LCoS) microdisplays,” IEEE Trans. Compon. Packag. Tech. 28(2), 303–310 (2005).
[Crossref]

Baets, R.

Bengtsson, J.

D. Engström, J. Bengtsson, E. Eriksson, and M. Goksör, “Steering accuracy of a spatial light modulator-based single beam steerer: guidelines and limitations,” Proc. SPIE 7038, 703829 (2008).
[Crossref]

D. Engström, J. Bengtsson, E. Eriksson, and M. Goksör, “Improved beam steering accuracy of a single beam with a 1D phase-only spatial light modulator,” Opt. Express 16(22), 18275–18287 (2008).
[Crossref] [PubMed]

Bogaerts, W.

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 eystems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Choubey, A.

A. Choubey, F. Andros, and B. Sammakia, “Study of assembly processes for liquid crystal on silicon (LCoS) microdisplays,” IEEE Trans. Compon. Packag. Tech. 28(2), 303–310 (2005).
[Crossref]

Chu, D.

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

Chu, D. P.

H. Yang, B. Robertson, D. Yu, Z. Zhang, and D. P. Chu, “Origin of transient crosstalk and its reduction in phase-only LCOS wavelength selective switches,” J. Lightwave Technol. 31(23), 3822–3829 (2013).
[Crossref]

Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivnenko, J. Moore, B. Crossland, D. P. Chu, and B. Milne, “High quality assembly of phase-only Liquid Crystal on Silicon (LCOS) devices,” J. Disp. Technol. 7(3), 120–126 (2011).
[Crossref]

Collings, N.

Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivnenko, J. Moore, B. Crossland, D. P. Chu, and B. Milne, “High quality assembly of phase-only Liquid Crystal on Silicon (LCOS) devices,” J. Disp. Technol. 7(3), 120–126 (2011).
[Crossref]

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]

Crossland, B.

Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivnenko, J. Moore, B. Crossland, D. P. Chu, and B. Milne, “High quality assembly of phase-only Liquid Crystal on Silicon (LCOS) devices,” J. Disp. Technol. 7(3), 120–126 (2011).
[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]

Du, J.

Z. Tang, X. Wang, Z. Huang, Q. Tan, Y. Duan, G. Suo, J. Du, and Q. Qiu, “Sub-aperture coherence method to realize ultra-high resolution laser beam deflection,” Opt. Commun. 335, 1–6 (2015).
[Crossref]

Duan, Y.

Z. Tang, X. Wang, Z. Huang, Q. Tan, Y. Duan, G. Suo, J. Du, and Q. Qiu, “Sub-aperture coherence method to realize ultra-high resolution laser beam deflection,” Opt. Commun. 335, 1–6 (2015).
[Crossref]

Engström, D.

D. Engström, J. Bengtsson, E. Eriksson, and M. Goksör, “Steering accuracy of a spatial light modulator-based single beam steerer: guidelines and limitations,” Proc. SPIE 7038, 703829 (2008).
[Crossref]

D. Engström, J. Bengtsson, E. Eriksson, and M. Goksör, “Improved beam steering accuracy of a single beam with a 1D phase-only spatial light modulator,” Opt. Express 16(22), 18275–18287 (2008).
[Crossref] [PubMed]

Eriksson, E.

D. Engström, J. Bengtsson, E. Eriksson, and M. Goksör, “Improved beam steering accuracy of a single beam with a 1D phase-only spatial light modulator,” Opt. Express 16(22), 18275–18287 (2008).
[Crossref] [PubMed]

D. Engström, J. Bengtsson, E. Eriksson, and M. Goksör, “Steering accuracy of a spatial light modulator-based single beam steerer: guidelines and limitations,” Proc. SPIE 7038, 703829 (2008).
[Crossref]

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 eystems,” Proc. IEEE 97(6), 1078–1096 (2009).
[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]

Goksör, M.

D. Engström, J. Bengtsson, E. Eriksson, and M. Goksör, “Steering accuracy of a spatial light modulator-based single beam steerer: guidelines and limitations,” Proc. SPIE 7038, 703829 (2008).
[Crossref]

D. Engström, J. Bengtsson, E. Eriksson, and M. Goksör, “Improved beam steering accuracy of a single beam with a 1D phase-only spatial light modulator,” Opt. Express 16(22), 18275–18287 (2008).
[Crossref] [PubMed]

Haellstig, E.

E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” Proc. SPIE 5087(10), 13 (2003).
[Crossref]

He, X.

X. Wang, L. Wu, X. He, X. Huang, and Q. Tan, “Theoretical analysis on power stability and switch time of the non-mechanical beam steering using liquid crystal optical phased array,” Liq. Cryst. 45(10), 1477–1486 (2018).
[Crossref]

X. He, X. Wang, L. Wu, Q. Tan, M. Li, J. Shang, S. Wu, and Z. Huang, “Theoretical modeling on the laser induced effect of liquid crystal optical phased beam steering,” Opt. Commun. 382, 437–443 (2017).
[Crossref]

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 eystems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

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]

Houdré, R.

Huang, X.

X. Wang, L. Wu, X. He, X. Huang, and Q. Tan, “Theoretical analysis on power stability and switch time of the non-mechanical beam steering using liquid crystal optical phased array,” Liq. Cryst. 45(10), 1477–1486 (2018).
[Crossref]

Huang, Z.

X. He, X. Wang, L. Wu, Q. Tan, M. Li, J. Shang, S. Wu, and Z. Huang, “Theoretical modeling on the laser induced effect of liquid crystal optical phased beam steering,” Opt. Commun. 382, 437–443 (2017).
[Crossref]

Z. Tang, X. Wang, Z. Huang, Q. Tan, Y. Duan, G. Suo, J. Du, and Q. Qiu, “Sub-aperture coherence method to realize ultra-high resolution laser beam deflection,” Opt. Commun. 335, 1–6 (2015).
[Crossref]

Jágerská, J.

Jeziorska-Chapman, A. M.

Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivnenko, J. Moore, B. Crossland, D. P. Chu, and B. Milne, “High quality assembly of phase-only Liquid Crystal on Silicon (LCOS) devices,” J. Disp. Technol. 7(3), 120–126 (2011).
[Crossref]

Khoo, I. C.

I. C. Khoo and S. L. Zhuang, “Nonlinear optical amplification in a nematic liquid crystal above the Frederiks transition,” Appl. Phys. Lett. 37(1), 3–4 (1980).
[Crossref]

Kong, L.

Lane, S. A.

Le Thomas, N.

Li, M.

X. He, X. Wang, L. Wu, Q. Tan, M. Li, J. Shang, S. Wu, and Z. Huang, “Theoretical modeling on the laser induced effect of liquid crystal optical phased beam steering,” Opt. Commun. 382, 437–443 (2017).
[Crossref]

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]

Lin, Y.

Y. Lin, M. Mahajan, D. Taber, B. Wen, and B. Winker, “Compact 4 cm aperture transmissive liquid crystal optical phased array for free-space optical communications,” Proc. SPIE 5892(3077), 58920C (2005).
[Crossref]

Lindgren, M.

E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” Proc. SPIE 5087(10), 13 (2003).
[Crossref]

Linnenberger, A.

A. Linnenberger, S. Serati, and J. Stockley, “Advances in optical phased array technology,” Proc. SPIE 6304(2), 268–298 (2006).

Maddalena, P.

E. Santamato, G. Abbate, P. Maddalena, L. Marrucci, and Y. R. Shen, “Laser-induced nonlinear dynamics in a nematic liquid-crystal film,” Phys. Rev. Lett. 64(12), 1377–1380 (1990).
[Crossref] [PubMed]

Mahajan, M.

Y. Lin, M. Mahajan, D. Taber, B. Wen, and B. Winker, “Compact 4 cm aperture transmissive liquid crystal optical phased array for free-space optical communications,” Proc. SPIE 5892(3077), 58920C (2005).
[Crossref]

Marrucci, L.

E. Santamato, G. Abbate, P. Maddalena, L. Marrucci, and Y. R. Shen, “Laser-induced nonlinear dynamics in a nematic liquid-crystal film,” Phys. Rev. Lett. 64(12), 1377–1380 (1990).
[Crossref] [PubMed]

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 eystems,” 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]

Milne, B.

Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivnenko, J. Moore, B. Crossland, D. P. Chu, and B. Milne, “High quality assembly of phase-only Liquid Crystal on Silicon (LCOS) devices,” J. Disp. Technol. 7(3), 120–126 (2011).
[Crossref]

Miniscalco, W. J.

Moore, J.

Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivnenko, J. Moore, B. Crossland, D. P. Chu, and B. Milne, “High quality assembly of phase-only Liquid Crystal on Silicon (LCOS) devices,” J. Disp. Technol. 7(3), 120–126 (2011).
[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]

Pivnenko, M.

Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivnenko, J. Moore, B. Crossland, D. P. Chu, and B. Milne, “High quality assembly of phase-only Liquid Crystal on Silicon (LCOS) devices,” J. Disp. Technol. 7(3), 120–126 (2011).
[Crossref]

Qiu, Q.

Z. Tang, X. Wang, Z. Huang, Q. Tan, Y. Duan, G. Suo, J. Du, and Q. Qiu, “Sub-aperture coherence method to realize ultra-high resolution laser beam deflection,” Opt. Commun. 335, 1–6 (2015).
[Crossref]

Repasky, K. S.

N. L. Seldomridge, J. A. Shaw, and K. S. Repasky, “Dual-polarization lidar using a liquid crystal variable retarder,” Opt. Eng. 45(10), 106202 (2006).
[Crossref]

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]

Robertson, B.

Sammakia, B.

A. Choubey, F. Andros, and B. Sammakia, “Study of assembly processes for liquid crystal on silicon (LCoS) microdisplays,” IEEE Trans. Compon. Packag. Tech. 28(2), 303–310 (2005).
[Crossref]

Santamato, E.

E. Santamato, G. Abbate, P. Maddalena, L. Marrucci, and Y. R. Shen, “Laser-induced nonlinear dynamics in a nematic liquid-crystal film,” Phys. Rev. Lett. 64(12), 1377–1380 (1990).
[Crossref] [PubMed]

Seldomridge, N. L.

N. L. Seldomridge, J. A. Shaw, and K. S. Repasky, “Dual-polarization lidar using a liquid crystal variable retarder,” Opt. Eng. 45(10), 106202 (2006).
[Crossref]

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 eystems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

A. Linnenberger, S. Serati, and J. Stockley, “Advances in optical phased array technology,” Proc. SPIE 6304(2), 268–298 (2006).

Shang, J.

X. He, X. Wang, L. Wu, Q. Tan, M. Li, J. Shang, S. Wu, and Z. Huang, “Theoretical modeling on the laser induced effect of liquid crystal optical phased beam steering,” Opt. Commun. 382, 437–443 (2017).
[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]

Shaw, J. A.

N. L. Seldomridge, J. A. Shaw, and K. S. Repasky, “Dual-polarization lidar using a liquid crystal variable retarder,” Opt. Eng. 45(10), 106202 (2006).
[Crossref]

Shen, Y. R.

E. Santamato, G. Abbate, P. Maddalena, L. Marrucci, and Y. R. Shen, “Laser-induced nonlinear dynamics in a nematic liquid-crystal film,” Phys. Rev. Lett. 64(12), 1377–1380 (1990).
[Crossref] [PubMed]

Sjoqvist, L.

E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” Proc. SPIE 5087(10), 13 (2003).
[Crossref]

Song, Y.

Stigwall, J.

E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” Proc. SPIE 5087(10), 13 (2003).
[Crossref]

Stockley, J.

A. Linnenberger, S. Serati, and J. Stockley, “Advances in optical phased array technology,” Proc. SPIE 6304(2), 268–298 (2006).

Suo, G.

Z. Tang, X. Wang, Z. Huang, Q. Tan, Y. Duan, G. Suo, J. Du, and Q. Qiu, “Sub-aperture coherence method to realize ultra-high resolution laser beam deflection,” Opt. Commun. 335, 1–6 (2015).
[Crossref]

Taber, D.

Y. Lin, M. Mahajan, D. Taber, B. Wen, and B. Winker, “Compact 4 cm aperture transmissive liquid crystal optical phased array for free-space optical communications,” Proc. SPIE 5892(3077), 58920C (2005).
[Crossref]

Tan, Q.

X. Wang, L. Wu, X. He, X. Huang, and Q. Tan, “Theoretical analysis on power stability and switch time of the non-mechanical beam steering using liquid crystal optical phased array,” Liq. Cryst. 45(10), 1477–1486 (2018).
[Crossref]

X. He, X. Wang, L. Wu, Q. Tan, M. Li, J. Shang, S. Wu, and Z. Huang, “Theoretical modeling on the laser induced effect of liquid crystal optical phased beam steering,” Opt. Commun. 382, 437–443 (2017).
[Crossref]

Z. Tang, X. Wang, Z. Huang, Q. Tan, Y. Duan, G. Suo, J. Du, and Q. Qiu, “Sub-aperture coherence method to realize ultra-high resolution laser beam deflection,” Opt. Commun. 335, 1–6 (2015).
[Crossref]

Tang, Z.

Z. Tang, X. Wang, Z. Huang, Q. Tan, Y. Duan, G. Suo, J. Du, and Q. Qiu, “Sub-aperture coherence method to realize ultra-high resolution laser beam deflection,” Opt. Commun. 335, 1–6 (2015).
[Crossref]

Van Acoleyen, K.

Vettese, D.

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

Wang, X.

X. Wang, L. Wu, X. He, X. Huang, and Q. Tan, “Theoretical analysis on power stability and switch time of the non-mechanical beam steering using liquid crystal optical phased array,” Liq. Cryst. 45(10), 1477–1486 (2018).
[Crossref]

X. He, X. Wang, L. Wu, Q. Tan, M. Li, J. Shang, S. Wu, and Z. Huang, “Theoretical modeling on the laser induced effect of liquid crystal optical phased beam steering,” Opt. Commun. 382, 437–443 (2017).
[Crossref]

Z. Tang, X. Wang, Z. Huang, Q. Tan, Y. Duan, G. Suo, J. Du, and Q. Qiu, “Sub-aperture coherence method to realize ultra-high resolution laser beam deflection,” Opt. Commun. 335, 1–6 (2015).
[Crossref]

Wang, Y.

Y. Wang and M. C. Wu, “An optical phased array for LIDAR,” J. Phys. Conf. Ser. 772(1), 012004 (2016).
[Crossref]

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 eystems,” 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]

Wen, B.

Y. Lin, M. Mahajan, D. Taber, B. Wen, and B. Winker, “Compact 4 cm aperture transmissive liquid crystal optical phased array for free-space optical communications,” Proc. SPIE 5892(3077), 58920C (2005).
[Crossref]

Winker, B.

Y. Lin, M. Mahajan, D. Taber, B. Wen, and B. Winker, “Compact 4 cm aperture transmissive liquid crystal optical phased array for free-space optical communications,” Proc. SPIE 5892(3077), 58920C (2005).
[Crossref]

Wu, L.

X. Wang, L. Wu, X. He, X. Huang, and Q. Tan, “Theoretical analysis on power stability and switch time of the non-mechanical beam steering using liquid crystal optical phased array,” Liq. Cryst. 45(10), 1477–1486 (2018).
[Crossref]

X. He, X. Wang, L. Wu, Q. Tan, M. Li, J. Shang, S. Wu, and Z. Huang, “Theoretical modeling on the laser induced effect of liquid crystal optical phased beam steering,” Opt. Commun. 382, 437–443 (2017).
[Crossref]

Wu, M. C.

Y. Wang and M. C. Wu, “An optical phased array for LIDAR,” J. Phys. Conf. Ser. 772(1), 012004 (2016).
[Crossref]

Wu, S.

X. He, X. Wang, L. Wu, Q. Tan, M. Li, J. Shang, S. Wu, and Z. Huang, “Theoretical modeling on the laser induced effect of liquid crystal optical phased beam steering,” Opt. Commun. 382, 437–443 (2017).
[Crossref]

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 eystems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Yang, H.

Yang, J.

You, Z.

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

Yu, D.

Zhang, Z.

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

H. Yang, B. Robertson, D. Yu, Z. Zhang, and D. P. Chu, “Origin of transient crosstalk and its reduction in phase-only LCOS wavelength selective switches,” J. Lightwave Technol. 31(23), 3822–3829 (2013).
[Crossref]

Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivnenko, J. Moore, B. Crossland, D. P. Chu, and B. Milne, “High quality assembly of phase-only Liquid Crystal on Silicon (LCOS) devices,” J. Disp. Technol. 7(3), 120–126 (2011).
[Crossref]

Zhu, Y.

Zhuang, S. L.

I. C. Khoo and S. L. Zhuang, “Nonlinear optical amplification in a nematic liquid crystal above the Frederiks transition,” Appl. Phys. Lett. 37(1), 3–4 (1980).
[Crossref]

Appl. Phys. Lett. (1)

I. C. Khoo and S. L. Zhuang, “Nonlinear optical amplification in a nematic liquid crystal above the Frederiks transition,” Appl. Phys. Lett. 37(1), 3–4 (1980).
[Crossref]

Chin. Opt. Lett. (1)

IEEE Trans. Compon. Packag. Tech. (1)

A. Choubey, F. Andros, and B. Sammakia, “Study of assembly processes for liquid crystal on silicon (LCoS) microdisplays,” IEEE Trans. Compon. Packag. Tech. 28(2), 303–310 (2005).
[Crossref]

J. Disp. Technol. (1)

Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivnenko, J. Moore, B. Crossland, D. P. Chu, and B. Milne, “High quality assembly of phase-only Liquid Crystal on Silicon (LCOS) devices,” J. Disp. Technol. 7(3), 120–126 (2011).
[Crossref]

J. Lightwave Technol. (2)

J. Phys. Conf. Ser. (1)

Y. Wang and M. C. Wu, “An optical phased array for LIDAR,” J. Phys. Conf. Ser. 772(1), 012004 (2016).
[Crossref]

Light Sci. Appl. (1)

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

Liq. Cryst. (1)

X. Wang, L. Wu, X. He, X. Huang, and Q. Tan, “Theoretical analysis on power stability and switch time of the non-mechanical beam steering using liquid crystal optical phased array,” Liq. Cryst. 45(10), 1477–1486 (2018).
[Crossref]

Nat. Photonics (1)

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

Opt. Commun. (2)

Z. Tang, X. Wang, Z. Huang, Q. Tan, Y. Duan, G. Suo, J. Du, and Q. Qiu, “Sub-aperture coherence method to realize ultra-high resolution laser beam deflection,” Opt. Commun. 335, 1–6 (2015).
[Crossref]

X. He, X. Wang, L. Wu, Q. Tan, M. Li, J. Shang, S. Wu, and Z. Huang, “Theoretical modeling on the laser induced effect of liquid crystal optical phased beam steering,” Opt. Commun. 382, 437–443 (2017).
[Crossref]

Opt. Eng. (1)

N. L. Seldomridge, J. A. Shaw, and K. S. Repasky, “Dual-polarization lidar using a liquid crystal variable retarder,” Opt. Eng. 45(10), 106202 (2006).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

E. Santamato, G. Abbate, P. Maddalena, L. Marrucci, and Y. R. Shen, “Laser-induced nonlinear dynamics in a nematic liquid-crystal film,” Phys. Rev. Lett. 64(12), 1377–1380 (1990).
[Crossref] [PubMed]

Proc. IEEE (2)

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 eystems,” 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]

Proc. SPIE (4)

Y. Lin, M. Mahajan, D. Taber, B. Wen, and B. Winker, “Compact 4 cm aperture transmissive liquid crystal optical phased array for free-space optical communications,” Proc. SPIE 5892(3077), 58920C (2005).
[Crossref]

E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” Proc. SPIE 5087(10), 13 (2003).
[Crossref]

A. Linnenberger, S. Serati, and J. Stockley, “Advances in optical phased array technology,” Proc. SPIE 6304(2), 268–298 (2006).

D. Engström, J. Bengtsson, E. Eriksson, and M. Goksör, “Steering accuracy of a spatial light modulator-based single beam steerer: guidelines and limitations,” Proc. SPIE 7038, 703829 (2008).
[Crossref]

Other (1)

B. Winker, M. Mahajan, and M. Hunwardsen, “Liquid crystal beam directors for airborne free-space optical communications,” Aerospace Conference, Proc. IEEE Vol.3, 1702 (2004)
[Crossref]

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Figures (19)

Fig. 1
Fig. 1 Normalized phase diagrams of two sub-aperture algorithm. (a) SAC (b) RSAC
Fig. 2
Fig. 2 Contrast diagram of θnormII curves of two sub-aperture algorithms under different incident light aperture. (a) SAC (b) RSAC
Fig. 3
Fig. 3 Normalized phase diagram of SRSAC.
Fig. 4
Fig. 4 Schematic diagram of alignment error based on SRSAC.
Fig. 5
Fig. 5 Simulation diagram of the relationship between the RMS of normalized steering angle error and the beam aperture.
Fig. 6
Fig. 6 The x-direction output error surface (μrad) based on RSAC.
Fig. 7
Fig. 7 The y-direction output error surface (μrad) based on RSAC.
Fig. 8
Fig. 8 The x-direction output error surface (μrad) based on SRSAC.
Fig. 9
Fig. 9 The y-direction output error surface (μrad) based on SRSAC.
Fig. 10
Fig. 10 Simulation diagram of the RMS of normalized steering angle error in x-direction with different alignment error. (a) SAC (b) RSAC (c) SRSAC
Fig. 11
Fig. 11 Schematic diagram of Zernike coefficients of the accessary aberration.
Fig. 12
Fig. 12 Schematic diagram of high precision measuring system.
Fig. 13
Fig. 13 Actual measuring system.
Fig. 14
Fig. 14 Continuous measurement interface of reference zero error and steering angles.
Fig. 15
Fig. 15 The contrast diagram of RSAC simulated scanning curves and their approximate formulas.
Fig. 16
Fig. 16 The contrast diagram of RSAC scanning curves with different beam apertures.
Fig. 17
Fig. 17 Schematic diagram of the RSAC measured angles. (a) The normalized steering angle sequences before linearized reconstruction and their custom fitting curves. (b) The normalized steering angle sequences after linearized reconstruction and the desired straight line.
Fig. 18
Fig. 18 The contrast diagram of SRSAC simulated curves and their approximate formula.
Fig. 19
Fig. 19 Schematic diagram of the SRSAC measured angles. (a) The normalized steering angle sequences before linearized reconstruction and their custom fitting curves. (b) The normalized steering angle sequences after linearized reconstruction and the desired straight line.

Tables (1)

Tables Icon

Table 1 The statistical parameters of RSAC data error withδin, x = ± 0.2mm.

Equations (20)

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

ϕ(x)=mod( 2πd λ round(x/d) θ ideal ,2π )
ϕ GL (x)= 2π N gray round( N gray 2π φ(x))
max( θ error ) λ N gray L
θ step = θ II θ I
η I = L I L , η II = L II L
P I = I I(x,y)dxdy , P II = II I(x,y)dxdy
η I = α I 2π , η II = α II 2π
P I ( P I + P II ) = η I , P II ( P I + P II ) = η II
θ norm = θθ I θ II θ I
η I = α I π , η II = α II π
S + =2Rsin( α II /2 ) δ in,x +O( δ in,x 2 )
S =2Rsin( α II /2 ) δ in,x O( δ in,x 2 )
lim δ in,x 0 Δ P II = lim δ in,x 0 ( S + S )I( R )=O( δ in,x ) 2
P II δ in,x =0, P I δ in,x = (P P II ) δ in,x =0
P I δ in,y =0, P II δ in,y = (P P I ) δ in,y =0
d P I = P I δ in,x d δ in,x + P I δ in,y d δ in,y =0
d P II = P II δ in,x d δ in,x + P II δ in,y d δ in,y =0
F ~ δ C (x)={ ( 2 3 2 +3 δ C (1/2x) 5 2 +3 δ C +1/2 )( 1+2 δ c ) x1/2 ( 2 3 2 3 δ C (x1/2) 5 2 3 δ C 1/2 )( 12 δ c )+1 x>1/2
F ~ δ c =0 =2 2 sgn(x0.5) | x0.5 | 5/2 +0.5
F s ~ (x)=2 F ~ δ C =0 (x/2)= (1x) 5 2 +1

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