Abstract

An experimental setup and simple method were proposed to investigate and control the actual phase profile in a high-spatial-resolution liquid-crystal optical-phased array (LCOPA). A crossed polarizer and high-resolution microscope objective were employed to transform the light distribution out of the liquid-crystal layer into a polarization-interference pattern in which the phase-profile information was wrapped. The polarization-interference pattern was then directly translated into the actual phase profile. Based on this setup, a method was developed to accurately control the actual phase profile, and the steering efficiency at the steering angle of 16 mrad was increased from 80% to 90%. The proposed method also helps in increasing the steering efficiency when disclination lines appear.

© 2013 Optical Society of America

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  1. D. Dayton, J. Gonglewski, and S. Brown, “Control algorithms of liquid crystal phased arrays used as adaptive optic correctors,” Proc. SPIE 6306, 630604 (2006).
    [CrossRef]
  2. P. McManamon, “An overview of optical phased array technology and status,” Proc. SPIE 5947, 59470I (2005).
    [CrossRef]
  3. X. H. Wang, B. Wang, and J. Pouch, “Performance evaluation of a liquid crystal on silicon spatial light modulator,” Opt. Eng. 43, 2769–2774 (2004).
    [CrossRef]
  4. D. P. Resler, D. S. Hobbs, R. C. Sharp, L. J. Friedman, and T. A. Dorschner, “High efficiency liquid crystal optical phased array beam steering,” Opt. Lett. 21, 689–691 (1996).
    [CrossRef]
  5. I. Smith and M. K. O. Holz, “Wide angle beam steering system,” U.S. Patent7,215,472 (8May2007).
  6. P. F. McManamon, “Agile nonmechanical beam steering,” Opt. Photon. News 17(3), 24–29 (2006).
    [CrossRef]
  7. S. A. Khan and N. A. Riza, “Demonstration of 3-D wide angle laser beam scanner using liquid crystal,” Opt. Express 12, 868–882 (2004).
    [CrossRef]
  8. J. Kim, C. Oh, M. J. Escuti, L. Hosting, and S. Serati, “Wide angle nonmechanical beam steering using liquid crystal polarization gratings,” Proc. SPIE 7093, 709302 (2008).
    [CrossRef]
  9. J. Kim, C. Oh, S. Serati, and M. J. Escuti, “Wide angle, nonmechanical beam steering with high throughput utilizing polarization gratings,” Appl. Opt. 50, 2636–2639 (2011).
    [CrossRef]
  10. L. Shi, P. F. McManamon, and P. J. Bos, “Liquid crystal optical phase plate with a variable continuous in plane gradient,” J. Appl. Phys. 104, 1–7 (2008).
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    [CrossRef]
  12. S. Harris, “Numerical optimization of the performance of nematic liquid crystal optical phased array,” Proc. SPIE 5162, 157–171 (2003).
    [CrossRef]
  13. X. H. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid crystal optical phased array,” J. Appl. Phys. 98, 073101 (2005).
    [CrossRef]
  14. E. Hallstig, L. Sjoqvist, and M. Lindgren, “Intensity variations using a quantized spatial light modulator for non-mechanical beam steering,” Opt. Eng. 42, 613–619 (2003).
    [CrossRef]
  15. X. Zhao, C. Liu, D. Zhang, and Y. Luo, “Tunable liquid crystal microlens array using hole patterned electrode structure with ultrathin glass slab,” Appl. Opt. 51, 3024–3030 (2012).
    [CrossRef]

2012 (1)

2011 (1)

2008 (2)

L. Shi, P. F. McManamon, and P. J. Bos, “Liquid crystal optical phase plate with a variable continuous in plane gradient,” J. Appl. Phys. 104, 1–7 (2008).

J. Kim, C. Oh, M. J. Escuti, L. Hosting, and S. Serati, “Wide angle nonmechanical beam steering using liquid crystal polarization gratings,” Proc. SPIE 7093, 709302 (2008).
[CrossRef]

2006 (2)

P. F. McManamon, “Agile nonmechanical beam steering,” Opt. Photon. News 17(3), 24–29 (2006).
[CrossRef]

D. Dayton, J. Gonglewski, and S. Brown, “Control algorithms of liquid crystal phased arrays used as adaptive optic correctors,” Proc. SPIE 6306, 630604 (2006).
[CrossRef]

2005 (2)

P. McManamon, “An overview of optical phased array technology and status,” Proc. SPIE 5947, 59470I (2005).
[CrossRef]

X. H. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid crystal optical phased array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

2004 (2)

X. H. Wang, B. Wang, and J. Pouch, “Performance evaluation of a liquid crystal on silicon spatial light modulator,” Opt. Eng. 43, 2769–2774 (2004).
[CrossRef]

S. A. Khan and N. A. Riza, “Demonstration of 3-D wide angle laser beam scanner using liquid crystal,” Opt. Express 12, 868–882 (2004).
[CrossRef]

2003 (2)

E. Hallstig, L. Sjoqvist, and M. Lindgren, “Intensity variations using a quantized spatial light modulator for non-mechanical beam steering,” Opt. Eng. 42, 613–619 (2003).
[CrossRef]

S. Harris, “Numerical optimization of the performance of nematic liquid crystal optical phased array,” Proc. SPIE 5162, 157–171 (2003).
[CrossRef]

1996 (2)

P. F. McManamon, T. A. Dorschner, D. L. Corkum, and L. J. Friedman, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

D. P. Resler, D. S. Hobbs, R. C. Sharp, L. J. Friedman, and T. A. Dorschner, “High efficiency liquid crystal optical phased array beam steering,” Opt. Lett. 21, 689–691 (1996).
[CrossRef]

Anderson, J. E.

X. H. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid crystal optical phased array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

Bos, P. J.

L. Shi, P. F. McManamon, and P. J. Bos, “Liquid crystal optical phase plate with a variable continuous in plane gradient,” J. Appl. Phys. 104, 1–7 (2008).

X. H. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid crystal optical phased array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

Brown, S.

D. Dayton, J. Gonglewski, and S. Brown, “Control algorithms of liquid crystal phased arrays used as adaptive optic correctors,” Proc. SPIE 6306, 630604 (2006).
[CrossRef]

Corkum, D. L.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, and L. J. Friedman, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

Dayton, D.

D. Dayton, J. Gonglewski, and S. Brown, “Control algorithms of liquid crystal phased arrays used as adaptive optic correctors,” Proc. SPIE 6306, 630604 (2006).
[CrossRef]

Dorschner, T. A.

D. P. Resler, D. S. Hobbs, R. C. Sharp, L. J. Friedman, and T. A. Dorschner, “High efficiency liquid crystal optical phased array beam steering,” Opt. Lett. 21, 689–691 (1996).
[CrossRef]

P. F. McManamon, T. A. Dorschner, D. L. Corkum, and L. J. Friedman, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

Escuti, M. J.

J. Kim, C. Oh, S. Serati, and M. J. Escuti, “Wide angle, nonmechanical beam steering with high throughput utilizing polarization gratings,” Appl. Opt. 50, 2636–2639 (2011).
[CrossRef]

J. Kim, C. Oh, M. J. Escuti, L. Hosting, and S. Serati, “Wide angle nonmechanical beam steering using liquid crystal polarization gratings,” Proc. SPIE 7093, 709302 (2008).
[CrossRef]

Friedman, L. J.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, and L. J. Friedman, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

D. P. Resler, D. S. Hobbs, R. C. Sharp, L. J. Friedman, and T. A. Dorschner, “High efficiency liquid crystal optical phased array beam steering,” Opt. Lett. 21, 689–691 (1996).
[CrossRef]

Gonglewski, J.

D. Dayton, J. Gonglewski, and S. Brown, “Control algorithms of liquid crystal phased arrays used as adaptive optic correctors,” Proc. SPIE 6306, 630604 (2006).
[CrossRef]

Hallstig, E.

E. Hallstig, L. Sjoqvist, and M. Lindgren, “Intensity variations using a quantized spatial light modulator for non-mechanical beam steering,” Opt. Eng. 42, 613–619 (2003).
[CrossRef]

Harris, S.

S. Harris, “Numerical optimization of the performance of nematic liquid crystal optical phased array,” Proc. SPIE 5162, 157–171 (2003).
[CrossRef]

Hobbs, D. S.

Holz, M. K. O.

I. Smith and M. K. O. Holz, “Wide angle beam steering system,” U.S. Patent7,215,472 (8May2007).

Hosting, L.

J. Kim, C. Oh, M. J. Escuti, L. Hosting, and S. Serati, “Wide angle nonmechanical beam steering using liquid crystal polarization gratings,” Proc. SPIE 7093, 709302 (2008).
[CrossRef]

Khan, S. A.

Kim, J.

J. Kim, C. Oh, S. Serati, and M. J. Escuti, “Wide angle, nonmechanical beam steering with high throughput utilizing polarization gratings,” Appl. Opt. 50, 2636–2639 (2011).
[CrossRef]

J. Kim, C. Oh, M. J. Escuti, L. Hosting, and S. Serati, “Wide angle nonmechanical beam steering using liquid crystal polarization gratings,” Proc. SPIE 7093, 709302 (2008).
[CrossRef]

Lindgren, M.

E. Hallstig, L. Sjoqvist, and M. Lindgren, “Intensity variations using a quantized spatial light modulator for non-mechanical beam steering,” Opt. Eng. 42, 613–619 (2003).
[CrossRef]

Liu, C.

Luo, Y.

McManamon, P.

P. McManamon, “An overview of optical phased array technology and status,” Proc. SPIE 5947, 59470I (2005).
[CrossRef]

McManamon, P. F.

L. Shi, P. F. McManamon, and P. J. Bos, “Liquid crystal optical phase plate with a variable continuous in plane gradient,” J. Appl. Phys. 104, 1–7 (2008).

P. F. McManamon, “Agile nonmechanical beam steering,” Opt. Photon. News 17(3), 24–29 (2006).
[CrossRef]

X. H. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid crystal optical phased array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

P. F. McManamon, T. A. Dorschner, D. L. Corkum, and L. J. Friedman, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

Miranda, F. A.

X. H. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid crystal optical phased array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

Oh, C.

J. Kim, C. Oh, S. Serati, and M. J. Escuti, “Wide angle, nonmechanical beam steering with high throughput utilizing polarization gratings,” Appl. Opt. 50, 2636–2639 (2011).
[CrossRef]

J. Kim, C. Oh, M. J. Escuti, L. Hosting, and S. Serati, “Wide angle nonmechanical beam steering using liquid crystal polarization gratings,” Proc. SPIE 7093, 709302 (2008).
[CrossRef]

Pouch, J.

X. H. Wang, B. Wang, and J. Pouch, “Performance evaluation of a liquid crystal on silicon spatial light modulator,” Opt. Eng. 43, 2769–2774 (2004).
[CrossRef]

Pouch, J. J.

X. H. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid crystal optical phased array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

Resler, D. P.

Riza, N. A.

Serati, S.

J. Kim, C. Oh, S. Serati, and M. J. Escuti, “Wide angle, nonmechanical beam steering with high throughput utilizing polarization gratings,” Appl. Opt. 50, 2636–2639 (2011).
[CrossRef]

J. Kim, C. Oh, M. J. Escuti, L. Hosting, and S. Serati, “Wide angle nonmechanical beam steering using liquid crystal polarization gratings,” Proc. SPIE 7093, 709302 (2008).
[CrossRef]

Sharp, R. C.

Shi, L.

L. Shi, P. F. McManamon, and P. J. Bos, “Liquid crystal optical phase plate with a variable continuous in plane gradient,” J. Appl. Phys. 104, 1–7 (2008).

Sjoqvist, L.

E. Hallstig, L. Sjoqvist, and M. Lindgren, “Intensity variations using a quantized spatial light modulator for non-mechanical beam steering,” Opt. Eng. 42, 613–619 (2003).
[CrossRef]

Smith, I.

I. Smith and M. K. O. Holz, “Wide angle beam steering system,” U.S. Patent7,215,472 (8May2007).

Wang, B.

X. H. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid crystal optical phased array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

X. H. Wang, B. Wang, and J. Pouch, “Performance evaluation of a liquid crystal on silicon spatial light modulator,” Opt. Eng. 43, 2769–2774 (2004).
[CrossRef]

Wang, X. H.

X. H. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid crystal optical phased array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

X. H. Wang, B. Wang, and J. Pouch, “Performance evaluation of a liquid crystal on silicon spatial light modulator,” Opt. Eng. 43, 2769–2774 (2004).
[CrossRef]

Zhang, D.

Zhao, X.

Appl. Opt. (2)

J. Appl. Phys. (2)

X. H. Wang, B. Wang, P. J. Bos, P. F. McManamon, J. J. Pouch, F. A. Miranda, and J. E. Anderson, “Modeling and design of an optimized liquid crystal optical phased array,” J. Appl. Phys. 98, 073101 (2005).
[CrossRef]

L. Shi, P. F. McManamon, and P. J. Bos, “Liquid crystal optical phase plate with a variable continuous in plane gradient,” J. Appl. Phys. 104, 1–7 (2008).

Opt. Eng. (2)

X. H. Wang, B. Wang, and J. Pouch, “Performance evaluation of a liquid crystal on silicon spatial light modulator,” Opt. Eng. 43, 2769–2774 (2004).
[CrossRef]

E. Hallstig, L. Sjoqvist, and M. Lindgren, “Intensity variations using a quantized spatial light modulator for non-mechanical beam steering,” Opt. Eng. 42, 613–619 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Opt. Photon. News (1)

P. F. McManamon, “Agile nonmechanical beam steering,” Opt. Photon. News 17(3), 24–29 (2006).
[CrossRef]

Proc. IEEE (1)

P. F. McManamon, T. A. Dorschner, D. L. Corkum, and L. J. Friedman, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[CrossRef]

Proc. SPIE (4)

S. Harris, “Numerical optimization of the performance of nematic liquid crystal optical phased array,” Proc. SPIE 5162, 157–171 (2003).
[CrossRef]

D. Dayton, J. Gonglewski, and S. Brown, “Control algorithms of liquid crystal phased arrays used as adaptive optic correctors,” Proc. SPIE 6306, 630604 (2006).
[CrossRef]

P. McManamon, “An overview of optical phased array technology and status,” Proc. SPIE 5947, 59470I (2005).
[CrossRef]

J. Kim, C. Oh, M. J. Escuti, L. Hosting, and S. Serati, “Wide angle nonmechanical beam steering using liquid crystal polarization gratings,” Proc. SPIE 7093, 709302 (2008).
[CrossRef]

Other (1)

I. Smith and M. K. O. Holz, “Wide angle beam steering system,” U.S. Patent7,215,472 (8May2007).

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Figures (8)

Fig. 1.
Fig. 1.

Schematic of experimental setup to measure the actual phase profile in LCOPA.

Fig. 2.
Fig. 2.

Bulk response of LCOPA phase delay on loaded gray-scale command.

Fig. 3.
Fig. 3.

Measured interference pattern of light distribution out of liquid crystal layer. (a) Light distribution of I. (b) Light distribution of I. (c) Light distribution of I45.

Fig. 4.
Fig. 4.

(a) The processed light distribution of polarization interference pattern and the measured error estimation by mean deviation method for I45. (b) Corresponding measured actual phase profile after data processing in real LCOPA. (c) Numerical simulation result of phase profile in LCOPA.

Fig. 5.
Fig. 5.

Accurate control of phase profile in LCOPA with the proposed method.

Fig. 6.
Fig. 6.

Formation of disclination lines when the optimized applied voltage in Fig. 5 was further pinned at the phase-reset point and the steering angle was 16 mrad. (a) 10 s after pinned voltage was applied. (b) 40 s after pinned voltage was applied.

Fig. 7.
Fig. 7.

Formation of disclination lines when the optimized voltage in Fig. 5 was further pinned at the phase-reset point and the steering angle was shifted from 0 to 16 mrad.

Fig. 8.
Fig. 8.

Square difference of the averaged cosine value of ϕ(x) between adjacent iterative steps, which was used as the indicator for judging the appearance or disappearance of disclination lines. (a) Square difference when optimization step was implemented by Eq. (1), and no disclination lines appear. (b) Square difference when disclination lines appear. (c) Square difference when voltage change was implemented according to Eq. (3), and disclination lines still exist. (d) Square difference when disclination lines disappeared.

Tables (1)

Tables Icon

Table 1. Steering Efficiency Obtained When Steering Angle was 16 mrad and Different Control Method was Applied

Equations (3)

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

cos(ϕ(x))=(I45I2I2)/II.
ΔV=k(V(φideal)V(φ¯actual)).
{Vmax=Vmaxk×(VmaxVmin)Vmin=Vmin+k×(VmaxVmin)

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