Abstract

Phase imaging is used to compare near-field measurements with the corresponding far-field intensity distribution. A liquid-crystal device serves as a phase object that can be programmed as a variable grating. Real-time phase visualization then provides an avenue for direct optimization of complex phase gratings.

© 1996 Optical Society of America

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References

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  1. M. M. Weffers, K. A. Nelson, “Programmable phase and amplitude femtosecond pulse shaping,” Opt. Lett. 18, 2032–2034 (1993).
    [CrossRef]
  2. H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
    [CrossRef]
  3. A. Tanone, Z. Zhang, C. M. Uang, T. S. Yu, D. Gregory, “Optical beam steering using a liquid-crystal television panel,” Microwave Opt. Technol. Lett. 7, 285–289 (1994).
    [CrossRef]
  4. R. M. Matic, “Blazed phase liquid crystal beam steering,” Laser Beam Propagation and Control Laser Power Beaming, H. Weichel, L. F. DeSandre, eds., Proc. SPIE2120, 194–205 (1994).
  5. B. Cassarly, J. M. Finlan, “Phase control of coherent diode laser arrays using liquid crystals,” in Laser Diode Technology and Applications, L. Figueroa, ed., Proc. SPIE1043, 130–137 (1989).
  6. D. P. Resler, D. S. Hobbs, R. C. Sharp, L. J. Friedman, T. A. Dorschner, “Optical phased array beam steering,” Opt. Lett. 21, 689–691 (1996).
    [CrossRef] [PubMed]
  7. J. E. Greivenkamp, J. H. Gruning, “Phase shifting interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.
  8. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1987), Chap. 14, p. 695.
  9. Z. Zhang, G. Lu, F. T. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
    [CrossRef]
  10. D. A. Yocky, T. H. Barnes, K. Matsumoto, N. Ooyama, K. Matsuda, “Simple measurement of the phase modulation capability of liquid crystal phase-only light modulators,” Optik 84, 140–144 (1990).
  11. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1987), Chap. 7, p. 305.
  12. P. F. McManamon, T. A. Dorschner, D. C. Corkum, L. J. Friedman, D. S. Hobbs, M. K. Holz, S. Liberman, H. Nguyen, D. P. Resler, R. C. Sharp, E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
    [CrossRef]
  13. U. Killat, G. Rabe, W. Rave, “Binary phase gratings for star couplers with high splitting ratio,” Fiber Integr. Opt. 4, 159–167 (1982).
    [CrossRef]
  14. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef] [PubMed]

1996 (2)

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

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

1994 (2)

A. Tanone, Z. Zhang, C. M. Uang, T. S. Yu, D. Gregory, “Optical beam steering using a liquid-crystal television panel,” Microwave Opt. Technol. Lett. 7, 285–289 (1994).
[CrossRef]

Z. Zhang, G. Lu, F. T. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

1993 (1)

1990 (1)

D. A. Yocky, T. H. Barnes, K. Matsumoto, N. Ooyama, K. Matsuda, “Simple measurement of the phase modulation capability of liquid crystal phase-only light modulators,” Optik 84, 140–144 (1990).

1982 (2)

U. Killat, G. Rabe, W. Rave, “Binary phase gratings for star couplers with high splitting ratio,” Fiber Integr. Opt. 4, 159–167 (1982).
[CrossRef]

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[CrossRef] [PubMed]

1971 (1)

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Barnes, T. H.

D. A. Yocky, T. H. Barnes, K. Matsumoto, N. Ooyama, K. Matsuda, “Simple measurement of the phase modulation capability of liquid crystal phase-only light modulators,” Optik 84, 140–144 (1990).

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1987), Chap. 14, p. 695.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1987), Chap. 7, p. 305.

Cassarly, B.

B. Cassarly, J. M. Finlan, “Phase control of coherent diode laser arrays using liquid crystals,” in Laser Diode Technology and Applications, L. Figueroa, ed., Proc. SPIE1043, 130–137 (1989).

Corkum, D. C.

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

Dammann, H.

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Dorschner, T. A.

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

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

Fienup, J. R.

Finlan, J. M.

B. Cassarly, J. M. Finlan, “Phase control of coherent diode laser arrays using liquid crystals,” in Laser Diode Technology and Applications, L. Figueroa, ed., Proc. SPIE1043, 130–137 (1989).

Friedman, L. J.

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

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

Gortler, K.

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Gregory, D.

A. Tanone, Z. Zhang, C. M. Uang, T. S. Yu, D. Gregory, “Optical beam steering using a liquid-crystal television panel,” Microwave Opt. Technol. Lett. 7, 285–289 (1994).
[CrossRef]

Greivenkamp, J. E.

J. E. Greivenkamp, J. H. Gruning, “Phase shifting interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.

Gruning, J. H.

J. E. Greivenkamp, J. H. Gruning, “Phase shifting interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.

Hobbs, D. S.

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

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

Holz, M. K.

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

Killat, U.

U. Killat, G. Rabe, W. Rave, “Binary phase gratings for star couplers with high splitting ratio,” Fiber Integr. Opt. 4, 159–167 (1982).
[CrossRef]

Liberman, S.

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

Lu, G.

Z. Zhang, G. Lu, F. T. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

Matic, R. M.

R. M. Matic, “Blazed phase liquid crystal beam steering,” Laser Beam Propagation and Control Laser Power Beaming, H. Weichel, L. F. DeSandre, eds., Proc. SPIE2120, 194–205 (1994).

Matsuda, K.

D. A. Yocky, T. H. Barnes, K. Matsumoto, N. Ooyama, K. Matsuda, “Simple measurement of the phase modulation capability of liquid crystal phase-only light modulators,” Optik 84, 140–144 (1990).

Matsumoto, K.

D. A. Yocky, T. H. Barnes, K. Matsumoto, N. Ooyama, K. Matsuda, “Simple measurement of the phase modulation capability of liquid crystal phase-only light modulators,” Optik 84, 140–144 (1990).

McManamon, P. F.

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

Nelson, K. A.

Nguyen, H.

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

Ooyama, N.

D. A. Yocky, T. H. Barnes, K. Matsumoto, N. Ooyama, K. Matsuda, “Simple measurement of the phase modulation capability of liquid crystal phase-only light modulators,” Optik 84, 140–144 (1990).

Rabe, G.

U. Killat, G. Rabe, W. Rave, “Binary phase gratings for star couplers with high splitting ratio,” Fiber Integr. Opt. 4, 159–167 (1982).
[CrossRef]

Rave, W.

U. Killat, G. Rabe, W. Rave, “Binary phase gratings for star couplers with high splitting ratio,” Fiber Integr. Opt. 4, 159–167 (1982).
[CrossRef]

Resler, D. P.

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

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

Sharp, R. C.

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

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

Tanone, A.

A. Tanone, Z. Zhang, C. M. Uang, T. S. Yu, D. Gregory, “Optical beam steering using a liquid-crystal television panel,” Microwave Opt. Technol. Lett. 7, 285–289 (1994).
[CrossRef]

Uang, C. M.

A. Tanone, Z. Zhang, C. M. Uang, T. S. Yu, D. Gregory, “Optical beam steering using a liquid-crystal television panel,” Microwave Opt. Technol. Lett. 7, 285–289 (1994).
[CrossRef]

Watson, E. A.

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

Weffers, M. M.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1987), Chap. 14, p. 695.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1987), Chap. 7, p. 305.

Yocky, D. A.

D. A. Yocky, T. H. Barnes, K. Matsumoto, N. Ooyama, K. Matsuda, “Simple measurement of the phase modulation capability of liquid crystal phase-only light modulators,” Optik 84, 140–144 (1990).

Yu, F. T.

Z. Zhang, G. Lu, F. T. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

Yu, T. S.

A. Tanone, Z. Zhang, C. M. Uang, T. S. Yu, D. Gregory, “Optical beam steering using a liquid-crystal television panel,” Microwave Opt. Technol. Lett. 7, 285–289 (1994).
[CrossRef]

Zhang, Z.

A. Tanone, Z. Zhang, C. M. Uang, T. S. Yu, D. Gregory, “Optical beam steering using a liquid-crystal television panel,” Microwave Opt. Technol. Lett. 7, 285–289 (1994).
[CrossRef]

Z. Zhang, G. Lu, F. T. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

Appl. Opt. (1)

Fiber Integr. Opt. (1)

U. Killat, G. Rabe, W. Rave, “Binary phase gratings for star couplers with high splitting ratio,” Fiber Integr. Opt. 4, 159–167 (1982).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

A. Tanone, Z. Zhang, C. M. Uang, T. S. Yu, D. Gregory, “Optical beam steering using a liquid-crystal television panel,” Microwave Opt. Technol. Lett. 7, 285–289 (1994).
[CrossRef]

Opt. Commun. (1)

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Opt. Eng. (1)

Z. Zhang, G. Lu, F. T. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

Opt. Lett. (2)

Optik (1)

D. A. Yocky, T. H. Barnes, K. Matsumoto, N. Ooyama, K. Matsuda, “Simple measurement of the phase modulation capability of liquid crystal phase-only light modulators,” Optik 84, 140–144 (1990).

Proc. IEEE (1)

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

Other (5)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1987), Chap. 7, p. 305.

J. E. Greivenkamp, J. H. Gruning, “Phase shifting interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1987), Chap. 14, p. 695.

R. M. Matic, “Blazed phase liquid crystal beam steering,” Laser Beam Propagation and Control Laser Power Beaming, H. Weichel, L. F. DeSandre, eds., Proc. SPIE2120, 194–205 (1994).

B. Cassarly, J. M. Finlan, “Phase control of coherent diode laser arrays using liquid crystals,” in Laser Diode Technology and Applications, L. Figueroa, ed., Proc. SPIE1043, 130–137 (1989).

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Figures (4)

Fig. 1
Fig. 1

Block diagram showing a Mach–Zehnder arrangement for transmissive tests. An imaging CCD records interferograms that are used to extract phase information. With the reference beam blocked, the far-field CCD records the diffraction pattern corresponding to the measured near-field phase.

Fig. 2
Fig. 2

With the liquid-crystal device operating as a uniform wave plate, the relative phase (birefringence) measured with conventional ellipsometry (solid dots) and measured with phase-stepping interferometry (solid curve) are compared. The two methods agree to within a standard deviation of λ/60.

Fig. 3
Fig. 3

Beam fan-out pattern realized with the use of only the phase images. (a) Electrode voltages altered until the measured phase profile (open circles) agrees closely with the computed target phase profile (solid curve). (b) Measured two-dimensional phase image corresponding to the situation also shown in (a). (c) Measured far-field diffraction pattern following the described phase optimization. In the table are listed the measured integrated efficiency η for the pattern together with the target efficiency predicted from the computer-optimized phase profile.

Fig. 4
Fig. 4

Phase images that optimize a blazed grating. (a) The measured phase profile (connected points) follow the ideal blazed saw tooth (solid straight line) for most of the ramp, but there is obvious rounding in the region of the 2π phase reset. In the inset are listed the steering efficiency as directly measured in the far field and as calculated from the measured phase profile. (b) Two-dimensional phase image corresponding to the situation in (a). (c) This phase profile is more optimized than that in (a) as seen in the sharper reset region. (d) Two-dimensional phase image corresponding to the situation in (c).

Equations (2)

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ϕ ( x ) = k o n e ( x ) d ,
e j ϕ ( x ) = m a m exp ( j m Kx ) = a 0 + a 1 exp ( j Kx ) + a 1 exp ( j Kx ) + a 2 exp ( 2 j Kx ) + ,

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