Abstract

Phase retarders usually show strong wavelength dependence. A novel and simple configuration with the combination of two twisted nematic liquid-crystal cells is proposed for the design of a true zero-order achromatic quarter-wave plate. The present optimization method considers the material dispersion. Simulation computations show a good achromatic behavior of the optimized waveplate. Compared with other types of broadband quarter-wave plates, the present device is compatible with classical liquid-crystal displays and can be expected to be used in precision polarimeters with low cost and enhanced light efficiency.

© 2005 Optical Society of America

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  1. R. J. King, “Quarter-wave retardation systems based on the Fresnel rhomb principle,” J. Sci. Instrum. 43, 617–622 (1966).
    [CrossRef]
  2. S. Pancharatnam, “Achromatic combinations of birefringent plates,” Proc. Indian Acad. Sci. Sect. A 41, 130–144 (1955).
  3. A. V. Samoylov, V. S. Samoylov, “Achromatic and super-achromatic zero order waveplates,” in Proceedings of LFNM 2003: 5th International Workshop on Laser and Fiber-Optical Networks Modeling (IEEE Press, Piscataway, N.J., 2003), pp. 119–121. (ieeexplore.ieee.org/Xplore).
  4. S. Guimond, D. Elmore, “Designing effective crystal waveplates requires understanding the engineering tradeoffs,” (SPIE) Mag. Photon. Technol. Appl., May 2004, 26–29; http://oemagazine.com.
  5. G. P. Nordin, P. C. Deguzman, “Broadband form birefringent quarter-wave plate for the mid-infrared wavelength region,” Opt. Express 5, 163–168 (2001).
    [CrossRef]
  6. J. Schirmer, P. Kohns, T. Schmidt-Kaler, S. Y. Yakovenko, A. A. Muravski, R. S. Dabrowski, P. Adomenas, Z. Stolarz, “Achromatic phase retarders using double-layer liquid cells,” in Liquid Crystals: Physics, Technology, and Applications, J. Rutkowska, S. J. Klosowicz, J. Zielinski, and J. Zmija, eds., Proc. SPIE3318, 358–363 (1998).
  7. D. Wang, Y. Deng, G. Ai, “Analysis of a new polarimeter for space solar telescope,” Polarimetry in Astronomy, S. Fineschi, ed., Proc. SPIE4843, 406–413 (2003).
  8. J. Schirmer, T. S. Kaler, “Liquid crystal phase retarder with broad spectral range,” Opt. Commun. 176, 313–317 (2000).
    [CrossRef]
  9. I. Abdulhalim, “Continuous phase-only or amplitude light modulation using ferroelectric liquid crystal with fixed boundary orientations,” Opt. Commun. 108, 119–224 (1994).
    [CrossRef]
  10. Z. Zhuang, Y. Kim, J. S. Patel, “Achromatic linear polarization rotator using twisted nematic liquid crystals,” Appl. Phys. Lett. 76, 3995–3997 (2000).
    [CrossRef]
  11. T. X. Wu, Y. Huang, S. T. Wu, “Design optimization of broadband linear polarization converter using twisted nematic liquid crystal,” Jpn. J. Appl. Phys. Part 1 42, 39–41 (2003).
    [CrossRef]
  12. Q. H. Wang, T. X. Wu, X. Zhu, S. T. Wu, “Achromatic polarization switch using a film-compensated twisted nematic liquid crystal cell,” Liq. Cryst. 31, 535–539 (2004).
    [CrossRef]
  13. L. Ingber, “Genetic algorithms and very fast simulated reannealing: a comparison,” Math. Comput. Modell., 16, 87–100 (1992).
    [CrossRef]
  14. C. Z. Shi, N. Zeng, M. Zhang, Y. B. Liao, S. R. Lai, “Adaptive simulated annealing algorithm for the fiber Bragg grating distributed strain sensing,” Opt. Commun. 266, 167–173 (2003).
    [CrossRef]

2004 (1)

Q. H. Wang, T. X. Wu, X. Zhu, S. T. Wu, “Achromatic polarization switch using a film-compensated twisted nematic liquid crystal cell,” Liq. Cryst. 31, 535–539 (2004).
[CrossRef]

2003 (2)

C. Z. Shi, N. Zeng, M. Zhang, Y. B. Liao, S. R. Lai, “Adaptive simulated annealing algorithm for the fiber Bragg grating distributed strain sensing,” Opt. Commun. 266, 167–173 (2003).
[CrossRef]

T. X. Wu, Y. Huang, S. T. Wu, “Design optimization of broadband linear polarization converter using twisted nematic liquid crystal,” Jpn. J. Appl. Phys. Part 1 42, 39–41 (2003).
[CrossRef]

2001 (1)

2000 (2)

Z. Zhuang, Y. Kim, J. S. Patel, “Achromatic linear polarization rotator using twisted nematic liquid crystals,” Appl. Phys. Lett. 76, 3995–3997 (2000).
[CrossRef]

J. Schirmer, T. S. Kaler, “Liquid crystal phase retarder with broad spectral range,” Opt. Commun. 176, 313–317 (2000).
[CrossRef]

1994 (1)

I. Abdulhalim, “Continuous phase-only or amplitude light modulation using ferroelectric liquid crystal with fixed boundary orientations,” Opt. Commun. 108, 119–224 (1994).
[CrossRef]

1992 (1)

L. Ingber, “Genetic algorithms and very fast simulated reannealing: a comparison,” Math. Comput. Modell., 16, 87–100 (1992).
[CrossRef]

1966 (1)

R. J. King, “Quarter-wave retardation systems based on the Fresnel rhomb principle,” J. Sci. Instrum. 43, 617–622 (1966).
[CrossRef]

1955 (1)

S. Pancharatnam, “Achromatic combinations of birefringent plates,” Proc. Indian Acad. Sci. Sect. A 41, 130–144 (1955).

Abdulhalim, I.

I. Abdulhalim, “Continuous phase-only or amplitude light modulation using ferroelectric liquid crystal with fixed boundary orientations,” Opt. Commun. 108, 119–224 (1994).
[CrossRef]

Adomenas, P.

J. Schirmer, P. Kohns, T. Schmidt-Kaler, S. Y. Yakovenko, A. A. Muravski, R. S. Dabrowski, P. Adomenas, Z. Stolarz, “Achromatic phase retarders using double-layer liquid cells,” in Liquid Crystals: Physics, Technology, and Applications, J. Rutkowska, S. J. Klosowicz, J. Zielinski, and J. Zmija, eds., Proc. SPIE3318, 358–363 (1998).

Ai, G.

D. Wang, Y. Deng, G. Ai, “Analysis of a new polarimeter for space solar telescope,” Polarimetry in Astronomy, S. Fineschi, ed., Proc. SPIE4843, 406–413 (2003).

Dabrowski, R. S.

J. Schirmer, P. Kohns, T. Schmidt-Kaler, S. Y. Yakovenko, A. A. Muravski, R. S. Dabrowski, P. Adomenas, Z. Stolarz, “Achromatic phase retarders using double-layer liquid cells,” in Liquid Crystals: Physics, Technology, and Applications, J. Rutkowska, S. J. Klosowicz, J. Zielinski, and J. Zmija, eds., Proc. SPIE3318, 358–363 (1998).

Deguzman, P. C.

Deng, Y.

D. Wang, Y. Deng, G. Ai, “Analysis of a new polarimeter for space solar telescope,” Polarimetry in Astronomy, S. Fineschi, ed., Proc. SPIE4843, 406–413 (2003).

Elmore, D.

S. Guimond, D. Elmore, “Designing effective crystal waveplates requires understanding the engineering tradeoffs,” (SPIE) Mag. Photon. Technol. Appl., May 2004, 26–29; http://oemagazine.com.

Guimond, S.

S. Guimond, D. Elmore, “Designing effective crystal waveplates requires understanding the engineering tradeoffs,” (SPIE) Mag. Photon. Technol. Appl., May 2004, 26–29; http://oemagazine.com.

Huang, Y.

T. X. Wu, Y. Huang, S. T. Wu, “Design optimization of broadband linear polarization converter using twisted nematic liquid crystal,” Jpn. J. Appl. Phys. Part 1 42, 39–41 (2003).
[CrossRef]

Ingber, L.

L. Ingber, “Genetic algorithms and very fast simulated reannealing: a comparison,” Math. Comput. Modell., 16, 87–100 (1992).
[CrossRef]

Kaler, T. S.

J. Schirmer, T. S. Kaler, “Liquid crystal phase retarder with broad spectral range,” Opt. Commun. 176, 313–317 (2000).
[CrossRef]

Kim, Y.

Z. Zhuang, Y. Kim, J. S. Patel, “Achromatic linear polarization rotator using twisted nematic liquid crystals,” Appl. Phys. Lett. 76, 3995–3997 (2000).
[CrossRef]

King, R. J.

R. J. King, “Quarter-wave retardation systems based on the Fresnel rhomb principle,” J. Sci. Instrum. 43, 617–622 (1966).
[CrossRef]

Kohns, P.

J. Schirmer, P. Kohns, T. Schmidt-Kaler, S. Y. Yakovenko, A. A. Muravski, R. S. Dabrowski, P. Adomenas, Z. Stolarz, “Achromatic phase retarders using double-layer liquid cells,” in Liquid Crystals: Physics, Technology, and Applications, J. Rutkowska, S. J. Klosowicz, J. Zielinski, and J. Zmija, eds., Proc. SPIE3318, 358–363 (1998).

Lai, S. R.

C. Z. Shi, N. Zeng, M. Zhang, Y. B. Liao, S. R. Lai, “Adaptive simulated annealing algorithm for the fiber Bragg grating distributed strain sensing,” Opt. Commun. 266, 167–173 (2003).
[CrossRef]

Liao, Y. B.

C. Z. Shi, N. Zeng, M. Zhang, Y. B. Liao, S. R. Lai, “Adaptive simulated annealing algorithm for the fiber Bragg grating distributed strain sensing,” Opt. Commun. 266, 167–173 (2003).
[CrossRef]

Muravski, A. A.

J. Schirmer, P. Kohns, T. Schmidt-Kaler, S. Y. Yakovenko, A. A. Muravski, R. S. Dabrowski, P. Adomenas, Z. Stolarz, “Achromatic phase retarders using double-layer liquid cells,” in Liquid Crystals: Physics, Technology, and Applications, J. Rutkowska, S. J. Klosowicz, J. Zielinski, and J. Zmija, eds., Proc. SPIE3318, 358–363 (1998).

Nordin, G. P.

Pancharatnam, S.

S. Pancharatnam, “Achromatic combinations of birefringent plates,” Proc. Indian Acad. Sci. Sect. A 41, 130–144 (1955).

Patel, J. S.

Z. Zhuang, Y. Kim, J. S. Patel, “Achromatic linear polarization rotator using twisted nematic liquid crystals,” Appl. Phys. Lett. 76, 3995–3997 (2000).
[CrossRef]

Samoylov, A. V.

A. V. Samoylov, V. S. Samoylov, “Achromatic and super-achromatic zero order waveplates,” in Proceedings of LFNM 2003: 5th International Workshop on Laser and Fiber-Optical Networks Modeling (IEEE Press, Piscataway, N.J., 2003), pp. 119–121. (ieeexplore.ieee.org/Xplore).

Samoylov, V. S.

A. V. Samoylov, V. S. Samoylov, “Achromatic and super-achromatic zero order waveplates,” in Proceedings of LFNM 2003: 5th International Workshop on Laser and Fiber-Optical Networks Modeling (IEEE Press, Piscataway, N.J., 2003), pp. 119–121. (ieeexplore.ieee.org/Xplore).

Schirmer, J.

J. Schirmer, T. S. Kaler, “Liquid crystal phase retarder with broad spectral range,” Opt. Commun. 176, 313–317 (2000).
[CrossRef]

J. Schirmer, P. Kohns, T. Schmidt-Kaler, S. Y. Yakovenko, A. A. Muravski, R. S. Dabrowski, P. Adomenas, Z. Stolarz, “Achromatic phase retarders using double-layer liquid cells,” in Liquid Crystals: Physics, Technology, and Applications, J. Rutkowska, S. J. Klosowicz, J. Zielinski, and J. Zmija, eds., Proc. SPIE3318, 358–363 (1998).

Schmidt-Kaler, T.

J. Schirmer, P. Kohns, T. Schmidt-Kaler, S. Y. Yakovenko, A. A. Muravski, R. S. Dabrowski, P. Adomenas, Z. Stolarz, “Achromatic phase retarders using double-layer liquid cells,” in Liquid Crystals: Physics, Technology, and Applications, J. Rutkowska, S. J. Klosowicz, J. Zielinski, and J. Zmija, eds., Proc. SPIE3318, 358–363 (1998).

Shi, C. Z.

C. Z. Shi, N. Zeng, M. Zhang, Y. B. Liao, S. R. Lai, “Adaptive simulated annealing algorithm for the fiber Bragg grating distributed strain sensing,” Opt. Commun. 266, 167–173 (2003).
[CrossRef]

Stolarz, Z.

J. Schirmer, P. Kohns, T. Schmidt-Kaler, S. Y. Yakovenko, A. A. Muravski, R. S. Dabrowski, P. Adomenas, Z. Stolarz, “Achromatic phase retarders using double-layer liquid cells,” in Liquid Crystals: Physics, Technology, and Applications, J. Rutkowska, S. J. Klosowicz, J. Zielinski, and J. Zmija, eds., Proc. SPIE3318, 358–363 (1998).

Wang, D.

D. Wang, Y. Deng, G. Ai, “Analysis of a new polarimeter for space solar telescope,” Polarimetry in Astronomy, S. Fineschi, ed., Proc. SPIE4843, 406–413 (2003).

Wang, Q. H.

Q. H. Wang, T. X. Wu, X. Zhu, S. T. Wu, “Achromatic polarization switch using a film-compensated twisted nematic liquid crystal cell,” Liq. Cryst. 31, 535–539 (2004).
[CrossRef]

Wu, S. T.

Q. H. Wang, T. X. Wu, X. Zhu, S. T. Wu, “Achromatic polarization switch using a film-compensated twisted nematic liquid crystal cell,” Liq. Cryst. 31, 535–539 (2004).
[CrossRef]

T. X. Wu, Y. Huang, S. T. Wu, “Design optimization of broadband linear polarization converter using twisted nematic liquid crystal,” Jpn. J. Appl. Phys. Part 1 42, 39–41 (2003).
[CrossRef]

Wu, T. X.

Q. H. Wang, T. X. Wu, X. Zhu, S. T. Wu, “Achromatic polarization switch using a film-compensated twisted nematic liquid crystal cell,” Liq. Cryst. 31, 535–539 (2004).
[CrossRef]

T. X. Wu, Y. Huang, S. T. Wu, “Design optimization of broadband linear polarization converter using twisted nematic liquid crystal,” Jpn. J. Appl. Phys. Part 1 42, 39–41 (2003).
[CrossRef]

Yakovenko, S. Y.

J. Schirmer, P. Kohns, T. Schmidt-Kaler, S. Y. Yakovenko, A. A. Muravski, R. S. Dabrowski, P. Adomenas, Z. Stolarz, “Achromatic phase retarders using double-layer liquid cells,” in Liquid Crystals: Physics, Technology, and Applications, J. Rutkowska, S. J. Klosowicz, J. Zielinski, and J. Zmija, eds., Proc. SPIE3318, 358–363 (1998).

Zeng, N.

C. Z. Shi, N. Zeng, M. Zhang, Y. B. Liao, S. R. Lai, “Adaptive simulated annealing algorithm for the fiber Bragg grating distributed strain sensing,” Opt. Commun. 266, 167–173 (2003).
[CrossRef]

Zhang, M.

C. Z. Shi, N. Zeng, M. Zhang, Y. B. Liao, S. R. Lai, “Adaptive simulated annealing algorithm for the fiber Bragg grating distributed strain sensing,” Opt. Commun. 266, 167–173 (2003).
[CrossRef]

Zhu, X.

Q. H. Wang, T. X. Wu, X. Zhu, S. T. Wu, “Achromatic polarization switch using a film-compensated twisted nematic liquid crystal cell,” Liq. Cryst. 31, 535–539 (2004).
[CrossRef]

Zhuang, Z.

Z. Zhuang, Y. Kim, J. S. Patel, “Achromatic linear polarization rotator using twisted nematic liquid crystals,” Appl. Phys. Lett. 76, 3995–3997 (2000).
[CrossRef]

Appl. Phys. Lett. (1)

Z. Zhuang, Y. Kim, J. S. Patel, “Achromatic linear polarization rotator using twisted nematic liquid crystals,” Appl. Phys. Lett. 76, 3995–3997 (2000).
[CrossRef]

J. Sci. Instrum. (1)

R. J. King, “Quarter-wave retardation systems based on the Fresnel rhomb principle,” J. Sci. Instrum. 43, 617–622 (1966).
[CrossRef]

Jpn. J. Appl. Phys. Part 1 (1)

T. X. Wu, Y. Huang, S. T. Wu, “Design optimization of broadband linear polarization converter using twisted nematic liquid crystal,” Jpn. J. Appl. Phys. Part 1 42, 39–41 (2003).
[CrossRef]

Liq. Cryst. (1)

Q. H. Wang, T. X. Wu, X. Zhu, S. T. Wu, “Achromatic polarization switch using a film-compensated twisted nematic liquid crystal cell,” Liq. Cryst. 31, 535–539 (2004).
[CrossRef]

Math. Comput. Modell. (1)

L. Ingber, “Genetic algorithms and very fast simulated reannealing: a comparison,” Math. Comput. Modell., 16, 87–100 (1992).
[CrossRef]

Opt. Commun. (3)

C. Z. Shi, N. Zeng, M. Zhang, Y. B. Liao, S. R. Lai, “Adaptive simulated annealing algorithm for the fiber Bragg grating distributed strain sensing,” Opt. Commun. 266, 167–173 (2003).
[CrossRef]

J. Schirmer, T. S. Kaler, “Liquid crystal phase retarder with broad spectral range,” Opt. Commun. 176, 313–317 (2000).
[CrossRef]

I. Abdulhalim, “Continuous phase-only or amplitude light modulation using ferroelectric liquid crystal with fixed boundary orientations,” Opt. Commun. 108, 119–224 (1994).
[CrossRef]

Opt. Express (1)

Proc. Indian Acad. Sci. Sect. A (1)

S. Pancharatnam, “Achromatic combinations of birefringent plates,” Proc. Indian Acad. Sci. Sect. A 41, 130–144 (1955).

Other (4)

A. V. Samoylov, V. S. Samoylov, “Achromatic and super-achromatic zero order waveplates,” in Proceedings of LFNM 2003: 5th International Workshop on Laser and Fiber-Optical Networks Modeling (IEEE Press, Piscataway, N.J., 2003), pp. 119–121. (ieeexplore.ieee.org/Xplore).

S. Guimond, D. Elmore, “Designing effective crystal waveplates requires understanding the engineering tradeoffs,” (SPIE) Mag. Photon. Technol. Appl., May 2004, 26–29; http://oemagazine.com.

J. Schirmer, P. Kohns, T. Schmidt-Kaler, S. Y. Yakovenko, A. A. Muravski, R. S. Dabrowski, P. Adomenas, Z. Stolarz, “Achromatic phase retarders using double-layer liquid cells,” in Liquid Crystals: Physics, Technology, and Applications, J. Rutkowska, S. J. Klosowicz, J. Zielinski, and J. Zmija, eds., Proc. SPIE3318, 358–363 (1998).

D. Wang, Y. Deng, G. Ai, “Analysis of a new polarimeter for space solar telescope,” Polarimetry in Astronomy, S. Fineschi, ed., Proc. SPIE4843, 406–413 (2003).

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Figures (7)

Fig. 1
Fig. 1

Configuration and operating principle of the designed achromatic quarter-wave plate. (a) Cell configuration, (b) relative angle.

Fig. 2
Fig. 2

Emergent SOP (points in the dashed square) and evolution of the SOP inside the device at two incident wavelengths: λ = 458 nm , (solid line) and λ = 598 nm (dotted line).

Fig. 3
Fig. 3

Cell-gap tolerance of the quarter-wave plate. (a) Solid curve, optimum design d 1 = 4.5 μ m ; dotted curve, d 1 = 4.6 μ m ; dashed curve, d 1 = 4.4 μ m . The other parameters are the same as in the optimized design. (b) Analogous to (a), solid curve, d 2 = 1.8 μ m ; dotted curve, d 2 = 1.9 μ m ; dashed curve, d 2 = 1.7 μ m .

Fig. 4
Fig. 4

Twist-angle tolerance of the quarter-wave plate. (a) Solid line, optimum design ϕ 1 = 33.61 ° ; dotted curve, ϕ 1 = 32.61 ° ; dashed curve, ϕ 1 = 34.61 ° . The other parameters as in Fig. 3. (b) Analogous to (a), solid curve, ϕ 2 = 65.31 ° ; dotted curve, ϕ 2 = 66.31 ° ; dashed curve, ϕ 2 = 64.31 ° .

Fig. 5
Fig. 5

Misalignment angle tolerance of the quarter-wave plate. (a) Solid curve, optimum design α 1 = 1.12 ° ; dotted curve, α 1 = 2.12 ° ; dashed curve, α 1 = 0.12 ° . The other parameters are unchanged. (b) Analogous to (a), solid curve, optimum design α 2 = 52.71 ° ; dotted curve, α 2 = 53.71 ° ; dashed curve, α 2 = 51.71 ° . The other parameters as in Fig. 3.

Fig. 6
Fig. 6

Theoretical temperature response of the designed achromatic TNLC quarter-wave plate: solid curve, 20 °C; dashed curve, 50 °C.

Fig. 7
Fig. 7

Comparison of the TNLC type (solid curve) with three-element Pancharatnam’s type (dashed curve) and the NLC type (dotted curve).

Equations (7)

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

( E x out E y out ) = M LC 2 M LC 1 ( E x in E y in ) ,
M LC , j = [ cos ( ϕ j + α j ) sin ( ϕ j + α j ) sin ( ϕ j + α j ) cos ( ϕ j + α j ) ] × [ cos X j i Γ j 2 sin X j X j ϕ j sin X j X j ϕ j sin X j X j cos X j + i Γ j 2 sin X j X j ] × [ cos α j sin α j sin α j cos α j ] .
Δ n ( λ * , T ) = G ( T ) λ * λ * 2 λ 2 λ * 2 .
S 3 = i ( E x E y E y E x ) ,
F cost = 400 nm 700 nm 1 S 3 ( λ ) d λ .
Δ n 1 ( λ a ) d 1 Δ n 2 ( λ a ) d 2 = λ a 4 ,
Δ n 1 ( λ b ) d 1 Δ n 2 ( λ b ) d 2 = λ b 4 .

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