Abstract

We report on a family of complex birefringent elements, called Multi-Twist Retarders (MTRs), which offer remarkably effective control of broadband polarization transformation. MTRs consist of two or more twisted liquid crystal (LC) layers on a single substrate and with a single alignment layer. Importantly, subsequent LC layers are aligned directly by prior layers, allowing simple fabrication, achieving automatic layer registration, and resulting in a monolithic film with a continuously varying optic axis. In this work, we employ a numerical design method and focus on achromatic quarter- and half-wave MTRs. In just two or three layers, these have bandwidths and general behavior that matches or exceeds all traditional approaches using multiple homogenous retarders. We validate the concept by fabricating several quarter-wave retarders using a commercial polymerizeable LC, and show excellent achromaticity across bandwidths of 450–650 nm and 400–800 nm. Due to their simple fabrication and many degrees of freedom, MTRs are especially well suited for patterned achromatic retarders, and can easily achieve large bandwidth and/or low-variation of retardation within visible through infrared wavelengths.

© 2013 OSA

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  1. D. H. Goldstein, Polarized Light (CRC Press, 2011), 3rd ed.
  2. H. Mattoussi, M. Srinviasarao, P. Kaatz, and G. C. Berry, “Birefringence and dispersion of uniaxial media,” Mol. Cryst. and Liq. Cryst.223, 69–84 (1992).
    [CrossRef]
  3. O. Parri, G. Smith, R. Harding, H. Yoon, I. Gardiner, J. Sargent, and K. Skjonnemand, “Patterned retarder films using reactive mesogen technology,” Proc. SPIE7956, 1–11 (2011).
  4. D. Clarke, “Achromatic halfwave plates and linear polarization rotators,” Opt. Acta14, 343–350 (1967).
    [CrossRef]
  5. P. Hariharan, “Achromatic and apochromatic halfwave and quarterwave retarders,” Opt. Eng.35, 3335–3337 (1996).
    [CrossRef]
  6. J. Schirmer and T. Schmidt-Kaler, “Liquid crystal phase retarder with broad spectral range,” Opt. Commun.176, 313–317 (2000).
    [CrossRef]
  7. B. Boulbry, B. Bousquet, B. Le Jeune, Y. Guern, and J. Lotrian, “Polarization errors associated with zero-order achromatic quarter-wave plates in the whole visible spectral range,” Opt. Express9, 225–235 (2001).
    [CrossRef]
  8. M. G. Destriau and J. Prouteau, “Realisation dun quart donde quasi achromatique par juxtaposition de 2 lames cristallines de meme nature,” J. Phys. Radium10, 53–55 (1949).
    [CrossRef]
  9. S. Pancharatnam, “Achromatic combinations of birefringent plates. Part I. An achromatic circular polarizer,” Proc. Ind. Acad. Sci. A41, 130–136 (1955).
  10. S. Pancharatnam, “Achromatic combinations of birefringent plates. Part II. An achromatic quarter-wave plate,” Proc. Ind. Acad. Sci. A41, 137–144 (1955).
  11. A. Samoylov, V. Samoylov, A. Vidmachenko, and A. Perekhod, “Achromatic and super-achromatic zero-order waveplates,” J. Quant. Spectrosc. Radiat. Transfer88, 319–325 (2004).
    [CrossRef]
  12. C. M. McIntyre and S. E. Harris, “Achromatic wave plates for visible spectrum,” J. Opt. Soc. Am.58, 1575–1580 (1968).
    [CrossRef]
  13. S. Tang and H. Kwok, “Mueller calculus and perfect polarization conversion modes in liquid crystal displays,” J. Appl. Phys.89, 5288–5294 (2001).
    [CrossRef]
  14. K. Yoon, H. Yoon, K. Kim, H. Cui, J. Park, W. Jang, and O. Park, “Application of twisted retarders to a cholesteric liquid crystal polarizer for the control of output polarization states,” Jap. J. Appl. Phys.48, 1–6 (2009).
    [CrossRef]
  15. O. Parri, K. Skjonnemand, K. Slaney, and M. Verrall, “Combination of optical films comprising a twisted a-plate and a polarizer,” US Patent7,187424 (2007).
  16. M. Lavrentovich, T. Sergan, and J. Kelly, “Switchable broadband achromatic half-wave plate with nematic liquid crystals,” Opt. Lett.29, 1411–1413 (2004).
    [CrossRef] [PubMed]
  17. Z. Zhuang, Y. Kim, and J. Patel, “Achromatic linear polarization rotator using twisted nematic liquid crystals,” Appl. Phys. Lett.76, 3995–3997 (2000).
    [CrossRef]
  18. T. X. Wu, Y. Huang, and S.-T. Wu, “Design optimization of broadband linear polarization converter using twisted nematic liquid crystal,” Jap. J. Appl. Phys.42, L39–L41 (2003).
    [CrossRef]
  19. S. Shen, J. She, and T. Tao, “Optimal design of achromatic true zero-order waveplates using twisted nematic liquid crystal,” J. Opt. Soc. Am. A22, 961–965 (2005).
    [CrossRef]
  20. D. Clarke, “Interference effects in Pancharatnam wave plates,” J. Opt. A - Pure Appl. Opt.6, 1047–1051 (2004).
    [CrossRef]
  21. R. Komanduri, J. Kim, K. Lawler, and M. Escuti, “Multi-twist retarders for broadband polarization transformation,” Proc. SPIE8279, 1–10 (2012).
  22. J. Kim, R. Komanduri, K. Lawler, D. Kekas, and M. Escuti, “Efficient and monolithic polarization conversion system based on a polarization grating,” Appl. Opt.51, 4852–4857 (2012).
    [CrossRef] [PubMed]
  23. Y. Li, J. Kim, and M. Escuti, “Broadband orbital angular momentum manipulation using liquid crystal thin films,” Proc. SPIE8274, 1–8 (2012).
  24. D. Mawet, “Taking the vector vortex coronagraph to the next level for ground- and space-based exoplanet imaging instruments: review of technology developments in the usa, japan, and europe,” Proc. SPIE8151, 1–14 (2011).
  25. C. Oh and M. Escuti, “Achromatic diffraction from polarization gratings with high efficiency,” Opt. Lett.33, 2287–2289 (2008).
    [CrossRef] [PubMed]
  26. D. Broer and I. Heynderickx, “3 dimensionally ordered polymer networks with a helicoidal structure,” Macromolecules23, 2474–2477 (1990).
    [CrossRef]
  27. S. Kelly, “Anisotropic networks,” J. Mater. Chem.5, 2047–2061 (1995).
    [CrossRef]
  28. M. Schadt, H. Seiberle, A. Schuster, and S. M. Kelly, “Photo-induced alignment and patterning of hybrid liquid-crystalline polymer films on single substrates,” Jap. J. Appl. Phys.34, L764–L767 (1995).
    [CrossRef]
  29. D. Broer, J. Lub, and G. Mol, “Wide-band reflective polarizers from cholesteric polymer networks with a pitch gradient,” Nature378, 467–469 (1995).
    [CrossRef]
  30. C. J. Koester, “Achromatic combinations of half-wave plates,” J. Opt. Soc. Am.49, 405–409 (1959).
    [CrossRef]

2012 (3)

R. Komanduri, J. Kim, K. Lawler, and M. Escuti, “Multi-twist retarders for broadband polarization transformation,” Proc. SPIE8279, 1–10 (2012).

J. Kim, R. Komanduri, K. Lawler, D. Kekas, and M. Escuti, “Efficient and monolithic polarization conversion system based on a polarization grating,” Appl. Opt.51, 4852–4857 (2012).
[CrossRef] [PubMed]

Y. Li, J. Kim, and M. Escuti, “Broadband orbital angular momentum manipulation using liquid crystal thin films,” Proc. SPIE8274, 1–8 (2012).

2011 (2)

D. Mawet, “Taking the vector vortex coronagraph to the next level for ground- and space-based exoplanet imaging instruments: review of technology developments in the usa, japan, and europe,” Proc. SPIE8151, 1–14 (2011).

O. Parri, G. Smith, R. Harding, H. Yoon, I. Gardiner, J. Sargent, and K. Skjonnemand, “Patterned retarder films using reactive mesogen technology,” Proc. SPIE7956, 1–11 (2011).

2009 (1)

K. Yoon, H. Yoon, K. Kim, H. Cui, J. Park, W. Jang, and O. Park, “Application of twisted retarders to a cholesteric liquid crystal polarizer for the control of output polarization states,” Jap. J. Appl. Phys.48, 1–6 (2009).
[CrossRef]

2008 (1)

2005 (1)

2004 (3)

D. Clarke, “Interference effects in Pancharatnam wave plates,” J. Opt. A - Pure Appl. Opt.6, 1047–1051 (2004).
[CrossRef]

M. Lavrentovich, T. Sergan, and J. Kelly, “Switchable broadband achromatic half-wave plate with nematic liquid crystals,” Opt. Lett.29, 1411–1413 (2004).
[CrossRef] [PubMed]

A. Samoylov, V. Samoylov, A. Vidmachenko, and A. Perekhod, “Achromatic and super-achromatic zero-order waveplates,” J. Quant. Spectrosc. Radiat. Transfer88, 319–325 (2004).
[CrossRef]

2003 (1)

T. X. Wu, Y. Huang, and S.-T. Wu, “Design optimization of broadband linear polarization converter using twisted nematic liquid crystal,” Jap. J. Appl. Phys.42, L39–L41 (2003).
[CrossRef]

2001 (2)

S. Tang and H. Kwok, “Mueller calculus and perfect polarization conversion modes in liquid crystal displays,” J. Appl. Phys.89, 5288–5294 (2001).
[CrossRef]

B. Boulbry, B. Bousquet, B. Le Jeune, Y. Guern, and J. Lotrian, “Polarization errors associated with zero-order achromatic quarter-wave plates in the whole visible spectral range,” Opt. Express9, 225–235 (2001).
[CrossRef]

2000 (2)

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

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

1996 (1)

P. Hariharan, “Achromatic and apochromatic halfwave and quarterwave retarders,” Opt. Eng.35, 3335–3337 (1996).
[CrossRef]

1995 (3)

S. Kelly, “Anisotropic networks,” J. Mater. Chem.5, 2047–2061 (1995).
[CrossRef]

M. Schadt, H. Seiberle, A. Schuster, and S. M. Kelly, “Photo-induced alignment and patterning of hybrid liquid-crystalline polymer films on single substrates,” Jap. J. Appl. Phys.34, L764–L767 (1995).
[CrossRef]

D. Broer, J. Lub, and G. Mol, “Wide-band reflective polarizers from cholesteric polymer networks with a pitch gradient,” Nature378, 467–469 (1995).
[CrossRef]

1992 (1)

H. Mattoussi, M. Srinviasarao, P. Kaatz, and G. C. Berry, “Birefringence and dispersion of uniaxial media,” Mol. Cryst. and Liq. Cryst.223, 69–84 (1992).
[CrossRef]

1990 (1)

D. Broer and I. Heynderickx, “3 dimensionally ordered polymer networks with a helicoidal structure,” Macromolecules23, 2474–2477 (1990).
[CrossRef]

1968 (1)

1967 (1)

D. Clarke, “Achromatic halfwave plates and linear polarization rotators,” Opt. Acta14, 343–350 (1967).
[CrossRef]

1959 (1)

1955 (2)

S. Pancharatnam, “Achromatic combinations of birefringent plates. Part I. An achromatic circular polarizer,” Proc. Ind. Acad. Sci. A41, 130–136 (1955).

S. Pancharatnam, “Achromatic combinations of birefringent plates. Part II. An achromatic quarter-wave plate,” Proc. Ind. Acad. Sci. A41, 137–144 (1955).

1949 (1)

M. G. Destriau and J. Prouteau, “Realisation dun quart donde quasi achromatique par juxtaposition de 2 lames cristallines de meme nature,” J. Phys. Radium10, 53–55 (1949).
[CrossRef]

Berry, G. C.

H. Mattoussi, M. Srinviasarao, P. Kaatz, and G. C. Berry, “Birefringence and dispersion of uniaxial media,” Mol. Cryst. and Liq. Cryst.223, 69–84 (1992).
[CrossRef]

Boulbry, B.

B. Boulbry, B. Bousquet, B. Le Jeune, Y. Guern, and J. Lotrian, “Polarization errors associated with zero-order achromatic quarter-wave plates in the whole visible spectral range,” Opt. Express9, 225–235 (2001).
[CrossRef]

Bousquet, B.

B. Boulbry, B. Bousquet, B. Le Jeune, Y. Guern, and J. Lotrian, “Polarization errors associated with zero-order achromatic quarter-wave plates in the whole visible spectral range,” Opt. Express9, 225–235 (2001).
[CrossRef]

Broer, D.

D. Broer, J. Lub, and G. Mol, “Wide-band reflective polarizers from cholesteric polymer networks with a pitch gradient,” Nature378, 467–469 (1995).
[CrossRef]

D. Broer and I. Heynderickx, “3 dimensionally ordered polymer networks with a helicoidal structure,” Macromolecules23, 2474–2477 (1990).
[CrossRef]

Clarke, D.

D. Clarke, “Interference effects in Pancharatnam wave plates,” J. Opt. A - Pure Appl. Opt.6, 1047–1051 (2004).
[CrossRef]

D. Clarke, “Achromatic halfwave plates and linear polarization rotators,” Opt. Acta14, 343–350 (1967).
[CrossRef]

Cui, H.

K. Yoon, H. Yoon, K. Kim, H. Cui, J. Park, W. Jang, and O. Park, “Application of twisted retarders to a cholesteric liquid crystal polarizer for the control of output polarization states,” Jap. J. Appl. Phys.48, 1–6 (2009).
[CrossRef]

Destriau, M. G.

M. G. Destriau and J. Prouteau, “Realisation dun quart donde quasi achromatique par juxtaposition de 2 lames cristallines de meme nature,” J. Phys. Radium10, 53–55 (1949).
[CrossRef]

Escuti, M.

J. Kim, R. Komanduri, K. Lawler, D. Kekas, and M. Escuti, “Efficient and monolithic polarization conversion system based on a polarization grating,” Appl. Opt.51, 4852–4857 (2012).
[CrossRef] [PubMed]

Y. Li, J. Kim, and M. Escuti, “Broadband orbital angular momentum manipulation using liquid crystal thin films,” Proc. SPIE8274, 1–8 (2012).

R. Komanduri, J. Kim, K. Lawler, and M. Escuti, “Multi-twist retarders for broadband polarization transformation,” Proc. SPIE8279, 1–10 (2012).

C. Oh and M. Escuti, “Achromatic diffraction from polarization gratings with high efficiency,” Opt. Lett.33, 2287–2289 (2008).
[CrossRef] [PubMed]

Gardiner, I.

O. Parri, G. Smith, R. Harding, H. Yoon, I. Gardiner, J. Sargent, and K. Skjonnemand, “Patterned retarder films using reactive mesogen technology,” Proc. SPIE7956, 1–11 (2011).

Goldstein, D. H.

D. H. Goldstein, Polarized Light (CRC Press, 2011), 3rd ed.

Guern, Y.

B. Boulbry, B. Bousquet, B. Le Jeune, Y. Guern, and J. Lotrian, “Polarization errors associated with zero-order achromatic quarter-wave plates in the whole visible spectral range,” Opt. Express9, 225–235 (2001).
[CrossRef]

Harding, R.

O. Parri, G. Smith, R. Harding, H. Yoon, I. Gardiner, J. Sargent, and K. Skjonnemand, “Patterned retarder films using reactive mesogen technology,” Proc. SPIE7956, 1–11 (2011).

Hariharan, P.

P. Hariharan, “Achromatic and apochromatic halfwave and quarterwave retarders,” Opt. Eng.35, 3335–3337 (1996).
[CrossRef]

Harris, S. E.

Heynderickx, I.

D. Broer and I. Heynderickx, “3 dimensionally ordered polymer networks with a helicoidal structure,” Macromolecules23, 2474–2477 (1990).
[CrossRef]

Huang, Y.

T. X. Wu, Y. Huang, and S.-T. Wu, “Design optimization of broadband linear polarization converter using twisted nematic liquid crystal,” Jap. J. Appl. Phys.42, L39–L41 (2003).
[CrossRef]

Jang, W.

K. Yoon, H. Yoon, K. Kim, H. Cui, J. Park, W. Jang, and O. Park, “Application of twisted retarders to a cholesteric liquid crystal polarizer for the control of output polarization states,” Jap. J. Appl. Phys.48, 1–6 (2009).
[CrossRef]

Kaatz, P.

H. Mattoussi, M. Srinviasarao, P. Kaatz, and G. C. Berry, “Birefringence and dispersion of uniaxial media,” Mol. Cryst. and Liq. Cryst.223, 69–84 (1992).
[CrossRef]

Kekas, D.

Kelly, J.

Kelly, S.

S. Kelly, “Anisotropic networks,” J. Mater. Chem.5, 2047–2061 (1995).
[CrossRef]

Kelly, S. M.

M. Schadt, H. Seiberle, A. Schuster, and S. M. Kelly, “Photo-induced alignment and patterning of hybrid liquid-crystalline polymer films on single substrates,” Jap. J. Appl. Phys.34, L764–L767 (1995).
[CrossRef]

Kim, J.

R. Komanduri, J. Kim, K. Lawler, and M. Escuti, “Multi-twist retarders for broadband polarization transformation,” Proc. SPIE8279, 1–10 (2012).

Y. Li, J. Kim, and M. Escuti, “Broadband orbital angular momentum manipulation using liquid crystal thin films,” Proc. SPIE8274, 1–8 (2012).

J. Kim, R. Komanduri, K. Lawler, D. Kekas, and M. Escuti, “Efficient and monolithic polarization conversion system based on a polarization grating,” Appl. Opt.51, 4852–4857 (2012).
[CrossRef] [PubMed]

Kim, K.

K. Yoon, H. Yoon, K. Kim, H. Cui, J. Park, W. Jang, and O. Park, “Application of twisted retarders to a cholesteric liquid crystal polarizer for the control of output polarization states,” Jap. J. Appl. Phys.48, 1–6 (2009).
[CrossRef]

Kim, Y.

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

Koester, C. J.

Komanduri, R.

J. Kim, R. Komanduri, K. Lawler, D. Kekas, and M. Escuti, “Efficient and monolithic polarization conversion system based on a polarization grating,” Appl. Opt.51, 4852–4857 (2012).
[CrossRef] [PubMed]

R. Komanduri, J. Kim, K. Lawler, and M. Escuti, “Multi-twist retarders for broadband polarization transformation,” Proc. SPIE8279, 1–10 (2012).

Kwok, H.

S. Tang and H. Kwok, “Mueller calculus and perfect polarization conversion modes in liquid crystal displays,” J. Appl. Phys.89, 5288–5294 (2001).
[CrossRef]

Lavrentovich, M.

Lawler, K.

R. Komanduri, J. Kim, K. Lawler, and M. Escuti, “Multi-twist retarders for broadband polarization transformation,” Proc. SPIE8279, 1–10 (2012).

J. Kim, R. Komanduri, K. Lawler, D. Kekas, and M. Escuti, “Efficient and monolithic polarization conversion system based on a polarization grating,” Appl. Opt.51, 4852–4857 (2012).
[CrossRef] [PubMed]

Le Jeune, B.

B. Boulbry, B. Bousquet, B. Le Jeune, Y. Guern, and J. Lotrian, “Polarization errors associated with zero-order achromatic quarter-wave plates in the whole visible spectral range,” Opt. Express9, 225–235 (2001).
[CrossRef]

Li, Y.

Y. Li, J. Kim, and M. Escuti, “Broadband orbital angular momentum manipulation using liquid crystal thin films,” Proc. SPIE8274, 1–8 (2012).

Lotrian, J.

B. Boulbry, B. Bousquet, B. Le Jeune, Y. Guern, and J. Lotrian, “Polarization errors associated with zero-order achromatic quarter-wave plates in the whole visible spectral range,” Opt. Express9, 225–235 (2001).
[CrossRef]

Lub, J.

D. Broer, J. Lub, and G. Mol, “Wide-band reflective polarizers from cholesteric polymer networks with a pitch gradient,” Nature378, 467–469 (1995).
[CrossRef]

Mattoussi, H.

H. Mattoussi, M. Srinviasarao, P. Kaatz, and G. C. Berry, “Birefringence and dispersion of uniaxial media,” Mol. Cryst. and Liq. Cryst.223, 69–84 (1992).
[CrossRef]

Mawet, D.

D. Mawet, “Taking the vector vortex coronagraph to the next level for ground- and space-based exoplanet imaging instruments: review of technology developments in the usa, japan, and europe,” Proc. SPIE8151, 1–14 (2011).

McIntyre, C. M.

Mol, G.

D. Broer, J. Lub, and G. Mol, “Wide-band reflective polarizers from cholesteric polymer networks with a pitch gradient,” Nature378, 467–469 (1995).
[CrossRef]

Oh, C.

Pancharatnam, S.

S. Pancharatnam, “Achromatic combinations of birefringent plates. Part II. An achromatic quarter-wave plate,” Proc. Ind. Acad. Sci. A41, 137–144 (1955).

S. Pancharatnam, “Achromatic combinations of birefringent plates. Part I. An achromatic circular polarizer,” Proc. Ind. Acad. Sci. A41, 130–136 (1955).

Park, J.

K. Yoon, H. Yoon, K. Kim, H. Cui, J. Park, W. Jang, and O. Park, “Application of twisted retarders to a cholesteric liquid crystal polarizer for the control of output polarization states,” Jap. J. Appl. Phys.48, 1–6 (2009).
[CrossRef]

Park, O.

K. Yoon, H. Yoon, K. Kim, H. Cui, J. Park, W. Jang, and O. Park, “Application of twisted retarders to a cholesteric liquid crystal polarizer for the control of output polarization states,” Jap. J. Appl. Phys.48, 1–6 (2009).
[CrossRef]

Parri, O.

O. Parri, G. Smith, R. Harding, H. Yoon, I. Gardiner, J. Sargent, and K. Skjonnemand, “Patterned retarder films using reactive mesogen technology,” Proc. SPIE7956, 1–11 (2011).

O. Parri, K. Skjonnemand, K. Slaney, and M. Verrall, “Combination of optical films comprising a twisted a-plate and a polarizer,” US Patent7,187424 (2007).

Patel, J.

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

Perekhod, A.

A. Samoylov, V. Samoylov, A. Vidmachenko, and A. Perekhod, “Achromatic and super-achromatic zero-order waveplates,” J. Quant. Spectrosc. Radiat. Transfer88, 319–325 (2004).
[CrossRef]

Prouteau, J.

M. G. Destriau and J. Prouteau, “Realisation dun quart donde quasi achromatique par juxtaposition de 2 lames cristallines de meme nature,” J. Phys. Radium10, 53–55 (1949).
[CrossRef]

Samoylov, A.

A. Samoylov, V. Samoylov, A. Vidmachenko, and A. Perekhod, “Achromatic and super-achromatic zero-order waveplates,” J. Quant. Spectrosc. Radiat. Transfer88, 319–325 (2004).
[CrossRef]

Samoylov, V.

A. Samoylov, V. Samoylov, A. Vidmachenko, and A. Perekhod, “Achromatic and super-achromatic zero-order waveplates,” J. Quant. Spectrosc. Radiat. Transfer88, 319–325 (2004).
[CrossRef]

Sargent, J.

O. Parri, G. Smith, R. Harding, H. Yoon, I. Gardiner, J. Sargent, and K. Skjonnemand, “Patterned retarder films using reactive mesogen technology,” Proc. SPIE7956, 1–11 (2011).

Schadt, M.

M. Schadt, H. Seiberle, A. Schuster, and S. M. Kelly, “Photo-induced alignment and patterning of hybrid liquid-crystalline polymer films on single substrates,” Jap. J. Appl. Phys.34, L764–L767 (1995).
[CrossRef]

Schirmer, J.

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

Schmidt-Kaler, T.

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

Schuster, A.

M. Schadt, H. Seiberle, A. Schuster, and S. M. Kelly, “Photo-induced alignment and patterning of hybrid liquid-crystalline polymer films on single substrates,” Jap. J. Appl. Phys.34, L764–L767 (1995).
[CrossRef]

Seiberle, H.

M. Schadt, H. Seiberle, A. Schuster, and S. M. Kelly, “Photo-induced alignment and patterning of hybrid liquid-crystalline polymer films on single substrates,” Jap. J. Appl. Phys.34, L764–L767 (1995).
[CrossRef]

Sergan, T.

She, J.

Shen, S.

Skjonnemand, K.

O. Parri, G. Smith, R. Harding, H. Yoon, I. Gardiner, J. Sargent, and K. Skjonnemand, “Patterned retarder films using reactive mesogen technology,” Proc. SPIE7956, 1–11 (2011).

O. Parri, K. Skjonnemand, K. Slaney, and M. Verrall, “Combination of optical films comprising a twisted a-plate and a polarizer,” US Patent7,187424 (2007).

Slaney, K.

O. Parri, K. Skjonnemand, K. Slaney, and M. Verrall, “Combination of optical films comprising a twisted a-plate and a polarizer,” US Patent7,187424 (2007).

Smith, G.

O. Parri, G. Smith, R. Harding, H. Yoon, I. Gardiner, J. Sargent, and K. Skjonnemand, “Patterned retarder films using reactive mesogen technology,” Proc. SPIE7956, 1–11 (2011).

Srinviasarao, M.

H. Mattoussi, M. Srinviasarao, P. Kaatz, and G. C. Berry, “Birefringence and dispersion of uniaxial media,” Mol. Cryst. and Liq. Cryst.223, 69–84 (1992).
[CrossRef]

Tang, S.

S. Tang and H. Kwok, “Mueller calculus and perfect polarization conversion modes in liquid crystal displays,” J. Appl. Phys.89, 5288–5294 (2001).
[CrossRef]

Tao, T.

Verrall, M.

O. Parri, K. Skjonnemand, K. Slaney, and M. Verrall, “Combination of optical films comprising a twisted a-plate and a polarizer,” US Patent7,187424 (2007).

Vidmachenko, A.

A. Samoylov, V. Samoylov, A. Vidmachenko, and A. Perekhod, “Achromatic and super-achromatic zero-order waveplates,” J. Quant. Spectrosc. Radiat. Transfer88, 319–325 (2004).
[CrossRef]

Wu, S.-T.

T. X. Wu, Y. Huang, and S.-T. Wu, “Design optimization of broadband linear polarization converter using twisted nematic liquid crystal,” Jap. J. Appl. Phys.42, L39–L41 (2003).
[CrossRef]

Wu, T. X.

T. X. Wu, Y. Huang, and S.-T. Wu, “Design optimization of broadband linear polarization converter using twisted nematic liquid crystal,” Jap. J. Appl. Phys.42, L39–L41 (2003).
[CrossRef]

Yoon, H.

O. Parri, G. Smith, R. Harding, H. Yoon, I. Gardiner, J. Sargent, and K. Skjonnemand, “Patterned retarder films using reactive mesogen technology,” Proc. SPIE7956, 1–11 (2011).

K. Yoon, H. Yoon, K. Kim, H. Cui, J. Park, W. Jang, and O. Park, “Application of twisted retarders to a cholesteric liquid crystal polarizer for the control of output polarization states,” Jap. J. Appl. Phys.48, 1–6 (2009).
[CrossRef]

Yoon, K.

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Figures (11)

Fig. 1
Fig. 1

Representative prior achromatic retarder approaches. Some use homogenous plates with (a) different materials [4], and others use a single material in designs with (b) two [8] (DP), (c) three [9] (Pancharatnam), and (d) five [11] (APSAW) elements. Some others use two twisted liquid crystal (LC) elements, (e) with [16] and (f) without [19] an additional element, having six and four substrates with LC alignment layers, respectively.

Fig. 2
Fig. 2

Illustration of the multi-twist retarder (MTR) monolithic structure, with one substrate and alignment layer, and M twisted layers. Cylinders correspond to the optical axis (and the nematic director field). Subsequent layers are aligned by the prior one.

Fig. 3
Fig. 3

(a) Illustration of the two layer MTR (2TR). (b) The polarization evolution within the 2TR QW-A design, on the Poincaré sphere (450 to 650 nm shown, spacing of 25 nm).

Fig. 4
Fig. 4

Simulated output of the achromatic 2TR QW designs, and the comparative DP example, assuming a linear (horizontal) input: (a) Stokes S3; (b) effective retardation; (c) ellipticity; and (d) effective optical axis orientation angle. Curves: QW-A (solid), QW-B (dashed), QW-C (dash dot), and DP (dotted).

Fig. 5
Fig. 5

(a) Illustration of the three layer MTR (3TR). (b) The polarization evolution within the 3TR QW-A design, on the Poincaré sphere (425 to 750 nm shown, spacing of 50 nm).

Fig. 6
Fig. 6

Simulated output of the super-achromatic 3TR QW designs, and the comparative Pancharatnam example, assuming a linear (horizontal) input: (a) Stokes S3; (b) effective retardation; (c) ellipticity; and (d) effective optical axis orientation angle. Curves: QW-A (solid), QW-B (dash dot), and Pancharatnam (dotted).

Fig. 7
Fig. 7

Simulated output of the (achromatic) 2TR and (super-achromatic) 3TR HW designs, and their comparative Pancharatnam examples: (a) and (b) show the output for the lin-lin HW MTRs, with a linear (horizontal) input polarization; whereas (c) and (d) show the output from cir-cir HW MTRs, with a circular (right) input. Curves: 2TR (dashed), 3TR (bold), and corresponding Pancharatnam (dotted and dash dot, respectively).

Fig. 8
Fig. 8

The MTR fabrication procedure resulting in a monolithic broadband element, on a single substrate and alignment layer: (a) alignment layer processing; (b) LCP coating (m = 1); (c) LCP photo-polymerization; and (d) repeat LCP coating and curing for (m ≥ 2).

Fig. 9
Fig. 9

Measured retardation spectra fabricated MTR QW elements, with linear (horizontal) input polarization. (a) Achromatic 2TR QW-A (solid) output, with the best fit simulation (dash dot), and the comparison AQW2 film (dotted) measured in the same way; (b) Super-achromatic 3TR QW-A (solid) output, with the best fit simulation (dash dot), and the comparison AQWO05M-600 element (dotted) from vendor-measured data.

Fig. 10
Fig. 10

Normalized bandwidth of achromatic MTRs (both QW and HW), and comparative examples in the prior art based on homogenous plates.

Fig. 11
Fig. 11

Analytic estimation of 2TR QW-A design parameters. In part (a), the thicknesses of the first (bold) and second (dashed) layers are shown, while in part (b) the twist angle (bold) of the second layer and the start angle (dashed) have been calculated.

Tables (4)

Tables Icon

Table 1 Summary of 2TR (achromatic) and 3TR (super-achromatic) QW designs.

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Table 2 Summary of 2TR and 3TR HW designs (lin-lin =“A” and cir-cir =“B”).

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Table 3 LCP mixtures for 2TR and 3TR QW designs.

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Table 4 Recipes for the 2TR and 3TR QW designs.

Equations (15)

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T m = ( 1 0 0 0 0 1 2 ( c 2 + d 2 ) 2 ( b d a c ) 2 ( a d + b c ) 0 2 ( a c + b d ) 1 2 ( b 2 + c 2 ) 2 ( a b c d ) 0 2 ( a d b c ) 2 ( a b + c d ) 1 2 ( b 2 + d 2 ) ) , with
a = cos X m cos ϕ m + ϕ m sin ϕ m sinc X m ,
b = ζ m cos ( 2 m ϕ ¯ ϕ m ) sinc X m ,
c = cos X m sin ϕ m ϕ m cos ϕ m sinc X m ,
d = ζ m sin ( 2 m ϕ ¯ ϕ m ) sinc X m .
T M T R = T M T 2 T 1 ,
T 2 T R [ 2 , 2 ] = ( 1 2 ( c 2 2 + d 2 2 ) ) ( 1 2 d 1 2 ) + 4 b 1 d 1 ( b 2 d 2 a 2 c 2 ) 4 a 1 d 1 ( a 2 d 2 + b 2 c 2 ) = 0
T 2 T R [ 3 , 2 ] = 2 ( a 2 c 2 + b 2 d 2 ) ( 1 2 d 1 2 ) + 2 b 1 d 1 ( 1 2 ( b 2 2 + c 2 2 ) ) + 4 a 1 d 1 ( a 2 b 2 c 2 d 2 ) = 0
T 2 T R [ 4 , 2 ] = 2 ( a 2 d 2 b 2 c 2 ) ( 1 2 d 1 2 ) 4 b 1 d 1 ( a 2 b 2 + c 2 d 2 ) + 2 a 1 d 1 ( 1 2 ( b 2 2 + d 2 2 ) ) = 1
1 2 d 1 2 = 2 ( a 2 d 2 b 2 c 2 )
2 b 1 d 1 = 2 ( a 2 b 2 + c 2 d 2 )
2 a 1 d 1 = 1 2 b 2 2 2 d 2 2
sin 2 ϕ 0 ( Eq . ( 10 a ) ) + cos 2 ϕ 0 ( Eq . ( 10 b ) ) sin 2 ϕ 0 cos 2 ζ 1 = 2 ζ 2 sinc 2 X 2
cos 2 ϕ 0 ( Eq . ( 10 a ) ) sin 2 ϕ 0 ( Eq . ( 10 b ) ) cos 2 ϕ 0 = 2 ζ 2 ϕ 2 sinc 2 X 2
Eq . ( 10 c ) 1 sin 2 ϕ 0 sin 2 ζ 1 = 2 ζ 2 2 sinc 2 X 2

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