Abstract

We report on a direct-write system for patterning of arbitrary, high-quality, continuous liquid crystal (LC) alignment patterns. The system uses a focused UV laser and XY scanning stages to expose a photoalignment layer, which then aligns a subsequent LC layer. We intentionally arrange for multiple overlapping exposures of the photoalignment material by a scanned Gaussian beam, often with a plurality of polarizations and intensities, in order to promote continuous and precise LC alignment. This type of exposure protocol has not been well investigated, and sometimes results in unexpected LC responses. Ultimately, this enables us to create continuous alignment patterns with feature sizes smaller than the recording beam. We describe the system design along with a thorough mathematical system description, starting from the direct-write system inputs and ending with the estimated alignment of the LC. We fabricate a number of test patterns to validate our system model, then design and fabricate a number of interesting well-known elements, including a q-plate and polarization grating.

© 2014 Optical Society of America

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References

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  1. J. Kim, C. Oh, S. Serati, M. J. Escuti, “Wide-angle, nonmechanical beam steering with high throughput utilizing polarization gratings,” Appl. Opt. 50, 2636–2639 (2011).
    [Crossref] [PubMed]
  2. S. C. McEldowney, D. M. Shemo, R. A. Chipman, P. K. Smith, “Creating vortex retarders using photoaligned liquid crystal polymers,” Opt. Lett. 33, 134–136 (2008).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  5. C. D. Modes, M. Warner, C. Sanchez-Somolinos, L. T. de Haan, D. Broer, “Mechanical frustration and spontaneous polygonal folding in active nematic sheets,” Phys. Rev. E 86, 3 (2012).
    [Crossref]
  6. M. Schadt, K. Schmitt, V. Kozinkov, V. Chigrinov, “Surface-induced parallel alignment of liquid-crystals by linearly polymerized photopolymers,” Jpn. J. Appl. Phys., Part 1 31, 2155–2164 (1992).
    [Crossref]
  7. P. J. Shannon, W. M. Gibbons, S. T. Sun, “Patterned optical-properties in photopolymerized surface-aligned liquid-crystal films,” Nature 368, 532–533 (1994).
    [Crossref]
  8. G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102(2005).
    [Crossref]
  9. H. Ono, T. Wada, N. Kawatsuki, “Polarization imaging screen using vector gratings fabricated by photocrosslinkable polymer liquid crystals,” Jpn. J. Appl. Phys. 51, 030202(2012).
    [Crossref]
  10. S. C. McEldowney, D. M. Shemo, R. A. Chipman, P. K. Smith, “Creating vortex retarders using photoaligned liquid crystal polymers,” Opt. Lett. 33, 134–136 (2008).
    [Crossref] [PubMed]
  11. S. Nersisyan, N. Tabiryan, D. M. Steeves, B. R. Kimball, “Fabrication of liquid crystal polymer axial wave-plates for uv-ir wavelengths,” Opt. Express 17, 11926–11934 (2009).
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  14. O. Yaroshchuk, Y. Reznikov, “Photoalignment of liquid crystals: basics and current trends,” J. Mat. Chem. 22, 286–300 (2012).
    [Crossref]
  15. N. Kawatsuki, “Photoalignment and photoinduced molecular reorientation of photosensitive materials,” Chem. Lett. 40, 548–554 (2011).
    [Crossref]
  16. V. G. Chigrinov, V. M. Kozenkov, H. S. Kwok, Photoalignment of Liquid Crystalline Materials: Physics and Applications (John Wiley & Sons, Ltd, West Sussex, 2008).
    [Crossref]
  17. B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, New York, 1991), chap. 3, pp. 80–107.
    [Crossref]
  18. R. K. Komanduri, M. J. Escuti, “Elastic continuum analysis of the liquid crystal polarization grating,” Phys. Rev. E 76, 021701(2007).
    [Crossref]
  19. H. Ono, M. Hishida, A. Emoto, T. Shioda, N. Kawatsuki, “Elastic continuum analysis and diffraction properties of two-dimensional liquid crystalline grating cells,” J. Opt. Soc. Am. B. 26, 1151–1156 (2009).
    [Crossref]
  20. S. R. Nersisyan, N. V. Tabiryan, D. Mawet, E. Serabyn, “Improving vector vortex waveplates for high-contrast coronagraphy,” Opt. Express 21, 8205–8213 (2013).
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  21. M. W. Kudenov, M. N. Miskiewicz, M. J. Escuti, E. L. Dereniak, “Spatial heterodyne interferometry with polarization gratings,” Opt. Lett. 37, 4413–4415 (2012).
    [Crossref] [PubMed]
  22. C. Oh, R. Komanduri, M. J. Escuti, “Fdtd analysis of 100%-efficient polarization-independent liquid crystal polarization gratings,” (Spie-Int Soc Optical Engineering, 2006), vol. 6332 of Proc. of SPIE, pp. 33212.
  23. E. Nicolescu, C. C. Mao, A. Fardad, M. Escuti, “Polarization-insensitive variable optical attenuator and wavelength blocker using liquid crystal polarization gratings,” J. Lightwave Technol. 28, 3121–3127 (2010).
  24. M. N. Miskiewicz, J. Kim, Y. M. Li, R. K. Komanduri, M. J. Escuti, “Progress on large-area polarization grating fabrication,” (2012), vol. 8395 of Proc. of SPIE.
    [Crossref]

2013 (1)

2012 (5)

M. W. Kudenov, M. N. Miskiewicz, M. J. Escuti, E. L. Dereniak, “Spatial heterodyne interferometry with polarization gratings,” Opt. Lett. 37, 4413–4415 (2012).
[Crossref] [PubMed]

O. Yaroshchuk, Y. Reznikov, “Photoalignment of liquid crystals: basics and current trends,” J. Mat. Chem. 22, 286–300 (2012).
[Crossref]

U. Ruiz, C. Provenzano, P. Pagliusi, G. Cipparrone, “Single-step polarization holographic method for programmable microlens arrays,” Opt. Lett. 37, 4958–4960 (2012).
[Crossref] [PubMed]

C. D. Modes, M. Warner, C. Sanchez-Somolinos, L. T. de Haan, D. Broer, “Mechanical frustration and spontaneous polygonal folding in active nematic sheets,” Phys. Rev. E 86, 3 (2012).
[Crossref]

H. Ono, T. Wada, N. Kawatsuki, “Polarization imaging screen using vector gratings fabricated by photocrosslinkable polymer liquid crystals,” Jpn. J. Appl. Phys. 51, 030202(2012).
[Crossref]

2011 (2)

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

N. Kawatsuki, “Photoalignment and photoinduced molecular reorientation of photosensitive materials,” Chem. Lett. 40, 548–554 (2011).
[Crossref]

2010 (1)

2009 (3)

2008 (2)

2007 (1)

R. K. Komanduri, M. J. Escuti, “Elastic continuum analysis of the liquid crystal polarization grating,” Phys. Rev. E 76, 021701(2007).
[Crossref]

2005 (1)

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102(2005).
[Crossref]

1994 (1)

P. J. Shannon, W. M. Gibbons, S. T. Sun, “Patterned optical-properties in photopolymerized surface-aligned liquid-crystal films,” Nature 368, 532–533 (1994).
[Crossref]

1992 (1)

M. Schadt, K. Schmitt, V. Kozinkov, V. Chigrinov, “Surface-induced parallel alignment of liquid-crystals by linearly polymerized photopolymers,” Jpn. J. Appl. Phys., Part 1 31, 2155–2164 (1992).
[Crossref]

1976 (1)

Broer, D.

C. D. Modes, M. Warner, C. Sanchez-Somolinos, L. T. de Haan, D. Broer, “Mechanical frustration and spontaneous polygonal folding in active nematic sheets,” Phys. Rev. E 86, 3 (2012).
[Crossref]

Callan-Jones, A.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102(2005).
[Crossref]

Chigrinov, V.

M. Schadt, K. Schmitt, V. Kozinkov, V. Chigrinov, “Surface-induced parallel alignment of liquid-crystals by linearly polymerized photopolymers,” Jpn. J. Appl. Phys., Part 1 31, 2155–2164 (1992).
[Crossref]

Chigrinov, V. G.

V. G. Chigrinov, V. M. Kozenkov, H. S. Kwok, Photoalignment of Liquid Crystalline Materials: Physics and Applications (John Wiley & Sons, Ltd, West Sussex, 2008).
[Crossref]

Chipman, R. A.

Cipparrone, G.

Codona, J.

F. Snik, G. Otten, M. Kenworthy, M. Miskiewicz, M. Escuti, C. Packham, J. Codona, “The vector-app: a broadband apodizing phase plate that yields complementary psfs,” (2012), vol. 8450 of Proc. of SPIE.
[Crossref]

Crawford, G. P.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102(2005).
[Crossref]

de Haan, L. T.

C. D. Modes, M. Warner, C. Sanchez-Somolinos, L. T. de Haan, D. Broer, “Mechanical frustration and spontaneous polygonal folding in active nematic sheets,” Phys. Rev. E 86, 3 (2012).
[Crossref]

Dereniak, E. L.

Eakin, J. N.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102(2005).
[Crossref]

Emoto, A.

H. Ono, M. Hishida, A. Emoto, T. Shioda, N. Kawatsuki, “Elastic continuum analysis and diffraction properties of two-dimensional liquid crystalline grating cells,” J. Opt. Soc. Am. B. 26, 1151–1156 (2009).
[Crossref]

Escuti, M.

E. Nicolescu, C. C. Mao, A. Fardad, M. Escuti, “Polarization-insensitive variable optical attenuator and wavelength blocker using liquid crystal polarization gratings,” J. Lightwave Technol. 28, 3121–3127 (2010).

F. Snik, G. Otten, M. Kenworthy, M. Miskiewicz, M. Escuti, C. Packham, J. Codona, “The vector-app: a broadband apodizing phase plate that yields complementary psfs,” (2012), vol. 8450 of Proc. of SPIE.
[Crossref]

Escuti, M. J.

M. W. Kudenov, M. N. Miskiewicz, M. J. Escuti, E. L. Dereniak, “Spatial heterodyne interferometry with polarization gratings,” Opt. Lett. 37, 4413–4415 (2012).
[Crossref] [PubMed]

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

R. K. Komanduri, M. J. Escuti, “Elastic continuum analysis of the liquid crystal polarization grating,” Phys. Rev. E 76, 021701(2007).
[Crossref]

C. Oh, R. Komanduri, M. J. Escuti, “Fdtd analysis of 100%-efficient polarization-independent liquid crystal polarization gratings,” (Spie-Int Soc Optical Engineering, 2006), vol. 6332 of Proc. of SPIE, pp. 33212.

M. N. Miskiewicz, J. Kim, Y. M. Li, R. K. Komanduri, M. J. Escuti, “Progress on large-area polarization grating fabrication,” (2012), vol. 8395 of Proc. of SPIE.
[Crossref]

Fardad, A.

Fratz, M.

Gibbons, W. M.

P. J. Shannon, W. M. Gibbons, S. T. Sun, “Patterned optical-properties in photopolymerized surface-aligned liquid-crystal films,” Nature 368, 532–533 (1994).
[Crossref]

Giel, D.

Hishida, M.

H. Ono, M. Hishida, A. Emoto, T. Shioda, N. Kawatsuki, “Elastic continuum analysis and diffraction properties of two-dimensional liquid crystalline grating cells,” J. Opt. Soc. Am. B. 26, 1151–1156 (2009).
[Crossref]

Kawatsuki, N.

H. Ono, T. Wada, N. Kawatsuki, “Polarization imaging screen using vector gratings fabricated by photocrosslinkable polymer liquid crystals,” Jpn. J. Appl. Phys. 51, 030202(2012).
[Crossref]

N. Kawatsuki, “Photoalignment and photoinduced molecular reorientation of photosensitive materials,” Chem. Lett. 40, 548–554 (2011).
[Crossref]

H. Ono, M. Hishida, A. Emoto, T. Shioda, N. Kawatsuki, “Elastic continuum analysis and diffraction properties of two-dimensional liquid crystalline grating cells,” J. Opt. Soc. Am. B. 26, 1151–1156 (2009).
[Crossref]

Kenworthy, M.

F. Snik, G. Otten, M. Kenworthy, M. Miskiewicz, M. Escuti, C. Packham, J. Codona, “The vector-app: a broadband apodizing phase plate that yields complementary psfs,” (2012), vol. 8450 of Proc. of SPIE.
[Crossref]

Kim, J.

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

M. N. Miskiewicz, J. Kim, Y. M. Li, R. K. Komanduri, M. J. Escuti, “Progress on large-area polarization grating fabrication,” (2012), vol. 8395 of Proc. of SPIE.
[Crossref]

Kimball, B. R.

Komanduri, R.

C. Oh, R. Komanduri, M. J. Escuti, “Fdtd analysis of 100%-efficient polarization-independent liquid crystal polarization gratings,” (Spie-Int Soc Optical Engineering, 2006), vol. 6332 of Proc. of SPIE, pp. 33212.

Komanduri, R. K.

R. K. Komanduri, M. J. Escuti, “Elastic continuum analysis of the liquid crystal polarization grating,” Phys. Rev. E 76, 021701(2007).
[Crossref]

M. N. Miskiewicz, J. Kim, Y. M. Li, R. K. Komanduri, M. J. Escuti, “Progress on large-area polarization grating fabrication,” (2012), vol. 8395 of Proc. of SPIE.
[Crossref]

Komatsu, H.

Kozenkov, V. M.

V. G. Chigrinov, V. M. Kozenkov, H. S. Kwok, Photoalignment of Liquid Crystalline Materials: Physics and Applications (John Wiley & Sons, Ltd, West Sussex, 2008).
[Crossref]

Kozinkov, V.

M. Schadt, K. Schmitt, V. Kozinkov, V. Chigrinov, “Surface-induced parallel alignment of liquid-crystals by linearly polymerized photopolymers,” Jpn. J. Appl. Phys., Part 1 31, 2155–2164 (1992).
[Crossref]

Kudenov, M. W.

Kwok, H. S.

V. G. Chigrinov, V. M. Kozenkov, H. S. Kwok, Photoalignment of Liquid Crystalline Materials: Physics and Applications (John Wiley & Sons, Ltd, West Sussex, 2008).
[Crossref]

Li, Y. M.

M. N. Miskiewicz, J. Kim, Y. M. Li, R. K. Komanduri, M. J. Escuti, “Progress on large-area polarization grating fabrication,” (2012), vol. 8395 of Proc. of SPIE.
[Crossref]

Mao, C. C.

Mawet, D.

McEldowney, S. C.

Miskiewicz, M.

F. Snik, G. Otten, M. Kenworthy, M. Miskiewicz, M. Escuti, C. Packham, J. Codona, “The vector-app: a broadband apodizing phase plate that yields complementary psfs,” (2012), vol. 8450 of Proc. of SPIE.
[Crossref]

Miskiewicz, M. N.

M. W. Kudenov, M. N. Miskiewicz, M. J. Escuti, E. L. Dereniak, “Spatial heterodyne interferometry with polarization gratings,” Opt. Lett. 37, 4413–4415 (2012).
[Crossref] [PubMed]

M. N. Miskiewicz, J. Kim, Y. M. Li, R. K. Komanduri, M. J. Escuti, “Progress on large-area polarization grating fabrication,” (2012), vol. 8395 of Proc. of SPIE.
[Crossref]

Mitsuhashi, Y.

Modes, C. D.

C. D. Modes, M. Warner, C. Sanchez-Somolinos, L. T. de Haan, D. Broer, “Mechanical frustration and spontaneous polygonal folding in active nematic sheets,” Phys. Rev. E 86, 3 (2012).
[Crossref]

Morikawa, T.

Nakajima, M.

Nersisyan, S.

Nersisyan, S. R.

Nicolescu, E.

Oh, C.

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

C. Oh, R. Komanduri, M. J. Escuti, “Fdtd analysis of 100%-efficient polarization-independent liquid crystal polarization gratings,” (Spie-Int Soc Optical Engineering, 2006), vol. 6332 of Proc. of SPIE, pp. 33212.

Ono, H.

H. Ono, T. Wada, N. Kawatsuki, “Polarization imaging screen using vector gratings fabricated by photocrosslinkable polymer liquid crystals,” Jpn. J. Appl. Phys. 51, 030202(2012).
[Crossref]

H. Ono, M. Hishida, A. Emoto, T. Shioda, N. Kawatsuki, “Elastic continuum analysis and diffraction properties of two-dimensional liquid crystalline grating cells,” J. Opt. Soc. Am. B. 26, 1151–1156 (2009).
[Crossref]

Otten, G.

F. Snik, G. Otten, M. Kenworthy, M. Miskiewicz, M. Escuti, C. Packham, J. Codona, “The vector-app: a broadband apodizing phase plate that yields complementary psfs,” (2012), vol. 8450 of Proc. of SPIE.
[Crossref]

Packham, C.

F. Snik, G. Otten, M. Kenworthy, M. Miskiewicz, M. Escuti, C. Packham, J. Codona, “The vector-app: a broadband apodizing phase plate that yields complementary psfs,” (2012), vol. 8450 of Proc. of SPIE.
[Crossref]

Pagliusi, P.

Pelcovits, R. A.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102(2005).
[Crossref]

Provenzano, C.

Radcliffe, M. D.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102(2005).
[Crossref]

Reznikov, Y.

O. Yaroshchuk, Y. Reznikov, “Photoalignment of liquid crystals: basics and current trends,” J. Mat. Chem. 22, 286–300 (2012).
[Crossref]

Ruiz, U.

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, New York, 1991), chap. 3, pp. 80–107.
[Crossref]

Sanchez-Somolinos, C.

C. D. Modes, M. Warner, C. Sanchez-Somolinos, L. T. de Haan, D. Broer, “Mechanical frustration and spontaneous polygonal folding in active nematic sheets,” Phys. Rev. E 86, 3 (2012).
[Crossref]

Schadt, M.

M. Schadt, K. Schmitt, V. Kozinkov, V. Chigrinov, “Surface-induced parallel alignment of liquid-crystals by linearly polymerized photopolymers,” Jpn. J. Appl. Phys., Part 1 31, 2155–2164 (1992).
[Crossref]

Schmitt, K.

M. Schadt, K. Schmitt, V. Kozinkov, V. Chigrinov, “Surface-induced parallel alignment of liquid-crystals by linearly polymerized photopolymers,” Jpn. J. Appl. Phys., Part 1 31, 2155–2164 (1992).
[Crossref]

Serabyn, E.

Serati, S.

Shannon, P. J.

P. J. Shannon, W. M. Gibbons, S. T. Sun, “Patterned optical-properties in photopolymerized surface-aligned liquid-crystal films,” Nature 368, 532–533 (1994).
[Crossref]

Shemo, D. M.

Shioda, T.

H. Ono, M. Hishida, A. Emoto, T. Shioda, N. Kawatsuki, “Elastic continuum analysis and diffraction properties of two-dimensional liquid crystalline grating cells,” J. Opt. Soc. Am. B. 26, 1151–1156 (2009).
[Crossref]

Sinzinger, S.

Smith, P. K.

Snik, F.

F. Snik, G. Otten, M. Kenworthy, M. Miskiewicz, M. Escuti, C. Packham, J. Codona, “The vector-app: a broadband apodizing phase plate that yields complementary psfs,” (2012), vol. 8450 of Proc. of SPIE.
[Crossref]

Steeves, D. M.

Sun, S. T.

P. J. Shannon, W. M. Gibbons, S. T. Sun, “Patterned optical-properties in photopolymerized surface-aligned liquid-crystal films,” Nature 368, 532–533 (1994).
[Crossref]

Tabiryan, N.

Tabiryan, N. V.

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, New York, 1991), chap. 3, pp. 80–107.
[Crossref]

Wada, T.

H. Ono, T. Wada, N. Kawatsuki, “Polarization imaging screen using vector gratings fabricated by photocrosslinkable polymer liquid crystals,” Jpn. J. Appl. Phys. 51, 030202(2012).
[Crossref]

Warner, M.

C. D. Modes, M. Warner, C. Sanchez-Somolinos, L. T. de Haan, D. Broer, “Mechanical frustration and spontaneous polygonal folding in active nematic sheets,” Phys. Rev. E 86, 3 (2012).
[Crossref]

Yaroshchuk, O.

O. Yaroshchuk, Y. Reznikov, “Photoalignment of liquid crystals: basics and current trends,” J. Mat. Chem. 22, 286–300 (2012).
[Crossref]

Appl. Opt. (3)

Chem. Lett. (1)

N. Kawatsuki, “Photoalignment and photoinduced molecular reorientation of photosensitive materials,” Chem. Lett. 40, 548–554 (2011).
[Crossref]

J. Appl. Phys. (1)

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102(2005).
[Crossref]

J. Lightwave Technol. (1)

J. Mat. Chem. (1)

O. Yaroshchuk, Y. Reznikov, “Photoalignment of liquid crystals: basics and current trends,” J. Mat. Chem. 22, 286–300 (2012).
[Crossref]

J. Opt. Soc. Am. B. (1)

H. Ono, M. Hishida, A. Emoto, T. Shioda, N. Kawatsuki, “Elastic continuum analysis and diffraction properties of two-dimensional liquid crystalline grating cells,” J. Opt. Soc. Am. B. 26, 1151–1156 (2009).
[Crossref]

Jpn. J. Appl. Phys (1)

M. Schadt, K. Schmitt, V. Kozinkov, V. Chigrinov, “Surface-induced parallel alignment of liquid-crystals by linearly polymerized photopolymers,” Jpn. J. Appl. Phys., Part 1 31, 2155–2164 (1992).
[Crossref]

Jpn. J. Appl. Phys. (1)

H. Ono, T. Wada, N. Kawatsuki, “Polarization imaging screen using vector gratings fabricated by photocrosslinkable polymer liquid crystals,” Jpn. J. Appl. Phys. 51, 030202(2012).
[Crossref]

Nature (1)

P. J. Shannon, W. M. Gibbons, S. T. Sun, “Patterned optical-properties in photopolymerized surface-aligned liquid-crystal films,” Nature 368, 532–533 (1994).
[Crossref]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. E (2)

C. D. Modes, M. Warner, C. Sanchez-Somolinos, L. T. de Haan, D. Broer, “Mechanical frustration and spontaneous polygonal folding in active nematic sheets,” Phys. Rev. E 86, 3 (2012).
[Crossref]

R. K. Komanduri, M. J. Escuti, “Elastic continuum analysis of the liquid crystal polarization grating,” Phys. Rev. E 76, 021701(2007).
[Crossref]

Other (5)

V. G. Chigrinov, V. M. Kozenkov, H. S. Kwok, Photoalignment of Liquid Crystalline Materials: Physics and Applications (John Wiley & Sons, Ltd, West Sussex, 2008).
[Crossref]

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, New York, 1991), chap. 3, pp. 80–107.
[Crossref]

F. Snik, G. Otten, M. Kenworthy, M. Miskiewicz, M. Escuti, C. Packham, J. Codona, “The vector-app: a broadband apodizing phase plate that yields complementary psfs,” (2012), vol. 8450 of Proc. of SPIE.
[Crossref]

C. Oh, R. Komanduri, M. J. Escuti, “Fdtd analysis of 100%-efficient polarization-independent liquid crystal polarization gratings,” (Spie-Int Soc Optical Engineering, 2006), vol. 6332 of Proc. of SPIE, pp. 33212.

M. N. Miskiewicz, J. Kim, Y. M. Li, R. K. Komanduri, M. J. Escuti, “Progress on large-area polarization grating fabrication,” (2012), vol. 8395 of Proc. of SPIE.
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 High-level schematic of the kind of polarization direct-write system studied in this paper.

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Fig. 2
Fig. 2 High-level view of our direct-write system description, which starts with the system inputs and ends with the LC response. The transformation functions H and T relate to material properties of the LPP and LC respectively; all other operations are purely mathematical and make no assumptions about material properties.

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Fig. 3
Fig. 3 Graphical representation of some properties of our chosen H, which takes the average of all input Stokes vectors. Each diagram is a 2D cross-section of the Poincare sphere (since we are only concerned with linear polarization), and the ring in each diagram represents a DOLP of 1. a) Non-causality and orientation averaging. b) Depolarization by superposition of orthogonal polarizations.

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Fig. 4
Fig. 4 Threshold functions used to predict the magnitude of the LC anchoring vector from key parameters. a) Fluence threshold function TF. b) DOLP threshold function TD.

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Fig. 5
Fig. 5 a) Polarizing optical microscope setup used to capture the images in this paper. The Full-Wave Plate (FWP) is used to distinguish between 0° and 90° polarized light. b) The full-color colormap for differently aligned liquid crystals, acquired when using the FWP. c) The grayscale colormap acquired without the FWP (0° and 90° are indistinguishable). Orientation angle profiles of films were measured by matching the film’s color with b) using the least squares algorithm.

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Fig. 6
Fig. 6 The first validation experiment, designed to test the effect of fluence on LC alignment. Pattern a) was created by scanning adjacent, uniform vertical lines and varying the fluence in the horizontal dimension. Pattern c) is the reverse of pattern a), and pattern b) is the superposition of a) and c). From this experiment we determined a fluence threshold to be used in subsequent simulations.

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Fig. 7
Fig. 7 The second validation experiment, designed to test 1) the effect of DOLP on LC alignment quality, and 2) if the LC aligns to the average exposure angle of the LPP. Pattern a) was created by scanning adjacent, uniform vertical lines and varying the polarization angle in the horizontal dimension from 0° to 90°. Pattern c) is the same as a), except the polarization varies from 0° to −90°. Pattern b) is the superposition of a) and c) with half fluence each (equivalent total fluence). From this experiment we determine a DOLP threshold to be used in subsequent simulations and confirm the aligning properties of the LC.

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Fig. 8
Fig. 8 Adjacent, uniform scan lines with polarization orientations of ψ0 − 50°, ψ 0 °, and ψ0 + 50°. The distance between the scan lines decreases from a) to c), and we observe an averaging of the LC orientation angle. By sufficiently overlapping neighboring scan lines, we can create continuously varying orientation profiles. The LC orientation angles are only plotted where the fluence is ¿0; in the other regions, the alignment confidence is very low, the LC becomes randomly aligned, and ψavg becomes undefined

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Fig. 9
Fig. 9 Two intersecting scan lines with polarization orientations 0° and 90°. The average polarization angle at every location is either 0°, 90°, or undefined where the fluence delivered by each line is equal. As a result, discrete domains are produced. a) Simulated F, b) Davg, c) |A|, d) ψavg using the color bar in Fig. 5(b), e) A, created by overlaying c) and d). f) Actual image of fabricated film, color bar in Fig. 5(b).

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Fig. 10
Fig. 10 A simulated and fabricated q-plate, which is a kind of azimuthal waveplate. a) Simulated F, b) Davg, c) |A|, d) ψavg using the color bar in Fig. 5(b), e) A, created by overlaying c) and d). f) Actual image of fabricated film, color bar in Fig. 5(b).

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Fig. 11
Fig. 11 A PG fabricated by scanning adjacent scan lines, where the polarization rotates from line to line. The target PG pitch is 50 μm and the scan lines were spaced 7 μm apart using a beam width of 7.5 μm. a), b), and c) are images obtained using different magnification objective lenses and the plots below show the desired orientation profile compared to our measured profile.

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Equations (24)

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I ( r , t ) = I b ( r − r b ( t ) )
S ( r , t ) = [ S 0 S 1 S 2 S 3 ] = I ( r , t )     [ 1 cos 2 ψ ( t ) sin 2 ψ ( t ) 0 ]
S ( r ) = H ( S ( r , t ) ) = 1 τ ∫ 0 τ S ( r , t ) d t
F ( r ) = S 0 ( r ) τ
ψ avg ( r ) = atan 2 ( S 2 ( r ) , S 1 ( r ) )
atan 2 ( y , x ) = 2 tan − 1 y x 2 + y 2 + x
D avg ( r ) = S 1 ( r ) 2 + S 2 ( r ) 2 S 0 ( r )
A ( r ) = T ( ψ avg ( r ) , F ( r ) , D avg ( r ) )
∠ A ( r ) = ψ avg ( r )
| A ( r ) | = T F ( F ) T D ( D avg )
T F ( F ) = 1 2 ( tanh ( F ( r ) − F T H w F T H ) + 1 )
T D ( D avg ) = 1 2 ( tanh ( D ( r ) − D T H w D T H ) + 1 )
I b ( r ) = I 0 exp ( − 2 x 2 + y 2 w 0 2 )
r b 1 ( t ) = x ^ d + y ^ t
r b 2 ( t ) = t y ^
r b 3 ( t ) = − x ^ d + y ^ t
I b ( r ) = I 0 exp ( − 2 x 2 + y 2 w 0 2 )
r b 1 ( t ) = x ^ t
r b 2 ( t ) = y ^ t
ψ b 1 ( t ) = 0
ψ b 2 ( t ) = π 2
I b ( r ) = I 0 exp ( − 2 x 2 + y 2 w 0 2 )
r b ( t ) = ( m + r t 2 π ) ( x ^ cos ( 2 π t ) + y ^ sin ( 2 π t ) )
ψ b ( t ) = q t

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