Abstract

Fabrication of multiple arbitrary diffractive optical elements (DOEs) on multiple curved surfaces is always a challenge; here we propose an effective optimization method to fabricate complicated DOEs on several curved surfaces at the same time. First we design phase distribution to modulate complicated three-dimensional (3D) intensity distribution on multiple curved surfaces simultaneously, and then by exposure, the intensity distribution is transferred into the pure-phase or depth distribution. Numerical simulations and optical fabrication are performed for different intensity distributions: 3D binary patterns and 3D gray level patterns, on two or three curved surfaces, and both are in nice agreement. Since multiple DOEs are fabricated on curved surfaces simultaneously, the collimation of different curved surfaces is avoided, and it could improve the fabrication efficiency. It is expected that this proposed method would be employed in various precision 3D optical fabrication and processing in the future.

© 2015 Optical Society of America

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References

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2014 (1)

2013 (1)

2011 (3)

2010 (4)

2009 (1)

J. G. Kim, N. Takama, B. J. Kim, and H. Fujita, “Optical-softlithographic technology for patterning on curved surfaces,” J. Micromech. Microeng. 19(5), 055017 (2009).
[Crossref]

2008 (2)

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A, Pure Appl. Opt. 10(3), 035302 (2008).
[Crossref]

H. Nishiyama, M. Mizoshiri, T. Kawahara, J. Nishii, and Y. Hirata, “SiO2-based nonplanar structures fabricated using femtosecond laser lithography,” Opt. Express 16(22), 17288–17294 (2008).
[Crossref] [PubMed]

2007 (2)

2003 (1)

2000 (2)

K. Kintaka, J. Nishii, and N. Tohge, “Diffraction gratings of photosensitive ZrO2 gel films fabricated with the two-ultraviolet-beam interference method,” Appl. Opt. 39(4), 489–493 (2000).
[Crossref] [PubMed]

A. J. Turberfield, M. Campbell, D. N. Sharp, M. T. Harrison, and R. G. Denning, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

1999 (2)

K. M. Baker, “Highly corrected close-packed microlens arrays and moth-eye structuring on curved surfaces,” Appl. Opt. 38(2), 352–356 (1999).
[Crossref] [PubMed]

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B 17(6), 2965–2969 (1999).
[Crossref]

1998 (1)

R. J. Jackman, S. T. Brittain, A. Adams, M. G. Prentiss, and G. M. Whitesides, “Design and fabrication of topologically complex, three-dimensional microstructures,” Science 280(5372), 2089–2091 (1998).
[Crossref] [PubMed]

1995 (1)

T. A. Savas, S. N. Shah, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Achromatic interferometric lithography for 100-nm-period gratings and grids,” J. Vac. Sci. Technol. B 13(6), 2732–2735 (1995).
[Crossref]

1968 (1)

Adams, A.

R. J. Jackman, S. T. Brittain, A. Adams, M. G. Prentiss, and G. M. Whitesides, “Design and fabrication of topologically complex, three-dimensional microstructures,” Science 280(5372), 2089–2091 (1998).
[Crossref] [PubMed]

Bailey, T.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B 17(6), 2965–2969 (1999).
[Crossref]

Baker, K. M.

Brittain, S. T.

R. J. Jackman, S. T. Brittain, A. Adams, M. G. Prentiss, and G. M. Whitesides, “Design and fabrication of topologically complex, three-dimensional microstructures,” Science 280(5372), 2089–2091 (1998).
[Crossref] [PubMed]

Campbell, M.

A. J. Turberfield, M. Campbell, D. N. Sharp, M. T. Harrison, and R. G. Denning, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

Carter, J. M.

T. A. Savas, S. N. Shah, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Achromatic interferometric lithography for 100-nm-period gratings and grids,” J. Vac. Sci. Technol. B 13(6), 2732–2735 (1995).
[Crossref]

Cheung, W.-K.

Choi, B.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B 17(6), 2965–2969 (1999).
[Crossref]

Christmas, J.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A, Pure Appl. Opt. 10(3), 035302 (2008).
[Crossref]

Colburn, M.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B 17(6), 2965–2969 (1999).
[Crossref]

Collings, N.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A, Pure Appl. Opt. 10(3), 035302 (2008).
[Crossref]

Crossland, W. A.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A, Pure Appl. Opt. 10(3), 035302 (2008).
[Crossref]

Damle, S.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B 17(6), 2965–2969 (1999).
[Crossref]

Denning, R. G.

A. J. Turberfield, M. Campbell, D. N. Sharp, M. T. Harrison, and R. G. Denning, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

Duparré, J.

Ekerdt, J.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B 17(6), 2965–2969 (1999).
[Crossref]

Esquivel, J. P.

T. Senn, J. P. Esquivel, N. Sabate, and B. Lochel, “Fabrication of high aspect ratio nanostructures on 3D surfaces,” Microelectron. Eng. 88(9), 3043–3048 (2011).
[Crossref]

Fujita, H.

J. G. Kim, N. Takama, B. J. Kim, and H. Fujita, “Optical-softlithographic technology for patterning on curved surfaces,” J. Micromech. Microeng. 19(5), 055017 (2009).
[Crossref]

Georgiou, A.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A, Pure Appl. Opt. 10(3), 035302 (2008).
[Crossref]

Han, J.

Harrison, M. T.

A. J. Turberfield, M. Campbell, D. N. Sharp, M. T. Harrison, and R. G. Denning, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

Hirata, Y.

Hu, B.

Ito, T.

Jackman, R. J.

R. J. Jackman, S. T. Brittain, A. Adams, M. G. Prentiss, and G. M. Whitesides, “Design and fabrication of topologically complex, three-dimensional microstructures,” Science 280(5372), 2089–2091 (1998).
[Crossref] [PubMed]

Johnson, S.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B 17(6), 2965–2969 (1999).
[Crossref]

Kanicki, J.

G. Yoo, H. Lee, D. Radtke, M. Stumpf, U. Zeitner, and J. Kanicki, “A maskless laser-write lithography processing of thin-film transistors on a hemispherical surface,” Microelectron. Eng. 87(1), 83–87 (2010).
[Crossref]

Kawahara, T.

Kikuta, H.

Kim, B. J.

J. G. Kim, N. Takama, B. J. Kim, and H. Fujita, “Optical-softlithographic technology for patterning on curved surfaces,” J. Micromech. Microeng. 19(5), 055017 (2009).
[Crossref]

Kim, J. G.

J. G. Kim, N. Takama, B. J. Kim, and H. Fujita, “Optical-softlithographic technology for patterning on curved surfaces,” J. Micromech. Microeng. 19(5), 055017 (2009).
[Crossref]

Kintaka, K.

Lee, H.

G. Yoo, H. Lee, D. Radtke, M. Stumpf, U. Zeitner, and J. Kanicki, “A maskless laser-write lithography processing of thin-film transistors on a hemispherical surface,” Microelectron. Eng. 87(1), 83–87 (2010).
[Crossref]

Li, C.

Li, F.

Li, X.

Liu, D.

Liu, H.

Liu, J.

Liu, P.

Lochel, B.

T. Senn, J. P. Esquivel, N. Sabate, and B. Lochel, “Fabrication of high aspect ratio nanostructures on 3D surfaces,” Microelectron. Eng. 88(9), 3043–3048 (2011).
[Crossref]

Lu, Z.

Masuda, N.

Mizoshiri, M.

Mizutani, A.

Moore, J.

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A, Pure Appl. Opt. 10(3), 035302 (2008).
[Crossref]

Nakayama, H.

Nishii, J.

Nishiyama, H.

Nounu, H.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B 17(6), 2965–2969 (1999).
[Crossref]

Pan, Y.

Poon, T.-C.

Prentiss, M. G.

R. J. Jackman, S. T. Brittain, A. Adams, M. G. Prentiss, and G. M. Whitesides, “Design and fabrication of topologically complex, three-dimensional microstructures,” Science 280(5372), 2089–2091 (1998).
[Crossref] [PubMed]

Radtke, D.

Ruchhoeft, P.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B 17(6), 2965–2969 (1999).
[Crossref]

Sabate, N.

T. Senn, J. P. Esquivel, N. Sabate, and B. Lochel, “Fabrication of high aspect ratio nanostructures on 3D surfaces,” Microelectron. Eng. 88(9), 3043–3048 (2011).
[Crossref]

Savas, T. A.

T. A. Savas, S. N. Shah, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Achromatic interferometric lithography for 100-nm-period gratings and grids,” J. Vac. Sci. Technol. B 13(6), 2732–2735 (1995).
[Crossref]

Schattenburg, M. L.

T. A. Savas, S. N. Shah, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Achromatic interferometric lithography for 100-nm-period gratings and grids,” J. Vac. Sci. Technol. B 13(6), 2732–2735 (1995).
[Crossref]

Senn, T.

T. Senn, J. P. Esquivel, N. Sabate, and B. Lochel, “Fabrication of high aspect ratio nanostructures on 3D surfaces,” Microelectron. Eng. 88(9), 3043–3048 (2011).
[Crossref]

Shah, S. N.

T. A. Savas, S. N. Shah, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Achromatic interferometric lithography for 100-nm-period gratings and grids,” J. Vac. Sci. Technol. B 13(6), 2732–2735 (1995).
[Crossref]

Sharp, D. N.

A. J. Turberfield, M. Campbell, D. N. Sharp, M. T. Harrison, and R. G. Denning, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

Shewell, J. R.

Shi, R.

Shimobaba, T.

Smith, H. I.

T. A. Savas, S. N. Shah, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Achromatic interferometric lithography for 100-nm-period gratings and grids,” J. Vac. Sci. Technol. B 13(6), 2732–2735 (1995).
[Crossref]

Sreenivasan, S. V.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B 17(6), 2965–2969 (1999).
[Crossref]

Stewart, M.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B 17(6), 2965–2969 (1999).
[Crossref]

Stumpf, M.

G. Yoo, H. Lee, D. Radtke, M. Stumpf, U. Zeitner, and J. Kanicki, “A maskless laser-write lithography processing of thin-film transistors on a hemispherical surface,” Microelectron. Eng. 87(1), 83–87 (2010).
[Crossref]

Sun, Q.

Takahira, S.

Takama, N.

J. G. Kim, N. Takama, B. J. Kim, and H. Fujita, “Optical-softlithographic technology for patterning on curved surfaces,” J. Micromech. Microeng. 19(5), 055017 (2009).
[Crossref]

Tohge, N.

Tsang, P.

Tünnermann, A.

Turberfield, A. J.

A. J. Turberfield, M. Campbell, D. N. Sharp, M. T. Harrison, and R. G. Denning, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

Wang, T.

Wang, X.

Wang, Y.

Whitesides, G. M.

R. J. Jackman, S. T. Brittain, A. Adams, M. G. Prentiss, and G. M. Whitesides, “Design and fabrication of topologically complex, three-dimensional microstructures,” Science 280(5372), 2089–2091 (1998).
[Crossref] [PubMed]

Willson, C. G.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B 17(6), 2965–2969 (1999).
[Crossref]

Wolf, E.

Wolfe, J. C.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B 17(6), 2965–2969 (1999).
[Crossref]

Xiao, R.

Xie, J.

Xie, Y.

Xu, J.

Xu, W.

Xu, Z.

Yoo, G.

G. Yoo, H. Lee, D. Radtke, M. Stumpf, U. Zeitner, and J. Kanicki, “A maskless laser-write lithography processing of thin-film transistors on a hemispherical surface,” Microelectron. Eng. 87(1), 83–87 (2010).
[Crossref]

Yu, W.

Zeitner, U.

G. Yoo, H. Lee, D. Radtke, M. Stumpf, U. Zeitner, and J. Kanicki, “A maskless laser-write lithography processing of thin-film transistors on a hemispherical surface,” Microelectron. Eng. 87(1), 83–87 (2010).
[Crossref]

Zeitner, U. D.

Zhang, D.

Zhang, H.

Zhang, N.

Zhao, H.

Zhong, H.

Zhou, C.

Zou, B.

Appl. Opt. (3)

J. Micromech. Microeng. (1)

J. G. Kim, N. Takama, B. J. Kim, and H. Fujita, “Optical-softlithographic technology for patterning on curved surfaces,” J. Micromech. Microeng. 19(5), 055017 (2009).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

A. Georgiou, J. Christmas, N. Collings, J. Moore, and W. A. Crossland, “Aspects of hologram calculation for video frames,” J. Opt. A, Pure Appl. Opt. 10(3), 035302 (2008).
[Crossref]

J. Opt. Soc. Am. (1)

J. Vac. Sci. Technol. B (2)

T. A. Savas, S. N. Shah, M. L. Schattenburg, J. M. Carter, and H. I. Smith, “Achromatic interferometric lithography for 100-nm-period gratings and grids,” J. Vac. Sci. Technol. B 13(6), 2732–2735 (1995).
[Crossref]

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, “Patterning curved surfaces: template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography,” J. Vac. Sci. Technol. B 17(6), 2965–2969 (1999).
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Figures (9)

Fig. 1
Fig. 1 Schematic view of the light propagation between the plane H and the curved surfaces P 1 , P 2 .
Fig. 2
Fig. 2 Flowchart of the proposed optimization method.
Fig. 3
Fig. 3 (a) Top view and (b) sampling schematic diagram of cylindrical surfaces.
Fig. 4
Fig. 4 Numerical simulation of 3D patterns on cylindrical surfaces: (a) the intensity distributions of the initial patterns, (b) the intensity distribution of the reconstructed patterns after 30 iterations, (c) the relationship between relative errors and the number of iteration.
Fig. 5
Fig. 5 Numerical simulation of 3D patterns on complicated surfaces: (a) the intensity distributions of the original patterns, (b) the intensity distribution of the reconstructed patterns after 30 iterations, (c) the relationship between relative errors and the number of iteration.
Fig. 6
Fig. 6 Numerical simulation of 3D patterns with 128 × 128 pixels on multiple surfaces: (a) the intensity distribution of the original patterns, (b) the intensity distribution of the reconstructed patterns after 20 iterations, (c) the relationship between relative error and the number of iteration.
Fig. 7
Fig. 7 Schematic view of the optical experimental setup.
Fig. 8
Fig. 8 (a) Picture of the binary pattern fabricated on cylindrical surface P 1 and (b) its partial enlarged picture.
Fig. 9
Fig. 9 (a) Picture of the gray level pattern fabricated on cylindrical surface P 2 and (b) its partial enlarged picture.

Equations (2)

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P i ( Χ i ) = 1 j λ Γ H ( Ξ ) exp ( j 2 π r i / λ ) r i d σ ( i = 1 , 2 )
H ( Ξ ) = i = 1 2 j λ Γ ' i P i ( X i ) exp ( j 2 π r ' i / λ ) r ' i d σ i '

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