Abstract

Two-photon polymerization enables the fabrication of micron sized structures with submicron resolution. Spatial light modulators (SLM) have already been used to create multiple polymerizing foci in the photoresist by holographic beam shaping, thus enabling the parallel fabrication of multiple microstructures. Here we demonstrate the parallel two-photon polymerization of single 3D microstructures by multiple holographically translated foci. Multiple foci were created by phase holograms, which were calculated real-time on an NVIDIA CUDA GPU, and displayed on an electronically addressed SLM. A 3D demonstrational structure was designed that is built up from a nested set of dodecahedron frames of decreasing size. Each individual microstructure was fabricated with the parallel and coordinated motion of 5 holographic foci. The reproducibility and the high uniformity of features of the microstructures were verified by scanning electron microscopy.

© 2014 Optical Society of America

Full Article  |  PDF Article

Corrections

Lucas A. Shaw, Samira Chizari, Maxim Shusteff, Hamed Naghsh-Nilchi, Dino Di Carlo, and Jonathan B. Hopkins, "Scanning two-photon continuous flow lithography for synthesis of high-resolution 3D microparticles: erratum," Opt. Express 26, 14718-14718 (2018)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-26-11-14718
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References

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  1. S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices - micromachines can be created with higher resolution using two-photon absorption,” Nature 412(6848), 697–698 (2001).
    [Crossref] [PubMed]
  2. P. Galajda and P. Ormos, “Complex micromachines produced and driven by light,” Appl. Phys. Lett. 78, 249–251 (2001).
    [Crossref]
  3. S. Maruo and H. Inoue, “Optically driven micropump produced by three-dimensional two-photon microfabrication,” Appl. Phys. Lett. 89, 144101 (2006).
    [Crossref]
  4. M. Straub and M. Gu, “Near-infrared photonic crystals with higher-order bandgaps generated by two-photon photopolymerization,” Opt. Lett. 27, 1824–1826 (2002).
    [Crossref]
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    [Crossref] [PubMed]
  6. Y. Liu, D. D. Nolte, and L. J. Pyrak-Nolte, “Large-format fabrication by two-photon polymerization in SU-8,” Appl. Phys. A 100(1), 181–191 (2010).
    [Crossref]
  7. R. Di Leonardo, A. Búzás, L. Kelemen, G. Vizsnyiczai, L. Oroszi, and P. Ormos, “Hydrodynamic synchronization of light driven microrotors,” Phys. Rev. Lett. 109, 034104 (2012).
    [Crossref] [PubMed]
  8. D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99, 58004 (2012).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  11. F. Formanek, N. Takeyasu, T. Tanaka, K. Chiyoda, A. Ishikawa, and S. Kawata, “Three-dimensional fabrication of metallic nanostructures over large areas by two-photon polymerization,” Opt. Express 14, 800–809 (2006).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  14. K. Obata, J. Koch, U. Hinze, and B. Chichkov, “Multi-focus two-photon polymerization technique based on individually controlled phase modulation,” Opt. Express 18, 17193–17200 (2010).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  17. N. Jenness, K. Wulff, M. Johannes, M. Padgett, D. Cole, and R. Clark, “Three-dimensional parallel holographic micropatterning using a spatial lightmodulator,” Opt. Express 16, 15942–15948 (2008).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2012 (3)

R. Di Leonardo, A. Búzás, L. Kelemen, G. Vizsnyiczai, L. Oroszi, and P. Ormos, “Hydrodynamic synchronization of light driven microrotors,” Phys. Rev. Lett. 109, 034104 (2012).
[Crossref] [PubMed]

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99, 58004 (2012).
[Crossref]

E. T. Ritschdorff, R. Nielson, and J. B. Shear, “Multi-focal multiphoton lithography,” LAB ON A CHIP 12(5), 867–871 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (5)

2008 (1)

2007 (2)

2006 (2)

2005 (1)

J. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micro-nanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
[Crossref]

2004 (1)

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[Crossref] [PubMed]

2002 (1)

2001 (2)

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices - micromachines can be created with higher resolution using two-photon absorption,” Nature 412(6848), 697–698 (2001).
[Crossref] [PubMed]

P. Galajda and P. Ormos, “Complex micromachines produced and driven by light,” Appl. Phys. Lett. 78, 249–251 (2001).
[Crossref]

Adachi, Y.

J. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micro-nanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
[Crossref]

Backsten, J.

Bengtsson, J.

Bianchi, S.

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181(8), 1444–1448 (2010).
[Crossref]

Booth, M.

Bowman, R.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99, 58004 (2012).
[Crossref]

Busch, K.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[Crossref] [PubMed]

Búzás, A.

R. Di Leonardo, A. Búzás, L. Kelemen, G. Vizsnyiczai, L. Oroszi, and P. Ormos, “Hydrodynamic synchronization of light driven microrotors,” Phys. Rev. Lett. 109, 034104 (2012).
[Crossref] [PubMed]

Carberry, D. M.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99, 58004 (2012).
[Crossref]

Chichkov, B.

Chiyoda, K.

Clark, R.

Cole, D.

Deubel, M.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[Crossref] [PubMed]

Di Leonardo, R.

R. Di Leonardo, A. Búzás, L. Kelemen, G. Vizsnyiczai, L. Oroszi, and P. Ormos, “Hydrodynamic synchronization of light driven microrotors,” Phys. Rev. Lett. 109, 034104 (2012).
[Crossref] [PubMed]

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181(8), 1444–1448 (2010).
[Crossref]

R. Di Leonardo, F. Ianni, and G. Ruocco, “Computer generation of optimal holograms for optical trap arrays,” Opt. Express 15, 1913–1922 (2007).
[Crossref] [PubMed]

Engström, D.

Formanek, F.

Frank, A.

Galajda, P.

P. Galajda and P. Ormos, “Complex micromachines produced and driven by light,” Appl. Phys. Lett. 78, 249–251 (2001).
[Crossref]

Gibson, G. M.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99, 58004 (2012).
[Crossref]

Gittard, S.

Goksör, M.

Grieve, J. A.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99, 58004 (2012).
[Crossref]

Gu, M.

Hanna, S.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99, 58004 (2012).
[Crossref]

Hinze, U.

Ianni, F.

Inoue, H.

S. Maruo and H. Inoue, “Optically driven micropump produced by three-dimensional two-photon microfabrication,” Appl. Phys. Lett. 89, 144101 (2006).
[Crossref]

Ishikawa, A.

Jenness, N.

Jesacher, A.

Johannes, M.

Kato, J.

J. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micro-nanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
[Crossref]

Kawata, S.

F. Formanek, N. Takeyasu, T. Tanaka, K. Chiyoda, A. Ishikawa, and S. Kawata, “Three-dimensional fabrication of metallic nanostructures over large areas by two-photon polymerization,” Opt. Express 14, 800–809 (2006).
[Crossref] [PubMed]

J. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micro-nanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
[Crossref]

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices - micromachines can be created with higher resolution using two-photon absorption,” Nature 412(6848), 697–698 (2001).
[Crossref] [PubMed]

Kelemen, L

L Kelemen, P. Ormos, and G. Vizsnyiczai, “Two-photon polymerization with optimized spatial light modulator,” J. Eur. Opt. Soc. Rapid Publ. 6, 11029 (2011).
[Crossref]

Kelemen, L.

R. Di Leonardo, A. Búzás, L. Kelemen, G. Vizsnyiczai, L. Oroszi, and P. Ormos, “Hydrodynamic synchronization of light driven microrotors,” Phys. Rev. Lett. 109, 034104 (2012).
[Crossref] [PubMed]

L. Kelemen, S. Valkai, and P. Ormos, “Parallel photopolymerisation with complex light patterns generated by diffractive optical elements,” Opt. Express 15, 14488–14497 (2007).
[Crossref] [PubMed]

Koch, J.

Koroleva, A.

Liu, Y.

Y. Liu, D. D. Nolte, and L. J. Pyrak-Nolte, “Large-format fabrication by two-photon polymerization in SU-8,” Appl. Phys. A 100(1), 181–191 (2010).
[Crossref]

Maruo, S.

S. Maruo and H. Inoue, “Optically driven micropump produced by three-dimensional two-photon microfabrication,” Appl. Phys. Lett. 89, 144101 (2006).
[Crossref]

Miles, M. J.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99, 58004 (2012).
[Crossref]

Narayan, R.

Nguyen, A.

Nielson, R.

E. T. Ritschdorff, R. Nielson, and J. B. Shear, “Multi-focal multiphoton lithography,” LAB ON A CHIP 12(5), 867–871 (2012).
[Crossref] [PubMed]

Nolte, D. D.

Y. Liu, D. D. Nolte, and L. J. Pyrak-Nolte, “Large-format fabrication by two-photon polymerization in SU-8,” Appl. Phys. A 100(1), 181–191 (2010).
[Crossref]

Obata, K.

Ormos, P.

R. Di Leonardo, A. Búzás, L. Kelemen, G. Vizsnyiczai, L. Oroszi, and P. Ormos, “Hydrodynamic synchronization of light driven microrotors,” Phys. Rev. Lett. 109, 034104 (2012).
[Crossref] [PubMed]

L Kelemen, P. Ormos, and G. Vizsnyiczai, “Two-photon polymerization with optimized spatial light modulator,” J. Eur. Opt. Soc. Rapid Publ. 6, 11029 (2011).
[Crossref]

L. Kelemen, S. Valkai, and P. Ormos, “Parallel photopolymerisation with complex light patterns generated by diffractive optical elements,” Opt. Express 15, 14488–14497 (2007).
[Crossref] [PubMed]

P. Galajda and P. Ormos, “Complex micromachines produced and driven by light,” Appl. Phys. Lett. 78, 249–251 (2001).
[Crossref]

Oroszi, L.

R. Di Leonardo, A. Búzás, L. Kelemen, G. Vizsnyiczai, L. Oroszi, and P. Ormos, “Hydrodynamic synchronization of light driven microrotors,” Phys. Rev. Lett. 109, 034104 (2012).
[Crossref] [PubMed]

Padgett, M.

Padgett, M. J.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99, 58004 (2012).
[Crossref]

Pereira, S.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[Crossref] [PubMed]

Persson, M.

Phillips, D. B.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99, 58004 (2012).
[Crossref]

Pyrak-Nolte, L. J.

Y. Liu, D. D. Nolte, and L. J. Pyrak-Nolte, “Large-format fabrication by two-photon polymerization in SU-8,” Appl. Phys. A 100(1), 181–191 (2010).
[Crossref]

Rarity, J. G.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99, 58004 (2012).
[Crossref]

Ritschdorff, E. T.

E. T. Ritschdorff, R. Nielson, and J. B. Shear, “Multi-focal multiphoton lithography,” LAB ON A CHIP 12(5), 867–871 (2012).
[Crossref] [PubMed]

Ruocco, G.

Shear, J. B.

E. T. Ritschdorff, R. Nielson, and J. B. Shear, “Multi-focal multiphoton lithography,” LAB ON A CHIP 12(5), 867–871 (2012).
[Crossref] [PubMed]

Simpson, S. H.

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99, 58004 (2012).
[Crossref]

Soukoulis, C. M.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[Crossref] [PubMed]

Straub, M.

Sun, H. B.

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices - micromachines can be created with higher resolution using two-photon absorption,” Nature 412(6848), 697–698 (2001).
[Crossref] [PubMed]

Sun, H.-B.

J. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micro-nanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
[Crossref]

Takada, K.

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices - micromachines can be created with higher resolution using two-photon absorption,” Nature 412(6848), 697–698 (2001).
[Crossref] [PubMed]

Takeyasu, N.

F. Formanek, N. Takeyasu, T. Tanaka, K. Chiyoda, A. Ishikawa, and S. Kawata, “Three-dimensional fabrication of metallic nanostructures over large areas by two-photon polymerization,” Opt. Express 14, 800–809 (2006).
[Crossref] [PubMed]

J. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micro-nanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
[Crossref]

Tanaka, T.

F. Formanek, N. Takeyasu, T. Tanaka, K. Chiyoda, A. Ishikawa, and S. Kawata, “Three-dimensional fabrication of metallic nanostructures over large areas by two-photon polymerization,” Opt. Express 14, 800–809 (2006).
[Crossref] [PubMed]

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices - micromachines can be created with higher resolution using two-photon absorption,” Nature 412(6848), 697–698 (2001).
[Crossref] [PubMed]

Valkai, S.

Vizsnyiczai, G.

R. Di Leonardo, A. Búzás, L. Kelemen, G. Vizsnyiczai, L. Oroszi, and P. Ormos, “Hydrodynamic synchronization of light driven microrotors,” Phys. Rev. Lett. 109, 034104 (2012).
[Crossref] [PubMed]

L Kelemen, P. Ormos, and G. Vizsnyiczai, “Two-photon polymerization with optimized spatial light modulator,” J. Eur. Opt. Soc. Rapid Publ. 6, 11029 (2011).
[Crossref]

von Freymann, G.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[Crossref] [PubMed]

Wegener, M.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[Crossref] [PubMed]

Wulff, K.

Appl. Phys. A (1)

Y. Liu, D. D. Nolte, and L. J. Pyrak-Nolte, “Large-format fabrication by two-photon polymerization in SU-8,” Appl. Phys. A 100(1), 181–191 (2010).
[Crossref]

Appl. Phys. Lett. (3)

P. Galajda and P. Ormos, “Complex micromachines produced and driven by light,” Appl. Phys. Lett. 78, 249–251 (2001).
[Crossref]

S. Maruo and H. Inoue, “Optically driven micropump produced by three-dimensional two-photon microfabrication,” Appl. Phys. Lett. 89, 144101 (2006).
[Crossref]

J. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micro-nanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
[Crossref]

Biomed. Opt. Express (1)

Comput. Phys. Commun. (1)

S. Bianchi and R. Di Leonardo, “Real-time optical micro-manipulation using optimized holograms generated on the GPU,” Comput. Phys. Commun. 181(8), 1444–1448 (2010).
[Crossref]

Europhys. Lett. (1)

D. B. Phillips, S. H. Simpson, J. A. Grieve, R. Bowman, G. M. Gibson, M. J. Padgett, J. G. Rarity, S. Hanna, M. J. Miles, and D. M. Carberry, “Force sensing with a shaped dielectric micro-tool,” Europhys. Lett. 99, 58004 (2012).
[Crossref]

J. Eur. Opt. Soc. Rapid Publ. (1)

L Kelemen, P. Ormos, and G. Vizsnyiczai, “Two-photon polymerization with optimized spatial light modulator,” J. Eur. Opt. Soc. Rapid Publ. 6, 11029 (2011).
[Crossref]

LAB ON A CHIP (1)

E. T. Ritschdorff, R. Nielson, and J. B. Shear, “Multi-focal multiphoton lithography,” LAB ON A CHIP 12(5), 867–871 (2012).
[Crossref] [PubMed]

Nat. Mater. (1)

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[Crossref] [PubMed]

Nature (1)

S. Kawata, H. B. Sun, T. Tanaka, and K. Takada, “Finer features for functional microdevices - micromachines can be created with higher resolution using two-photon absorption,” Nature 412(6848), 697–698 (2001).
[Crossref] [PubMed]

Opt. Express (7)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

R. Di Leonardo, A. Búzás, L. Kelemen, G. Vizsnyiczai, L. Oroszi, and P. Ormos, “Hydrodynamic synchronization of light driven microrotors,” Phys. Rev. Lett. 109, 034104 (2012).
[Crossref] [PubMed]

Other (2)

http://www.nvidia.com/object/cuda_home_new.htm

http:freeglut.sourceforge.net

Supplementary Material (2)

» Media 1: MOV (10285 KB)     
» Media 2: MOV (5271 KB)     

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Figures (5)

Fig. 1
Fig. 1 Schematic layout of the holographic two-photon polymerization system.

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Fig. 2
Fig. 2 (a) Three dimensional plot of the test microstructure voxel coordinates. Z-coordinates are relative to the focal plane of the objective. Different colors show voxels exposed by foci of different holographic beams. See Media 1 for the visualization of the scanning trajectories of the five foci. (b) Y–Z plot of the test microstructure revealing the relative positions of the focal plane and the coverglass-SU-8 interface. Axis units are in micrometers.

Download Full Size | PPT Slide | PDF

Fig. 3
Fig. 3 Brightfield microscope images of the fabrication process visualized in IPL photoresist ( Media 2).

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Fig. 4
Fig. 4 Scanning electron microscope images of a holographically polymerized test structure, with viewing angle 45° (a) and top view (b).

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Fig. 5
Fig. 5 The average and the standard deviation of thicknesses of the outermost line segments numbered on Fig. 3(b).

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Equations (5)

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ϕ j = arg [ ∑ m w m e i ( Δ j m + θ m ) ]
Δ j m = 2 π λ f [ x j x m + y j y m + z m f 2 n i 2 − ( x j 2 + y j 2 ) ]
V m = 1 N ∑ j = 1 N e i ( ϕ j − Δ j m )
w m = w m 〈 | V m | 〉 | V m |
θ m = arg ( V m )

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