Abstract

We present a unique method that utilizes high intensity core of the zero-order nondiffracting beam (NDB) to fabricate a homogeneous polymer fiber as narrow as 2 µm and as long as centimeters. The constant diameter of the fiber along all its length is done by the propagation invariant properties of the NDB. The length of the fiber is determined by the maximum propagation distance of the NDB which is much longer than the classical Gaussian beam of comparable width. Moreover, we also proved that the self-writing waveguide mechanism prolongs the length of the developed fibers. Circular movement of the NDB creates hollow fiber, several co-axial, or overlapping fibers.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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  6. P. Galajda and P. Ormos, “Orientation of flat particles in optical tweezers by linearly polarized light,” Opt. Express 11, 446–451 (2003).
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    [CrossRef] [PubMed]
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    [CrossRef]
  12. R. C. Rumpf and E. G. Johnson, “Comprehensive modeling of near-field nanopatterning,” Opt. Express 13, 7198–7208 (2005).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  24. J. Kim, K.-H. Jeong, and L. P. Lee, “Artificial ommatidia by self-aligned microlenses and waveguides,” Opt. Lett. 30, 5–7 (2005).
    [CrossRef] [PubMed]
  25. J. Durnin, J. J. Miceli, and J. H. Eberly, “Difraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef] [PubMed]
  26. Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Com. 251, 207–211 (1998).
    [CrossRef]
  27. M. R. Lapointe“Review of non-diffracting Bessel beam experiments,” Opt. Laser Technol. 24, 315–321 (1992).
    [CrossRef]
  28. D. McGloin and K. Dholakia, “Bessel beam: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
    [CrossRef]
  29. T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
    [CrossRef]
  30. T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8, 43 (2006).
    [CrossRef]
  31. L. Patersona, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A. C. Riches, and K. Dholakia, “Light-induced cell separation in a tailored optical landscape,” Appl. Phys. Lett. 87, 123901 (2005).
    [CrossRef]
  32. K. Okamoto, Y. Inouye, and S. Kawata, “Use of Bessel J (1) laser beam to focus an atomic beam into a nano-scale dot,” Jpn. J. of Appl. Phys. Part 1 40, 4544–4548 (2001).
    [CrossRef]
  33. V. Jarutis, R. Paskauskas, and A. Stabinis, “Focusing of Laguerre±Gaussian beams by axicon,” Opt. Commun. 184, 105–112 (2000).
    [CrossRef]
  34. S. Shoji, S. Kawata, A. A. Sukhorukov, and Y. S. Kivshar, “Self-written waveguides in photopolymerizable resins,” Opt. Lett. 27, 185–187 (2002).
    [CrossRef]
  35. K. Dorkenoo, O. Crégut, L. Mager, F. Gillot, C. Carre, and A. Fort, “Quasi-solitonic behavior of self-written waveguides created by photopolymerization,” Opt. Lett. 27, 1782–1784 (2002).
    [CrossRef]

2006 (3)

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]

A. Argyros, M. A. van Eijkelenborg, M. C. J. Large, and I. M. Bassett, “Hollow-core microstructured polymer optical fiber,” Opt. Letters 31, 172–174 (2006).
[CrossRef]

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8, 43 (2006).
[CrossRef]

2005 (9)

L. Patersona, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A. C. Riches, and K. Dholakia, “Light-induced cell separation in a tailored optical landscape,” Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

D. McGloin and K. Dholakia, “Bessel beam: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

J. Kim, K.-H. Jeong, and L. P. Lee, “Artificial ommatidia by self-aligned microlenses and waveguides,” Opt. Lett. 30, 5–7 (2005).
[CrossRef] [PubMed]

T. Yamashita and M. Kagami, “Fabrication of Light-Induced Self-Written Waveguides with a W-Shaped Refractive Index Profile,” J. Light. Tech. 23, 2542–2548 (2005).
[CrossRef]

L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, “Fabrication of large area two- and threedimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. 86, 241102 (2005).
[CrossRef]

R. C. Rumpf and E. G. Johnson, “Comprehensive modeling of near-field nanopatterning,” Opt. Express 13, 7198–7208 (2005).
[CrossRef] [PubMed]

C. Jensen-McMullin, H. P. Lee, and E. R. Lyons, “Demonstration of trapping, motion control, sensing and fluorescence detection of polystyrene beads in a multi-fiber optical trap,” Opt. Express 13, 2634–2642 (2005).
[CrossRef] [PubMed]

Z. Bayindir, Y. Sun, M. J. Naughtona, C. N. LaFratta, T. Baldacchini, J. T. Fourkas, J. Stewart, B. E. A. Saleh, and M. C. Teich, “Polymer microcantilevers fabricated via multiphoton absorption polymerization,” Appl. Phys. Lett. 86, 064105 (2005).
[CrossRef]

2004 (4)

M. van Eijkelenborg, “Imaging with microstructured polymer fibre,” Opt. Express 12, 342–346 (2004).
[CrossRef] [PubMed]

J. Zagari, A. Argyros, N. A. Issa, G. Barton, G. Henry, M. C. J. Large, L. Poladian, and M. A. van Eijkelenborg, “Small-core single-mode microstructured polymer optical fiber with large external diameter,” Opt. Letters 29, 1560–1560 (2004).
[CrossRef]

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the Refractive Index in Photopolymerizable Materials for (2+1)D SolitaryWave Guide Formation,” Phys. Rev. Lett. 93, 143905 (2004).
[CrossRef] [PubMed]

R. Bachelot, A. Fares, R. Fikri, D. Barchiesi, G. Lerondel, and P. Royer, “Coupling semiconductor lasers into single-mode optical fibers by use of tips grown by photopolymerization,” Opt. Lett. 29, 1971–1973 (2004).
[CrossRef] [PubMed]

2003 (4)

P. Galajda and P. Ormos, “Orientation of flat particles in optical tweezers by linearly polarized light,” Opt. Express 11, 446–451 (2003).
[CrossRef] [PubMed]

S. Maruo, K. Ikuta, and H. Korugi, “Submicron manipulation tools driven by light in a liquid,” Appl. Phys. Lett. 82, 133–135 (2003).
[CrossRef]

M. J. Escuti, J. Qi, and G. P. Crawford, “Tunable-face-centered-cubic photonic crystal formed in holographic polymer dispersed liquid crystals,” Opt. Lett. 28, 522–524 (2003).
[CrossRef] [PubMed]

K. Kaneko, H. B. Sun, X. M. Duan, and S. Kawata, “Submicron diamond-lattice photonic crystals produced by two-photon laser nanofabrication,” Appl. Phys. Lett. 83, 2091–2093 (2003).
[CrossRef]

2002 (2)

2001 (4)

K. Okamoto, Y. Inouye, and S. Kawata, “Use of Bessel J (1) laser beam to focus an atomic beam into a nano-scale dot,” Jpn. J. of Appl. Phys. Part 1 40, 4544–4548 (2001).
[CrossRef]

T. M. Monroi, C. M. de Sterke, and L. Poladian, “Catching light in its own trap,” J. Mod. Opt. 48, 191–238 (2001).

R. Bachelot, C. Ecoffet, D. Deloeil, P. Royer, and D.-J. Lougnot, “Integration of micrometer-sized polymer elements at the end of optical fibers by free-radical photopolymerization,” Appl. Opt. 40, 5860–5871 (2001).
[CrossRef]

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

2000 (2)

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

V. Jarutis, R. Paskauskas, and A. Stabinis, “Focusing of Laguerre±Gaussian beams by axicon,” Opt. Commun. 184, 105–112 (2000).
[CrossRef]

1999 (1)

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

1998 (1)

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Com. 251, 207–211 (1998).
[CrossRef]

1997 (1)

1996 (1)

A. S. Kewitsch and A. Yariv, “Self-focusing and self-trapping of optical beams upon photopolymerization,” Opt. Letters 21, 24–26 (1996).
[CrossRef]

1993 (1)

S. J. Frisken, “Light-induced optical waveguide uptapers,” Opt. Letters 19, 1035–1037 (1993).
[CrossRef]

1992 (1)

M. R. Lapointe“Review of non-diffracting Bessel beam experiments,” Opt. Laser Technol. 24, 315–321 (1992).
[CrossRef]

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Difraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Ananthavel, S. P.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Argyros, A.

A. Argyros, M. A. van Eijkelenborg, M. C. J. Large, and I. M. Bassett, “Hollow-core microstructured polymer optical fiber,” Opt. Letters 31, 172–174 (2006).
[CrossRef]

J. Zagari, A. Argyros, N. A. Issa, G. Barton, G. Henry, M. C. J. Large, L. Poladian, and M. A. van Eijkelenborg, “Small-core single-mode microstructured polymer optical fiber with large external diameter,” Opt. Letters 29, 1560–1560 (2004).
[CrossRef]

Bachelot, R.

Baldacchini, T.

Z. Bayindir, Y. Sun, M. J. Naughtona, C. N. LaFratta, T. Baldacchini, J. T. Fourkas, J. Stewart, B. E. A. Saleh, and M. C. Teich, “Polymer microcantilevers fabricated via multiphoton absorption polymerization,” Appl. Phys. Lett. 86, 064105 (2005).
[CrossRef]

Barchiesi, D.

Barlow, S.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Barton, G.

J. Zagari, A. Argyros, N. A. Issa, G. Barton, G. Henry, M. C. J. Large, L. Poladian, and M. A. van Eijkelenborg, “Small-core single-mode microstructured polymer optical fiber with large external diameter,” Opt. Letters 29, 1560–1560 (2004).
[CrossRef]

Bassett, I. M.

A. Argyros, M. A. van Eijkelenborg, M. C. J. Large, and I. M. Bassett, “Hollow-core microstructured polymer optical fiber,” Opt. Letters 31, 172–174 (2006).
[CrossRef]

Bayindir, Z.

Z. Bayindir, Y. Sun, M. J. Naughtona, C. N. LaFratta, T. Baldacchini, J. T. Fourkas, J. Stewart, B. E. A. Saleh, and M. C. Teich, “Polymer microcantilevers fabricated via multiphoton absorption polymerization,” Appl. Phys. Lett. 86, 064105 (2005).
[CrossRef]

Bouchal, Z.

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8, 43 (2006).
[CrossRef]

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Com. 251, 207–211 (1998).
[CrossRef]

Bryant, P. E.

L. Patersona, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A. C. Riches, and K. Dholakia, “Light-induced cell separation in a tailored optical landscape,” Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

Campbell, M.

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

Carre, C.

Chan, C. T.

L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, “Fabrication of large area two- and threedimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. 86, 241102 (2005).
[CrossRef]

Chiyoda, K.

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Com. 251, 207–211 (1998).
[CrossRef]

Cižmár, T.

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8, 43 (2006).
[CrossRef]

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

Crawford, G. P.

Crégut, O.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the Refractive Index in Photopolymerizable Materials for (2+1)D SolitaryWave Guide Formation,” Phys. Rev. Lett. 93, 143905 (2004).
[CrossRef] [PubMed]

K. Dorkenoo, O. Crégut, L. Mager, F. Gillot, C. Carre, and A. Fort, “Quasi-solitonic behavior of self-written waveguides created by photopolymerization,” Opt. Lett. 27, 1782–1784 (2002).
[CrossRef]

Cumpston, B. H.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

de Sterke, C. M.

T. M. Monroi, C. M. de Sterke, and L. Poladian, “Catching light in its own trap,” J. Mod. Opt. 48, 191–238 (2001).

Deloeil, D.

Denning, R. G.

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

Dholakia, K.

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

D. McGloin and K. Dholakia, “Bessel beam: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

L. Patersona, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A. C. Riches, and K. Dholakia, “Light-induced cell separation in a tailored optical landscape,” Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

Dorkenoo, K.

Dorkenoo, K. D.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the Refractive Index in Photopolymerizable Materials for (2+1)D SolitaryWave Guide Formation,” Phys. Rev. Lett. 93, 143905 (2004).
[CrossRef] [PubMed]

Duan, X. M.

K. Kaneko, H. B. Sun, X. M. Duan, and S. Kawata, “Submicron diamond-lattice photonic crystals produced by two-photon laser nanofabrication,” Appl. Phys. Lett. 83, 2091–2093 (2003).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Difraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Dyer, D. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Difraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Ecoffet, C.

Ehrlich, J. E.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Erskine, L. L.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Escuti, M. J.

Fares, A.

Fikri, R.

Formanek, F.

Fort, A.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the Refractive Index in Photopolymerizable Materials for (2+1)D SolitaryWave Guide Formation,” Phys. Rev. Lett. 93, 143905 (2004).
[CrossRef] [PubMed]

K. Dorkenoo, O. Crégut, L. Mager, F. Gillot, C. Carre, and A. Fort, “Quasi-solitonic behavior of self-written waveguides created by photopolymerization,” Opt. Lett. 27, 1782–1784 (2002).
[CrossRef]

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Z. Bayindir, Y. Sun, M. J. Naughtona, C. N. LaFratta, T. Baldacchini, J. T. Fourkas, J. Stewart, B. E. A. Saleh, and M. C. Teich, “Polymer microcantilevers fabricated via multiphoton absorption polymerization,” Appl. Phys. Lett. 86, 064105 (2005).
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P. Galajda and P. Ormos, “Orientation of flat particles in optical tweezers by linearly polarized light,” Opt. Express 11, 446–451 (2003).
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P. Galajda and P. Ormos, “Complex micromachines produced and driven by light,” Appl. Phys. Lett. 78, 249–251 (2001).
[CrossRef]

Garcés-Chávez, V.

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

L. Patersona, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A. C. Riches, and K. Dholakia, “Light-induced cell separation in a tailored optical landscape,” Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

Gillot, F.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the Refractive Index in Photopolymerizable Materials for (2+1)D SolitaryWave Guide Formation,” Phys. Rev. Lett. 93, 143905 (2004).
[CrossRef] [PubMed]

K. Dorkenoo, O. Crégut, L. Mager, F. Gillot, C. Carre, and A. Fort, “Quasi-solitonic behavior of self-written waveguides created by photopolymerization,” Opt. Lett. 27, 1782–1784 (2002).
[CrossRef]

Gunn-Moore, F. J.

L. Patersona, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A. C. Riches, and K. Dholakia, “Light-induced cell separation in a tailored optical landscape,” Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

Harrison, M. T.

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

Heikal, A. A.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Henry, G.

J. Zagari, A. Argyros, N. A. Issa, G. Barton, G. Henry, M. C. J. Large, L. Poladian, and M. A. van Eijkelenborg, “Small-core single-mode microstructured polymer optical fiber with large external diameter,” Opt. Letters 29, 1560–1560 (2004).
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S. Maruo, K. Ikuta, and H. Korugi, “Submicron manipulation tools driven by light in a liquid,” Appl. Phys. Lett. 82, 133–135 (2003).
[CrossRef]

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K. Okamoto, Y. Inouye, and S. Kawata, “Use of Bessel J (1) laser beam to focus an atomic beam into a nano-scale dot,” Jpn. J. of Appl. Phys. Part 1 40, 4544–4548 (2001).
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Issa, N. A.

J. Zagari, A. Argyros, N. A. Issa, G. Barton, G. Henry, M. C. J. Large, L. Poladian, and M. A. van Eijkelenborg, “Small-core single-mode microstructured polymer optical fiber with large external diameter,” Opt. Letters 29, 1560–1560 (2004).
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V. Jarutis, R. Paskauskas, and A. Stabinis, “Focusing of Laguerre±Gaussian beams by axicon,” Opt. Commun. 184, 105–112 (2000).
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Jeong, K.-H.

Johnson, E. G.

Kagami, M.

T. Yamashita and M. Kagami, “Fabrication of Light-Induced Self-Written Waveguides with a W-Shaped Refractive Index Profile,” J. Light. Tech. 23, 2542–2548 (2005).
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K. Kaneko, H. B. Sun, X. M. Duan, and S. Kawata, “Submicron diamond-lattice photonic crystals produced by two-photon laser nanofabrication,” Appl. Phys. Lett. 83, 2091–2093 (2003).
[CrossRef]

Kawata, S.

Kewitsch, A. S.

A. S. Kewitsch and A. Yariv, “Self-focusing and self-trapping of optical beams upon photopolymerization,” Opt. Letters 21, 24–26 (1996).
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Kivshar, Y. S.

Kollárová, V.

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8, 43 (2006).
[CrossRef]

Korugi, H.

S. Maruo, K. Ikuta, and H. Korugi, “Submicron manipulation tools driven by light in a liquid,” Appl. Phys. Lett. 82, 133–135 (2003).
[CrossRef]

Kuebler, S. M.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

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Z. Bayindir, Y. Sun, M. J. Naughtona, C. N. LaFratta, T. Baldacchini, J. T. Fourkas, J. Stewart, B. E. A. Saleh, and M. C. Teich, “Polymer microcantilevers fabricated via multiphoton absorption polymerization,” Appl. Phys. Lett. 86, 064105 (2005).
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A. Argyros, M. A. van Eijkelenborg, M. C. J. Large, and I. M. Bassett, “Hollow-core microstructured polymer optical fiber,” Opt. Letters 31, 172–174 (2006).
[CrossRef]

J. Zagari, A. Argyros, N. A. Issa, G. Barton, G. Henry, M. C. J. Large, L. Poladian, and M. A. van Eijkelenborg, “Small-core single-mode microstructured polymer optical fiber with large external diameter,” Opt. Letters 29, 1560–1560 (2004).
[CrossRef]

Leblond, H.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the Refractive Index in Photopolymerizable Materials for (2+1)D SolitaryWave Guide Formation,” Phys. Rev. Lett. 93, 143905 (2004).
[CrossRef] [PubMed]

Lee, H. P.

Lee, I.-Y. S.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Lee, L. P.

Lerondel, G.

Lougnot, D.-J.

Lyons, E. R.

Mager, L.

Marder, S. R.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Maruo, S.

S. Maruo, K. Ikuta, and H. Korugi, “Submicron manipulation tools driven by light in a liquid,” Appl. Phys. Lett. 82, 133–135 (2003).
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S. Maruo, O. Nakamura, and S. Kawata, “Three-dimensional microfabrication with two-photon-absorbed photopolymerization,” Opt. Lett. 22, 132–134 (1997).
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B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
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D. McGloin and K. Dholakia, “Bessel beam: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
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L. Patersona, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A. C. Riches, and K. Dholakia, “Light-induced cell separation in a tailored optical landscape,” Appl. Phys. Lett. 87, 123901 (2005).
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T. M. Monroi, C. M. de Sterke, and L. Poladian, “Catching light in its own trap,” J. Mod. Opt. 48, 191–238 (2001).

Nakamura, O.

Naughtona, M. J.

Z. Bayindir, Y. Sun, M. J. Naughtona, C. N. LaFratta, T. Baldacchini, J. T. Fourkas, J. Stewart, B. E. A. Saleh, and M. C. Teich, “Polymer microcantilevers fabricated via multiphoton absorption polymerization,” Appl. Phys. Lett. 86, 064105 (2005).
[CrossRef]

Okamoto, K.

K. Okamoto, Y. Inouye, and S. Kawata, “Use of Bessel J (1) laser beam to focus an atomic beam into a nano-scale dot,” Jpn. J. of Appl. Phys. Part 1 40, 4544–4548 (2001).
[CrossRef]

Ormos, P.

P. Galajda and P. Ormos, “Orientation of flat particles in optical tweezers by linearly polarized light,” Opt. Express 11, 446–451 (2003).
[CrossRef] [PubMed]

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

Papagiakoumou, E.

L. Patersona, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A. C. Riches, and K. Dholakia, “Light-induced cell separation in a tailored optical landscape,” Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

Paskauskas, R.

V. Jarutis, R. Paskauskas, and A. Stabinis, “Focusing of Laguerre±Gaussian beams by axicon,” Opt. Commun. 184, 105–112 (2000).
[CrossRef]

Patersona, L.

L. Patersona, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A. C. Riches, and K. Dholakia, “Light-induced cell separation in a tailored optical landscape,” Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

Perry, J. W.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Poladian, L.

J. Zagari, A. Argyros, N. A. Issa, G. Barton, G. Henry, M. C. J. Large, L. Poladian, and M. A. van Eijkelenborg, “Small-core single-mode microstructured polymer optical fiber with large external diameter,” Opt. Letters 29, 1560–1560 (2004).
[CrossRef]

T. M. Monroi, C. M. de Sterke, and L. Poladian, “Catching light in its own trap,” J. Mod. Opt. 48, 191–238 (2001).

Qi, J.

Qin, J.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Riches, A. C.

L. Patersona, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A. C. Riches, and K. Dholakia, “Light-induced cell separation in a tailored optical landscape,” Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

Röckel, H.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Royer, P.

Rumi, M.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Rumpf, R. C.

Saleh, B. E. A.

Z. Bayindir, Y. Sun, M. J. Naughtona, C. N. LaFratta, T. Baldacchini, J. T. Fourkas, J. Stewart, B. E. A. Saleh, and M. C. Teich, “Polymer microcantilevers fabricated via multiphoton absorption polymerization,” Appl. Phys. Lett. 86, 064105 (2005).
[CrossRef]

Sharp, D. N.

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

Shoji, S.

Sibbett, W.

L. Patersona, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A. C. Riches, and K. Dholakia, “Light-induced cell separation in a tailored optical landscape,” Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

Sonnefraud, Y.

K. D. Dorkenoo, F. Gillot, O. Crégut, Y. Sonnefraud, A. Fort, and H. Leblond, “Control of the Refractive Index in Photopolymerizable Materials for (2+1)D SolitaryWave Guide Formation,” Phys. Rev. Lett. 93, 143905 (2004).
[CrossRef] [PubMed]

Stabinis, A.

V. Jarutis, R. Paskauskas, and A. Stabinis, “Focusing of Laguerre±Gaussian beams by axicon,” Opt. Commun. 184, 105–112 (2000).
[CrossRef]

Stewart, J.

Z. Bayindir, Y. Sun, M. J. Naughtona, C. N. LaFratta, T. Baldacchini, J. T. Fourkas, J. Stewart, B. E. A. Saleh, and M. C. Teich, “Polymer microcantilevers fabricated via multiphoton absorption polymerization,” Appl. Phys. Lett. 86, 064105 (2005).
[CrossRef]

Sukhorukov, A. A.

Sun, H. B.

K. Kaneko, H. B. Sun, X. M. Duan, and S. Kawata, “Submicron diamond-lattice photonic crystals produced by two-photon laser nanofabrication,” Appl. Phys. Lett. 83, 2091–2093 (2003).
[CrossRef]

Sun, Y.

Z. Bayindir, Y. Sun, M. J. Naughtona, C. N. LaFratta, T. Baldacchini, J. T. Fourkas, J. Stewart, B. E. A. Saleh, and M. C. Teich, “Polymer microcantilevers fabricated via multiphoton absorption polymerization,” Appl. Phys. Lett. 86, 064105 (2005).
[CrossRef]

Takeyasu, N.

Tanaka, T.

Tatarkova, S. A.

L. Patersona, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A. C. Riches, and K. Dholakia, “Light-induced cell separation in a tailored optical landscape,” Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

Teich, M. C.

Z. Bayindir, Y. Sun, M. J. Naughtona, C. N. LaFratta, T. Baldacchini, J. T. Fourkas, J. Stewart, B. E. A. Saleh, and M. C. Teich, “Polymer microcantilevers fabricated via multiphoton absorption polymerization,” Appl. Phys. Lett. 86, 064105 (2005).
[CrossRef]

Turberfeld, A. J.

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

van Eijkelenborg, M.

van Eijkelenborg, M. A.

A. Argyros, M. A. van Eijkelenborg, M. C. J. Large, and I. M. Bassett, “Hollow-core microstructured polymer optical fiber,” Opt. Letters 31, 172–174 (2006).
[CrossRef]

J. Zagari, A. Argyros, N. A. Issa, G. Barton, G. Henry, M. C. J. Large, L. Poladian, and M. A. van Eijkelenborg, “Small-core single-mode microstructured polymer optical fiber with large external diameter,” Opt. Letters 29, 1560–1560 (2004).
[CrossRef]

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Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Com. 251, 207–211 (1998).
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L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, “Fabrication of large area two- and threedimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. 86, 241102 (2005).
[CrossRef]

Wong, K. S.

L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, “Fabrication of large area two- and threedimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. 86, 241102 (2005).
[CrossRef]

Wu, L.

L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, “Fabrication of large area two- and threedimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. 86, 241102 (2005).
[CrossRef]

Wu, X.

B. H. Cumpston, S. P. Ananthavel, S. Barlow, D. L. Dyer, J. E. Ehrlich, L. L. Erskine, A. A. Heikal, S. M. Kuebler, I.-Y. S. Lee, D. McCord-Maughon, J. Qin, H. Röckel, M. Rumi, X. Wu, S. R. Marder, and J. W. Perry, “Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication,” Nature 398, 51–54 (1999).
[CrossRef]

Yamashita, T.

T. Yamashita and M. Kagami, “Fabrication of Light-Induced Self-Written Waveguides with a W-Shaped Refractive Index Profile,” J. Light. Tech. 23, 2542–2548 (2005).
[CrossRef]

Yariv, A.

A. S. Kewitsch and A. Yariv, “Self-focusing and self-trapping of optical beams upon photopolymerization,” Opt. Letters 21, 24–26 (1996).
[CrossRef]

Zagari, J.

J. Zagari, A. Argyros, N. A. Issa, G. Barton, G. Henry, M. C. J. Large, L. Poladian, and M. A. van Eijkelenborg, “Small-core single-mode microstructured polymer optical fiber with large external diameter,” Opt. Letters 29, 1560–1560 (2004).
[CrossRef]

Zemánek, P.

T. Čižmár, V. Kollárová, Z. Bouchal, and P. Zemánek, “Sub-micron particle organization by self-imaging of non-diffracting beams,” New J. Phys. 8, 43 (2006).
[CrossRef]

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

Zhong, Y.

L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, “Fabrication of large area two- and threedimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. 86, 241102 (2005).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (7)

S. Maruo, K. Ikuta, and H. Korugi, “Submicron manipulation tools driven by light in a liquid,” Appl. Phys. Lett. 82, 133–135 (2003).
[CrossRef]

Z. Bayindir, Y. Sun, M. J. Naughtona, C. N. LaFratta, T. Baldacchini, J. T. Fourkas, J. Stewart, B. E. A. Saleh, and M. C. Teich, “Polymer microcantilevers fabricated via multiphoton absorption polymerization,” Appl. Phys. Lett. 86, 064105 (2005).
[CrossRef]

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

K. Kaneko, H. B. Sun, X. M. Duan, and S. Kawata, “Submicron diamond-lattice photonic crystals produced by two-photon laser nanofabrication,” Appl. Phys. Lett. 83, 2091–2093 (2003).
[CrossRef]

L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, “Fabrication of large area two- and threedimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. 86, 241102 (2005).
[CrossRef]

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[CrossRef]

L. Patersona, E. Papagiakoumou, G. Milne, V. Garcés-Chávez, S. A. Tatarkova, W. Sibbett, F. J. Gunn-Moore, P. E. Bryant, A. C. Riches, and K. Dholakia, “Light-induced cell separation in a tailored optical landscape,” Appl. Phys. Lett. 87, 123901 (2005).
[CrossRef]

Contemp. Phys. (1)

D. McGloin and K. Dholakia, “Bessel beam: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

J. Light. Tech. (1)

T. Yamashita and M. Kagami, “Fabrication of Light-Induced Self-Written Waveguides with a W-Shaped Refractive Index Profile,” J. Light. Tech. 23, 2542–2548 (2005).
[CrossRef]

J. Mod. Opt. (1)

T. M. Monroi, C. M. de Sterke, and L. Poladian, “Catching light in its own trap,” J. Mod. Opt. 48, 191–238 (2001).

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

K. Okamoto, Y. Inouye, and S. Kawata, “Use of Bessel J (1) laser beam to focus an atomic beam into a nano-scale dot,” Jpn. J. of Appl. Phys. Part 1 40, 4544–4548 (2001).
[CrossRef]

Nature (2)

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfeld, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
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Figures (9)

Fig. 1.
Fig. 1.

Parameters of the experimental set-up. The incident Gaussian beam of half-width w passes through an axicon with apex angle α and is transformed to the Bessel beam existing over a distance zmax. Telescope made of lenses L1 and L2 scales down the original Bessel beam radius and the maximal BB propagation distance zmax to new values z’max in the air and z’maxp inside the cuvette filled with liquid optical glue.

Fig. 2.
Fig. 2.

Top row: Lateral intensity profiles of three types of generated BBs with different diameters of the BB cores (2r’B ). Corresponding parameters of the set-up and the created fiber diameter (dfiber ) and its length (Lfiber ). Bottom row: ESEM image of the polymer fibers. In all three cases we used the same output laser power 3 W giving laser power 1.5 W in the cuvette.

Fig. 3.
Fig. 3.

ESEM images of the left (a), middle (b) and right (c) part of one fiber long 15 mm (see the column B in Fig. 2). Each of the image rows keeps the same scale but uses different magnifications to demonstrate the fiber homogeneity.

Fig. 4.
Fig. 4.

Formation of the fiber in the short BB. The BB core radius was 0.8 µm and the maximum propagation distance of the BB was about 100 µm. The laser power in the cuvette was 90 mW. The top plot shows the calculated on-axis intensity profile of the BB for the parameters used in the experiment.

Fig. 5.
Fig. 5.

Time evolution of the length of the fiber formed by different laser powers in the cuvette. The BB has the same parameters as in the previous case in Fig. 4.

Fig. 6.
Fig. 6.

Top plots show the calculated on-axis intensity distribution for the used experimental parameters. The first image shows on the right a short fiber segment created after 2 s of illumination. The beam was blocked and the cuvette was shifted along the beam propagation. Unblocked beam created on the left side the second segment after 2 s of illumination (2nd row). This segment gradually grew till it reached the first segment on the right (3rd row). Both segments interconnected (4th row) and immediately the first fiber segment continued in its growth on the right (4th–6th rows). Laser power in the cuvette equaled to 130 mW.

Fig. 7.
Fig. 7.

Chaotic growth of the polymer fibers. Single fiber is formed if the illumination is shorter than 2 s. Later on more fibers started to grow especially at the ripples of the older fiber where the leakage of the light from the fiber is probably higher. The light is backscattered in the formed structures and via the self-written waveguide mechanism initiated a reverse growth. Laser power in the cuvette equaled 400 mW.

Fig. 8.
Fig. 8.

Images of the front end (A), middle part (B) and rear end (C) of a free the hollow fiber taken by an optical microscope at different image planes. The diameter and length of this cylinder (dashed contours) was 10 µm and 90 µm, respectively.

Fig. 9.
Fig. 9.

The front (A) and rear (B) side of the hollow fiber structures. Top row: two intersected hollow fibers long 150 µm and wide 40 µm. Bottom row: two hollow concentric fibers. The diameter of the inner and outer hollow fiber is 10 µm and 35 µm, respectively.

Equations (8)

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I ( r , z ) = 4 P k sin θ w z z max J 0 2 ( k r sin θ ) exp { 2 z 2 z max 2 } ,
θ ( π 2 α 2 ) ( n a n m 1 ) ,
z max = w cos θ sin θ .
r B = 2.4048 k sin θ .
I ( r ' , z ' ) = 4 P T k sin θ ' w ' z ' z ' max J 0 2 ( k r ' sin θ ' ) exp { 2 z ' 2 z ' max 2 } ,
sin θ ' = sin θ M , w ' = M w , z ' max = w ' cos θ ' sin θ ' , r ' B = M r B ,
I ( r ' , z ' ) 4 P T k sin θ M 4 w z ' z max J 0 2 ( k r ' sin θ M ) exp { 2 z ' 2 M 2 z max 2 } .
z ' max p = w ' cos θ p ' sin θ p ' n p z ' max .

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