Abstract

Manufacturing end-of-fiber optical components able to realize optical functions ranging from a simple lens to more complex functions such as mode-selective components is a decisive but a priori complex task owing to the fiber-core dimensions. Effective low-cost methods allowing researchers to grow polymer components by free-radical photopolymerization using the light coming out of the fiber have recently been reported. A novel, to our knowledge, phenomenological model of the underlying photopolymerization process is here given and used to simulate the polymer-component growth in a three-dimensional time-resolved manner. The simulation results are thus used to understand and optimize the component growth conditions, focusing particularly on the role of oxygen either present in the atmosphere or dissolved in the solution.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  9. M. Hocine, R. Bachelot, C. Ecoffet, N. Fressengeas, P. Royer, and G. Kugel, "End-of-fiber polymer tip: manufacturing and modeling," Synth. Met. 127, 313-318 (2002).
    [CrossRef]
  10. R. Bachelot, A. Fares, D. Barchiesi, G. Lerondel, and P. Royer, "Coupling semiconductor lasers into single-mode optical fibers by use of tips grown by photopolymerization," Opt. Lett. 17, 1971-1973 (2004).
    [CrossRef]
  11. J. Tyrrell, "Tiny polymer tips boost fibre coupling efficiency," Opt. Laser Europe, November 2004, pp. 29-31.
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    [CrossRef]
  13. T. M. Monro, C. M. D. Sterke, and L. Poladian, "Topical review: catching light in its own trap," J. Mod. Opt. 48, 191-238 (2001).
  14. K. Dorkenoo, O. Cregut, 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]
  15. A. Barthelemy, S. Maneuf, and C. Froehly, "Propagation soliton et autoconfinement de faisceau laser," Opt. Commun. 55, 201-206 (1985).
    [CrossRef]
  16. M. Segev, B. Crosignani, and A. Yariv, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
    [CrossRef] [PubMed]
  17. N. Fressengeas, J. Maufoy, and G. Kugel, "Temporal behavior of bidimensional photorefractive bright spatial solitons," Phys. Rev. E 54, 6866-6875 (1996).
    [CrossRef]
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    [CrossRef] [PubMed]
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  21. C. Ecoffet, A. Espanet, and D. J. Lougnot, "Photopolymerization by evanescent waves: a new method to obtain nanoparts," Adv. Mater. (Weinheim, Ger.) 10, 411-414 (1998).
    [CrossRef]
  22. A. Espanet, C. Ecoffet, and D. J. Lougnot, "Photopolymerisation by evanescent waves II: revealing dramatic inhibiting effects of oxygen at submicrometer scale," J. Polym. Sci., Part A: Polym. Chem. 37, 2075-2085 (1999).
    [CrossRef]
  23. A. Espanet, G. D. Santos, C. Ecoffet, and D. J. Lougnot, "Photopolymerization by evanescent waves: characterization of photopolymerizable formulation for photolithography with nanometric resolution," Appl. Surf. Sci. 138-139, 87-92 (1999).
    [CrossRef]
  24. C. Decker and A. Jenkins, "Kinetic approach of O2 inhibition in ultraviolet and laser-induced polymerizations," Macromolecules 18, 1241-1244 (1985).
    [CrossRef]
  25. L. B. Jeunhomme, Single-Mode Fiber Optics: Principles and Applications (Marcel Dekker, 1990).
  26. K. Dorkenoo, A. J. V. Wonderen, H. Bulou, M. Romeo, O. Cregut, and A. Fort, "Time-resolved measurement of the refractive index for photopolymerization processes," Appl. Phys. Lett. 83, 2474-2476 (2003).
    [CrossRef]
  27. S. R. Logan, "Spatial inhomogeneity effects in photochemical kinetics," J. Chem. Educ. 67, 872-875 (1990).
    [CrossRef]
  28. C. H. Wang and J. L. Xia, "Holographic method for investigating the diffusion of dye molecules in the polymer host," J. Chem. Phys. 92, 2603-2613 (1990).
    [CrossRef]
  29. H. Hervet, W. Urbach, and F. Rondelez, "Mass diffusion measurements in liquid crystals by a novel optical method," J. Chem. Phys. 68, 2725-2729 (1978).
    [CrossRef]
  30. R. C. Reid, J. M. Prausnitz, and T. K. Sternood, The Properties of Gases and Liquids (McGraw-Hill, 1977).

2004

R. Bachelot, A. Fares, D. Barchiesi, G. Lerondel, and P. Royer, "Coupling semiconductor lasers into single-mode optical fibers by use of tips grown by photopolymerization," Opt. Lett. 17, 1971-1973 (2004).
[CrossRef]

2003

K. Dorkenoo, A. J. V. Wonderen, H. Bulou, M. Romeo, O. Cregut, and A. Fort, "Time-resolved measurement of the refractive index for photopolymerization processes," Appl. Phys. Lett. 83, 2474-2476 (2003).
[CrossRef]

2002

M. Hocine, R. Bachelot, C. Ecoffet, N. Fressengeas, P. Royer, and G. Kugel, "End-of-fiber polymer tip: manufacturing and modeling," Synth. Met. 127, 313-318 (2002).
[CrossRef]

K. Dorkenoo, O. Cregut, 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]

2001

1999

T. M. Monro, C. M. de Sterke, and L. Poladian, "Analysis of self-written waveguide experiments," J. Opt. Soc. Am. B 16, 1680-1685 (1999).
[CrossRef]

A. Espanet, C. Ecoffet, and D. J. Lougnot, "Photopolymerisation by evanescent waves II: revealing dramatic inhibiting effects of oxygen at submicrometer scale," J. Polym. Sci., Part A: Polym. Chem. 37, 2075-2085 (1999).
[CrossRef]

A. Espanet, G. D. Santos, C. Ecoffet, and D. J. Lougnot, "Photopolymerization by evanescent waves: characterization of photopolymerizable formulation for photolithography with nanometric resolution," Appl. Surf. Sci. 138-139, 87-92 (1999).
[CrossRef]

1998

C. Ecoffet, A. Espanet, and D. J. Lougnot, "Photopolymerization by evanescent waves: a new method to obtain nanoparts," Adv. Mater. (Weinheim, Ger.) 10, 411-414 (1998).
[CrossRef]

1996

N. Fressengeas, J. Maufoy, and G. Kugel, "Temporal behavior of bidimensional photorefractive bright spatial solitons," Phys. Rev. E 54, 6866-6875 (1996).
[CrossRef]

1992

M. Segev, B. Crosignani, and A. Yariv, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
[CrossRef] [PubMed]

1990

H. M. Presby, A. F. Benner, and C. A. Edwards, "Laser micromachining of efficient fiber microlenses," Appl. Opt. 29, 2692-2695 (1990).
[CrossRef] [PubMed]

S. R. Logan, "Spatial inhomogeneity effects in photochemical kinetics," J. Chem. Educ. 67, 872-875 (1990).
[CrossRef]

C. H. Wang and J. L. Xia, "Holographic method for investigating the diffusion of dye molecules in the polymer host," J. Chem. Phys. 92, 2603-2613 (1990).
[CrossRef]

1985

C. Decker and A. Jenkins, "Kinetic approach of O2 inhibition in ultraviolet and laser-induced polymerizations," Macromolecules 18, 1241-1244 (1985).
[CrossRef]

K. S. Lee and F. S. Barnes, "Microlenses on the end of single-mode optical fibers for laser applications," Appl. Opt. 24, 3134-3139 (1985).
[CrossRef] [PubMed]

A. Barthelemy, S. Maneuf, and C. Froehly, "Propagation soliton et autoconfinement de faisceau laser," Opt. Commun. 55, 201-206 (1985).
[CrossRef]

1982

1980

1978

M. D. Feit and J. A. Fleck, "Light propagation in graded-index optical fibers," Appl. Opt. 17, 3990-3998 (1978).
[CrossRef] [PubMed]

H. Hervet, W. Urbach, and F. Rondelez, "Mass diffusion measurements in liquid crystals by a novel optical method," J. Chem. Phys. 68, 2725-2729 (1978).
[CrossRef]

1974

1973

D. Kato, "Light coupling from a stripe-geometry GaAs diode laser into an optical fiber with spherical end," J. Appl. Phys. 44, 2756-2758 (1973).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1989).

Bachelot, R.

R. Bachelot, A. Fares, D. Barchiesi, G. Lerondel, and P. Royer, "Coupling semiconductor lasers into single-mode optical fibers by use of tips grown by photopolymerization," Opt. Lett. 17, 1971-1973 (2004).
[CrossRef]

M. Hocine, R. Bachelot, C. Ecoffet, N. Fressengeas, P. Royer, and G. Kugel, "End-of-fiber polymer tip: manufacturing and modeling," Synth. Met. 127, 313-318 (2002).
[CrossRef]

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

Banerjee, P. P.

J. M. Jarem and P. P. Banerjee, Computational Methods for Electromagnetic and Optical Systems (Marcel Dekker, 2000).

Barchiesi, D.

R. Bachelot, A. Fares, D. Barchiesi, G. Lerondel, and P. Royer, "Coupling semiconductor lasers into single-mode optical fibers by use of tips grown by photopolymerization," Opt. Lett. 17, 1971-1973 (2004).
[CrossRef]

Barnes, F. S.

Barthelemy, A.

A. Barthelemy, S. Maneuf, and C. Froehly, "Propagation soliton et autoconfinement de faisceau laser," Opt. Commun. 55, 201-206 (1985).
[CrossRef]

Bear, P. D.

Benner, A. F.

Bulou, H.

K. Dorkenoo, A. J. V. Wonderen, H. Bulou, M. Romeo, O. Cregut, and A. Fort, "Time-resolved measurement of the refractive index for photopolymerization processes," Appl. Phys. Lett. 83, 2474-2476 (2003).
[CrossRef]

Carre, C.

Cohen, L. G.

Cregut, O.

K. Dorkenoo, A. J. V. Wonderen, H. Bulou, M. Romeo, O. Cregut, and A. Fort, "Time-resolved measurement of the refractive index for photopolymerization processes," Appl. Phys. Lett. 83, 2474-2476 (2003).
[CrossRef]

K. Dorkenoo, O. Cregut, 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]

Crosignani, B.

M. Segev, B. Crosignani, and A. Yariv, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
[CrossRef] [PubMed]

de Sterke, C. M.

Decker, C.

C. Decker and A. Jenkins, "Kinetic approach of O2 inhibition in ultraviolet and laser-induced polymerizations," Macromolecules 18, 1241-1244 (1985).
[CrossRef]

Deloeil, D.

Dorkenoo, K.

K. Dorkenoo, A. J. V. Wonderen, H. Bulou, M. Romeo, O. Cregut, and A. Fort, "Time-resolved measurement of the refractive index for photopolymerization processes," Appl. Phys. Lett. 83, 2474-2476 (2003).
[CrossRef]

K. Dorkenoo, O. Cregut, 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]

Ecoffet, C.

M. Hocine, R. Bachelot, C. Ecoffet, N. Fressengeas, P. Royer, and G. Kugel, "End-of-fiber polymer tip: manufacturing and modeling," Synth. Met. 127, 313-318 (2002).
[CrossRef]

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

A. Espanet, C. Ecoffet, and D. J. Lougnot, "Photopolymerisation by evanescent waves II: revealing dramatic inhibiting effects of oxygen at submicrometer scale," J. Polym. Sci., Part A: Polym. Chem. 37, 2075-2085 (1999).
[CrossRef]

A. Espanet, G. D. Santos, C. Ecoffet, and D. J. Lougnot, "Photopolymerization by evanescent waves: characterization of photopolymerizable formulation for photolithography with nanometric resolution," Appl. Surf. Sci. 138-139, 87-92 (1999).
[CrossRef]

C. Ecoffet, A. Espanet, and D. J. Lougnot, "Photopolymerization by evanescent waves: a new method to obtain nanoparts," Adv. Mater. (Weinheim, Ger.) 10, 411-414 (1998).
[CrossRef]

Edwards, C. A.

Eisenstein, G.

Espanet, A.

A. Espanet, G. D. Santos, C. Ecoffet, and D. J. Lougnot, "Photopolymerization by evanescent waves: characterization of photopolymerizable formulation for photolithography with nanometric resolution," Appl. Surf. Sci. 138-139, 87-92 (1999).
[CrossRef]

A. Espanet, C. Ecoffet, and D. J. Lougnot, "Photopolymerisation by evanescent waves II: revealing dramatic inhibiting effects of oxygen at submicrometer scale," J. Polym. Sci., Part A: Polym. Chem. 37, 2075-2085 (1999).
[CrossRef]

C. Ecoffet, A. Espanet, and D. J. Lougnot, "Photopolymerization by evanescent waves: a new method to obtain nanoparts," Adv. Mater. (Weinheim, Ger.) 10, 411-414 (1998).
[CrossRef]

Fares, A.

R. Bachelot, A. Fares, D. Barchiesi, G. Lerondel, and P. Royer, "Coupling semiconductor lasers into single-mode optical fibers by use of tips grown by photopolymerization," Opt. Lett. 17, 1971-1973 (2004).
[CrossRef]

Feit, M. D.

Fleck, J. A.

Fort, A.

K. Dorkenoo, A. J. V. Wonderen, H. Bulou, M. Romeo, O. Cregut, and A. Fort, "Time-resolved measurement of the refractive index for photopolymerization processes," Appl. Phys. Lett. 83, 2474-2476 (2003).
[CrossRef]

K. Dorkenoo, O. Cregut, 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]

Fressengeas, N.

M. Hocine, R. Bachelot, C. Ecoffet, N. Fressengeas, P. Royer, and G. Kugel, "End-of-fiber polymer tip: manufacturing and modeling," Synth. Met. 127, 313-318 (2002).
[CrossRef]

N. Fressengeas, J. Maufoy, and G. Kugel, "Temporal behavior of bidimensional photorefractive bright spatial solitons," Phys. Rev. E 54, 6866-6875 (1996).
[CrossRef]

Froehly, C.

A. Barthelemy, S. Maneuf, and C. Froehly, "Propagation soliton et autoconfinement de faisceau laser," Opt. Commun. 55, 201-206 (1985).
[CrossRef]

Gillot, F.

Hervet, H.

H. Hervet, W. Urbach, and F. Rondelez, "Mass diffusion measurements in liquid crystals by a novel optical method," J. Chem. Phys. 68, 2725-2729 (1978).
[CrossRef]

Hocine, M.

M. Hocine, R. Bachelot, C. Ecoffet, N. Fressengeas, P. Royer, and G. Kugel, "End-of-fiber polymer tip: manufacturing and modeling," Synth. Met. 127, 313-318 (2002).
[CrossRef]

Jarem, J. M.

J. M. Jarem and P. P. Banerjee, Computational Methods for Electromagnetic and Optical Systems (Marcel Dekker, 2000).

Jenkins, A.

C. Decker and A. Jenkins, "Kinetic approach of O2 inhibition in ultraviolet and laser-induced polymerizations," Macromolecules 18, 1241-1244 (1985).
[CrossRef]

Jeunhomme, L. B.

L. B. Jeunhomme, Single-Mode Fiber Optics: Principles and Applications (Marcel Dekker, 1990).

Kato, D.

D. Kato, "Light coupling from a stripe-geometry GaAs diode laser into an optical fiber with spherical end," J. Appl. Phys. 44, 2756-2758 (1973).
[CrossRef]

Kugel, G.

M. Hocine, R. Bachelot, C. Ecoffet, N. Fressengeas, P. Royer, and G. Kugel, "End-of-fiber polymer tip: manufacturing and modeling," Synth. Met. 127, 313-318 (2002).
[CrossRef]

N. Fressengeas, J. Maufoy, and G. Kugel, "Temporal behavior of bidimensional photorefractive bright spatial solitons," Phys. Rev. E 54, 6866-6875 (1996).
[CrossRef]

Lee, K. S.

Lerondel, G.

R. Bachelot, A. Fares, D. Barchiesi, G. Lerondel, and P. Royer, "Coupling semiconductor lasers into single-mode optical fibers by use of tips grown by photopolymerization," Opt. Lett. 17, 1971-1973 (2004).
[CrossRef]

Logan, S. R.

S. R. Logan, "Spatial inhomogeneity effects in photochemical kinetics," J. Chem. Educ. 67, 872-875 (1990).
[CrossRef]

Lougnot, D.

Lougnot, D. J.

A. Espanet, C. Ecoffet, and D. J. Lougnot, "Photopolymerisation by evanescent waves II: revealing dramatic inhibiting effects of oxygen at submicrometer scale," J. Polym. Sci., Part A: Polym. Chem. 37, 2075-2085 (1999).
[CrossRef]

A. Espanet, G. D. Santos, C. Ecoffet, and D. J. Lougnot, "Photopolymerization by evanescent waves: characterization of photopolymerizable formulation for photolithography with nanometric resolution," Appl. Surf. Sci. 138-139, 87-92 (1999).
[CrossRef]

C. Ecoffet, A. Espanet, and D. J. Lougnot, "Photopolymerization by evanescent waves: a new method to obtain nanoparts," Adv. Mater. (Weinheim, Ger.) 10, 411-414 (1998).
[CrossRef]

Mager, L.

Maneuf, S.

A. Barthelemy, S. Maneuf, and C. Froehly, "Propagation soliton et autoconfinement de faisceau laser," Opt. Commun. 55, 201-206 (1985).
[CrossRef]

Maufoy, J.

N. Fressengeas, J. Maufoy, and G. Kugel, "Temporal behavior of bidimensional photorefractive bright spatial solitons," Phys. Rev. E 54, 6866-6875 (1996).
[CrossRef]

Monro, T. M.

T. M. Monro, C. M. D. Sterke, and L. Poladian, "Topical review: catching light in its own trap," J. Mod. Opt. 48, 191-238 (2001).

T. M. Monro, C. M. de Sterke, and L. Poladian, "Analysis of self-written waveguide experiments," J. Opt. Soc. Am. B 16, 1680-1685 (1999).
[CrossRef]

Poladian, L.

T. M. Monro, C. M. D. Sterke, and L. Poladian, "Topical review: catching light in its own trap," J. Mod. Opt. 48, 191-238 (2001).

T. M. Monro, C. M. de Sterke, and L. Poladian, "Analysis of self-written waveguide experiments," J. Opt. Soc. Am. B 16, 1680-1685 (1999).
[CrossRef]

Prausnitz, J. M.

R. C. Reid, J. M. Prausnitz, and T. K. Sternood, The Properties of Gases and Liquids (McGraw-Hill, 1977).

Presby, H. M.

Reid, R. C.

R. C. Reid, J. M. Prausnitz, and T. K. Sternood, The Properties of Gases and Liquids (McGraw-Hill, 1977).

Romeo, M.

K. Dorkenoo, A. J. V. Wonderen, H. Bulou, M. Romeo, O. Cregut, and A. Fort, "Time-resolved measurement of the refractive index for photopolymerization processes," Appl. Phys. Lett. 83, 2474-2476 (2003).
[CrossRef]

Rondelez, F.

H. Hervet, W. Urbach, and F. Rondelez, "Mass diffusion measurements in liquid crystals by a novel optical method," J. Chem. Phys. 68, 2725-2729 (1978).
[CrossRef]

Royer, P.

R. Bachelot, A. Fares, D. Barchiesi, G. Lerondel, and P. Royer, "Coupling semiconductor lasers into single-mode optical fibers by use of tips grown by photopolymerization," Opt. Lett. 17, 1971-1973 (2004).
[CrossRef]

M. Hocine, R. Bachelot, C. Ecoffet, N. Fressengeas, P. Royer, and G. Kugel, "End-of-fiber polymer tip: manufacturing and modeling," Synth. Met. 127, 313-318 (2002).
[CrossRef]

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

Santos, G. D.

A. Espanet, G. D. Santos, C. Ecoffet, and D. J. Lougnot, "Photopolymerization by evanescent waves: characterization of photopolymerizable formulation for photolithography with nanometric resolution," Appl. Surf. Sci. 138-139, 87-92 (1999).
[CrossRef]

Schneider, M. V.

Segev, M.

M. Segev, B. Crosignani, and A. Yariv, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
[CrossRef] [PubMed]

Sterke, C. M.

T. M. Monro, C. M. D. Sterke, and L. Poladian, "Topical review: catching light in its own trap," J. Mod. Opt. 48, 191-238 (2001).

Sternood, T. K.

R. C. Reid, J. M. Prausnitz, and T. K. Sternood, The Properties of Gases and Liquids (McGraw-Hill, 1977).

Tyrrell, J.

J. Tyrrell, "Tiny polymer tips boost fibre coupling efficiency," Opt. Laser Europe, November 2004, pp. 29-31.

Urbach, W.

H. Hervet, W. Urbach, and F. Rondelez, "Mass diffusion measurements in liquid crystals by a novel optical method," J. Chem. Phys. 68, 2725-2729 (1978).
[CrossRef]

Vitello, D.

Wang, C. H.

C. H. Wang and J. L. Xia, "Holographic method for investigating the diffusion of dye molecules in the polymer host," J. Chem. Phys. 92, 2603-2613 (1990).
[CrossRef]

Wonderen, A. J.

K. Dorkenoo, A. J. V. Wonderen, H. Bulou, M. Romeo, O. Cregut, and A. Fort, "Time-resolved measurement of the refractive index for photopolymerization processes," Appl. Phys. Lett. 83, 2474-2476 (2003).
[CrossRef]

Xia, J. L.

C. H. Wang and J. L. Xia, "Holographic method for investigating the diffusion of dye molecules in the polymer host," J. Chem. Phys. 92, 2603-2613 (1990).
[CrossRef]

Yariv, A.

M. Segev, B. Crosignani, and A. Yariv, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
[CrossRef] [PubMed]

Adv. Mater. (Weinheim, Ger.)

C. Ecoffet, A. Espanet, and D. J. Lougnot, "Photopolymerization by evanescent waves: a new method to obtain nanoparts," Adv. Mater. (Weinheim, Ger.) 10, 411-414 (1998).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

K. Dorkenoo, A. J. V. Wonderen, H. Bulou, M. Romeo, O. Cregut, and A. Fort, "Time-resolved measurement of the refractive index for photopolymerization processes," Appl. Phys. Lett. 83, 2474-2476 (2003).
[CrossRef]

Appl. Surf. Sci.

A. Espanet, G. D. Santos, C. Ecoffet, and D. J. Lougnot, "Photopolymerization by evanescent waves: characterization of photopolymerizable formulation for photolithography with nanometric resolution," Appl. Surf. Sci. 138-139, 87-92 (1999).
[CrossRef]

J. Appl. Phys.

D. Kato, "Light coupling from a stripe-geometry GaAs diode laser into an optical fiber with spherical end," J. Appl. Phys. 44, 2756-2758 (1973).
[CrossRef]

J. Chem. Educ.

S. R. Logan, "Spatial inhomogeneity effects in photochemical kinetics," J. Chem. Educ. 67, 872-875 (1990).
[CrossRef]

J. Chem. Phys.

C. H. Wang and J. L. Xia, "Holographic method for investigating the diffusion of dye molecules in the polymer host," J. Chem. Phys. 92, 2603-2613 (1990).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Experimental setup: He–Ne 543.5 nm laser light emerges from the fiber into the surface-tension-driven photosensitive droplet, thus initiating the polymerization reaction.

Fig. 2
Fig. 2

Electron micrograph of a 30 μ m long polymer tip grown on the end of a monomode fiber at 543.5 nm. Its basis width is of the order of the fiber core: 3 μ m .

Fig. 3
Fig. 3

Detail of the end of the polymer tip shown in Fig. 2.

Fig. 4
Fig. 4

Polymer tip grown with a L P 21 mode on the end of a standard telecommunication fiber.

Fig. 5
Fig. 5

Typical polymerization curve expressed in terms of index-of-refraction variation as a function of the accumulated energy E acc , the maximum index variation between the monomer and the polymer being d n = 0.04 . The existence of a threshold energy E s below which no polymerization can occur is evidenced.

Fig. 6
Fig. 6

(Color online) Typical shape of a 30 μ m long polymer tip computed by using a standard BPM and the accumulated energy model shown on Fig. 5 without taking into account O 2 diffusion into the solution.

Fig. 7
Fig. 7

Simulated growth of a polymer tip on the cleaved end of monomode telecom 1.55 μ m fiber excited at 543.5 μ m in its fundamental mode (bottom), alongside the beam profile during the growth (top). The beam emerges from the fiber on the left.

Fig. 8
Fig. 8

Simulated growth of a polymer tip on the cleaved end of monomode 543.5 nm fiber (bottom), alongside the beam profile during the growth (top). The beam emerges from the fiber on the left.

Fig. 9
Fig. 9

(Color online) Simulated influence of dissolved oxygen ( C s ) and atmosphere O 2 concentration ( C s max ) for a diffusion length D diff = 1 μ m . (a)–(e) C s = 10 3 J m 2 , and C s max rises. (f)–(j) C s = 10 4 J m 2 , and C s max rises. (k)–(o) C s = 10 5 J m 2 , and C s max rises. Precise values are given in Table 1. The fiber end to which the tip is attached is located on the left-hand side. The hollow ends of tips that can be seen on Figs. 9, 10, 11 are a rendering artifact and mean that the tips are actually flat.

Fig. 10
Fig. 10

(Color online) Simulated influence of dissolved oxygen ( C s ) and atmosphere O 2 concentration ( C s max ) for a diffusion length D diff = 2 μ m . (a)–(e) C s = 10 3 J m 2 , and C s max rises. (f)–(j) C s = 10 4 J m 2 , and C s max rises. (k)–(o) C s = 10 5 J m 2 , and C s max rises. Precise values are given in Table 2. The fiber end to which the tip is attached is located on the left-hand side.

Fig. 11
Fig. 11

(Color online) Simulated influence of dissolved oxygen ( C s ) and atmosphere O 2 concentration ( C s max ) for a diffusion length D diff = 3 μ m . (a)–(e) C s = 10 3 J m 2 , and C s max rises. (f)–(j) C s = 10 4 J m 2 , and C s max rises. (k)–(o) C s = 10 5 J m 2 , and C s max rises. Precise values are given in Table 3. The fiber end to which the tip is attached is located on the left-hand side.

Fig. 12
Fig. 12

Left: simulated polymer tip without taking into account diffusion within the droplet. Right: droplet inner diffusion taken into account. Simulation data: C s = 5 × 10 2 J m 2 , C s max = 10 8 J m 2 , D diff 2 = D diff = 0.1 μ m , C s max 2 = 10 4 J m 2 , and an exposure time of 1 s. The dotted curve around the right-hand tip is a shadow of the left-hand one meant to help in the comparison.

Fig. 13
Fig. 13

Experimentally measured curvature radii are compared with simulated ones for varying exposure times and for a beam power of 2.5 μ W , an experimental eosin concentration of 3%, and the following simulation data: C s = 5 × 10 2 J m 2 , C s max = 10 8 J m 2 , D diff = D diff 2 = 0.1 μ m , C s max 2 = 10 4 J m 2 , and α = 10 .

Fig. 14
Fig. 14

Experimentally measured curvature radii are compared with simulated ones for varying output beam powers and for an exposure time of 1 s, an experimental eosin concentration of 3%, and the following simulation data: C s = 5 × 10 2 J m 2 , C s max = 10 8 J m 2 , D diff = D diff 2 = 0.1 μ m , C s max 2 = 10 4 J m 2 , and α = 10 . The straight lines are guides to the eyes.

Fig. 15
Fig. 15

Simulated propagation of light in a sample polymer tip: the initial plane wave undergoes strong focusing prior to reaching the tip end, thus providing high enlargement of the numerical aperture of the system.

Tables (3)

Tables Icon

Table 1 Simulation Values for Fig. 9 a

Tables Icon

Table 2 Simulation Values for Fig. 10 a

Tables Icon

Table 3 Simulation Values for Fig. 11 a

Equations (6)

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Δ n = d n tanh ( E acc E s α E s ) h ( E acc E s ) ,
γ = 1 d ln [ 1 + exp ( d γ 0 ) 1 exp ( E acc κ ) ] ,
C s max exp ( z d D diff ) ,
C s max 2 exp ( r d 2 D diff 2 ) ,
E s = C s + C s max exp ( z d D diff ) + C s max 2 exp ( r d 2 D diff 2 ) ,
C s C s max C s exp ( d D diff ) .

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