Abstract

We present a novel fabrication technology for nano-structured graded index micro-optical components, based on the stack-and-draw method used for photonic crystal fibres. These discrete structures can be described with an effective refractive index distribution. Furthermore we present spherical nano-structured microlenses with a flat facet fabricated with this method and designed using an algorithm based on the Maxwell-Garnett mixing formula. Finally we show theoretical verification by using FDTD simulations for a nano-structured lens as well as experimental data obtained in the microwave regime.

© 2009 Optical Society of America

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    [CrossRef]

2008

H. Kurt, E. Colak, O. Cakmak, H. Caglayan, and E. Ozbay, "The focusing effect of graded index photonic crystals," Appl. Phys. Lett. 93, 171,108 (2008), http://link.aip.org/link/?APL/93/171108/1.
[CrossRef]

2007

L. Hao, S. Bangren, W. Jijiang, G. Lijun, and L. Aimei, "Fabrication of gradient refractive index ball lenses," Opt. Lasers Eng. 46, 252-256 (2007).

2005

2004

T. Huang, Z. Li, M. Li, D. Chetwynd, and C. Gosselin, "Conceptual design and dimensional synthesis of a novel 2-DOF translational parallel robot for pick-and-place operations," Journal of Mechanical Design 126, 449-455 (2004).
[CrossRef]

F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight, and P. S. J. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369-2371 (2004), http://ol.osa.org/abstract.cfm?URI=ol-29-20-2369.
[CrossRef] [PubMed]

2003

2001

1997

1995

Z. Sacks, D. Kingsland, R. Lee, and J. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition." IEEE Trans. Antenn. Propag. 43, 1460-1463 (1995).
[CrossRef]

1994

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

1983

S. Kirkpatrick, C. GelattJr, and M. Vecchi, "Optimization by Simulated Annealing," Science 220, 671 (1983).
[CrossRef] [PubMed]

Afsar, M.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Aimei, L.

L. Hao, S. Bangren, W. Jijiang, G. Lijun, and L. Aimei, "Fabrication of gradient refractive index ball lenses," Opt. Lasers Eng. 46, 252-256 (2007).

Bangren, S.

L. Hao, S. Bangren, W. Jijiang, G. Lijun, and L. Aimei, "Fabrication of gradient refractive index ball lenses," Opt. Lasers Eng. 46, 252-256 (2007).

Bigot, L.

Birch, J.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Bird, D. M.

Bouwmans, G.

Caglayan, H.

H. Kurt, E. Colak, O. Cakmak, H. Caglayan, and E. Ozbay, "The focusing effect of graded index photonic crystals," Appl. Phys. Lett. 93, 171,108 (2008), http://link.aip.org/link/?APL/93/171108/1.
[CrossRef]

Cakmak, O.

H. Kurt, E. Colak, O. Cakmak, H. Caglayan, and E. Ozbay, "The focusing effect of graded index photonic crystals," Appl. Phys. Lett. 93, 171,108 (2008), http://link.aip.org/link/?APL/93/171108/1.
[CrossRef]

Chetwynd, D.

T. Huang, Z. Li, M. Li, D. Chetwynd, and C. Gosselin, "Conceptual design and dimensional synthesis of a novel 2-DOF translational parallel robot for pick-and-place operations," Journal of Mechanical Design 126, 449-455 (2004).
[CrossRef]

Clarke, R.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Colak, E.

H. Kurt, E. Colak, O. Cakmak, H. Caglayan, and E. Ozbay, "The focusing effect of graded index photonic crystals," Appl. Phys. Lett. 93, 171,108 (2008), http://link.aip.org/link/?APL/93/171108/1.
[CrossRef]

Douay, M.

Dutta, J.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Feng, X.

Finazzi, V.

Frost, H.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Gelatt, C.

S. Kirkpatrick, C. GelattJr, and M. Vecchi, "Optimization by Simulated Annealing," Science 220, 671 (1983).
[CrossRef] [PubMed]

George, A. K.

Gerbaux, X.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Gosselin, C.

T. Huang, Z. Li, M. Li, D. Chetwynd, and C. Gosselin, "Conceptual design and dimensional synthesis of a novel 2-DOF translational parallel robot for pick-and-place operations," Journal of Mechanical Design 126, 449-455 (2004).
[CrossRef]

Hadni, A.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Hall, W.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Hao, L.

L. Hao, S. Bangren, W. Jijiang, G. Lijun, and L. Aimei, "Fabrication of gradient refractive index ball lenses," Opt. Lasers Eng. 46, 252-256 (2007).

Hedley, T. D.

Heidinger, R.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Hewak, D.

Ho, W.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Huang, T.

T. Huang, Z. Li, M. Li, D. Chetwynd, and C. Gosselin, "Conceptual design and dimensional synthesis of a novel 2-DOF translational parallel robot for pick-and-place operations," Journal of Mechanical Design 126, 449-455 (2004).
[CrossRef]

Jijiang, W.

L. Hao, S. Bangren, W. Jijiang, G. Lijun, and L. Aimei, "Fabrication of gradient refractive index ball lenses," Opt. Lasers Eng. 46, 252-256 (2007).

Jones, C.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Kingsland, D.

Z. Sacks, D. Kingsland, R. Lee, and J. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition." IEEE Trans. Antenn. Propag. 43, 1460-1463 (1995).
[CrossRef]

Kirkpatrick, S.

S. Kirkpatrick, C. GelattJr, and M. Vecchi, "Optimization by Simulated Annealing," Science 220, 671 (1983).
[CrossRef] [PubMed]

Knight, J. C.

Koniger, F.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Kurt, H.

H. Kurt, E. Colak, O. Cakmak, H. Caglayan, and E. Ozbay, "The focusing effect of graded index photonic crystals," Appl. Phys. Lett. 93, 171,108 (2008), http://link.aip.org/link/?APL/93/171108/1.
[CrossRef]

Lee, J.

Z. Sacks, D. Kingsland, R. Lee, and J. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition." IEEE Trans. Antenn. Propag. 43, 1460-1463 (1995).
[CrossRef]

Lee, R.

Z. Sacks, D. Kingsland, R. Lee, and J. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition." IEEE Trans. Antenn. Propag. 43, 1460-1463 (1995).
[CrossRef]

Li, L.

Li, M.

T. Huang, Z. Li, M. Li, D. Chetwynd, and C. Gosselin, "Conceptual design and dimensional synthesis of a novel 2-DOF translational parallel robot for pick-and-place operations," Journal of Mechanical Design 126, 449-455 (2004).
[CrossRef]

Li, Z.

T. Huang, Z. Li, M. Li, D. Chetwynd, and C. Gosselin, "Conceptual design and dimensional synthesis of a novel 2-DOF translational parallel robot for pick-and-place operations," Journal of Mechanical Design 126, 449-455 (2004).
[CrossRef]

Lijun, G.

L. Hao, S. Bangren, W. Jijiang, G. Lijun, and L. Aimei, "Fabrication of gradient refractive index ball lenses," Opt. Lasers Eng. 46, 252-256 (2007).

Lopez, F.

Luan, F.

Matsuo, H.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Monro, T.

Moore, R.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Nakano, T.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Neviere, M.

Ozbay, E.

H. Kurt, E. Colak, O. Cakmak, H. Caglayan, and E. Ozbay, "The focusing effect of graded index photonic crystals," Appl. Phys. Lett. 93, 171,108 (2008), http://link.aip.org/link/?APL/93/171108/1.
[CrossRef]

Pearce, G. J.

Petropoulos, P.

Popov, E.

Provino, L.

Quiquempois, Y.

Richter, W.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Russell, P. S. J.

Sacks, Z.

Z. Sacks, D. Kingsland, R. Lee, and J. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition." IEEE Trans. Antenn. Propag. 43, 1460-1463 (1995).
[CrossRef]

Sakai, K.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Simonis, G.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Stead, M.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Stumper, U.

J. Birch, G. Simonis, M. Afsar, R. Clarke, J. Dutta, H. Frost, X. Gerbaux, A. Hadni, W. Hall, R. Heidinger, W. Ho, C. Jones, F. Koniger, R. Moore, H. Matsuo, T. Nakano, W. Richter, K. Sakai, M. Stead, U. Stumper, R. Vigil, and T. Wells, "An intercomparison of measurement techniques for the determination of the dielectric properties of solids at near millimetre wavelengths," IEEE T. Microw. Theory. 42, 956-965 (1994).
[CrossRef]

Vecchi, M.

S. Kirkpatrick, C. GelattJr, and M. Vecchi, "Optimization by Simulated Annealing," Science 220, 671 (1983).
[CrossRef] [PubMed]

Vigil, R.

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Figures (8)

Fig. 1.
Fig. 1.

Design of a nano-structures microlens: (a) the index pattern of the nano-structured lens; (b) the effective index distribution of (a) calculated with equation 1; (c) the ideal parabolic distribution used for the reference lens.

Fig. 2.
Fig. 2.

FDTD simulations comparing an ideal GRIN lens with the structured lens

Fig. 3.
Fig. 3.

Comparison of the intensity distribution in the focal plane of the nano-structured lens (a) and the ideal gradient index lens (b) in a logarithmic color scale. (c) shows a cross section through the focal plane of both elements

Fig. 4.
Fig. 4.

The stack-and-draw technique used for the fabrication of nano-structures phase elements

Fig. 5.
Fig. 5.

Pictures of the intermediate preforms of the microlens: (a) the preform after the first drawing process, (b) the intermediate preform of the microlens array before the last drawing step

Fig. 6.
Fig. 6.

Results from the phase contrast microscope showing the nano structured GRIN lens drawn to a lens size of 6 μm : (a) the direct output of the phase contrast microscope; (b) false color plot of one microlens of the array; (c) cross section of the phase contrast image through the center of the lens

Fig. 7.
Fig. 7.

(a) The design of the microwave lens assembled from solid rods (red) and tubes (yellow); (b) the distribution of the effective refractive index; (c) photo of the assembled component used in the experiments.

Fig. 8.
Fig. 8.

Experimental measurements of the microwave lens: (a) a cross section of the phase directly after the element; (b) a cross section of the intensity in the focal plane; (c) the field distribution in the focal plane

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

ε eff = < ε > f ( ε 1 ε 2 ) ε 1 < ε > 3 < ε >
c = 1 P ( p = 1 P ( n eff ( p ) N ( p ) ) 2 ) 1 / 2
n ( r ) = n max ( 1 a r 2 / 2 )

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