Abstract

The light focusing by using dielectric nano-waveguides array with its length in micron is investigated via the finite-difference time domain (FDTD) method. Simulated results show that the focal length depends on the length and the total width of the arrays and can be altered from tens of micron to wavelength order. Both TM and TE mode incident light can be focused by the array. The wavelength-order focal length is achieved by employing the dielectric nano-waveguide array with variant separations. The unique focusing behavior is contributed to the radiation mode with longer decay length and the large evanescent field which appears in the nano-waveguide array. We believe this simulation results can be a promising guidance for the experiments.

© 2009 OSA

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References

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  1. Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
    [CrossRef]
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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]
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2009 (2)

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

A. H. J. Yang, T. Lerdsuchatawanich, and D. Erickson, “Forces and transport velocities for a particle in a slot waveguide,” Nano Lett. 9(3), 1182–1188 (2009).
[CrossRef] [PubMed]

2007 (3)

2006 (3)

2005 (2)

L. Tong, J. Lou, R. R. Gattass, S. He, X. Chen, L. Liu, and E. Mazur, “Assembly of silica nanowires on silica aerogels for microphotonic devices,” Nano Lett. 5(2), 259–262 (2005).
[CrossRef] [PubMed]

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express 13(18), 6815–6820 (2005).
[CrossRef] [PubMed]

2004 (3)

2003 (1)

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

2001 (1)

Y. Cui, Q. Wei, H. Park, and C. M. Lieber, “Nanowire nanosensors for highly sensitive and selective detection of biological and chemical species,” Science 293(5533), 1289–1292 (2001).
[CrossRef] [PubMed]

1996 (1)

J.-P. Berenger, “Perfectly Matched Layer for the FDTD Solution of Wave-Structure Interaction Problems,” IEEE Trans. Antenn. Propag. 44(1), 110–117 (1996).
[CrossRef]

1989 (1)

1988 (2)

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13(9), 794–796 (1988).
[CrossRef] [PubMed]

N. Kishi and E. Yamshita, “A Simple Coupled-Mode Analysis Method for Multiple-Core Optical Fiber and Coupled Dielectric Waveguide Structures,” IEEE Trans. Microw. Theory Tech. 36(12), 1861–1868 (1988).
[CrossRef]

1973 (1)

S. Somekh, E. Gamire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22(1), 46–47 (1973).
[CrossRef]

Ashcom, J. B.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Barnard, E. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

Berenger, J.-P.

J.-P. Berenger, “Perfectly Matched Layer for the FDTD Solution of Wave-Structure Interaction Problems,” IEEE Trans. Antenn. Propag. 44(1), 110–117 (1996).
[CrossRef]

Brongersma, M. L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

Chen, X.

L. Tong, J. Lou, R. R. Gattass, S. He, X. Chen, L. Liu, and E. Mazur, “Assembly of silica nanowires on silica aerogels for microphotonic devices,” Nano Lett. 5(2), 259–262 (2005).
[CrossRef] [PubMed]

Christodoulides, D. N.

Cui, Y.

Y. Cui, Q. Wei, H. Park, and C. M. Lieber, “Nanowire nanosensors for highly sensitive and selective detection of biological and chemical species,” Science 293(5533), 1289–1292 (2001).
[CrossRef] [PubMed]

Deng, Y.

Dong, X.

Du, C.

Erickson, D.

A. H. J. Yang, T. Lerdsuchatawanich, and D. Erickson, “Forces and transport velocities for a particle in a slot waveguide,” Nano Lett. 9(3), 1182–1188 (2009).
[CrossRef] [PubMed]

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

Fan, X.

Gamire, E.

S. Somekh, E. Gamire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22(1), 46–47 (1973).
[CrossRef]

Gao, H.

Garvin, H. L.

S. Somekh, E. Gamire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22(1), 46–47 (1973).
[CrossRef]

Gattass, R. R.

L. Tong, J. Lou, R. R. Gattass, S. He, X. Chen, L. Liu, and E. Mazur, “Assembly of silica nanowires on silica aerogels for microphotonic devices,” Nano Lett. 5(2), 259–262 (2005).
[CrossRef] [PubMed]

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Guo, Q.-Z.

He, S.

L. Tong, J. Lou, R. R. Gattass, S. He, X. Chen, L. Liu, and E. Mazur, “Assembly of silica nanowires on silica aerogels for microphotonic devices,” Nano Lett. 5(2), 259–262 (2005).
[CrossRef] [PubMed]

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Herzig, H. P.

Huang, K.

Huang, Z.-M.

Hunsperger, R. G.

S. Somekh, E. Gamire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22(1), 46–47 (1973).
[CrossRef]

Jiao, X.

Joseph, R. I.

Josten, G.

Kim, H. K.

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[CrossRef]

Kishi, N.

N. Kishi and E. Yamshita, “A Simple Coupled-Mode Analysis Method for Multiple-Core Optical Fiber and Coupled Dielectric Waveguide Structures,” IEEE Trans. Microw. Theory Tech. 36(12), 1861–1868 (1988).
[CrossRef]

Lerdsuchatawanich, T.

A. H. J. Yang, T. Lerdsuchatawanich, and D. Erickson, “Forces and transport velocities for a particle in a slot waveguide,” Nano Lett. 9(3), 1182–1188 (2009).
[CrossRef] [PubMed]

Lieber, C. M.

Y. Cui, Q. Wei, H. Park, and C. M. Lieber, “Nanowire nanosensors for highly sensitive and selective detection of biological and chemical species,” Science 293(5533), 1289–1292 (2001).
[CrossRef] [PubMed]

Liu, L.

L. Tong, J. Lou, R. R. Gattass, S. He, X. Chen, L. Liu, and E. Mazur, “Assembly of silica nanowires on silica aerogels for microphotonic devices,” Nano Lett. 5(2), 259–262 (2005).
[CrossRef] [PubMed]

Lou, J.

L. Tong, J. Lou, R. R. Gattass, S. He, X. Chen, L. Liu, and E. Mazur, “Assembly of silica nanowires on silica aerogels for microphotonic devices,” Nano Lett. 5(2), 259–262 (2005).
[CrossRef] [PubMed]

L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12(6), 1025–1035 (2004).
[CrossRef] [PubMed]

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Luethy, W.

Luo, X.

Maxwell, I.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Mazur, E.

L. Tong, J. Lou, R. R. Gattass, S. He, X. Chen, L. Liu, and E. Mazur, “Assembly of silica nanowires on silica aerogels for microphotonic devices,” Nano Lett. 5(2), 259–262 (2005).
[CrossRef] [PubMed]

L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12(6), 1025–1035 (2004).
[CrossRef] [PubMed]

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Meng, Y.-C.

Min, C.

Ming, H.

Park, H.

Y. Cui, Q. Wei, H. Park, and C. M. Lieber, “Nanowire nanosensors for highly sensitive and selective detection of biological and chemical species,” Science 293(5533), 1289–1292 (2001).
[CrossRef] [PubMed]

Ruffieux, P.

Scharf, T.

Shen, M.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Shi, H.

Somekh, S.

S. Somekh, E. Gamire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22(1), 46–47 (1973).
[CrossRef]

Sun, Z.

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[CrossRef]

Tan, W.-H.

Tong, L.

G. Zhai and L. Tong, “Roughness-induced radiation losses in optical micro or nanofibers,” Opt. Express 15(21), 13805–13816 (2007).
[CrossRef] [PubMed]

K. Huang, S. Yang, and L. Tong, “Modeling of evanescent coupling between two parallel optical nanowires,” Appl. Opt. 46(9), 1429–1434 (2006).
[CrossRef]

L. Tong, J. Lou, R. R. Gattass, S. He, X. Chen, L. Liu, and E. Mazur, “Assembly of silica nanowires on silica aerogels for microphotonic devices,” Nano Lett. 5(2), 259–262 (2005).
[CrossRef] [PubMed]

L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12(6), 1025–1035 (2004).
[CrossRef] [PubMed]

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

Völkel, R.

Wang, C.

Wang, G. P.

Wang, P.

Weber, H. P.

Wei, J. S.

J. S. Wei, “Power Transfer in a Large Parallel Array of Coupled Dielectric Waveguides,” IEEE Trans. Microw. Theory Tech. 55(11), 2345–2353 (2007).
[CrossRef]

Wei, Q.

Y. Cui, Q. Wei, H. Park, and C. M. Lieber, “Nanowire nanosensors for highly sensitive and selective detection of biological and chemical species,” Science 293(5533), 1289–1292 (2001).
[CrossRef] [PubMed]

Weible, K. J.

White, J. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

Yamshita, E.

N. Kishi and E. Yamshita, “A Simple Coupled-Mode Analysis Method for Multiple-Core Optical Fiber and Coupled Dielectric Waveguide Structures,” IEEE Trans. Microw. Theory Tech. 36(12), 1861–1868 (1988).
[CrossRef]

Yang, A. H. J.

A. H. J. Yang, T. Lerdsuchatawanich, and D. Erickson, “Forces and transport velocities for a particle in a slot waveguide,” Nano Lett. 9(3), 1182–1188 (2009).
[CrossRef] [PubMed]

Yang, S.

Yariv, A.

S. Somekh, E. Gamire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22(1), 46–47 (1973).
[CrossRef]

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

Zhai, G.

Appl. Opt. (2)

Appl. Phys. Lett. (2)

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[CrossRef]

S. Somekh, E. Gamire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22(1), 46–47 (1973).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

J.-P. Berenger, “Perfectly Matched Layer for the FDTD Solution of Wave-Structure Interaction Problems,” IEEE Trans. Antenn. Propag. 44(1), 110–117 (1996).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (2)

J. S. Wei, “Power Transfer in a Large Parallel Array of Coupled Dielectric Waveguides,” IEEE Trans. Microw. Theory Tech. 55(11), 2345–2353 (2007).
[CrossRef]

N. Kishi and E. Yamshita, “A Simple Coupled-Mode Analysis Method for Multiple-Core Optical Fiber and Coupled Dielectric Waveguide Structures,” IEEE Trans. Microw. Theory Tech. 36(12), 1861–1868 (1988).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nano Lett. (3)

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[CrossRef]

L. Tong, J. Lou, R. R. Gattass, S. He, X. Chen, L. Liu, and E. Mazur, “Assembly of silica nanowires on silica aerogels for microphotonic devices,” Nano Lett. 5(2), 259–262 (2005).
[CrossRef] [PubMed]

A. H. J. Yang, T. Lerdsuchatawanich, and D. Erickson, “Forces and transport velocities for a particle in a slot waveguide,” Nano Lett. 9(3), 1182–1188 (2009).
[CrossRef] [PubMed]

Nature (1)

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Opt. Express (5)

Opt. Lett. (2)

Science (1)

Y. Cui, Q. Wei, H. Park, and C. M. Lieber, “Nanowire nanosensors for highly sensitive and selective detection of biological and chemical species,” Science 293(5533), 1289–1292 (2001).
[CrossRef] [PubMed]

Other (4)

A. W. Snyder, and J. D. Love, Optical waveguide theory (Chapman and Hall, 1983).

A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed (Artech House, 2000).

B. E. A. Saleh, and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

P. Klocek, Handbook of infrared optical materials (Marcel Dekker, 1991).

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Figures (7)

Fig. 1
Fig. 1

The schematic of the nano-waveguide arrays. W is the width of the single nano-waveguide, D the wire separation and L the wire length.

Fig. 2
Fig. 2

The electric field distribution of the nano-waveguide array with N = 13, W = D = 300nm, L = 2.0μm. The FWHM of the incident light is 7.5μm. The white vertical line presents the end of the array.

Fig. 3
Fig. 3

The focal length f versus array length L with W = D = 300nm. The solid squares represent f for N = 13 (FWHM = 7.5μm), the solid circles for N = 11 (FWHM = 6.3μm) and the solid triangles for N = 9 (FWHM = 5.1μm). The solid line is just the guiding link between the values.

Fig. 4
Fig. 4

The focal length f versus the wire width W with D = 300nm and L = 1.0μm. The solid squares represent the values that N = 15; the solid circles, N = 13; the solid triangles, N = 11; the solid nablas, N = 9; the solid diamonds, N = 7. The solid line is just the guiding link between the values.

Fig. 5
Fig. 5

The focal length f versus the wire separation D with W = 300nm, L = 1.0μm. The solid squares represent the values that N = 15; the solid circles, N = 13; the solid triangles, N = 11; the solid nablas, N = 9; the solid diamonds, N = 7. The solid line is just the guiding link between the values.

Fig. 6
Fig. 6

The electric field distribution of the nano-waveguide array with variant separation and N = 7, W = 100nm, L = 2μm. D in the center is 0.05μm and increases linearly with a step of 0.05μm to the boundary of the array. The FWHM of the incident light is 1.6μm. The white vertical line presents the end of the array. The redcolor shows the energy peak as the focus.

Fig. 7
Fig. 7

The focal length for light of TE mode in the array with W = D = 300nm. The solid squares represent the value that N = 13 (FWHM = 7.5μm); the solid circles, N = 11 (FWHM = 6.3μm); the solid triangles, N = 9 (FWHM = 5.1μm). The solid line is just the guiding link between the values.

Equations (1)

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Lra=ρ2θcExp[V2]

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