Abstract

Bending losses of nanofibers or nanowires with circular 90° bends are simulated using a three- dimensional finite-difference time-domain (3D-FDTD) method. Dependences of bending losses on wavelength and polarization of guided light are investigated, as well as the diameters, refractive indices, and bending radii of nanowires. The acceptable bending losses (1dB/90°) predicted in glass, polymer, and semiconductor nanowires with bending radii down to micrometer level may offer valuable references for assembling highly compact photonic integrated circuits or devices with optical nanowires.

© 2009 Optical Society of America

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2008 (4)

Y. H. Li and L. M. Tong, “Mach--Zehnder interferometers assembled with optical microfibers or nanofibers,” Opt. Lett. 33, 303-305 (2008).
[CrossRef] [PubMed]

F. X. Gu, L. Zhang, X. F. Yin, and L. M. Tong, “Polymer single-nanowire optical sensors,” Nano Lett. 8, 2757-2761 (2008).
[CrossRef] [PubMed]

X. B. Xing, H. Zhu, Y. Q. Wang, and B. J. Li, “Ultracompact photonic coupling splitters twisted by PTT nanowires,” Nano Lett. 8, 2839-2843 (2008).
[CrossRef] [PubMed]

S. S. Wang, J. Fu, M. Qiu, K. J. Huang, Z. Ma, and L. M. Tong, “Modeling endface output patterns of optical micro/nanofibers,” Opt. Express 16, 8887-8895 (2008).
[CrossRef] [PubMed]

2007 (3)

2006 (5)

2005 (3)

Q. Wang, G. Farrell, and T. Freir, “Theoretical and experimental investigations of macro-bend losses for standard single mode fibers,” Opt. Express 13, 4476-4484 (2005).
[CrossRef] [PubMed]

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

M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, “Optical microfiber loop resonator,” Appl. Phys. Lett. 86, 161108 (2005).
[CrossRef]

2004 (8)

M. Law, J. Goldberger, and P. D. Yang, “Semiconductor nanowires and nanotubes,” Annu. Rev. Mater. Res. 34, 83-122(2004).
[CrossRef]

M. Law, D. J. Sirbuly, J. C. Johnson, J. Goldberger, R. J. Saykally, and P. D. Yang, “Nanoribbon waveguides for subwavelength photonics integration,” Science 305, 1269-1273 (2004).
[CrossRef] [PubMed]

S. A. Harfenist, S. D. Cambron, E. W. Nelson, S. M. Berry, A. W. Isham, M. M. Crain, K. M. Walsh, R. S. Keynton, and R. W. Cohn, “Direct drawing of suspended filamentary micro- and nanostructures from liquid polymers,” Nano Lett. 4, 1931-1937 (2004).
[CrossRef]

M. Sumetsky, “Optical fiber microcoil resonator,” Opt. Express 12, 2303-2316 (2004).
[CrossRef] [PubMed]

M. Sumetsky, Y. Dulashko, and A. Hale, “Fabrication and study of bent and coiled free silica nanowires: self-coupling microloop optical interferometer,” Opt. Express 12, 3521-3531(2004).
[CrossRef] [PubMed]

A. Sakai, T. Fukazawa, and T. Baba, “Estimation of polarization crosstalk at a micro-bend in Si-photonic wire waveguide,” J. Lightwave Technol. 22, 520-525 (2004).
[CrossRef]

F. L. Kien, J. Q. Liang, K. Hakuta, and V. I. Balykin, “Field intensity distributions and polarization orientations in a vacuum-clad subwavelength-diameter optical fiber,” Opt. Commun. 242, 445-455 (2004).
[CrossRef]

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

2003 (2)

J. H. Greene and A. Taflove, “Intial three-dimensional finite-difference time-domain phenomenology study of the transient response of a large vertically coupled photonic racetrack,” Opt. Lett. 28, 1733-1735 (2003).
[CrossRef] [PubMed]

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

1998 (2)

1997 (1)

L. Faustini and G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol. 15, 671-679 (1997).
[CrossRef]

1996 (1)

S. D. Gedney, “An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630-1639 (1996).
[CrossRef]

1995 (1)

M. Rivera, “A finite-difference BPM analysis of dielectric wave-guides,” J. Lightwave Technol. 13, 233-238 (1995).
[CrossRef]

1993 (1)

D. Marcuse, “Bend loss of slab and fiber modes computed with diffraction theory,” IEEE J. Quantum Electron. 29, 2957-2961 (1993).
[CrossRef]

1992 (1)

H. Renner, “Bending losses of coated single-mode fibers: a simple approach,” J. Lightwave Technol. 10, 544-551 (1992).
[CrossRef]

1985 (1)

C. Vassallo, “Perturbation of an LP mode of an optical fiber by a quasi-degenerate field: a simple formula,” Opt. Quantum Electron. 17, 201-205 (1985).
[CrossRef]

1976 (1)

1975 (1)

M. Heiblum and J. H. Harris, “Analysis of curved waveguides by conformal transformation,” IEEE J. Quantum Electron. 11, 75-83 (1975).
[CrossRef]

Ashcom, J. B.

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

Baba, T.

Balykin, V. I.

F. L. Kien, J. Q. Liang, K. Hakuta, and V. I. Balykin, “Field intensity distributions and polarization orientations in a vacuum-clad subwavelength-diameter optical fiber,” Opt. Commun. 242, 445-455 (2004).
[CrossRef]

Berry, S. M.

S. A. Harfenist, S. D. Cambron, E. W. Nelson, S. M. Berry, A. W. Isham, M. M. Crain, K. M. Walsh, R. S. Keynton, and R. W. Cohn, “Direct drawing of suspended filamentary micro- and nanostructures from liquid polymers,” Nano Lett. 4, 1931-1937 (2004).
[CrossRef]

Cambron, S. D.

S. A. Harfenist, S. D. Cambron, E. W. Nelson, S. M. Berry, A. W. Isham, M. M. Crain, K. M. Walsh, R. S. Keynton, and R. W. Cohn, “Direct drawing of suspended filamentary micro- and nanostructures from liquid polymers,” Nano Lett. 4, 1931-1937 (2004).
[CrossRef]

Chen, G. H.

Chen, X. W.

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

Cohn, R. W.

S. A. Harfenist, S. D. Cambron, E. W. Nelson, S. M. Berry, A. W. Isham, M. M. Crain, K. M. Walsh, R. S. Keynton, and R. W. Cohn, “Direct drawing of suspended filamentary micro- and nanostructures from liquid polymers,” Nano Lett. 4, 1931-1937 (2004).
[CrossRef]

Crain, M. M.

S. A. Harfenist, S. D. Cambron, E. W. Nelson, S. M. Berry, A. W. Isham, M. M. Crain, K. M. Walsh, R. S. Keynton, and R. W. Cohn, “Direct drawing of suspended filamentary micro- and nanostructures from liquid polymers,” Nano Lett. 4, 1931-1937 (2004).
[CrossRef]

Dai, D. X.

Dulashko, Y.

Fan, D. Y.

Farrell, G.

Faustini, L.

L. Faustini and G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol. 15, 671-679 (1997).
[CrossRef]

Fini, J. M.

M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, “Optical microfiber loop resonator,” Appl. Phys. Lett. 86, 161108 (2005).
[CrossRef]

Frarell, G.

Freir, T.

Fu, J.

Fukazawa, T.

Gattass, R. R.

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

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

Gedney, S. D.

S. D. Gedney, “An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630-1639 (1996).
[CrossRef]

Goldberger, J.

M. Law, J. Goldberger, and P. D. Yang, “Semiconductor nanowires and nanotubes,” Annu. Rev. Mater. Res. 34, 83-122(2004).
[CrossRef]

M. Law, D. J. Sirbuly, J. C. Johnson, J. Goldberger, R. J. Saykally, and P. D. Yang, “Nanoribbon waveguides for subwavelength photonics integration,” Science 305, 1269-1273 (2004).
[CrossRef] [PubMed]

Greene, J. H.

Gu, F. X.

F. X. Gu, L. Zhang, X. F. Yin, and L. M. Tong, “Polymer single-nanowire optical sensors,” Nano Lett. 8, 2757-2761 (2008).
[CrossRef] [PubMed]

Hagness, S. C.

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

Hakuta, K.

F. L. Kien, J. Q. Liang, K. Hakuta, and V. I. Balykin, “Field intensity distributions and polarization orientations in a vacuum-clad subwavelength-diameter optical fiber,” Opt. Commun. 242, 445-455 (2004).
[CrossRef]

Hale, A.

Harfenist, S. A.

S. A. Harfenist, S. D. Cambron, E. W. Nelson, S. M. Berry, A. W. Isham, M. M. Crain, K. M. Walsh, R. S. Keynton, and R. W. Cohn, “Direct drawing of suspended filamentary micro- and nanostructures from liquid polymers,” Nano Lett. 4, 1931-1937 (2004).
[CrossRef]

Harris, J. H.

M. Heiblum and J. H. Harris, “Analysis of curved waveguides by conformal transformation,” IEEE J. Quantum Electron. 11, 75-83 (1975).
[CrossRef]

He, J. L.

He, S. L.

D. X. Dai, Y. C. Shi, and S. L. He, “Characteristic analysis of nanosilicon rectangular waveguides for planar light-wave circuits of high integration,” Appl. Opt. 45, 4941-4946 (2006).
[CrossRef] [PubMed]

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

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

Heiblum, M.

M. Heiblum and J. H. Harris, “Analysis of curved waveguides by conformal transformation,” IEEE J. Quantum Electron. 11, 75-83 (1975).
[CrossRef]

Hirono, T.

Ho, K. M.

Z. Ye, X. H. Hu, M. Li, K. M. Ho, and P. D. Yang, “Propagation of guided modes in curved nanoribbon waveguides,” Appl. Phys. Lett. 89, 241108 (2006).
[CrossRef]

Hu, L. L.

Hu, X. H.

Z. Ye, X. H. Hu, M. Li, K. M. Ho, and P. D. Yang, “Propagation of guided modes in curved nanoribbon waveguides,” Appl. Phys. Lett. 89, 241108 (2006).
[CrossRef]

Huang, K. J.

Huang, W. P.

Isham, A. W.

S. A. Harfenist, S. D. Cambron, E. W. Nelson, S. M. Berry, A. W. Isham, M. M. Crain, K. M. Walsh, R. S. Keynton, and R. W. Cohn, “Direct drawing of suspended filamentary micro- and nanostructures from liquid polymers,” Nano Lett. 4, 1931-1937 (2004).
[CrossRef]

Johnson, J. C.

M. Law, D. J. Sirbuly, J. C. Johnson, J. Goldberger, R. J. Saykally, and P. D. Yang, “Nanoribbon waveguides for subwavelength photonics integration,” Science 305, 1269-1273 (2004).
[CrossRef] [PubMed]

Kakihara, K.

Kawano, K.

K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis: Solving Maxwell's Equations and the Schrödinger Equation (Wiley, 2001).
[PubMed]

Keynton, R. S.

S. A. Harfenist, S. D. Cambron, E. W. Nelson, S. M. Berry, A. W. Isham, M. M. Crain, K. M. Walsh, R. S. Keynton, and R. W. Cohn, “Direct drawing of suspended filamentary micro- and nanostructures from liquid polymers,” Nano Lett. 4, 1931-1937 (2004).
[CrossRef]

Kien, F. L.

F. L. Kien, J. Q. Liang, K. Hakuta, and V. I. Balykin, “Field intensity distributions and polarization orientations in a vacuum-clad subwavelength-diameter optical fiber,” Opt. Commun. 242, 445-455 (2004).
[CrossRef]

Kitoh, T.

K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis: Solving Maxwell's Equations and the Schrödinger Equation (Wiley, 2001).
[PubMed]

Kono, N.

Koshiba, M.

Law, M.

M. Law, J. Goldberger, and P. D. Yang, “Semiconductor nanowires and nanotubes,” Annu. Rev. Mater. Res. 34, 83-122(2004).
[CrossRef]

M. Law, D. J. Sirbuly, J. C. Johnson, J. Goldberger, R. J. Saykally, and P. D. Yang, “Nanoribbon waveguides for subwavelength photonics integration,” Science 305, 1269-1273 (2004).
[CrossRef] [PubMed]

Li, B. J.

X. B. Xing, H. Zhu, Y. Q. Wang, and B. J. Li, “Ultracompact photonic coupling splitters twisted by PTT nanowires,” Nano Lett. 8, 2839-2843 (2008).
[CrossRef] [PubMed]

Li, M.

Z. Ye, X. H. Hu, M. Li, K. M. Ho, and P. D. Yang, “Propagation of guided modes in curved nanoribbon waveguides,” Appl. Phys. Lett. 89, 241108 (2006).
[CrossRef]

Li, Y. H.

Liang, J. Q.

F. L. Kien, J. Q. Liang, K. Hakuta, and V. I. Balykin, “Field intensity distributions and polarization orientations in a vacuum-clad subwavelength-diameter optical fiber,” Opt. Commun. 242, 445-455 (2004).
[CrossRef]

Lieber, C. M.

A. M. Morales and C. M. Lieber, “A laser ablation method for the synthesis of crystalline semiconductor nanowires,” Science 279, 208-211 (1998).
[CrossRef] [PubMed]

Liu, L.

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

Liu, W. W.

Lou, J. Y.

L. M. Tong, L. L. Hu, J. J. Zhang, J. R. Qiu, Q. Yang, J. Y. Lou, Y. H. Shen, J. L. He, and Z. Z. Ye, “Photonic nanowires directly drawn from bulk glasses,” Opt. Express 14, 82-87 (2006).
[CrossRef] [PubMed]

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

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

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

Ma, Z.

Marcuse, D.

D. Marcuse, “Bend loss of slab and fiber modes computed with diffraction theory,” IEEE J. Quantum Electron. 29, 2957-2961 (1993).
[CrossRef]

D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. 66, 216-220 (1976).
[CrossRef]

Martini, G.

L. Faustini and G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol. 15, 671-679 (1997).
[CrossRef]

Maxwell, I.

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

Mazur, E.

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

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

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

Morales, A. M.

A. M. Morales and C. M. Lieber, “A laser ablation method for the synthesis of crystalline semiconductor nanowires,” Science 279, 208-211 (1998).
[CrossRef] [PubMed]

Mu, W.

Nelson, E. W.

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[CrossRef]

F. X. Gu, L. Zhang, X. F. Yin, and L. M. Tong, “Polymer single-nanowire optical sensors,” Nano Lett. 8, 2757-2761 (2008).
[CrossRef] [PubMed]

X. B. Xing, H. Zhu, Y. Q. Wang, and B. J. Li, “Ultracompact photonic coupling splitters twisted by PTT nanowires,” Nano Lett. 8, 2839-2843 (2008).
[CrossRef] [PubMed]

L. M. Tong, J. Y. Lou, R. R. Gattass, S. L. He, X. W. Chen, L. Liu, and E. Mazur, “Assembly of silica nanowires on silica aerogels for microphotonics devices,” Nano Lett. 5, 259-262(2005).
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Nature (1)

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816-819 (2003).
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Figures (6)

Fig. 1
Fig. 1

Mathematical model for 3D-FDTD simulation of a circular 90 ° bent nanowire. Inset, topography profile of the bent nanowire.

Fig. 2
Fig. 2

Electric field intensity distributions in x z plane ( y = 0 ) of (a)  5 μm and (c) 1 μm bent wires. The wavelength of the quasi-x-polarized light is 633 nm and the diameter of the nanowires is 450 nm . The output mode profiles of (a) 5 μm and (c) 1 μm bent wires at the P1 transverse cross planes as are located at black dashed lines are shown in (b) and (d), respectively. The black solid lines map the topography profile of the nanowires.

Fig. 3
Fig. 3

Bending-radius-dependent bending losses of (a) a 350 nm diameter silica nanowire, (b) a 350 nm diameter PS nanowire, and (c) a 270 nm diameter ZnO nanowire with a 633 nm wavelength source.

Fig. 4
Fig. 4

Wavelength-dependent bending losses of a 2 μm bent (a)  450 nm diameter silica nanowire and (b)  250 nm diameter ZnO nanowire with quasi-x-polarized sources.

Fig. 5
Fig. 5

Diameter-dependent bending losses of a 2 μm bent (a) silica nanowire and (b) ZnO nanowire with a 633 nm wavelength quasi-x-polarized source.

Fig. 6
Fig. 6

Refractive-index-dependent bending losses of a 2 μm bent (a)  450 nm diameter nanowire and (b)  250 nm diameter nanowire with a 633 nm wavelength quasi-x-polarized source.

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