Abstract

Based on exact solutions of Maxwell’s equations of a 3-layer-structured cylindrical waveguide, we calculated dispersion shifts in thin-dielectric-coated optical nanowires. Typical parameters of silica and silicon nanowires are used for numerical simulations. It shows that, the dispersion of a nanowire waveguide can be made highly sensitive to the thickness and index of the coating layer, and a thin coat may lead to considerable dispersion shift of the guided light. For example, in a 300-nm-diameter silicon nanowire, a 1% decrease in diameter of the silicon core by oxidation of silicon into silica shell leads to a 34% decrease in dispersion at 1450-nm wavelength. Results presented in this work suggest the possibility of tuning waveguide dispersions of optical nanowires by coating thin dielectric layers.

© 2006 Optical Society of America

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2005 (8)

2004 (10)

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]

G. Brambilla, V. Finazzi, and D. J. Richardson, "Ultra-low-loss optical fiber nanotapers," Opt. Express 12, 2258-2263 (2004).
[CrossRef] [PubMed]

S. G. Leon-Saval, T. A. Birks, W. J. Wadsworth, P. St. J. Russell, and M. W. Mason, "Supercontinuum generation in submicron fibre waveguides," Opt. Express 12, 2864-2869 (2004).
[CrossRef] [PubMed]

M. A. Foster, K. D. Moll, and A. L. Gaeta, "Optimal waveguide dimensions for nonlinear interactions," Opt. Express 12, 2880-2887 (2004).
[CrossRef] [PubMed]

Y. K. Lize, E. C. Magi, V. G. Ta'eed, J. A. Bolger, P. Steinvurzel, and B. J. Eggleton, "Microstructured optical fiber photonic wires with subwavelength core diameter," Opt. Express 12, 3209-3217 (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]

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

V. I. Balykin, K. Hakuta, F. Le Kien, J. Q. Liang, and M. Morinaga, "Atom trapping and guiding with a subwavelength-diameter optical fiber," Phys. Rev. A 70, 011401 (2004).
[CrossRef]

F. Le Kien, V. I. Balykin, and K. Hakuta, "Atom trap and waveguide using a two-color evanescent light field around a subwavelength-diameter optical fiber," Phys. Rev. A 70, 063403 (2004).
[CrossRef]

C. J. Barrelet, A. B. Greytak, and C. M. Lieber, "Nanowire photonic circuit elements," Nano Lett. 4, 1981-1985 (2004).
[CrossRef]

2003 (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).
[CrossRef] [PubMed]

2001 (1)

U. Schroter and A. Dereux, "Surface plasmon polaritons on metal cylinders with dielectric core," Phys. Rev. B 64, 125420 (2001).
[CrossRef]

2000 (1)

1999 (1)

1998 (2)

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]

J. L. Liu, Y. Lu, Y. Shi, S. L. Gu, R. L. Jiang, F. Wang, H. M. Bu, and Y. D. Zheng, "Study on thermal oxidation of Si nanowires," Phys. Stat. Sol. A 168, 441-446 (1998).
[CrossRef]

Ahuja, A.

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]

Balykin, V. I.

V. I. Balykin, K. Hakuta, F. Le Kien, J. Q. Liang, and M. Morinaga, "Atom trapping and guiding with a subwavelength-diameter optical fiber," Phys. Rev. A 70, 011401 (2004).
[CrossRef]

F. Le Kien, V. I. Balykin, and K. Hakuta, "Atom trap and waveguide using a two-color evanescent light field around a subwavelength-diameter optical fiber," Phys. Rev. A 70, 063403 (2004).
[CrossRef]

Barrelet, C. J.

C. J. Barrelet, A. B. Greytak, and C. M. Lieber, "Nanowire photonic circuit elements," Nano Lett. 4, 1981-1985 (2004).
[CrossRef]

Birks, T. A.

Bolger, J. A.

Brambilla, G.

G. Brambilla, E. Koizumi, X. Feng, and D. J. Richardson, "Compound-glass optical nanowires," Electron. Lett. 41, 400-402 (2005).
[CrossRef]

G. Brambilla, V. Finazzi, and D. J. Richardson, "Ultra-low-loss optical fiber nanotapers," Opt. Express 12, 2258-2263 (2004).
[CrossRef] [PubMed]

Bu, H. M.

J. L. Liu, Y. Lu, Y. Shi, S. L. Gu, R. L. Jiang, F. Wang, H. M. Bu, and Y. D. Zheng, "Study on thermal oxidation of Si nanowires," Phys. Stat. Sol. A 168, 441-446 (1998).
[CrossRef]

Bures, J.

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 microphotonic devices," Nano Lett. 5, 259-262 (2005).
[CrossRef] [PubMed]

Dereux, A.

U. Schroter and A. Dereux, "Surface plasmon polaritons on metal cylinders with dielectric core," Phys. Rev. B 64, 125420 (2001).
[CrossRef]

Dulashko, Y.

Eggleton, B. J.

Feng, X.

G. Brambilla, E. Koizumi, X. Feng, and D. J. Richardson, "Compound-glass optical nanowires," Electron. Lett. 41, 400-402 (2005).
[CrossRef]

Finazzi, V.

Fini, J. M.

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

Foster, M. A.

Gaeta, A. L.

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 microphotonic 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]

Ghosh, R.

Goldberger, J.

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

Greytak, A. B.

C. J. Barrelet, A. B. Greytak, and C. M. Lieber, "Nanowire photonic circuit elements," Nano Lett. 4, 1981-1985 (2004).
[CrossRef]

Gu, S. L.

J. L. Liu, Y. Lu, Y. Shi, S. L. Gu, R. L. Jiang, F. Wang, H. M. Bu, and Y. D. Zheng, "Study on thermal oxidation of Si nanowires," Phys. Stat. Sol. A 168, 441-446 (1998).
[CrossRef]

Hakuta, K.

F. Le Kien, V. I. Balykin, and K. Hakuta, "Atom trap and waveguide using a two-color evanescent light field around a subwavelength-diameter optical fiber," Phys. Rev. A 70, 063403 (2004).
[CrossRef]

V. I. Balykin, K. Hakuta, F. Le Kien, J. Q. Liang, and M. Morinaga, "Atom trapping and guiding with a subwavelength-diameter optical fiber," Phys. Rev. A 70, 011401 (2004).
[CrossRef]

Hale, A.

He, S. 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 microphotonic 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]

Jiang, R. L.

J. L. Liu, Y. Lu, Y. Shi, S. L. Gu, R. L. Jiang, F. Wang, H. M. Bu, and Y. D. Zheng, "Study on thermal oxidation of Si nanowires," Phys. Stat. Sol. A 168, 441-446 (1998).
[CrossRef]

Johnson, J. C.

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

Koizumi, E.

G. Brambilla, E. Koizumi, X. Feng, and D. J. Richardson, "Compound-glass optical nanowires," Electron. Lett. 41, 400-402 (2005).
[CrossRef]

Kuo, P.

Kutz, J. N.

Law, M.

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

Le Kien, F.

F. Le Kien, V. I. Balykin, and K. Hakuta, "Atom trap and waveguide using a two-color evanescent light field around a subwavelength-diameter optical fiber," Phys. Rev. A 70, 063403 (2004).
[CrossRef]

V. I. Balykin, K. Hakuta, F. Le Kien, J. Q. Liang, and M. Morinaga, "Atom trapping and guiding with a subwavelength-diameter optical fiber," Phys. Rev. A 70, 011401 (2004).
[CrossRef]

Leon-Saval, S. G.

Liang, J. Q.

V. I. Balykin, K. Hakuta, F. Le Kien, J. Q. Liang, and M. Morinaga, "Atom trapping and guiding with a subwavelength-diameter optical fiber," Phys. Rev. A 70, 011401 (2004).
[CrossRef]

Lieber, C. M.

C. J. Barrelet, A. B. Greytak, and C. M. Lieber, "Nanowire photonic circuit elements," Nano Lett. 4, 1981-1985 (2004).
[CrossRef]

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, J. L.

J. L. Liu, Y. Lu, Y. Shi, S. L. Gu, R. L. Jiang, F. Wang, H. M. Bu, and Y. D. Zheng, "Study on thermal oxidation of Si nanowires," Phys. Stat. Sol. A 168, 441-446 (1998).
[CrossRef]

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 microphotonic devices," Nano Lett. 5, 259-262 (2005).
[CrossRef] [PubMed]

Lize, Y. K.

Lou, J. Y.

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 microphotonic devices," Nano Lett. 5, 259-262 (2005).
[CrossRef] [PubMed]

J. Y. Lou, L. M. Tong, Z. Z. Ye, "Modeling of silica nanowires for optical sensing," Opt. Express 13, 2135-2140 (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]

Lu, Y.

J. L. Liu, Y. Lu, Y. Shi, S. L. Gu, R. L. Jiang, F. Wang, H. M. Bu, and Y. D. Zheng, "Study on thermal oxidation of Si nanowires," Phys. Stat. Sol. A 168, 441-446 (1998).
[CrossRef]

Lyngå, C.

Magi, E. C.

Mansuripur, M.

Mason, M. W.

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 microphotonic 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]

Mikkelsen, B.

Moll, K. D.

Monzón-Hernández, D.

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]

Morinaga, M.

V. I. Balykin, K. Hakuta, F. Le Kien, J. Q. Liang, and M. Morinaga, "Atom trapping and guiding with a subwavelength-diameter optical fiber," Phys. Rev. A 70, 011401 (2004).
[CrossRef]

Nielsen, T. N.

Peyghambarian, N.

Polynkin, A.

Polynkin, P.

Richardson, D. J.

G. Brambilla, E. Koizumi, X. Feng, and D. J. Richardson, "Compound-glass optical nanowires," Electron. Lett. 41, 400-402 (2005).
[CrossRef]

G. Brambilla, V. Finazzi, and D. J. Richardson, "Ultra-low-loss optical fiber nanotapers," Opt. Express 12, 2258-2263 (2004).
[CrossRef] [PubMed]

Rogers, J. A.

Russell, P. St. J.

Saykally, R. J.

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

Schroter, U.

U. Schroter and A. Dereux, "Surface plasmon polaritons on metal cylinders with dielectric core," Phys. Rev. B 64, 125420 (2001).
[CrossRef]

Shen, M. Y.

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]

Shi, Y.

J. L. Liu, Y. Lu, Y. Shi, S. L. Gu, R. L. Jiang, F. Wang, H. M. Bu, and Y. D. Zheng, "Study on thermal oxidation of Si nanowires," Phys. Stat. Sol. A 168, 441-446 (1998).
[CrossRef]

Sirbuly, D. J.

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

Steinvurzel, P.

Sumetsky, M.

Ta'eed, V. G.

Tong, L. M.

J. Y. Lou, L. M. Tong, Z. Z. Ye, "Modeling of silica nanowires for optical sensing," Opt. Express 13, 2135-2140 (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 microphotonic 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]

Villatoro, J.

Wadsworth, W. J.

Wang, F.

J. L. Liu, Y. Lu, Y. Shi, S. L. Gu, R. L. Jiang, F. Wang, H. M. Bu, and Y. D. Zheng, "Study on thermal oxidation of Si nanowires," Phys. Stat. Sol. A 168, 441-446 (1998).
[CrossRef]

Westbrook, P. S.

Yang, P.

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

Ye, Z. Z.

Zheltikov, A.

Zheng, Y. D.

J. L. Liu, Y. Lu, Y. Shi, S. L. Gu, R. L. Jiang, F. Wang, H. M. Bu, and Y. D. Zheng, "Study on thermal oxidation of Si nanowires," Phys. Stat. Sol. A 168, 441-446 (1998).
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Figures (4)

Fig. 1.
Fig. 1.

Mathematic model of an optical nanowire with a cylinder coat. (a) Cross-section view and (b) refractive index profile of the nanowire.

Fig. 2.
Fig. 2.

Modified dispersion of 400-nm-diameter silica wire with different coatings (dc =5nm). Dashed line: dispersion of 400-nm-diameter silica wire without coat.

Fig. 3.
Fig. 3.

(a) Modified dispersion of a 400-nm-diameter silica wire with different coating thickness. (b) Coat-thickness-dependent dispersion of a 400-nm-diameter silica wire at the wavelength of 633 nm. Refractive indices of the coats are assumed to be 2.7 and 1.45, respectively.

Fig. 4.
Fig. 4.

(a) Modified dispersion of 300-nm-diameter silicon wire with thickness reduction in silicon core by oxidization. (b) Thickness-reduction-dependent dispersion of a 300-nm-diameter silicon nanowire at the wavelength of 1450 nm.

Equations (9)

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

E r = ( i β k j Z m j ( k j r ) a m j m ω k j 2 r Z m j ( k j r ) b m j ) F m , H r = ( m n j 2 k 0 2 ω k j 2 r Z m j ( k j r ) a m j + i β k j Z m j ( k j r ) b m j ) F m ,
E θ = ( m β k j 2 r Z m j ( k j r ) a m j i ω k j Z m j ( k j r ) b m j ) F m , H θ = ( i n j 2 k 0 2 ω k j Z m j ( k j r ) a m j m β k j 2 r Z m j ( k j r ) b m j ) F m ,
E z = Z m j ( k j r ) a m j F m , H z = Z m j ( k j r ) b m j F m ,
F m = exp ( i m θ + i β z i ω t ) ,
k j 2 = n j 2 k 0 2 β 2 .
det [ M ( β ) ] = 0 ,
v g = d ω d β = 2 π c λ 2 d λ d β
D w = d ( v g 1 ) d λ
d c = d S i ρ S i M SiO 2 ρ SiO 2 M S i

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