Abstract

Internal physical structure can drastically modify the properties of waveguides: photonic crystal fibers are able to confine light inside a hollow air core by Bragg scattering from a periodic array of holes, while metamaterial loaded waveguides for microwaves can support propagation at frequencies well below cutoff. Anisotropic metamaterials assembled into cylindrically symmetric geometries constitute light-guiding structures that support new kinds of exotic modes. A microtube of anodized nanoporous alumina, with nanopores radially emanating from the inner wall to the outer surface, is a manifestation of such an anisotropic metamaterial optical fiber. The nanopores, when filled with a plasmonic metal such as silver or gold, greatly increase the electromagnetic anisotropy. The modal solutions in such anisotropic circular waveguides can be uncommon Bessel functions with imaginary orders.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]

2015 (1)

J. G. Pollock and A. K. Iyer, ”Miniaturized circular-waveguide probe antennas using metamaterial liners,” IEEE Trans. Antennas Propagat.,  63, 428–433 (2015).
[Crossref]

2013 (2)

J.G. Pollock and A.K. Iyer, “Below-cutoff propagation in metamaterial-lined circular waveguides,” IEEE Trans. Microw. Theory Techn. 61, 3169–3178 (2013).
[Crossref]

S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Hollow-core uniaxial metamaterial clad fibers with dispersive metamaterials,” J. Opt. Soc. Am. B 30, 851–867 (2013).
[Crossref]

2012 (5)

N. Singh, A. Tuniz, R. Lwin, S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Fiber-drawn double split ring resonators in the terahertz range,” Opt. Mat. Express 2, 1254–1259 (2012).
[Crossref]

S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Hollow-core waveguides with uniaxial meta-material cladding: modal equations and guidance conditions,” J. Opt. Soc. Am. B 29, 2462–2477 (2012).
[Crossref]

C. J. Chapman, “The asymptotic theory of dispersion relations containing Bessel functions of imaginary order,” Proc. R. Soc. A 468, 4008–4023 (2012).
[Crossref]

B. Ghosh and A. B. Kakade, “Guided modes in a metamaterial-filled circular waveguide,” Electromagnetics A 32, 465480 (2012).

C.R. Simovsky, P.A. Belov, A.V. Atrashenko, and Yu. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mat. 24, 4229–4248 (2012).
[Crossref]

2011 (1)

2010 (2)

B. D. F. Casse, W. T. Lu, Y. J. Huang, E. Gultepe, L. Menon, and S. Sridhar, “Super-resolution imaging using a three-dimensional metamaterials nanolens”, Appl. Phys. Lett. 96, 023114 (2010)
[Crossref]

E. J. Smith, Z. Liu, Y. Mei, and O.G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10, 1–5 (2010).
[Crossref]

2009 (4)

M. Yan, N. A. Mortensen, and M. Qui, “Engineering modes in optical fibers with metamaterial,” Front. Optoelectron. China 2, 153–158 (2009).
[Crossref]

M. Yan and N. A. Mortensen, “Hollow-core infrared fiber incorporating metal-wire metamaterial,” Opt. Express 17, 14851–14864 (2009).
[Crossref] [PubMed]

S. Chakrabarti, S. A. Ramakrishna, and H. Wanare, “Switching a plasmalike metamaterial via embedded resonant atoms exhibiting electromagnetically induced transparency,” Opt. Letters 34, 3728–3730 (2009).
[Crossref]

W. J. Zheng, G. T. Fei, B. Wang, and L. D. Zhang, “Modulation of transmission spectra of anodized alumina membrane distributed Bragg reflector by controlling anodization temperature,” Nanoscale Res Lett 4, 665667 (2009).
[Crossref]

2008 (3)

A. Nicolet, F. Zolla, and Y. Ould Agha, “Geometrical transformations and equivalent materials in computational electromagnetism,” COMPEL 27, 806–819 (2008).
[Crossref]

M. Farhat, S. Guenneau, A.B. Movchan, and S. Enoch, “Achieving invisibility over a finite range of frequencies,” Opt. Express 14, 5658–5661 (2008).

R. H. J. Grimshaw, K. R. Khusnutdinova, and L. A. Ostrovsky, “The effect of a depth-dependent bubble distribution on the normal modes of internal waves: quasistatic approximation,” Eur. J. Mech. B/Fluids 27, 24–41 (2008).
[Crossref]

2007 (2)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-Limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

2006 (3)

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261101 (2006).
[Crossref]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
[Crossref] [PubMed]

A. V. Novitsky, “Negative-refractive-index fibres:TEM modes,” J. Opt. A: Pure Appl. Opt. 8, 864866 (2006).
[Crossref]

2005 (3)

H. Cory and T. Blum, “Surface-wave propagation along a metamaterial cylindrical guide,” Microwave Opt. Tech. Lett. 44, 3135 (2005).
[Crossref]

S. Hrabar, J. Bartolic, and Z. Sipus, “Waveguide miniaturization using uniaxial negative permeability metamaterial,” IEEE Trans. Antennas Propag. 53, 110–119 (2005).
[Crossref]

A. V. Novitsky and L. M. Barkovsky, “Guided modes in negative-refractive-index fibres,” J. Opt. A: Pure Appl. Opt. 7, S51S56 (2005).
[Crossref]

2003 (3)

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[Crossref] [PubMed]

J. B. Pendry, “Perfect cylindrical lenses,” Opt. Express 11, 755–760 (2003).
[Crossref] [PubMed]

J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys.: Condens. Matter 15, 63456364 (2003).

1996 (1)

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[Crossref]

1995 (1)

H. Masuda and K. Fukuda, “Ordered metal nanohole arrays made by a two-step replication of honeycomb structure of anodic alumina,” Science 268, 1466–1468 (1995).
[Crossref] [PubMed]

1990 (1)

T.M. Dunster, “Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter,” SIAM J. Math. Anal. 21, 995–1018 (1990).
[Crossref]

1945 (1)

R. C. Jones, “A generalization of the dielectric ellipsoid problem,” Phys. Rev. 68, 93–96 (1945).
[Crossref]

Alekseyev, L. V.

Argyros, A.

S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Hollow-core uniaxial metamaterial clad fibers with dispersive metamaterials,” J. Opt. Soc. Am. B 30, 851–867 (2013).
[Crossref]

S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Hollow-core waveguides with uniaxial meta-material cladding: modal equations and guidance conditions,” J. Opt. Soc. Am. B 29, 2462–2477 (2012).
[Crossref]

N. Singh, A. Tuniz, R. Lwin, S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Fiber-drawn double split ring resonators in the terahertz range,” Opt. Mat. Express 2, 1254–1259 (2012).
[Crossref]

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, D. Felbacq, A. Argyros, and S. Leon-Saval, Foundations of Photonic Crystal Fibres, (Imperial College Press, 2008).

Atakaramians, S.

Atrashenko, A.V.

C.R. Simovsky, P.A. Belov, A.V. Atrashenko, and Yu. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mat. 24, 4229–4248 (2012).
[Crossref]

Barkovsky, L. M.

A. V. Novitsky and L. M. Barkovsky, “Guided modes in negative-refractive-index fibres,” J. Opt. A: Pure Appl. Opt. 7, S51S56 (2005).
[Crossref]

Bartolic, J.

S. Hrabar, J. Bartolic, and Z. Sipus, “Waveguide miniaturization using uniaxial negative permeability metamaterial,” IEEE Trans. Antennas Propag. 53, 110–119 (2005).
[Crossref]

Belov, P.A.

C.R. Simovsky, P.A. Belov, A.V. Atrashenko, and Yu. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mat. 24, 4229–4248 (2012).
[Crossref]

Blum, T.

H. Cory and T. Blum, “Surface-wave propagation along a metamaterial cylindrical guide,” Microwave Opt. Tech. Lett. 44, 3135 (2005).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley, New York, USA, 1983).

Cai, W.

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).
[Crossref]

Casse, B. D. F.

B. D. F. Casse, W. T. Lu, Y. J. Huang, E. Gultepe, L. Menon, and S. Sridhar, “Super-resolution imaging using a three-dimensional metamaterials nanolens”, Appl. Phys. Lett. 96, 023114 (2010)
[Crossref]

Chakrabarti, S.

S. Chakrabarti, S. A. Ramakrishna, and H. Wanare, “Switching a plasmalike metamaterial via embedded resonant atoms exhibiting electromagnetically induced transparency,” Opt. Letters 34, 3728–3730 (2009).
[Crossref]

Chapman, C. J.

C. J. Chapman, “The asymptotic theory of dispersion relations containing Bessel functions of imaginary order,” Proc. R. Soc. A 468, 4008–4023 (2012).
[Crossref]

Chiang, C. L.

Cory, H.

H. Cory and T. Blum, “Surface-wave propagation along a metamaterial cylindrical guide,” Microwave Opt. Tech. Lett. 44, 3135 (2005).
[Crossref]

Dunster, T.M.

T.M. Dunster, “Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter,” SIAM J. Math. Anal. 21, 995–1018 (1990).
[Crossref]

Elser, J.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261101 (2006).
[Crossref]

Enoch, S.

M. Farhat, S. Guenneau, A.B. Movchan, and S. Enoch, “Achieving invisibility over a finite range of frequencies,” Opt. Express 14, 5658–5661 (2008).

Fan, C. F.

Farhat, M.

M. Farhat, S. Guenneau, A.B. Movchan, and S. Enoch, “Achieving invisibility over a finite range of frequencies,” Opt. Express 14, 5658–5661 (2008).

Fei, G. T.

W. J. Zheng, G. T. Fei, B. Wang, and L. D. Zhang, “Modulation of transmission spectra of anodized alumina membrane distributed Bragg reflector by controlling anodization temperature,” Nanoscale Res Lett 4, 665667 (2009).
[Crossref]

Felbacq, D.

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, D. Felbacq, A. Argyros, and S. Leon-Saval, Foundations of Photonic Crystal Fibres, (Imperial College Press, 2008).

Fleming, S. C.

Fukuda, K.

H. Masuda and K. Fukuda, “Ordered metal nanohole arrays made by a two-step replication of honeycomb structure of anodic alumina,” Science 268, 1466–1468 (1995).
[Crossref] [PubMed]

Ghosh, B.

B. Ghosh and A. B. Kakade, “Guided modes in a metamaterial-filled circular waveguide,” Electromagnetics A 32, 465480 (2012).

Grimshaw, R. H. J.

R. H. J. Grimshaw, K. R. Khusnutdinova, and L. A. Ostrovsky, “The effect of a depth-dependent bubble distribution on the normal modes of internal waves: quasistatic approximation,” Eur. J. Mech. B/Fluids 27, 24–41 (2008).
[Crossref]

Grzegorczyk, T.M.

S. A. Ramakrishna and T.M. Grzegorczyk, Physics and Applications of Negative Refractive Index Materials (CRC Press, 2009).

Guenneau, S.

M. Farhat, S. Guenneau, A.B. Movchan, and S. Enoch, “Achieving invisibility over a finite range of frequencies,” Opt. Express 14, 5658–5661 (2008).

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, D. Felbacq, A. Argyros, and S. Leon-Saval, Foundations of Photonic Crystal Fibres, (Imperial College Press, 2008).

Gultepe, E.

B. D. F. Casse, W. T. Lu, Y. J. Huang, E. Gultepe, L. Menon, and S. Sridhar, “Super-resolution imaging using a three-dimensional metamaterials nanolens”, Appl. Phys. Lett. 96, 023114 (2010)
[Crossref]

Hrabar, S.

S. Hrabar, J. Bartolic, and Z. Sipus, “Waveguide miniaturization using uniaxial negative permeability metamaterial,” IEEE Trans. Antennas Propag. 53, 110–119 (2005).
[Crossref]

Huang, Y. J.

B. D. F. Casse, W. T. Lu, Y. J. Huang, E. Gultepe, L. Menon, and S. Sridhar, “Super-resolution imaging using a three-dimensional metamaterials nanolens”, Appl. Phys. Lett. 96, 023114 (2010)
[Crossref]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley, New York, USA, 1983).

Iyer, A. K.

J. G. Pollock and A. K. Iyer, ”Miniaturized circular-waveguide probe antennas using metamaterial liners,” IEEE Trans. Antennas Propagat.,  63, 428–433 (2015).
[Crossref]

Iyer, A.K.

J.G. Pollock and A.K. Iyer, “Below-cutoff propagation in metamaterial-lined circular waveguides,” IEEE Trans. Microw. Theory Techn. 61, 3169–3178 (2013).
[Crossref]

Jacob, Z.

Jones, R. C.

R. C. Jones, “A generalization of the dielectric ellipsoid problem,” Phys. Rev. 68, 93–96 (1945).
[Crossref]

Kakade, A. B.

B. Ghosh and A. B. Kakade, “Guided modes in a metamaterial-filled circular waveguide,” Electromagnetics A 32, 465480 (2012).

Khusnutdinova, K. R.

R. H. J. Grimshaw, K. R. Khusnutdinova, and L. A. Ostrovsky, “The effect of a depth-dependent bubble distribution on the normal modes of internal waves: quasistatic approximation,” Eur. J. Mech. B/Fluids 27, 24–41 (2008).
[Crossref]

Kivshar, Yu. S.

C.R. Simovsky, P.A. Belov, A.V. Atrashenko, and Yu. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mat. 24, 4229–4248 (2012).
[Crossref]

Kuhlmey, B.

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, D. Felbacq, A. Argyros, and S. Leon-Saval, Foundations of Photonic Crystal Fibres, (Imperial College Press, 2008).

Kuhlmey, B. T.

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-Limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

Leon-Saval, S.

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, D. Felbacq, A. Argyros, and S. Leon-Saval, Foundations of Photonic Crystal Fibres, (Imperial College Press, 2008).

Liu, Z.

E. J. Smith, Z. Liu, Y. Mei, and O.G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10, 1–5 (2010).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-Limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

Lu, W. T.

B. D. F. Casse, W. T. Lu, Y. J. Huang, E. Gultepe, L. Menon, and S. Sridhar, “Super-resolution imaging using a three-dimensional metamaterials nanolens”, Appl. Phys. Lett. 96, 023114 (2010)
[Crossref]

Lwin, R.

N. Singh, A. Tuniz, R. Lwin, S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Fiber-drawn double split ring resonators in the terahertz range,” Opt. Mat. Express 2, 1254–1259 (2012).
[Crossref]

Masuda, H.

H. Masuda and K. Fukuda, “Ordered metal nanohole arrays made by a two-step replication of honeycomb structure of anodic alumina,” Science 268, 1466–1468 (1995).
[Crossref] [PubMed]

Mei, Y.

E. J. Smith, Z. Liu, Y. Mei, and O.G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10, 1–5 (2010).
[Crossref]

Menon, L.

B. D. F. Casse, W. T. Lu, Y. J. Huang, E. Gultepe, L. Menon, and S. Sridhar, “Super-resolution imaging using a three-dimensional metamaterials nanolens”, Appl. Phys. Lett. 96, 023114 (2010)
[Crossref]

Mortensen, N. A.

M. Yan, N. A. Mortensen, and M. Qui, “Engineering modes in optical fibers with metamaterial,” Front. Optoelectron. China 2, 153–158 (2009).
[Crossref]

M. Yan and N. A. Mortensen, “Hollow-core infrared fiber incorporating metal-wire metamaterial,” Opt. Express 17, 14851–14864 (2009).
[Crossref] [PubMed]

Movchan, A.B.

M. Farhat, S. Guenneau, A.B. Movchan, and S. Enoch, “Achieving invisibility over a finite range of frequencies,” Opt. Express 14, 5658–5661 (2008).

Narimanov, E.

Narimanov, E. E.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261101 (2006).
[Crossref]

Nicolet, A.

A. Nicolet, F. Zolla, and Y. Ould Agha, “Geometrical transformations and equivalent materials in computational electromagnetism,” COMPEL 27, 806–819 (2008).
[Crossref]

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, D. Felbacq, A. Argyros, and S. Leon-Saval, Foundations of Photonic Crystal Fibres, (Imperial College Press, 2008).

Novitsky, A. V.

A. V. Novitsky, “Negative-refractive-index fibres:TEM modes,” J. Opt. A: Pure Appl. Opt. 8, 864866 (2006).
[Crossref]

A. V. Novitsky and L. M. Barkovsky, “Guided modes in negative-refractive-index fibres,” J. Opt. A: Pure Appl. Opt. 7, S51S56 (2005).
[Crossref]

Ostrovsky, L. A.

R. H. J. Grimshaw, K. R. Khusnutdinova, and L. A. Ostrovsky, “The effect of a depth-dependent bubble distribution on the normal modes of internal waves: quasistatic approximation,” Eur. J. Mech. B/Fluids 27, 24–41 (2008).
[Crossref]

Ould Agha, Y.

A. Nicolet, F. Zolla, and Y. Ould Agha, “Geometrical transformations and equivalent materials in computational electromagnetism,” COMPEL 27, 806–819 (2008).
[Crossref]

Pendry, J. B.

J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys.: Condens. Matter 15, 63456364 (2003).

J. B. Pendry, “Perfect cylindrical lenses,” Opt. Express 11, 755–760 (2003).
[Crossref] [PubMed]

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[Crossref]

Podolskiy, V. A.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261101 (2006).
[Crossref]

Pollock, J. G.

J. G. Pollock and A. K. Iyer, ”Miniaturized circular-waveguide probe antennas using metamaterial liners,” IEEE Trans. Antennas Propagat.,  63, 428–433 (2015).
[Crossref]

Pollock, J.G.

J.G. Pollock and A.K. Iyer, “Below-cutoff propagation in metamaterial-lined circular waveguides,” IEEE Trans. Microw. Theory Techn. 61, 3169–3178 (2013).
[Crossref]

Qui, M.

M. Yan, N. A. Mortensen, and M. Qui, “Engineering modes in optical fibers with metamaterial,” Front. Optoelectron. China 2, 153–158 (2009).
[Crossref]

Ramakrishna, S. A.

S. Chakrabarti, S. A. Ramakrishna, and H. Wanare, “Switching a plasmalike metamaterial via embedded resonant atoms exhibiting electromagnetically induced transparency,” Opt. Letters 34, 3728–3730 (2009).
[Crossref]

J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys.: Condens. Matter 15, 63456364 (2003).

S. A. Ramakrishna and T.M. Grzegorczyk, Physics and Applications of Negative Refractive Index Materials (CRC Press, 2009).

Renversez, G.

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, D. Felbacq, A. Argyros, and S. Leon-Saval, Foundations of Photonic Crystal Fibres, (Imperial College Press, 2008).

Russell, P.

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[Crossref] [PubMed]

Schmidt, O.G.

E. J. Smith, Z. Liu, Y. Mei, and O.G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10, 1–5 (2010).
[Crossref]

Shalaev, V.

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).
[Crossref]

Simovsky, C.R.

C.R. Simovsky, P.A. Belov, A.V. Atrashenko, and Yu. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mat. 24, 4229–4248 (2012).
[Crossref]

Singh, N.

N. Singh, A. Tuniz, R. Lwin, S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Fiber-drawn double split ring resonators in the terahertz range,” Opt. Mat. Express 2, 1254–1259 (2012).
[Crossref]

Sipus, Z.

S. Hrabar, J. Bartolic, and Z. Sipus, “Waveguide miniaturization using uniaxial negative permeability metamaterial,” IEEE Trans. Antennas Propag. 53, 110–119 (2005).
[Crossref]

Smith, E. J.

E. J. Smith, Z. Liu, Y. Mei, and O.G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10, 1–5 (2010).
[Crossref]

Sridhar, S.

B. D. F. Casse, W. T. Lu, Y. J. Huang, E. Gultepe, L. Menon, and S. Sridhar, “Super-resolution imaging using a three-dimensional metamaterials nanolens”, Appl. Phys. Lett. 96, 023114 (2010)
[Crossref]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-Limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

Tuniz, A.

N. Singh, A. Tuniz, R. Lwin, S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Fiber-drawn double split ring resonators in the terahertz range,” Opt. Mat. Express 2, 1254–1259 (2012).
[Crossref]

Wanare, H.

S. Chakrabarti, S. A. Ramakrishna, and H. Wanare, “Switching a plasmalike metamaterial via embedded resonant atoms exhibiting electromagnetically induced transparency,” Opt. Letters 34, 3728–3730 (2009).
[Crossref]

Wang, B.

W. J. Zheng, G. T. Fei, B. Wang, and L. D. Zhang, “Modulation of transmission spectra of anodized alumina membrane distributed Bragg reflector by controlling anodization temperature,” Nanoscale Res Lett 4, 665667 (2009).
[Crossref]

Wangberg, R.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261101 (2006).
[Crossref]

Ward, A. J.

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[Crossref]

Weber, M. J.

M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-Limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

Yan, M.

M. Yan, N. A. Mortensen, and M. Qui, “Engineering modes in optical fibers with metamaterial,” Front. Optoelectron. China 2, 153–158 (2009).
[Crossref]

M. Yan and N. A. Mortensen, “Hollow-core infrared fiber incorporating metal-wire metamaterial,” Opt. Express 17, 14851–14864 (2009).
[Crossref] [PubMed]

Yu, C. P.

Zhang, L. D.

W. J. Zheng, G. T. Fei, B. Wang, and L. D. Zhang, “Modulation of transmission spectra of anodized alumina membrane distributed Bragg reflector by controlling anodization temperature,” Nanoscale Res Lett 4, 665667 (2009).
[Crossref]

Zhang, X.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-Limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

Zheng, W. J.

W. J. Zheng, G. T. Fei, B. Wang, and L. D. Zhang, “Modulation of transmission spectra of anodized alumina membrane distributed Bragg reflector by controlling anodization temperature,” Nanoscale Res Lett 4, 665667 (2009).
[Crossref]

Zolla, F.

A. Nicolet, F. Zolla, and Y. Ould Agha, “Geometrical transformations and equivalent materials in computational electromagnetism,” COMPEL 27, 806–819 (2008).
[Crossref]

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, D. Felbacq, A. Argyros, and S. Leon-Saval, Foundations of Photonic Crystal Fibres, (Imperial College Press, 2008).

Adv. Mat. (1)

C.R. Simovsky, P.A. Belov, A.V. Atrashenko, and Yu. S. Kivshar, “Wire metamaterials: physics and applications,” Adv. Mat. 24, 4229–4248 (2012).
[Crossref]

Appl. Phys. Lett. (2)

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261101 (2006).
[Crossref]

B. D. F. Casse, W. T. Lu, Y. J. Huang, E. Gultepe, L. Menon, and S. Sridhar, “Super-resolution imaging using a three-dimensional metamaterials nanolens”, Appl. Phys. Lett. 96, 023114 (2010)
[Crossref]

COMPEL (1)

A. Nicolet, F. Zolla, and Y. Ould Agha, “Geometrical transformations and equivalent materials in computational electromagnetism,” COMPEL 27, 806–819 (2008).
[Crossref]

Electromagnetics A (1)

B. Ghosh and A. B. Kakade, “Guided modes in a metamaterial-filled circular waveguide,” Electromagnetics A 32, 465480 (2012).

Eur. J. Mech. B/Fluids (1)

R. H. J. Grimshaw, K. R. Khusnutdinova, and L. A. Ostrovsky, “The effect of a depth-dependent bubble distribution on the normal modes of internal waves: quasistatic approximation,” Eur. J. Mech. B/Fluids 27, 24–41 (2008).
[Crossref]

Front. Optoelectron. China (1)

M. Yan, N. A. Mortensen, and M. Qui, “Engineering modes in optical fibers with metamaterial,” Front. Optoelectron. China 2, 153–158 (2009).
[Crossref]

IEEE Trans. Antennas Propag. (1)

S. Hrabar, J. Bartolic, and Z. Sipus, “Waveguide miniaturization using uniaxial negative permeability metamaterial,” IEEE Trans. Antennas Propag. 53, 110–119 (2005).
[Crossref]

IEEE Trans. Antennas Propagat. (1)

J. G. Pollock and A. K. Iyer, ”Miniaturized circular-waveguide probe antennas using metamaterial liners,” IEEE Trans. Antennas Propagat.,  63, 428–433 (2015).
[Crossref]

IEEE Trans. Microw. Theory Techn. (1)

J.G. Pollock and A.K. Iyer, “Below-cutoff propagation in metamaterial-lined circular waveguides,” IEEE Trans. Microw. Theory Techn. 61, 3169–3178 (2013).
[Crossref]

J. Mod. Opt. (1)

A. J. Ward and J. B. Pendry, “Refraction and geometry in Maxwell’s equations,” J. Mod. Opt. 43, 773–793 (1996).
[Crossref]

J. Opt. A: Pure Appl. Opt. (2)

A. V. Novitsky and L. M. Barkovsky, “Guided modes in negative-refractive-index fibres,” J. Opt. A: Pure Appl. Opt. 7, S51S56 (2005).
[Crossref]

A. V. Novitsky, “Negative-refractive-index fibres:TEM modes,” J. Opt. A: Pure Appl. Opt. 8, 864866 (2006).
[Crossref]

J. Opt. Soc. Am. B (2)

J. Phys.: Condens. Matter (1)

J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys.: Condens. Matter 15, 63456364 (2003).

Microwave Opt. Tech. Lett. (1)

H. Cory and T. Blum, “Surface-wave propagation along a metamaterial cylindrical guide,” Microwave Opt. Tech. Lett. 44, 3135 (2005).
[Crossref]

Nano Lett. (1)

E. J. Smith, Z. Liu, Y. Mei, and O.G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10, 1–5 (2010).
[Crossref]

Nanoscale Res Lett (1)

W. J. Zheng, G. T. Fei, B. Wang, and L. D. Zhang, “Modulation of transmission spectra of anodized alumina membrane distributed Bragg reflector by controlling anodization temperature,” Nanoscale Res Lett 4, 665667 (2009).
[Crossref]

Opt. Express (5)

Opt. Letters (1)

S. Chakrabarti, S. A. Ramakrishna, and H. Wanare, “Switching a plasmalike metamaterial via embedded resonant atoms exhibiting electromagnetically induced transparency,” Opt. Letters 34, 3728–3730 (2009).
[Crossref]

Opt. Mat. Express (1)

N. Singh, A. Tuniz, R. Lwin, S. Atakaramians, A. Argyros, S. C. Fleming, and B. T. Kuhlmey, “Fiber-drawn double split ring resonators in the terahertz range,” Opt. Mat. Express 2, 1254–1259 (2012).
[Crossref]

Phys. Rev. (1)

R. C. Jones, “A generalization of the dielectric ellipsoid problem,” Phys. Rev. 68, 93–96 (1945).
[Crossref]

Proc. R. Soc. A (1)

C. J. Chapman, “The asymptotic theory of dispersion relations containing Bessel functions of imaginary order,” Proc. R. Soc. A 468, 4008–4023 (2012).
[Crossref]

Science (4)

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-Limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

H. Masuda and K. Fukuda, “Ordered metal nanohole arrays made by a two-step replication of honeycomb structure of anodic alumina,” Science 268, 1466–1468 (1995).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

SIAM J. Math. Anal. (1)

T.M. Dunster, “Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter,” SIAM J. Math. Anal. 21, 995–1018 (1990).
[Crossref]

Other (5)

S. A. Ramakrishna and T.M. Grzegorczyk, Physics and Applications of Negative Refractive Index Materials (CRC Press, 2009).

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).
[Crossref]

M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley, New York, USA, 1983).

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau, D. Felbacq, A. Argyros, and S. Leon-Saval, Foundations of Photonic Crystal Fibres, (Imperial College Press, 2008).

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Figures (5)

Fig. 1
Fig. 1 Left: A schematic of the anisotropic optical fiber with PEC core and outer boundary. Right: panels show the computed electric fields (Ez) of modes for R1 = 0.5 μm, R2 = 12.5 μm with m = 5 (left column), m = 20 (middle column) and m = 40 (right column). Top row shows the Bessel modes in an isotropic alumina fiber with real integral orders for εr = εϕ = εz = 3.118. The middle row shows Bessel modes in an anisotropic nanoporous alumina fiber with fractional order and positive dielectric permittivity components for εr = 2.467 and εϕ = εz = 2.638. The bottom row shows the fields for Bessel modes of anisotropic nanoporous alumina fiber with imaginary orders and εr = 2.638 and εϕ = εz = 2.467. Relative permittivity components are at wavelength 633 nm.
Fig. 2
Fig. 2 The behavior of low-order modes (TM1,1 and TM2,2) in a anisotropic nanoporous alumina fiber for dimensions R1 = 0.5 μm and R2 = 12.5 μm. Col. 1: Eigen modes at β = 0, ν = m integral order, Col. 2: modes at εr = 2.467, εϕ = εz = 2.638, and β ≠ 0, νm fractional order, Col. 3: modes at εr = 2.638, εϕ = εz = 2.467, and β ≠ 0, νm imaginary order. Dielectric constants are at wavelength 633 nm.
Fig. 3
Fig. 3 Scanning electron micrographs of the nanoporous alumina microtube. Note the presence of the radially oriented non-branching nanopores. The nanoporous outer surface and the impermeable barrier oxide layer at the inner tubular surface are shown in the insets. The brittle alumina microtube cracks when cleaved for SEM imaging.
Fig. 4
Fig. 4 A cylindrical shell is mapped to a flat slab. The nanopores along the radial direction in shell mapped along the -direction in the new frame.
Fig. 5
Fig. 5 Top: Picture of light (λ = 532 nm) propagating across a bent nanoporous alumina fiber with an aluminum core (Aluminium core diameter- 10 μm, nanoporous alumina shell diameter- 80 μm, length- 1.3 cm, nanopore diameter is 30 nm and nanopore periodicity is 100 nm at outer surface). The output from the fiber at λ = 633 nm is shown on the right. Plot of the variation of effective dielectric permittivity components in the Maxwell-Garnet approximation with the radial distance in a nanoporous alumina microtube for air inclusion (Bottom-left) and when the nanopores are filled with silver for nanopore radius q = 25 nm at outer surface and f = 0.23(bottom-right).

Tables (2)

Tables Icon

Table 1 Table showing the conditions on the material parameters and the propagation constant to obtain imaginary orders (ν) for the Bessel functions that describe the modes for the TE and TM polarizations in the anisotropic fiber. Note that k 0 2 = ω 2 / c 2.

Tables Icon

Table 2 Table showing the cutoff frequencies calculated for an anisotropic (coaxial) fiber of outer diameter 25 μm and inner diameter of 1 μm and the waveguide is homogeneously filled with a material of dielectric permittivity of εr = 2.638 and εϕ = εz = 2.467.

Equations (18)

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

ε ̿ = ε 0 ( ε r 0 0 0 ε φ 0 0 0 ε z ) .
H z = [ A J ν ( k r r ) + B Y ν ( k r r ) ] exp [ i ( m φ + β z ) ] ,
k r 2 = ε φ ω 2 c 2 β 2 , and ν 2 = ( ε φ ω 2 / c 2 β 2 ) ( ε r ω 2 / c 2 β 2 ) m 2 .
J ν ( k r R 1 ) Y ν ( k r R 2 ) J ν ( k r R 2 ) Y ν ( k r R 1 ) = 0 ,
E z = [ A J ν ( k r r ) + B Y ν ( k r r ) ] exp [ i ( m φ + β z ) ] ,
k r 2 = ε z ε r ( ε r ω 2 / c 2 β 2 ) , and ν 2 = ε φ ε r ( ε r ω 2 / c 2 β 2 ε φ ω 2 / c 2 β 2 ) m 2 .
J ν ( k r R 1 ) Y ν ( k r R 2 ) J ν ( k r R 2 ) Y ν ( k r R 1 ) = 0 ,
k r 2 ε φ + m 2 r 2 ε r = ω 2 c 2 .
x ˜ = ln r , y ˜ = φ , z ˜ = z ,
ε ˜ j = ε j S 1 S 2 S 3 S j , μ ˜ j = μ j S 1 S 2 S 3 S j , E ˜ j = S j E j , H ˜ j = S j H j ,
S j 2 = ( r q ˜ j ) 2 + ( r φ q ˜ j ) 2 + ( z q ˜ j ) 2 ,
ε x ˜ , s ˜ = ε r , s , ε y ˜ , s ˜ = ε φ , s , ε z ˜ , s ˜ = e 2 x ˜ ε z , s ; μ x ˜ , s ˜ = μ r , s , μ y ˜ , s ˜ = μ φ , s , μ z ˜ , s ˜ = e 2 x ˜ μ z , s ,
ε x ˜ eff = f ε r , i + ( 1 f ) ε r , h ,
ε y ˜ eff = ( 1 + f ) ε φ , i ε φ , h + ( 1 f ) ε φ , h 2 ( 1 f ) ε φ , i + ( 1 + f ) ε φ , h ,
ε z ˜ eff = e 2 x ˜ ( 1 + f ) ε z , i ε z , h + ( 1 f ) ε z , h 2 ( 1 f ) ε z , i + ( 1 + f ) ε z , h .
ε r eff = f ε r , i + ( 1 f ) ε r , h ,
ε φ eff = ( 1 + f ) ε φ , i ε φ , h + ( 1 f ) ε φ , h 2 ( 1 f ) ε φ , i + ( 1 + f ) ε φ , h ,
ε z eff = ( 1 + f ) ε z , i ε z , h + ( 1 f ) ε z , h 2 ( 1 f ) ε z , i + ( 1 + f ) ε z , h .

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