Abstract

We analyze the dependence of the electromagnetic properties of wire array metamaterial media on the choice of metal, and identify promising material combinations for use in the near and mid infrared. We propose a figure of merit for the metal optical quality and consider it as a function of several parameters, such as material loss, wavelength of operation and wire diameter. Accordingly, we select promising material combinations, based on optical quality and fabrication compatibility, and simulate the loss of the quasi-TEM mode, for different wavelengths between 1 and 10 μm. We conclude that wire arrays are unlikely to deliver on their many promises at 1 μm, but should prove useful beyond 3 μm.

© 2015 Optical Society of America

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2015 (2)

I. Ktorza, L. Ceresoli, S. Enoch, S. Guenneau, and R. Abdeddaim, “Single frequency microwave cloaking and subwavelength imaging with curved wired media,” Opt. Express 23(8), 10319–10326 (2015).
[Crossref] [PubMed]

J. S. Brownless, B. C. P. Sturmberg, A. Argyros, B. T. Kuhlmey, and C. M. de Sterke, “Guided modes of a wire medium slab: comparison of effective medium approaches with exact calculations,” Phys. Rev. B 91(15), 155427 (2015).
[Crossref]

2013 (5)

S. Laref, J. Cao, A. Asaduzzaman, K. Runge, P. Deymier, R. W. Ziolkowski, M. Miyawaki, and K. Muralidharan, “Size-dependent permittivity and intrinsic optical anisotropy of nanometric gold thin films: a density functional theory study,” Opt. Express 21(10), 11827–11838 (2013).
[Crossref] [PubMed]

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

O. T. Naman, M. R. New-Tolley, R. Lwin, A. Tuniz, A. H. Al-Janabi, I. Karatchevtseva, S. C. Fleming, B. T. Kuhlmey, and A. Argyros, “Indefinite media based on wire array metamaterials for THz and Mid-IR,” Adv. Opt. Mater. 1(12), 971–977 (2013).
[Crossref]

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Purcell effect in wire metamaterials,” Phys. Rev. B 87(3), 035136 (2013).
[Crossref]

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

2012 (3)

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat. Commun. 3, 1205 (2012).
[Crossref] [PubMed]

Y. Wang, Y. Ma, X. Guo, and L. Tong, “Single-mode plasmonic waveguiding properties of metal nanowires with dielectric substrates,” Opt. Express 20(17), 19006–19015 (2012).
[Crossref] [PubMed]

2011 (3)

M. Hövel, B. Gompf, and M. Dressel, “Electrodynamics of ultrathin gold films at the insulator-to-metal transition,” Thin Solid Films 519(9), 2955–2958 (2011).
[Crossref]

H. W. Lee, M. A. Schmidt, R. F. Russell, N. Y. Joly, H. K. Tyagi, P. Uebel, and P. St. J. Russell, “Pressure-assisted melt-filling and optical characterization of Au nano-wires in microstructured fibers,” Opt. Express 19(13), 12180–12189 (2011).
[Crossref] [PubMed]

P. Uebel, M. A. Schmidt, M. Scharrer, and P. St. J. Russell, “An azimuthally polarizing photonic crystal fibre with a central gold nanowire,” New J. Phys. 13(6), 063016 (2011).
[Crossref]

2010 (4)

H. K. Tyagi, H. W. Lee, P. Uebel, M. A. Schmidt, N. Joly, M. Scharrer, and P. St. J. Russell, “Plasmon resonances on gold nanowires directly drawn in a step-index fiber,” Opt. Lett. 35(15), 2573–2575 (2010).
[Crossref] [PubMed]

P. A. Belov, G. K. Palikaras, Y. Zhao, A. Rahman, C. R. Simovski, Y. Hao, and C. Parini, “Experimental demonstration of multiwire endoscopes capable of manipulating near-fields with subwavelength resolution,” Appl. Phys. Lett. 97(19), 191905 (2010).
[Crossref]

E. Badinter, A. Ioisher, E. Monaico, V. Postolache, and I. M. Tiginyanu, “Exceptional integration of metal or semimetal nanowires in human-hair-like glass fiber,” Mater. Lett. 64(17), 1902–1904 (2010).
[Crossref]

M. A. Noginov, H. Li, Y. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35(11), 1863–1865 (2010).
[Crossref] [PubMed]

2008 (6)

X. Zhang, Z. Ma, Z. Y. Yuan, and M. Su, “Mass-Production of vertically aligned extremely long metallic micro/nanowires using fiber drawing nanomanufacturing,” Adv. Mater. 20(7), 1310–1314 (2008).
[Crossref]

I. S. Nefedov, D. Chicherin, and A. J. Viitanen, “Infrared cloaking based on wire media,” Proc. SPIE 6987, 698728 (2008).
[Crossref]

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

J. Hou, D. Bird, A. George, S. Maier, B. Kuhlmey, and J. C. Knight, “Metallic mode confinement in microstructured fibres,” Opt. Express 16(9), 5983–5990 (2008).
[Crossref] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

M. A. Schmidt, L. N. P. Sempere, H. K. Tyagi, C. G. Poulton, and P. S. J. Russell, “Waveguiding and plasmon resonances in two-dimensional photonic lattice of gold and silver nanowires,” Phys. Rev. Lett. B 77(3), 033417 (2008).
[Crossref]

2007 (6)

R. Kitamura, L. Pilon, and M. Jonasz, “Optical constants of silica glass from extreme ultraviolet to far infrared at near room temperature,” Appl. Opt. 46(33), 8118–8133 (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(5819), 1686 (2007).
[Crossref] [PubMed]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[Crossref] [PubMed]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[Crossref]

G. Shvets, S. Trendafilov, J. B. Pendry, and A. Sarychev, “Guiding, focusing, and sensing on the subwavelength scale using metallic wire arrays,” Phys. Rev. Lett. 99(5), 053903 (2007).
[Crossref] [PubMed]

P. Ikonen, C. Simovski, S. Tretyakov, P. Belov, and Y. Hao, “Magnification of subwavelength field distributions at microwave frequencies using a wire medium slab operating in the canalization regime,” Appl. Phys. Lett. 91(10), 104102 (2007).
[Crossref]

2006 (2)

T. G. Mackay, A. Lakhtakia, and R. A. Depine, “Uniaxial dielectric media with hyperbolic dispersion relations,” Microw. Opt. Technol. Lett. 48(2), 363–367 (2006).
[Crossref]

M. G. Silveirinha, “Nonlocal homogenization model for a periodic array of ϵ -negative rods,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046612 (2006).
[Crossref] [PubMed]

2005 (1)

2003 (1)

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

2002 (1)

P. A. Belov, S. A. Tretyakov, and A. J. Viitanen, “Dispersion and reflection properties of artificial media formed by regular lattices of ideally conducting wires,” J. Electromagn. Waves Appl. 16(8), 1153–1170 (2002).
[Crossref]

2000 (1)

T. Kloss, G. Lautenschläger, and K. Schneider, “Advances in the process of floating borosilicate glasses and some recent applications for specialty borosilicate float glasses,” Glass Technol. 41(6), 177–181 (2000).

1997 (1)

1996 (1)

F. Dadabhai, F. Gaspari, S. Zukotynski, and C. Bland, “Reduction of silicon dioxide by aluminum in metal-oxide-semiconductor structures,” J. Appl. Phys. 80(11), 6505 (1996).
[Crossref]

1985 (2)

M. H. Hecht, R. P. Vasquez, F. J. Grunthaner, N. Zamani, and J. Maserjian, “A novel x-ray photoelectron spectroscopy study of the Al/SiO2 interface,” J. Appl. Phys. 57(12), 5256 (1985).
[Crossref]

M. Rubin, “Optical properties of soda lime silica glasses,” Sol. Energy Mater. 12(4), 275–288 (1985).
[Crossref]

1981 (1)

S. Roberts and P. J. Dobson, “Evidence for reaction at the Al-SiO2 interface,” J. Phys. D Appl. Phys. 14(3), L17–L22 (1981).
[Crossref]

1978 (1)

L. G. Aio, A. M. Efimov, and V. F. Kokorina, “Refractive index of chalcogenide glasses over a wide range on compositions,” J. Non-Cryst. Solids 27(3), 299–307 (1978).
[Crossref]

1969 (1)

L. A. B. Pilkington, “The float glass process,” Proc. R. Soc. Lond. A Math. Phys. Sci. 314(1516), 1–25 (1969).
[Crossref]

1935 (1)

S. Tomotika, “On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid,” Proc. R. Soc. Lon. A Math. 150(870), 322–337 (1935).

Abdeddaim, R.

Aio, L. G.

L. G. Aio, A. M. Efimov, and V. F. Kokorina, “Refractive index of chalcogenide glasses over a wide range on compositions,” J. Non-Cryst. Solids 27(3), 299–307 (1978).
[Crossref]

Al-Janabi, A. H.

O. T. Naman, M. R. New-Tolley, R. Lwin, A. Tuniz, A. H. Al-Janabi, I. Karatchevtseva, S. C. Fleming, B. T. Kuhlmey, and A. Argyros, “Indefinite media based on wire array metamaterials for THz and Mid-IR,” Adv. Opt. Mater. 1(12), 971–977 (2013).
[Crossref]

Argyros, A.

J. S. Brownless, B. C. P. Sturmberg, A. Argyros, B. T. Kuhlmey, and C. M. de Sterke, “Guided modes of a wire medium slab: comparison of effective medium approaches with exact calculations,” Phys. Rev. B 91(15), 155427 (2015).
[Crossref]

O. T. Naman, M. R. New-Tolley, R. Lwin, A. Tuniz, A. H. Al-Janabi, I. Karatchevtseva, S. C. Fleming, B. T. Kuhlmey, and A. Argyros, “Indefinite media based on wire array metamaterials for THz and Mid-IR,” Adv. Opt. Mater. 1(12), 971–977 (2013).
[Crossref]

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Asaduzzaman, A.

Badinter, E.

E. Badinter, A. Ioisher, E. Monaico, V. Postolache, and I. M. Tiginyanu, “Exceptional integration of metal or semimetal nanowires in human-hair-like glass fiber,” Mater. Lett. 64(17), 1902–1904 (2010).
[Crossref]

Barnakov, Y. A.

Belov, P.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

P. Ikonen, C. Simovski, S. Tretyakov, P. Belov, and Y. Hao, “Magnification of subwavelength field distributions at microwave frequencies using a wire medium slab operating in the canalization regime,” Appl. Phys. Lett. 91(10), 104102 (2007).
[Crossref]

Belov, P. A.

A. N. Poddubny, P. A. Belov, and Y. S. Kivshar, “Purcell effect in wire metamaterials,” Phys. Rev. B 87(3), 035136 (2013).
[Crossref]

P. A. Belov, G. K. Palikaras, Y. Zhao, A. Rahman, C. R. Simovski, Y. Hao, and C. Parini, “Experimental demonstration of multiwire endoscopes capable of manipulating near-fields with subwavelength resolution,” Appl. Phys. Lett. 97(19), 191905 (2010).
[Crossref]

P. A. Belov, Y. Zhao, S. Tse, P. Ikonen, M. G. Silveirinha, C. R. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

P. A. Belov, S. A. Tretyakov, and A. J. Viitanen, “Dispersion and reflection properties of artificial media formed by regular lattices of ideally conducting wires,” J. Electromagn. Waves Appl. 16(8), 1153–1170 (2002).
[Crossref]

Bird, D.

Bland, C.

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Figures (10)

Fig. 1
Fig. 1 Measured values of (a) the imaginary and (b) the real part of the permittivity for bulk metals [23,24], in the NIR and MIR. Figure of merit: the 0th order TM mode loss of a single metal wire waveguide embedded in vacuum for wire diameters of (c) d = 250 nm, (d) d = 500 nm.
Fig. 2
Fig. 2 Loss as a function of wavelength for several wire diameters. (a) Au, (b) Sn.
Fig. 3
Fig. 3 (a) Fractional energy in the metal for the lowest order TM mode in the single wire waveguide in vacuum, as a function of the wire diameter, for Au and Sn, at λ = 3 μm. (b) Difference in the imaginary part of the mode effective index for the TM mode of a single wire with and without the metallic loss, normalized by the wavelength.
Fig. 4
Fig. 4 (a) Loss and (b) fractional energy in the metal core as a function of the refractive index of the dielectric for Au and Sn wires (d = 250 nm), at λ = 3 μm.
Fig. 5
Fig. 5 (a) Isofrequency curves of the modes in the wire array, Sn/soda-lime system, d = 100 nm, L = 600 nm and λ = 3 μm. (b) Schematic of the hexagonal wire array (c) Field distribution of the calculated quasi-TEM mode with high spatial frequency (k = (π/Λ)*(2/√3)).
Fig. 6
Fig. 6 Quasi-TEM mode loss for the wire array (Au/SiO2 system) as a function of d and L, at λ = 1 μm, for (a) k = 0, and (b) kmax (corresponding to the edge of the Brillouin zone).
Fig. 7
Fig. 7 (a) Profile of the normalized electric field norm across the small diagonal of the unit cell (red line of the inset) from the four quasi-TEM modes showed in (b-e), Au/SiO2 system, L = 40 nm, at λ = 1 μm. Normalized electric field norm for the quasi-TEM modes with k = 0 and kmax, d = 10 nm (b,c) and d = 25 nm (d,e), respectively.
Fig. 8
Fig. 8 Quasi-TEM mode loss for wire arrays as functions of d and L, at 3 μm wavelength, for (a,c) k = 0 and (b,d) kmax (corresponding to the edge of the Brillouin zone). (a,b) Au/SiO2 and (c,d) Sn/soda-lime.
Fig. 9
Fig. 9 Quasi-TEM mode loss for wire array as functions of d and L, at 10 μm wavelength, for (a,c) k = 0 and (b,d) kmax (corresponding to the edge of the Brillouin zone). (a,b) Sn and (c,d) Au embedded in a glass with nd = 2.8.
Fig. 10
Fig. 10 Quasi-TEM mode loss for a wire array with Sn wires as a function of the refractive index of the dielectric nd, d = 250 nm and L = 500 nm, at 3 μm wavelength, for k = 0 (red curve) and for kmax (black curve), corresponding to the edge of the Brillouin zone.

Equations (10)

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

γ 2 I 1 ( γ 1 a) K 0 ( γ 2 a) γ 1 I 0 ( γ 1 a) K 1 ( γ 2 a) = ε 2 ε 1
γ j = k 0 ( n eff 2 ε j ) 1/2
α= 40π κ λln(10)
4Al+3SiO 2 2Al 2 O 3 +3Si. 
η= metal W(r)dA / All W(r)dA
W(r)= 1 2 ( d(ε(r)ω) dω |E(r) | 2 + μ 0 |H(r) | 2 )
Δκ= ( ε 0 μ 0 ) 1/2 metal ε i |E | 2 da All 2(| E r H ϕ | )da
k 2 ε | k | 2 | ε | = ( ω c ) 2
k 2 + k 2 = ε d ( ω c ) 2
k 2 + k 2 + k p 2 = ε d ( ω c ) 2

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