Abstract

The integration of nanoscale electronics with conventional optical devices is restricted by the diffraction limit of light. Metals can confine light at the subwavelength scales needed, but they are lossy, while dielectric materials do not confine evanescent waves outside a waveguide or resonator, leading to cross talk between components. We show that light can be confined below the diffraction limit using completely transparent artificial media (metamaterials with ε>1,μ=1). Our approach relies on controlling the optical momentum of evanescent waves—an important electromagnetic property overlooked in photonic devices. For practical applications, we propose a class of waveguides using this approach that outperforms the cross-talk performance by 1 order of magnitude as compared to any existing photonic structure. Our work overcomes a critical stumbling block for nanophotonics by completely averting the use of metals and can impact electromagnetic devices from the visible to microwave frequency ranges.

© 2014 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
  16. M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, A. J. Ouderkirk, “Giant birefringent optics in multilayer polymer mirrors,” Science 287, 2451–2456 (2000).
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    [Crossref]
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    [Crossref]

2013 (1)

Z. Han, S. I. Bozhevolnyi, “Radiation guiding with surface plasmon polaritons,” Rep. Prog. Phys. 76, 016402 (2013).
[Crossref]

2011 (1)

P. B. Catrysse, S. Fan, “Transverse electromagnetic modes in aperture waveguides containing a metamaterial with extreme anisotropy,” Phys. Rev. Lett. 106, 223902 (2011).
[Crossref]

2010 (1)

D. K. Gramotnev, S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[Crossref]

2009 (2)

D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97, 1166–1185 (2009).
[Crossref]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

2008 (2)

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

G. Veronis, S. Fan, “Crosstalk between three-dimensional plasmonic slot waveguides,” Opt. Express 16, 2129–2140 (2008).
[Crossref]

2007 (2)

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photonics 1, 115–118 (2007).
[Crossref]

D. Dai, Y. Shi, S. He, “Comparative study of the integration density for passive linear planar light-wave circuits based on three different kinds of nanophotonic waveguide,” Appl. Opt. 46, 1126–1131 (2007).
[Crossref]

2006 (2)

S. Tomljenovic-Hanic, C. Martijn de Sterke, M. J. Steel, “Packing density of conventional waveguides and photonic crystal waveguides,” Opt. Commun. 259, 142–148 (2006).
[Crossref]

S. A. Maier, “Plasmonic field enhancement and SERS in the effective mode volume picture,” Opt. Express 14, 1957–1964 (2006).
[Crossref]

2004 (2)

2003 (1)

T. F. Krauss, “Planar photonic crystal waveguide devices for integrated optics,” Phys. Status Solidi A 197, 688–702 (2003).
[Crossref]

2000 (1)

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, A. J. Ouderkirk, “Giant birefringent optics in multilayer polymer mirrors,” Science 287, 2451–2456 (2000).
[Crossref]

1998 (2)

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[Crossref]

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[Crossref]

1997 (1)

J. D. Joannopoulos, P. R. Villeneuve, S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

Almeida, V. R.

Baets, R.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Barrios, C. A.

Benabid, F.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photonics 1, 115–118 (2007).
[Crossref]

Berger, V.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[Crossref]

Biaggio, I.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Bogaerts, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Bozhevolnyi, S. I.

Z. Han, S. I. Bozhevolnyi, “Radiation guiding with surface plasmon polaritons,” Rep. Prog. Phys. 76, 016402 (2013).
[Crossref]

D. K. Gramotnev, S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[Crossref]

Bravetti, P.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[Crossref]

Brongersma, M. L.

Catrysse, P. B.

P. B. Catrysse, S. Fan, “Transverse electromagnetic modes in aperture waveguides containing a metamaterial with extreme anisotropy,” Phys. Rev. Lett. 106, 223902 (2011).
[Crossref]

R. Zia, M. D. Selker, P. B. Catrysse, M. L. Brongersma, “Geometries and materials for subwavelength surface plasmon modes,” J. Opt. Soc. Am. A 21, 2442–2446 (2004).
[Crossref]

Chow, E.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[Crossref]

Cordeiro, C. M. B.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photonics 1, 115–118 (2007).
[Crossref]

Couny, F.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photonics 1, 115–118 (2007).
[Crossref]

Cruz, C. H. B.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photonics 1, 115–118 (2007).
[Crossref]

Dai, D.

Diederich, F.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Dumon, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Esembeson, B.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Fan, S.

P. B. Catrysse, S. Fan, “Transverse electromagnetic modes in aperture waveguides containing a metamaterial with extreme anisotropy,” Phys. Rev. Lett. 106, 223902 (2011).
[Crossref]

G. Veronis, S. Fan, “Crosstalk between three-dimensional plasmonic slot waveguides,” Opt. Express 16, 2129–2140 (2008).
[Crossref]

J. D. Joannopoulos, P. R. Villeneuve, S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

Fiore, A.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[Crossref]

Fragnito, H. L.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photonics 1, 115–118 (2007).
[Crossref]

Freude, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Genov, D. A.

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

Gilbert, L. R.

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, A. J. Ouderkirk, “Giant birefringent optics in multilayer polymer mirrors,” Science 287, 2451–2456 (2000).
[Crossref]

Gramotnev, D. K.

D. K. Gramotnev, S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[Crossref]

Han, Z.

Z. Han, S. I. Bozhevolnyi, “Radiation guiding with surface plasmon polaritons,” Rep. Prog. Phys. 76, 016402 (2013).
[Crossref]

He, S.

Hietala, V.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[Crossref]

Joannopoulos, J. D.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[Crossref]

J. D. Joannopoulos, P. R. Villeneuve, S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

Knight, J. C.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photonics 1, 115–118 (2007).
[Crossref]

Koos, C.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Krauss, T. F.

T. F. Krauss, “Planar photonic crystal waveguide devices for integrated optics,” Phys. Status Solidi A 197, 688–702 (2003).
[Crossref]

Leuthold, J.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Lin, S.-Y.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[Crossref]

Lipson, M.

Maier, S. A.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photonics 1, 115–118 (2007).
[Crossref]

S. A. Maier, “Plasmonic field enhancement and SERS in the effective mode volume picture,” Opt. Express 14, 1957–1964 (2006).
[Crossref]

Martijn de Sterke, C.

S. Tomljenovic-Hanic, C. Martijn de Sterke, M. J. Steel, “Packing density of conventional waveguides and photonic crystal waveguides,” Opt. Commun. 259, 142–148 (2006).
[Crossref]

Michinobu, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Miller, D. A. B.

D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEEE 97, 1166–1185 (2009).
[Crossref]

Milton, G. W.

G. W. Milton, The Theory of Composites (Cambridge University, 2002).

Nagle, J.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[Crossref]

Nevitt, T. J.

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, A. J. Ouderkirk, “Giant birefringent optics in multilayer polymer mirrors,” Science 287, 2451–2456 (2000).
[Crossref]

Ouderkirk, A. J.

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, A. J. Ouderkirk, “Giant birefringent optics in multilayer polymer mirrors,” Science 287, 2451–2456 (2000).
[Crossref]

Oulton, R. F.

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

Pile, D. F. P.

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

Ramo, S.

S. Ramo, J. R. Whinnery, T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 1994).

Rosencher, E.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[Crossref]

Selker, M. D.

Shi, Y.

Sorger, V. J.

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

Steel, M. J.

S. Tomljenovic-Hanic, C. Martijn de Sterke, M. J. Steel, “Packing density of conventional waveguides and photonic crystal waveguides,” Opt. Commun. 259, 142–148 (2006).
[Crossref]

Stover, C. A.

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, A. J. Ouderkirk, “Giant birefringent optics in multilayer polymer mirrors,” Science 287, 2451–2456 (2000).
[Crossref]

Tomljenovic-Hanic, S.

S. Tomljenovic-Hanic, C. Martijn de Sterke, M. J. Steel, “Packing density of conventional waveguides and photonic crystal waveguides,” Opt. Commun. 259, 142–148 (2006).
[Crossref]

Vallaitis, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Van Duzer, T.

S. Ramo, J. R. Whinnery, T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 1994).

Veronis, G.

Villeneuve, P. R.

S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[Crossref]

J. D. Joannopoulos, P. R. Villeneuve, S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

Vorreau, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Weber, M. F.

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, A. J. Ouderkirk, “Giant birefringent optics in multilayer polymer mirrors,” Science 287, 2451–2456 (2000).
[Crossref]

Whinnery, J. R.

S. Ramo, J. R. Whinnery, T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, 1994).

Wiederhecker, G. S.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photonics 1, 115–118 (2007).
[Crossref]

Xu, Q.

Zhang, X.

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

Zia, R.

Appl. Opt. (1)

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

Nat. Photonics (4)

D. K. Gramotnev, S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[Crossref]

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

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photonics 1, 115–118 (2007).
[Crossref]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, J. Leuthold, “All-optical high-speed signal processing with silicon–organic hybrid slot waveguides,” Nat. Photonics 3, 216–219 (2009).
[Crossref]

Nature (2)

J. D. Joannopoulos, P. R. Villeneuve, S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature 391, 463–466 (1998).
[Crossref]

Opt. Commun. (1)

S. Tomljenovic-Hanic, C. Martijn de Sterke, M. J. Steel, “Packing density of conventional waveguides and photonic crystal waveguides,” Opt. Commun. 259, 142–148 (2006).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

P. B. Catrysse, S. Fan, “Transverse electromagnetic modes in aperture waveguides containing a metamaterial with extreme anisotropy,” Phys. Rev. Lett. 106, 223902 (2011).
[Crossref]

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Supplementary Material (1)

» Supplement 1: PDF (1517 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

(a) Conventional TIR: if n1>n2 and the incident angle is larger than the critical angle, the light is totally reflected to medium 1 and decays in medium 2. (b) Relaxed-TIR: if n1>εx and the incident angle is larger than the critical angle, the light is totally reflected. However, the penetration depth can be decreased considerably if εz1. (c) Wave propagation along the optical axis of a uniaxial medium. As the electric field is perpendicular to the momentum direction, permittivity in a specific direction controls the momentum in the perpendicular direction. (d) Conventional waveguide based on TIR: as the core size is decreased, most of the power lies outside and decays slowly in the cladding. (e) TCW: relaxed-TIR (n1>εx) preserves the conventional waveguiding mechanism. Furthermore, the light decays fast in the cladding as the optical momentum in the cladding is transformed using anisotropy (εz1). Thus, the wave can be confined inside the core, giving rise to subdiffraction optics with completely transparent media.

Fig. 2.
Fig. 2.

Normalized tangential electric field of the TM mode for a glass slab waveguide with a size of 0.1λ surrounded with all-dielectric metamaterial cladding. The metamaterial has dielectric constants of εx=1.1 and εz=15. On comparison with a conventional mode that has air as the surrounding medium, a rapid decay of the evanescent fields is observed. The plots are normalized to the same input electric energy. Inset: as the anisotropy of the cladding is increased, the mode length decreases significantly below the diffraction limit with completely transparent media. This can be achieved with a cladding size (width b) three times that of the core size (width a).

Fig. 3.
Fig. 3.

Mode length comparison of slab waveguides with core size. It shows that the anisotropic cladding (εx=1.1 and εz=15) can confine the TM mode to subdiffraction values. Inset: we emphasize that the net power in the core is also higher for the TCW as compared to conventional waveguides.

Fig. 4.
Fig. 4.

Dense photonic integration at optical telecommunication wavelength (λ=1550nm). (a) Extreme skin depth cladding with low cross talk between closely spaced waveguides. This can be achieved by surrounding the waveguide cores (thick blue layers) with multilayer all-dielectric metamaterials. The multilayer metamaterial consists of alternating subwavelength layers of germanium (26 nm) and silica (14 nm). This all-dielectric structure achieves anisotropy of εx=4.8 and εz=11.9. (b) Comparison of coupling length (cross talk) for conventional slab waveguides, slot waveguides, and TCWs. It is seen that the TCW improves the cross talk by 1 order of magnitude and the practical multilayer structure result is in excellent agreement with the effectively anisotropic cladding. The core is silicon with a center-to-center separation of 0.5λ between waveguides. Each slot waveguide has the same net size as the core of the other waveguides; the slot size is 0.01λ and is filled with glass. If the slot size is larger or the slot index is lower, the cross-talk performance is worse than that shown. Also note that the slot waveguide cross talk is, in fact, always more than that in the conventional waveguide.

Fig. 5.
Fig. 5.

Simulated distribution of the electric energy density inside a low-index 2D dielectric waveguide with arbitrary cross section using metamaterial claddings. (a) Waveguide without cladding, and (b) the waveguide with all-dielectric nonmagnetic cladding (εx=εy=1.2 and εz=15). When the anisotropic cladding is added, the mode area of the waveguide is decreased from about 80A0 to 0.7A0, and the fraction of power inside the core to the total power is increased from less than 1% to about 36%.

Equations (3)

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n1>εx,
(kz)2εx+(kx)2εz=(k0)2.
kx=εzεxεx(k0)2(kz)2.

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