Abstract

We describe a layered metal-dielectric waveguide, whose fundamental mode has an effective index as high as 7.35 at 1.55μm, enabling subwavelength spatial confinement. The loss is found to be reasonable in relation to the confinement. The indefinite dielectric tensor of the stratified metamaterial core generally leads to multimode operation of the waveguide, exhibiting a “reversed” mode ordering contrary to conventional waveguides. The waveguide features a strong leveraging in modal index change subject to a change of index in the dielectric layers, opening the design possibilities of very compact active electro-optic devices.

© 2011 OSA

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  1. B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24, 4600–4615 (2006).
    [CrossRef]
  2. L. Thylén, S. He, L. Wosinski, and D. Dai, “The Moore’s law for photonic integrated circuits,” J. Zhejiang Univ. Sci. 7, 1961–1967 (2006).
    [CrossRef]
  3. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  4. K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82, 1158–1160 (2003).
    [CrossRef]
  5. G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightwave Technol. 25, 2511–2521 (2007).
    [CrossRef]
  6. B. T. Schwartz and R. Piestun, “Waveguiding in air by total external reflection from ultralow index metamaterials,” Appl. Phys. Lett. 85, 1–3 (2004).
    [CrossRef]
  7. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
    [CrossRef] [PubMed]
  8. M. Yan and N. A. Mortensen, “Hollow-core infrared fiber incorporating metal-wire metamaterial,” Opt. Express 17, 14851–14864 (2009).
    [CrossRef] [PubMed]
  9. J. Elser, A. A. Govyadinov, I. Avrutsky, I. Salakhutdinov, and V. A. Podolskiy, “Plasmonic nanolayer composites: Coupled plasmon polaritons, effective-medium response, and subdiffraction light manipulation,” J. Nanomater. 2007, 79469 (2007).
    [CrossRef]
  10. C. H. Gan and P. Lalanne, “Well-confined surface plasmon polaritons for sensing applications in the near-infrared,” Opt. Lett. 35, 610–612 (2010).
    [CrossRef] [PubMed]
  11. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  12. Z. L. Sámson, S.-C. Yen, K. F. MacDonald, K. Knight, S. Li, D. W. Hewak, D.-P. Tsai, and N. I. Zheludev, “Chalcogenide glasses in active plasmonics,” Phys. Status Solidi (RRL) 4, 274–276 (2010).
    [CrossRef]
  13. This picture is only absolutely valid when the waveguide under consideration is infinitely extending along x, or of slab geometry. When the waveguide width is finite, the guided mode is always hybrid with both TM and transverse-electric (TE) field components. A plasmonic mode usually has a larger portion of TM components and is therefore a TM-like mode.
  14. Y. Ikuma, Y. Shoji, M. Kuwahara, X. Wang, K. Kintaka, H. Kawashima, D. Tanaka, and H. Tsuda, “Small-sized optical gate switch using ge2sb2te5 phase-change material integrated with silicon waveguide,” Electron. Lett. 46, 368–369 (2010).
    [CrossRef]
  15. A tensor is indefinite if its three principle tensor components are not of the same sign. A medium with such a permittivity and/or permeability tensor(s) is referred to as an indefinite medium [16].
  16. D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
    [CrossRef] [PubMed]

2010 (3)

Z. L. Sámson, S.-C. Yen, K. F. MacDonald, K. Knight, S. Li, D. W. Hewak, D.-P. Tsai, and N. I. Zheludev, “Chalcogenide glasses in active plasmonics,” Phys. Status Solidi (RRL) 4, 274–276 (2010).
[CrossRef]

Y. Ikuma, Y. Shoji, M. Kuwahara, X. Wang, K. Kintaka, H. Kawashima, D. Tanaka, and H. Tsuda, “Small-sized optical gate switch using ge2sb2te5 phase-change material integrated with silicon waveguide,” Electron. Lett. 46, 368–369 (2010).
[CrossRef]

C. H. Gan and P. Lalanne, “Well-confined surface plasmon polaritons for sensing applications in the near-infrared,” Opt. Lett. 35, 610–612 (2010).
[CrossRef] [PubMed]

2009 (1)

2007 (2)

G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightwave Technol. 25, 2511–2521 (2007).
[CrossRef]

J. Elser, A. A. Govyadinov, I. Avrutsky, I. Salakhutdinov, and V. A. Podolskiy, “Plasmonic nanolayer composites: Coupled plasmon polaritons, effective-medium response, and subdiffraction light manipulation,” J. Nanomater. 2007, 79469 (2007).
[CrossRef]

2006 (2)

B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24, 4600–4615 (2006).
[CrossRef]

L. Thylén, S. He, L. Wosinski, and D. Dai, “The Moore’s law for photonic integrated circuits,” J. Zhejiang Univ. Sci. 7, 1961–1967 (2006).
[CrossRef]

2005 (1)

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
[CrossRef] [PubMed]

2004 (1)

B. T. Schwartz and R. Piestun, “Waveguiding in air by total external reflection from ultralow index metamaterials,” Appl. Phys. Lett. 85, 1–3 (2004).
[CrossRef]

2003 (2)

K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82, 1158–1160 (2003).
[CrossRef]

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

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Avrutsky, I.

J. Elser, A. A. Govyadinov, I. Avrutsky, I. Salakhutdinov, and V. A. Podolskiy, “Plasmonic nanolayer composites: Coupled plasmon polaritons, effective-medium response, and subdiffraction light manipulation,” J. Nanomater. 2007, 79469 (2007).
[CrossRef]

Catrysse, P. B.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
[CrossRef] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Dai, D.

L. Thylén, S. He, L. Wosinski, and D. Dai, “The Moore’s law for photonic integrated circuits,” J. Zhejiang Univ. Sci. 7, 1961–1967 (2006).
[CrossRef]

Elser, J.

J. Elser, A. A. Govyadinov, I. Avrutsky, I. Salakhutdinov, and V. A. Podolskiy, “Plasmonic nanolayer composites: Coupled plasmon polaritons, effective-medium response, and subdiffraction light manipulation,” J. Nanomater. 2007, 79469 (2007).
[CrossRef]

Fan, S.

G. Veronis and S. Fan, “Modes of subwavelength plasmonic slot waveguides,” J. Lightwave Technol. 25, 2511–2521 (2007).
[CrossRef]

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
[CrossRef] [PubMed]

Fathpour, S.

Gan, C. H.

Govyadinov, A. A.

J. Elser, A. A. Govyadinov, I. Avrutsky, I. Salakhutdinov, and V. A. Podolskiy, “Plasmonic nanolayer composites: Coupled plasmon polaritons, effective-medium response, and subdiffraction light manipulation,” J. Nanomater. 2007, 79469 (2007).
[CrossRef]

He, S.

L. Thylén, S. He, L. Wosinski, and D. Dai, “The Moore’s law for photonic integrated circuits,” J. Zhejiang Univ. Sci. 7, 1961–1967 (2006).
[CrossRef]

Hewak, D. W.

Z. L. Sámson, S.-C. Yen, K. F. MacDonald, K. Knight, S. Li, D. W. Hewak, D.-P. Tsai, and N. I. Zheludev, “Chalcogenide glasses in active plasmonics,” Phys. Status Solidi (RRL) 4, 274–276 (2010).
[CrossRef]

Ikuma, Y.

Y. Ikuma, Y. Shoji, M. Kuwahara, X. Wang, K. Kintaka, H. Kawashima, D. Tanaka, and H. Tsuda, “Small-sized optical gate switch using ge2sb2te5 phase-change material integrated with silicon waveguide,” Electron. Lett. 46, 368–369 (2010).
[CrossRef]

Jalali, B.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Kawashima, H.

Y. Ikuma, Y. Shoji, M. Kuwahara, X. Wang, K. Kintaka, H. Kawashima, D. Tanaka, and H. Tsuda, “Small-sized optical gate switch using ge2sb2te5 phase-change material integrated with silicon waveguide,” Electron. Lett. 46, 368–369 (2010).
[CrossRef]

Kintaka, K.

Y. Ikuma, Y. Shoji, M. Kuwahara, X. Wang, K. Kintaka, H. Kawashima, D. Tanaka, and H. Tsuda, “Small-sized optical gate switch using ge2sb2te5 phase-change material integrated with silicon waveguide,” Electron. Lett. 46, 368–369 (2010).
[CrossRef]

Knight, K.

Z. L. Sámson, S.-C. Yen, K. F. MacDonald, K. Knight, S. Li, D. W. Hewak, D.-P. Tsai, and N. I. Zheludev, “Chalcogenide glasses in active plasmonics,” Phys. Status Solidi (RRL) 4, 274–276 (2010).
[CrossRef]

Kuwahara, M.

Y. Ikuma, Y. Shoji, M. Kuwahara, X. Wang, K. Kintaka, H. Kawashima, D. Tanaka, and H. Tsuda, “Small-sized optical gate switch using ge2sb2te5 phase-change material integrated with silicon waveguide,” Electron. Lett. 46, 368–369 (2010).
[CrossRef]

Lalanne, P.

Li, S.

Z. L. Sámson, S.-C. Yen, K. F. MacDonald, K. Knight, S. Li, D. W. Hewak, D.-P. Tsai, and N. I. Zheludev, “Chalcogenide glasses in active plasmonics,” Phys. Status Solidi (RRL) 4, 274–276 (2010).
[CrossRef]

MacDonald, K. F.

Z. L. Sámson, S.-C. Yen, K. F. MacDonald, K. Knight, S. Li, D. W. Hewak, D.-P. Tsai, and N. I. Zheludev, “Chalcogenide glasses in active plasmonics,” Phys. Status Solidi (RRL) 4, 274–276 (2010).
[CrossRef]

Maier, S. A.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Mortensen, N. A.

Piestun, R.

B. T. Schwartz and R. Piestun, “Waveguiding in air by total external reflection from ultralow index metamaterials,” Appl. Phys. Lett. 85, 1–3 (2004).
[CrossRef]

Podolskiy, V. A.

J. Elser, A. A. Govyadinov, I. Avrutsky, I. Salakhutdinov, and V. A. Podolskiy, “Plasmonic nanolayer composites: Coupled plasmon polaritons, effective-medium response, and subdiffraction light manipulation,” J. Nanomater. 2007, 79469 (2007).
[CrossRef]

Salakhutdinov, I.

J. Elser, A. A. Govyadinov, I. Avrutsky, I. Salakhutdinov, and V. A. Podolskiy, “Plasmonic nanolayer composites: Coupled plasmon polaritons, effective-medium response, and subdiffraction light manipulation,” J. Nanomater. 2007, 79469 (2007).
[CrossRef]

Sámson, Z. L.

Z. L. Sámson, S.-C. Yen, K. F. MacDonald, K. Knight, S. Li, D. W. Hewak, D.-P. Tsai, and N. I. Zheludev, “Chalcogenide glasses in active plasmonics,” Phys. Status Solidi (RRL) 4, 274–276 (2010).
[CrossRef]

Schurig, D.

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

Schwartz, B. T.

B. T. Schwartz and R. Piestun, “Waveguiding in air by total external reflection from ultralow index metamaterials,” Appl. Phys. Lett. 85, 1–3 (2004).
[CrossRef]

Shen, J. T.

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
[CrossRef] [PubMed]

Shoji, Y.

Y. Ikuma, Y. Shoji, M. Kuwahara, X. Wang, K. Kintaka, H. Kawashima, D. Tanaka, and H. Tsuda, “Small-sized optical gate switch using ge2sb2te5 phase-change material integrated with silicon waveguide,” Electron. Lett. 46, 368–369 (2010).
[CrossRef]

Smith, D. R.

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

Tanaka, D.

Y. Ikuma, Y. Shoji, M. Kuwahara, X. Wang, K. Kintaka, H. Kawashima, D. Tanaka, and H. Tsuda, “Small-sized optical gate switch using ge2sb2te5 phase-change material integrated with silicon waveguide,” Electron. Lett. 46, 368–369 (2010).
[CrossRef]

Tanaka, K.

K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82, 1158–1160 (2003).
[CrossRef]

Tanaka, M.

K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82, 1158–1160 (2003).
[CrossRef]

Thylén, L.

L. Thylén, S. He, L. Wosinski, and D. Dai, “The Moore’s law for photonic integrated circuits,” J. Zhejiang Univ. Sci. 7, 1961–1967 (2006).
[CrossRef]

Tsai, D.-P.

Z. L. Sámson, S.-C. Yen, K. F. MacDonald, K. Knight, S. Li, D. W. Hewak, D.-P. Tsai, and N. I. Zheludev, “Chalcogenide glasses in active plasmonics,” Phys. Status Solidi (RRL) 4, 274–276 (2010).
[CrossRef]

Tsuda, H.

Y. Ikuma, Y. Shoji, M. Kuwahara, X. Wang, K. Kintaka, H. Kawashima, D. Tanaka, and H. Tsuda, “Small-sized optical gate switch using ge2sb2te5 phase-change material integrated with silicon waveguide,” Electron. Lett. 46, 368–369 (2010).
[CrossRef]

Veronis, G.

Wang, X.

Y. Ikuma, Y. Shoji, M. Kuwahara, X. Wang, K. Kintaka, H. Kawashima, D. Tanaka, and H. Tsuda, “Small-sized optical gate switch using ge2sb2te5 phase-change material integrated with silicon waveguide,” Electron. Lett. 46, 368–369 (2010).
[CrossRef]

Wosinski, L.

L. Thylén, S. He, L. Wosinski, and D. Dai, “The Moore’s law for photonic integrated circuits,” J. Zhejiang Univ. Sci. 7, 1961–1967 (2006).
[CrossRef]

Yan, M.

Yen, S.-C.

Z. L. Sámson, S.-C. Yen, K. F. MacDonald, K. Knight, S. Li, D. W. Hewak, D.-P. Tsai, and N. I. Zheludev, “Chalcogenide glasses in active plasmonics,” Phys. Status Solidi (RRL) 4, 274–276 (2010).
[CrossRef]

Zheludev, N. I.

Z. L. Sámson, S.-C. Yen, K. F. MacDonald, K. Knight, S. Li, D. W. Hewak, D.-P. Tsai, and N. I. Zheludev, “Chalcogenide glasses in active plasmonics,” Phys. Status Solidi (RRL) 4, 274–276 (2010).
[CrossRef]

Appl. Phys. Lett. (2)

K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82, 1158–1160 (2003).
[CrossRef]

B. T. Schwartz and R. Piestun, “Waveguiding in air by total external reflection from ultralow index metamaterials,” Appl. Phys. Lett. 85, 1–3 (2004).
[CrossRef]

Electron. Lett. (1)

Y. Ikuma, Y. Shoji, M. Kuwahara, X. Wang, K. Kintaka, H. Kawashima, D. Tanaka, and H. Tsuda, “Small-sized optical gate switch using ge2sb2te5 phase-change material integrated with silicon waveguide,” Electron. Lett. 46, 368–369 (2010).
[CrossRef]

J. Lightwave Technol. (2)

J. Nanomater. (1)

J. Elser, A. A. Govyadinov, I. Avrutsky, I. Salakhutdinov, and V. A. Podolskiy, “Plasmonic nanolayer composites: Coupled plasmon polaritons, effective-medium response, and subdiffraction light manipulation,” J. Nanomater. 2007, 79469 (2007).
[CrossRef]

J. Zhejiang Univ. Sci. (1)

L. Thylén, S. He, L. Wosinski, and D. Dai, “The Moore’s law for photonic integrated circuits,” J. Zhejiang Univ. Sci. 7, 1961–1967 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Phys. Rev. Lett. (2)

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94, 197401 (2005).
[CrossRef] [PubMed]

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

Phys. Status Solidi (RRL) (1)

Z. L. Sámson, S.-C. Yen, K. F. MacDonald, K. Knight, S. Li, D. W. Hewak, D.-P. Tsai, and N. I. Zheludev, “Chalcogenide glasses in active plasmonics,” Phys. Status Solidi (RRL) 4, 274–276 (2010).
[CrossRef]

Other (3)

This picture is only absolutely valid when the waveguide under consideration is infinitely extending along x, or of slab geometry. When the waveguide width is finite, the guided mode is always hybrid with both TM and transverse-electric (TE) field components. A plasmonic mode usually has a larger portion of TM components and is therefore a TM-like mode.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

A tensor is indefinite if its three principle tensor components are not of the same sign. A medium with such a permittivity and/or permeability tensor(s) is referred to as an indefinite medium [16].

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic diagram of the waveguide cross-section. The blue region (air) is the cladding. Inset shows the multilayer medium in bulk. (b) Indices ( and neff) versus wavelength, and (c) Losses versus wavelength for a layered medium in bulk when examined in the MGT limit, and for the fundamental modes guided repectively by a slab and a stripe waveguides based on the layered medium.

Fig. 2
Fig. 2

The field patterns for the fundamental mode at 1.55μm. Domain: 300 × 300nm2. Values are in SI units.

Fig. 3
Fig. 3

Difference in the effective mode index when the dielectric index changes from 3 to 3.1.

Fig. 4
Fig. 4

Dispersion (a) and loss (b) curves of 5 modes guided in the waveguide. The mode numbers, from the fundamental mode to the highest-order mode, are denoted as 1 to 5 correspondingly. Insets show the Hx field distributions for the high-order modes.

Equations (3)

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ɛ y = ɛ m ɛ d f d ɛ m + f m ɛ d ,
ɛ x = ɛ z = f m ɛ m + f d ɛ d ,
2 H x y 2 = ɛ z ( n eff 2 ɛ y 1 ) k 0 2 H x ,

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