Abstract

We numerically demonstrate a kind of metal heterostructure (MHS) for high-efficiency nanofocusing and nanoguiding of light through finite-difference time-domain simulations. The results reveal that Al–Ag constructed MHSs with a trapezoid Ag guide can focus an incident light into a domain of about 0.004λ2 with higher than 96% focusing efficiency, whereas that with a rectangular Ag guide can transport light energy within 65 nm × 55 nm cross section with a propagation loss as low as 2.0 dBμm. The physics behind the above interesting nanophotonic properties is explained on the basis of the principle of conventional integrated optics, and potential applications of MHSs in other nanophotonic devices are also discussed.

© 2006 Optical Society of America

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  1. L. Novotny, D. W. Pohl, and B. Hecht, "Scanning near-field optical probe with ultrasmall spot size," Opt. Lett. 20, 970-972 (1995).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. D. G. Grier, "A revolution in optical manipulation," Anzen Kogaku 424, 810-816(2003).
  4. E. Betzig and R. J. Chichester, "Single molecules observed by near-field scanning optical microscopy," Science 262, 1422-1425(1993).
    [CrossRef] [PubMed]
  5. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669(1998).
    [CrossRef]
  6. J. C. Weeber, Y. Lacroute, and A. Dereux, "Optical near-field distributions of surface plasmon waveguide modes," Phys. Rev. B 68, 115401 (2003).
    [CrossRef]
  7. S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078(2001).
    [CrossRef]
  8. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
    [CrossRef] [PubMed]
  9. B. Wang and G. P. Wang, "Surface plasmon polariton propagation in nanoscale metal gap waveguides," Opt. Lett. 29, 1992-1994(2004).
    [CrossRef] [PubMed]
  10. M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, "Electromagnetic energy transport via linear chains of silver nanoparticles," Opt. Lett. 23, 1331-1333(1998).
    [CrossRef]
  11. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232(2003).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  15. J. X. Fang, Z. Q. Cao, and F. Z. Yang, Physical Foundations of Optical Waveguide Technology (Shanghai Jiaotong U. Press, 1987).
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  17. G. P. Wang, Y. Yi, and B. Wang, "Evanescent coupling of transmitted light through an array of holes in a metallic film assisted by transverse surface current," J. Phys.: Condens. Matter 15, 8147-8156 (2003).
    [CrossRef]
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    [CrossRef] [PubMed]
  21. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, "Guiding of a one-dimensional optical beam with nanometer diameter," Opt. Lett. 22, 475-477(1997).
    [CrossRef] [PubMed]
  22. B. Wang and G. P. Wang, "Plasmon Bragg reflectors and nanocavities on flat metallic surfaces," Appl. Phys. Lett. 87, 013107 (2005).
    [CrossRef]

2005

B. Wang and G. P. Wang, "Plasmon Bragg reflectors and nanocavities on flat metallic surfaces," Appl. Phys. Lett. 87, 013107 (2005).
[CrossRef]

2004

B. Wang and G. P. Wang, "Metal heterowaveguides for nanometric focusing of light," Appl. Phys. Lett. 85, 3599-3601(2004).
[CrossRef]

Z. Y. Li and K. M. Ho, "Anomalous propagation loss in photonic crystal waveguides," Phys. Rev. Lett. 92, 063904 (2004).
[CrossRef] [PubMed]

B. Wang and G. P. Wang, "Surface plasmon polariton propagation in nanoscale metal gap waveguides," Opt. Lett. 29, 1992-1994(2004).
[CrossRef] [PubMed]

2003

G. P. Wang, Y. Yi, and B. Wang, "Evanescent coupling of transmitted light through an array of holes in a metallic film assisted by transverse surface current," J. Phys.: Condens. Matter 15, 8147-8156 (2003).
[CrossRef]

Y. Yi, G. P. Wang, Y. B. Long, and H. Shang, "Optical transmission enhancement of two-dimensional subwavelength hole arrays in metallic films," Acta Phys. Sin. 52, 604-608(2003).

D. G. Grier, "A revolution in optical manipulation," Anzen Kogaku 424, 810-816(2003).

J. C. Weeber, Y. Lacroute, and A. Dereux, "Optical near-field distributions of surface plasmon waveguide modes," Phys. Rev. B 68, 115401 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232(2003).
[CrossRef] [PubMed]

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

2001

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078(2001).
[CrossRef]

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669(1998).
[CrossRef]

M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, "Electromagnetic energy transport via linear chains of silver nanoparticles," Opt. Lett. 23, 1331-1333(1998).
[CrossRef]

1997

J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, "Guiding of a one-dimensional optical beam with nanometer diameter," Opt. Lett. 22, 475-477(1997).
[CrossRef] [PubMed]

S. M. Nie and S. R. Emery, "Probing single molecules and single nanoparticles by surface-enhanced Raman scattering," Science 275, 1102-1106 (1997).
[CrossRef] [PubMed]

1995

1993

E. Betzig and R. J. Chichester, "Single molecules observed by near-field scanning optical microscopy," Science 262, 1422-1425(1993).
[CrossRef] [PubMed]

1974

Atwater, H. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232(2003).
[CrossRef] [PubMed]

Aussenegg, F. R.

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Betzig, E.

E. Betzig and R. J. Chichester, "Single molecules observed by near-field scanning optical microscopy," Science 262, 1422-1425(1993).
[CrossRef] [PubMed]

Boltasseva, A.

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078(2001).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078(2001).
[CrossRef]

Cao, Z. Q.

J. X. Fang, Z. Q. Cao, and F. Z. Yang, Physical Foundations of Optical Waveguide Technology (Shanghai Jiaotong U. Press, 1987).

Chichester, R. J.

E. Betzig and R. J. Chichester, "Single molecules observed by near-field scanning optical microscopy," Science 262, 1422-1425(1993).
[CrossRef] [PubMed]

Dereux, A.

J. C. Weeber, Y. Lacroute, and A. Dereux, "Optical near-field distributions of surface plasmon waveguide modes," Phys. Rev. B 68, 115401 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669(1998).
[CrossRef]

Emery, S. R.

S. M. Nie and S. R. Emery, "Probing single molecules and single nanoparticles by surface-enhanced Raman scattering," Science 275, 1102-1106 (1997).
[CrossRef] [PubMed]

Fang, J. X.

J. X. Fang, Z. Q. Cao, and F. Z. Yang, Physical Foundations of Optical Waveguide Technology (Shanghai Jiaotong U. Press, 1987).

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669(1998).
[CrossRef]

Grier, D. G.

D. G. Grier, "A revolution in optical manipulation," Anzen Kogaku 424, 810-816(2003).

Harel, E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232(2003).
[CrossRef] [PubMed]

Hecht, B.

Ho, K. M.

Z. Y. Li and K. M. Ho, "Anomalous propagation loss in photonic crystal waveguides," Phys. Rev. Lett. 92, 063904 (2004).
[CrossRef] [PubMed]

Kaminow, I. P.

Kik, P. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232(2003).
[CrossRef] [PubMed]

Kobayashi, T.

Koel, B. E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232(2003).
[CrossRef] [PubMed]

Krenn, J. R.

Lacroute, Y.

J. C. Weeber, Y. Lacroute, and A. Dereux, "Optical near-field distributions of surface plasmon waveguide modes," Phys. Rev. B 68, 115401 (2003).
[CrossRef]

Leitner, A.

Leosson, K.

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078(2001).
[CrossRef]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669(1998).
[CrossRef]

Li, Z. Y.

Z. Y. Li and K. M. Ho, "Anomalous propagation loss in photonic crystal waveguides," Phys. Rev. Lett. 92, 063904 (2004).
[CrossRef] [PubMed]

Long, Y. B.

Y. Yi, G. P. Wang, Y. B. Long, and H. Shang, "Optical transmission enhancement of two-dimensional subwavelength hole arrays in metallic films," Acta Phys. Sin. 52, 604-608(2003).

Maier, S. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232(2003).
[CrossRef] [PubMed]

Mammel, W. L.

Meltzer, S.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232(2003).
[CrossRef] [PubMed]

Morimoto, A.

Nie, S. M.

S. M. Nie and S. R. Emery, "Probing single molecules and single nanoparticles by surface-enhanced Raman scattering," Science 275, 1102-1106 (1997).
[CrossRef] [PubMed]

Novotny, L.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

Pohl, D. W.

Quinten, M.

Requicha, A. A. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232(2003).
[CrossRef] [PubMed]

Shang, H.

Y. Yi, G. P. Wang, Y. B. Long, and H. Shang, "Optical transmission enhancement of two-dimensional subwavelength hole arrays in metallic films," Acta Phys. Sin. 52, 604-608(2003).

Takahara, J.

Taki, H.

Tanaka, K.

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

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669(1998).
[CrossRef]

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078(2001).
[CrossRef]

Wang, B.

B. Wang and G. P. Wang, "Plasmon Bragg reflectors and nanocavities on flat metallic surfaces," Appl. Phys. Lett. 87, 013107 (2005).
[CrossRef]

B. Wang and G. P. Wang, "Surface plasmon polariton propagation in nanoscale metal gap waveguides," Opt. Lett. 29, 1992-1994(2004).
[CrossRef] [PubMed]

B. Wang and G. P. Wang, "Metal heterowaveguides for nanometric focusing of light," Appl. Phys. Lett. 85, 3599-3601(2004).
[CrossRef]

G. P. Wang, Y. Yi, and B. Wang, "Evanescent coupling of transmitted light through an array of holes in a metallic film assisted by transverse surface current," J. Phys.: Condens. Matter 15, 8147-8156 (2003).
[CrossRef]

Wang, G. P.

B. Wang and G. P. Wang, "Plasmon Bragg reflectors and nanocavities on flat metallic surfaces," Appl. Phys. Lett. 87, 013107 (2005).
[CrossRef]

B. Wang and G. P. Wang, "Surface plasmon polariton propagation in nanoscale metal gap waveguides," Opt. Lett. 29, 1992-1994(2004).
[CrossRef] [PubMed]

B. Wang and G. P. Wang, "Metal heterowaveguides for nanometric focusing of light," Appl. Phys. Lett. 85, 3599-3601(2004).
[CrossRef]

Y. Yi, G. P. Wang, Y. B. Long, and H. Shang, "Optical transmission enhancement of two-dimensional subwavelength hole arrays in metallic films," Acta Phys. Sin. 52, 604-608(2003).

G. P. Wang, Y. Yi, and B. Wang, "Evanescent coupling of transmitted light through an array of holes in a metallic film assisted by transverse surface current," J. Phys.: Condens. Matter 15, 8147-8156 (2003).
[CrossRef]

Weber, H. P.

Weeber, J. C.

J. C. Weeber, Y. Lacroute, and A. Dereux, "Optical near-field distributions of surface plasmon waveguide modes," Phys. Rev. B 68, 115401 (2003).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669(1998).
[CrossRef]

Yamagishi, S.

Yang, F. Z.

J. X. Fang, Z. Q. Cao, and F. Z. Yang, Physical Foundations of Optical Waveguide Technology (Shanghai Jiaotong U. Press, 1987).

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, 1997).

Yi, Y.

G. P. Wang, Y. Yi, and B. Wang, "Evanescent coupling of transmitted light through an array of holes in a metallic film assisted by transverse surface current," J. Phys.: Condens. Matter 15, 8147-8156 (2003).
[CrossRef]

Y. Yi, G. P. Wang, Y. B. Long, and H. Shang, "Optical transmission enhancement of two-dimensional subwavelength hole arrays in metallic films," Acta Phys. Sin. 52, 604-608(2003).

Acta Phys. Sin.

Y. Yi, G. P. Wang, Y. B. Long, and H. Shang, "Optical transmission enhancement of two-dimensional subwavelength hole arrays in metallic films," Acta Phys. Sin. 52, 604-608(2003).

Anzen Kogaku

D. G. Grier, "A revolution in optical manipulation," Anzen Kogaku 424, 810-816(2003).

Appl. Opt.

Appl. Phys. Lett.

B. Wang and G. P. Wang, "Plasmon Bragg reflectors and nanocavities on flat metallic surfaces," Appl. Phys. Lett. 87, 013107 (2005).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, K. Leosson, and A. Boltasseva, "Bend loss in surface plasmon polariton band-gap structures," Appl. Phys. Lett. 79, 1076-1078(2001).
[CrossRef]

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

B. Wang and G. P. Wang, "Metal heterowaveguides for nanometric focusing of light," Appl. Phys. Lett. 85, 3599-3601(2004).
[CrossRef]

J. Phys.: Condens. Matter

G. P. Wang, Y. Yi, and B. Wang, "Evanescent coupling of transmitted light through an array of holes in a metallic film assisted by transverse surface current," J. Phys.: Condens. Matter 15, 8147-8156 (2003).
[CrossRef]

Nat. Mater.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232(2003).
[CrossRef] [PubMed]

Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669(1998).
[CrossRef]

Opt. Lett.

Phys. Rev. B

J. C. Weeber, Y. Lacroute, and A. Dereux, "Optical near-field distributions of surface plasmon waveguide modes," Phys. Rev. B 68, 115401 (2003).
[CrossRef]

Phys. Rev. Lett.

Z. Y. Li and K. M. Ho, "Anomalous propagation loss in photonic crystal waveguides," Phys. Rev. Lett. 92, 063904 (2004).
[CrossRef] [PubMed]

Science

S. M. Nie and S. R. Emery, "Probing single molecules and single nanoparticles by surface-enhanced Raman scattering," Science 275, 1102-1106 (1997).
[CrossRef] [PubMed]

E. Betzig and R. J. Chichester, "Single molecules observed by near-field scanning optical microscopy," Science 262, 1422-1425(1993).
[CrossRef] [PubMed]

Other

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, 1997).

J. X. Fang, Z. Q. Cao, and F. Z. Yang, Physical Foundations of Optical Waveguide Technology (Shanghai Jiaotong U. Press, 1987).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

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Figures (8)

Fig. 1
Fig. 1

(a) Schemes of the cross sections of MHSs constructed with Ag (black) and Al (gray) in the xy and yz planes. L is the guide length; ε 0 is the permittivity of dielectric in the guiding region; b x and b y are the width and height of Al guide, respectively; and c x and c y are the sizes of MHS cross section. (b) Typical gray distribution of E 2 in the yz plane at x = 0 as SPPs pass through a MHS with h 1 = 405 nm and w = h 2 = 35 nm .

Fig. 2
Fig. 2

(a)–(d) Gray distributions of E 2 in a plane ( x - y plane) 15 nm away from the output end of MHSs. (e) and (f) Corresponding E 2 profiles in x- and y-directions, respectively. Geometric parameters: h 1 = 405 nm and (a) w = h 2 = 35 nm , (b) w = 35 nm , h 2 = 25 nm , (c) w = 35 nm , h 2 = 15 nm , (d) w = 25 nm , h 2 = 15 nm .

Fig. 3
Fig. 3

(a)–(d) Gray distributions of E 2 in a plane (the xy plane) 15 nm away from the output end of MHSs. (e) and (f) Corresponding E 2 profiles in x and y directions. Geometric parameters: w = h 2 = 15 nm and (a) h 1 = 405 nm , (b) h 1 = 305 nm , (c) h 1 = 205 nm , and (d) h 1 = 105 nm .

Fig. 4
Fig. 4

Dependence of the normalized phase velocity v P C and the imaginary part β I k 0 of propagation constants of SPPs in 2D Ag and Al WGs on guide width w.

Fig. 5
Fig. 5

Gray distributions of E 2 of SPPs at x = 0 of the yz plane of MHSs with a rectangular Ag guide ( h 1 = h 2 ) . The refractive index of dielectric in the guiding region is n = ε 0 = (a) 1.0, (b) 1.2, and (c) 1.5. (d) Normalized intensity (NI) profiles of E 2 in the y direction at the crests of standing waves ( x = 0 ) . (e) Dependence of the FWHM of E 2 in the y direction at the height h 1 of Ag WGs as w = 15 nm and n = 1.5 . Inset, dependence of the FWHM of E 2 on Ag and Al guide widths w = b x as h 1 = h 2 = 35 nm .

Fig. 6
Fig. 6

(a)–(c) Gray distributions of E 2 at x = 0 of the yz plane of MHSs. (d) NI profiles of E 2 in the y direction as SPPs pass through L = 800 nm long MHSs. The width of rectangular Ag WGs ( h 1 = h 2 ) is narrower than that of Al ( w < b x ) . (e) Dependence of E 2 of SPPs on propagation length. b x = 85 nm , h 1 = h 2 = 35 nm , n = 1.0 ; (a) w = 15 nm , (b) w = 55 nm , and (c) w = 35 nm .

Fig. 7
Fig. 7

ERI distributions of 2D Au and Al WGs at different wavelengths as WG width w = 25 nm and the dielectric filled in the guiding region is air ( n = 1.0 ) . The solid and dashed curves are the real ( n r ) and imaginary ( n i ) parts of ERIs, respectively.

Fig. 8
Fig. 8

(a) Scheme of designed SPPs Bragg reflectors with Al ( ε 1 , length d 1 , and n 1 ) and Au ( ε 3 , d 2 , and n 2 ). (b) Calculated transmission spectrum of SPPs passing through the Bragg reflectors by the transfer-matrix method. (c), (f) Gray distributions of E 2 as SPPs pass through the designed Bragg reflectors. (d) and (f) the normalized intensity (NI) profiles at x = 0 . The excited light is λ = 630 nm [(c), (d)] and 780 nm [(e), (f)].

Equations (2)

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ε 0 p ε i k = 1 exp ( k w ) 1 + exp ( k w ) , k , p = β 2 k 0 2 ε 0 , i ,
λ = 2 ( d 1 n 1 + d 2 n 2 ) ,

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