Abstract

We theoretically investigate planar heterostructures for subwavelength guiding of surface plasmon modes and optimize their design to enhance the waveguiding efficiency. We show that by appropriately selecting the thicknesses of metallic and dielectric layers of a two-layer waveguide, one can compensate the intrinsic damping of the mode by having minimal optical gain in the dielectric region. We also reveal that mode confinement can be significantly improved by the use of an additional metal layer adjacent to the dielectric, to form a metal–dielectric–metal (MDM) structure. By varying the layer thicknesses in the MDM waveguide, we demonstrate that the propagation length of the plasmonic mode can be maximized. We further show that the losses may be suppressed by minimal gain in the dielectric region by the careful choice of geometrical parameters. We note that the associated gain levels are relatively small; for example, the losses in a 300 nm thick Ag–ZnO–Ag waveguide can be compensated by a gain of 225cm1. Our results may prove useful for the realization of efficient optical interconnects in high-density nanophotonic circuity.

© 2012 Optical Society of America

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2011 (5)

2010 (2)

2009 (1)

A. Boltasseva, “Plasmonic components fabrication via nanoimprint,” J. Opt. A 11, 114001 (2009).
[CrossRef]

2008 (3)

2007 (2)

J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding,” Phys. Rev. B 76, 035434 (2007).
[CrossRef]

H. A. Atwater, “The promise of plasmonics,” Sci. Am. 296, 56–62 (2007).
[CrossRef]

2006 (4)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef]

S. A. Maier, “Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides,” Opt. Commun. 258, 295–299 (2006).
[CrossRef]

Z. K. Tang, M. Kawasaki, A. Ohtomo, H. Koinuma, and Y. Segawa, “Self-assembled ZnO nano-crystals and exciton lasing at room temperature,” J. Cryst. Growth 287, 169–179 (2006).
[CrossRef]

J. Wang, S. K. Hark, and Q. Li, “Electronic structure and luminescence properties of Er doped ZnO nanowires,” Microsc. Microanal. 12, 748–749 (2006).
[CrossRef]

2005 (3)

D. F. P. Pile, T. Ogawa, D. K. Gramontnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef]

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

2004 (1)

2003 (1)

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

2002 (1)

K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, “Surface-enhanced Raman scattering and biophysics,” J. Phys. Condens. Matter 14, R597–R624 (2002).
[CrossRef]

2001 (1)

Y. Chen, N. T. Tuan, Y. Segawa, H. Ko, S. Hong, and T. Yao, “Stimulated emission and optical gain in ZnO epilayers grown by plasma-assisted molecular-beam epitaxy with buffers,” Appl. Phys. Lett. 78, 1469–1471 (2001).
[CrossRef]

1999 (1)

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sensors Actuators B 54, 3–15 (1999).
[CrossRef]

1998 (1)

1997 (2)

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]

J. Koglin, U. C. Fischer, and H. Fuchs, “Material contrast in scanning near-field optical microscopy at 1–10 nm resolution,” Phys. Rev. B 55, 7977–7984 (1997).
[CrossRef]

1996 (1)

S. C. Fleming and T. J. Whitley, “Measurement and analysis of pump-dependent refractive index and dispersion effects in erbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 32, 1113–1121 (1996).
[CrossRef]

1995 (1)

L. Novotny, D. W. Pohl, and B. Hecht, “Light confinement in scanning near-field optical microscopy,” Ultramicroscopy 61, 1–9 (1995).
[CrossRef]

1991 (1)

S. C. Fleming and T. J. Whitley, “Measurement of pump induced refractive index change in erbium doped fibre amplifier,” Electron. Lett. 27, 1959–1961 (1991).
[CrossRef]

1990 (1)

E. Desurvire, “Study of the complex atomic susceptibility of erbium-doped fiber amplifiers,” J. Lightwave Technol. 8, 1517–1527 (1990).
[CrossRef]

1981 (1)

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927–1930 (1981).
[CrossRef]

1972 (1)

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

Adachi, S.

S. Adachi, Optical Constants of Crystalline and Amorphous Semiconductors—Numerical Data and Graphical Information (Springer, 1999).

Adegoke, J. A.

Agrawal, G. P.

Atwater, H. A.

H. A. Atwater, “The promise of plasmonics,” Sci. Am. 296, 56–62 (2007).
[CrossRef]

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Aussenegg, F. R.

Bahoura, M.

Barnes, W. L.

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

Boltasseva, A.

A. Boltasseva, “Plasmonic components fabrication via nanoimprint,” J. Opt. A 11, 114001 (2009).
[CrossRef]

Bozhevolnyi, S. I.

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

J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding,” Phys. Rev. B 76, 035434 (2007).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef]

Brueck, S. R. J.

Chen, J.

Chen, Y.

Y. Chen, N. T. Tuan, Y. Segawa, H. Ko, S. Hong, and T. Yao, “Stimulated emission and optical gain in ZnO epilayers grown by plasma-assisted molecular-beam epitaxy with buffers,” Appl. Phys. Lett. 78, 1469–1471 (2001).
[CrossRef]

Christy, R. W.

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

Dasari, R. R.

K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, “Surface-enhanced Raman scattering and biophysics,” J. Phys. Condens. Matter 14, R597–R624 (2002).
[CrossRef]

Dereux, A.

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

Desurvire, E.

E. Desurvire, “Study of the complex atomic susceptibility of erbium-doped fiber amplifiers,” J. Lightwave Technol. 8, 1517–1527 (1990).
[CrossRef]

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef]

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

Fainman, Y.

Feld, M. S.

K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, “Surface-enhanced Raman scattering and biophysics,” J. Phys. Condens. Matter 14, R597–R624 (2002).
[CrossRef]

Fischer, U. C.

J. Koglin, U. C. Fischer, and H. Fuchs, “Material contrast in scanning near-field optical microscopy at 1–10 nm resolution,” Phys. Rev. B 55, 7977–7984 (1997).
[CrossRef]

Fleming, S. C.

S. C. Fleming and T. J. Whitley, “Measurement and analysis of pump-dependent refractive index and dispersion effects in erbium-doped fiber amplifiers,” IEEE J. Quantum Electron. 32, 1113–1121 (1996).
[CrossRef]

S. C. Fleming and T. J. Whitley, “Measurement of pump induced refractive index change in erbium doped fibre amplifier,” Electron. Lett. 27, 1959–1961 (1991).
[CrossRef]

Fuchs, H.

J. Koglin, U. C. Fischer, and H. Fuchs, “Material contrast in scanning near-field optical microscopy at 1–10 nm resolution,” Phys. Rev. B 55, 7977–7984 (1997).
[CrossRef]

Fukui, M.

D. F. P. Pile, T. Ogawa, D. K. Gramontnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

Gauglitz, G.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sensors Actuators B 54, 3–15 (1999).
[CrossRef]

Genov, D. A.

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. Photon. 2, 496–500 (2008).
[CrossRef]

Gramontnev, D. K.

D. F. P. Pile, T. Ogawa, D. K. Gramontnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

Gramotnev, D. K.

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

Handapangoda, D.

Haraguchi, M.

D. F. P. Pile, T. Ogawa, D. K. Gramontnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

Hark, S. K.

J. Wang, S. K. Hark, and Q. Li, “Electronic structure and luminescence properties of Er doped ZnO nanowires,” Microsc. Microanal. 12, 748–749 (2006).
[CrossRef]

He, J.

J. Lo, W. Lien, C. Lin, and J. He, “Er-doped ZnO nanorod arrays with enhanced 1540 nm emission by employing Ag island films and high-temperature annealing,” ACS Appl. Mater. Interf. 3, 1009–1014 (2011).
[CrossRef]

Hecht, B.

L. Novotny, D. W. Pohl, and B. Hecht, “Light confinement in scanning near-field optical microscopy,” Ultramicroscopy 61, 1–9 (1995).
[CrossRef]

Hecht, J.

J. Hecht, The Laser Guidebook (McGraw-Hill, 1992).

Homola, J.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sensors Actuators B 54, 3–15 (1999).
[CrossRef]

Hong, S.

Y. Chen, N. T. Tuan, Y. Segawa, H. Ko, S. Hong, and T. Yao, “Stimulated emission and optical gain in ZnO epilayers grown by plasma-assisted molecular-beam epitaxy with buffers,” Appl. Phys. Lett. 78, 1469–1471 (2001).
[CrossRef]

Itzkan, I.

K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, “Surface-enhanced Raman scattering and biophysics,” J. Phys. Condens. Matter 14, R597–R624 (2002).
[CrossRef]

Jagadish, C.

Johnson, P. B.

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

Jung, J.

J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Theoretical analysis of square surface plasmon-polariton waveguides for long-range polarization-independent waveguiding,” Phys. Rev. B 76, 035434 (2007).
[CrossRef]

Kawasaki, M.

Z. K. Tang, M. Kawasaki, A. Ohtomo, H. Koinuma, and Y. Segawa, “Self-assembled ZnO nano-crystals and exciton lasing at room temperature,” J. Cryst. Growth 287, 169–179 (2006).
[CrossRef]

Kneipp, H.

K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, “Surface-enhanced Raman scattering and biophysics,” J. Phys. Condens. Matter 14, R597–R624 (2002).
[CrossRef]

Kneipp, K.

K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, “Surface-enhanced Raman scattering and biophysics,” J. Phys. Condens. Matter 14, R597–R624 (2002).
[CrossRef]

Ko, H.

Y. Chen, N. T. Tuan, Y. Segawa, H. Ko, S. Hong, and T. Yao, “Stimulated emission and optical gain in ZnO epilayers grown by plasma-assisted molecular-beam epitaxy with buffers,” Appl. Phys. Lett. 78, 1469–1471 (2001).
[CrossRef]

Kobayashi, T.

Koglin, J.

J. Koglin, U. C. Fischer, and H. Fuchs, “Material contrast in scanning near-field optical microscopy at 1–10 nm resolution,” Phys. Rev. B 55, 7977–7984 (1997).
[CrossRef]

Koinuma, H.

Z. K. Tang, M. Kawasaki, A. Ohtomo, H. Koinuma, and Y. Segawa, “Self-assembled ZnO nano-crystals and exciton lasing at room temperature,” J. Cryst. Growth 287, 169–179 (2006).
[CrossRef]

Krenn, J. R.

Leitner, A.

Li, Q.

J. Wang, S. K. Hark, and Q. Li, “Electronic structure and luminescence properties of Er doped ZnO nanowires,” Microsc. Microanal. 12, 748–749 (2006).
[CrossRef]

Lien, W.

J. Lo, W. Lien, C. Lin, and J. He, “Er-doped ZnO nanorod arrays with enhanced 1540 nm emission by employing Ag island films and high-temperature annealing,” ACS Appl. Mater. Interf. 3, 1009–1014 (2011).
[CrossRef]

Lin, C.

J. Lo, W. Lien, C. Lin, and J. He, “Er-doped ZnO nanorod arrays with enhanced 1540 nm emission by employing Ag island films and high-temperature annealing,” ACS Appl. Mater. Interf. 3, 1009–1014 (2011).
[CrossRef]

Lo, J.

J. Lo, W. Lien, C. Lin, and J. He, “Er-doped ZnO nanorod arrays with enhanced 1540 nm emission by employing Ag island films and high-temperature annealing,” ACS Appl. Mater. Interf. 3, 1009–1014 (2011).
[CrossRef]

Maier, S. A.

S. A. Maier, “Gain-assisted propagation of electromagnetic energy in subwavelength surface plasmon polariton gap waveguides,” Opt. Commun. 258, 295–299 (2006).
[CrossRef]

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

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

Malloy, K. J.

Matsuo, S.

D. F. P. Pile, T. Ogawa, D. K. Gramontnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

Mayy, M.

Morimoto, A.

Morkoc, H.

H. Morkoc and Ü. Özgür, Zinc Oxide: Fundamentals, Materials and Device Technology (Wiley-VCH Verlag, 2009).

Nezhad, M. P.

Noginov, M. A.

Novotny, L.

L. Novotny, D. W. Pohl, and B. Hecht, “Light confinement in scanning near-field optical microscopy,” Ultramicroscopy 61, 1–9 (1995).
[CrossRef]

Ogawa, T.

D. F. P. Pile, T. Ogawa, D. K. Gramontnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

Ohtomo, A.

Z. K. Tang, M. Kawasaki, A. Ohtomo, H. Koinuma, and Y. Segawa, “Self-assembled ZnO nano-crystals and exciton lasing at room temperature,” J. Cryst. Growth 287, 169–179 (2006).
[CrossRef]

Okamoto, T.

D. F. P. Pile, T. Ogawa, D. K. Gramontnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. 87, 061106 (2005).
[CrossRef]

Oulton, R. F.

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. Photon. 2, 496–500 (2008).
[CrossRef]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef]

Özgür, Ü.

H. Morkoc and Ü. Özgür, Zinc Oxide: Fundamentals, Materials and Device Technology (Wiley-VCH Verlag, 2009).

Pannipitiya, A.

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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. Photon. 2, 496–500 (2008).
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D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4, 83–91 (2010).
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D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927–1930 (1981).
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J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sensors Actuators B 54, 3–15 (1999).
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Figures (6)

Fig. 1.
Fig. 1.

Planar heterostructure consisting of n layers made of dielectrics and metals; ϵj is the permittivity of the jth layer. The heterostructure is assumed to extend infinitely in the y direction.

Fig. 2.
Fig. 2.

(a) Schematic of the metal–dielectric waveguide and the notations employed. (b) Density plot of electric field amplitude for a Ag–ZnO waveguide surrounded by air. It is assumed that d=250nm and h=50nm.

Fig. 3.
Fig. 3.

(a) Critical gain as a function of relative thickness p of the dielectric layer and (b) minimum critical gain γ0 (blue curve, left scale) and optimum thickness p0 (red curve, right scale) corresponding to γ0. The simulations were performed for a Ag–ZnO waveguide shown in Fig. 2(a); the material parameters are ε1=1, ϵ2=129+3.3i [22], ϵ3=3.73 [36].

Fig. 4.
Fig. 4.

(a) Schematic of MDM waveguide and the notations employed. (b) Density plot of electric field amplitude for a Ag–ZnO–Ag waveguide surrounded by air. The simulation parameters are d=120nm and h=90nm.

Fig. 5.
Fig. 5.

(a) Propagation length of SPPs as a function of q and (b) maximum values of LSPP (blue) with the corresponding optimum q values (red).

Fig. 6.
Fig. 6.

(a) Variation of critical gain with q and (b) minimal critical gain (blue) and the corresponding dielectric thickness (red).

Equations (7)

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

E(x,z,t)=12[x^Ex(x)+z^Ez(x)]exp[i(βzωt)]+c.c,
Exj=βϵjk[Ajexp(αjx)+Bjexp(αjx)],Ezj=iαjϵjk[Ajexp(αjx)Bjexp(αjx)],Hyj=Ajexp(αjx)+Bjexp(αjx),
ϵj=ϵjiϵj=ϵjiγϵj/k,
tanh(α2h)=α2ϵ2[2α1α3ϵ1ϵ3+tanh(α3d)(α32ϵ12+α12ϵ32)]α3ϵ3(α22ϵ12+α12ϵ22)+α1ϵ1tanh(α3d)(α32ϵ22+α22ϵ32).
p=d/w,
tanh(α3d2)=α2ϵ3α3ϵ2α2ϵ1tanh(α2h)+α1ϵ2α1ϵ2tanh(α2h)+α2ϵ1.
q=1d/w,

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