Abstract

We investigate in detail the crosstalk between plasmonic slot waveguides. We show that the coupling behavior of deep subwavelength three-dimensional (3-D) plasmonic slot waveguides is very different from the one of two-dimensional (2-D) metal-dielectric-metal (MDM) plasmonic waveguides. While in the 2-D case the coupling occurs only through the metal, in the 3-D case the coupling occurs primarily through the dielectric, in which the evanescent tail is much larger compared to the one in the metal. Thus, in most cases the coupling between 3-D plasmonic slot waveguides is much stronger than the coupling between the corresponding 2-D MDM plasmonic waveguides. Such strong coupling can be exploited to form directional couplers using plasmonic slot waveguides. On the other hand, with appropriate design, the crosstalk between 3-D plasmonic slot waveguides can be reduced even below the crosstalk levels of 2-D MDM plasmonic waveguides, without significantly affecting their modal size and attenuation length. Thus, 3-D plasmonic slot waveguides can be used for ultradense integration of optoelectronic components.

© 2008 Optical Society of America

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References

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2007

N. N. Feng, M. L. Brongersma, and L. Dal Negro, "Metal-dielectric slot-waveguide structures for the propagation of surface plasmon polaritons at 1.55 m," IEEE J. Quantum Electron. 43, 479-485 (2007).
[CrossRef]

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

E. Feigenbaum and M. Orenstein, "Modeling of complementary (Void) plasmon waveguiding," J. Lightwave Technol. 25, 2547-2562 (2007).
[CrossRef]

2006

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

2005

F. Kusunoki, T. Yotsuya, J. Takahara, and T. Kobayashi, "Propagation properties of guided waves in index-guided two-dimensional optical waveguides," Appl. Phys. Lett. 86, 211101 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, "Two-dimensionally localized modes of a nanoscale gap plasmon waveguide," Appl. Phys. Lett. 87, 261114 (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] [PubMed]

G. Veronis and S. Fan, "Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides," Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

L. Liu, Z. Han, and S. He, "Novel surface plasmon waveguide for high integration," Opt. Express 13, 6645-6650 (2005).
[CrossRef] [PubMed]

G. Veronis and S. Fan, "Guided subwavelength plasmonic mode supported by a slot in a thin metal film," Opt. Lett. 30, 3359-3361 (2005).
[CrossRef]

2004

2003

J. A. Pereda, A. Vegas, and A. Prieto, "An improved compact 2D full-wave FDFD method for general guided wave structures," Microwave Opt. Technol. Lett. 38, 331-335 (2003).
[CrossRef]

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

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]

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]

2002

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, "Nondiffraction-limited light transport by gold nanowires," Europhys. Lett. 60, 663-669 (2002).
[CrossRef]

2000

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B 62, R16356-R16359 (2000).
[CrossRef]

1999

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, "Plasmon polaritons of metallic nanowires for controlling submicron propagation of light," Phys. Rev. B 60, 9061-9068 (1999).
[CrossRef]

1997

1975

Appl. Phys. Lett.

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]

F. Kusunoki, T. Yotsuya, J. Takahara, and T. Kobayashi, "Propagation properties of guided waves in index-guided two-dimensional optical waveguides," Appl. Phys. Lett. 86, 211101 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, "Two-dimensionally localized modes of a nanoscale gap plasmon waveguide," Appl. Phys. Lett. 87, 261114 (2005).
[CrossRef]

G. Veronis and S. Fan, "Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides," Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

Europhys. Lett.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, "Nondiffraction-limited light transport by gold nanowires," Europhys. Lett. 60, 663-669 (2002).
[CrossRef]

IEEE J. Quantum Electron.

N. N. Feng, M. L. Brongersma, and L. Dal Negro, "Metal-dielectric slot-waveguide structures for the propagation of surface plasmon polaritons at 1.55 m," IEEE J. Quantum Electron. 43, 479-485 (2007).
[CrossRef]

S. J. Al-Bader, "Optical transmission on metallic wires - fundamental modes," IEEE J. Quantum Electron. 40, 325-329 (2004).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Microwave Opt. Technol. Lett.

J. A. Pereda, A. Vegas, and A. Prieto, "An improved compact 2D full-wave FDFD method for general guided wave structures," Microwave Opt. Technol. Lett. 38, 331-335 (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

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, "Channel plasmon subwavelength waveguide components including interferometers and ring resonators," Nature 440, 508-511 (2006).
[CrossRef] [PubMed]

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

Opt. Express

Opt. Lett.

Phys. Rev. B

J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, "Plasmon polaritons of metallic nanowires for controlling submicron propagation of light," Phys. Rev. B 60, 9061-9068 (1999).
[CrossRef]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, "Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit," Phys. Rev. B 62, R16356-R16359 (2000).
[CrossRef]

Phys. Rev. Lett.

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] [PubMed]

Other

D. M. Pozar, Microwave Engineering, (Wiley, New York, 1998).

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, (Oxford University Press, New York, 2006).

J. Jin, The Finite Element Method in Electromagnetics, (Wiley, New York, 2002).

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

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Figures (5)

Fig. 1.
Fig. 1.

Maximum transfer power p max as a function of Lc /p , under the approximation γ-≃i(βs βa )/2 (see Section 2). Here Lc is the coupling length, and p is the mean attenuation length. In all cases considered in this paper, this approximation results in less than 1% error in the calculated p max.

Fig. 2.
Fig. 2.

(a) Schematic of two coupled 2-D MDM plasmonic waveguides. (b) Schematic of two coupled symmetric plasmonic slot waveguides which are formed on the same thin metal film. (c) Schematic of two vertically-coupled symmetric plasmonic slot waveguides which are formed on parallel thin metal films. (d) Schematic of two coupled asymmetric plasmonic slot waveguides which are formed on the same thin metal film. (e) Coupling length Lc as a function of the distance D between two coupled plasmonic waveguides. Results are shown for 2-D MDM plasmonic waveguides (green line), symmetric plasmonic slot waveguides formed on the same metal film (red line), vertically-coupled symmetric plasmonic slot waveguides formed on parallel metal films (blue line), and asymmetric plasmonic slot waveguides formed on the same metal film (black line). In all cases, the slot widths are w=50 nm, the metal film thicknesses are h=50 nm, and the operating wavelength is λ 0=1.55 µm. (f) Maximum transfer power p max as a function of the distance D between two coupled plasmonic waveguides. All other parameters are as in (e).

Fig. 3.
Fig. 3.

(a) Schematic of a structure consisting of two coupled plasmonic slot waveguides, in which the metal film separating the two slots has an increased thickness h i. (b) Coupling length Lc as a function of h i (solid line). The distance between the two plasmonic slot waveguides is D=150 nm. All other parameters are as in Fig. 2(e). Also shown are the asymptotic value of Lc for h i→∞ (dash-dotted line), and Lc for two coupled 2-D MDM plasmonic waveguides with the same w and D (dashed line). (c) Maximum transfer power p max as a function of h i (solid line). Also shown are the asymptotic value of p max for h i→∞ (dash-dotted line), and p max for two coupled 2-D MDM plasmonic waveguides with the same w and D (dashed line). All other parameters are as in (b).

Fig. 4.
Fig. 4.

(a) Power density profile of the fundamental mode of a symmetric plasmonic slot waveguide consisting of a slot of width w=50 nm in a silver film of thickness h=50 nm embedded in silica (ns =1.44). (b) Power density profile of the mode with symmetric electric field distribution (E s (x,y)), supported by the structure of Fig. 3(a) for h i=1 µm. All other parameters are as in Fig. 3(b). Since the coupling between the two plasmonic slot waveguides is negligible for h i=1 µm (Figs. 3(b), 3(c)), the power density profiles of the symmetric (E s (x,y)) and antisymmetric (E a (x,y)) modes are almost identical. (c) Power density profile of the mode with symmetric electric field distribution (E s (x,y)), supported by the structure of Fig. 5(a) for w i=150 nm. All other parameters are as in Fig. 5(b). Since the coupling between the two plasmonic slot waveguides is negligible for w i=150 nm (Figs. 5(b), 5(c)), the power density profiles of the symmetric (E s (x,y)) and antisymmetric (E a (x,y)) modes are almost identical.

Fig. 5.
Fig. 5.

(a) Schematic of a structure consisting of two coupled plasmonic slot waveguides, in which the metal region separating the two slots is I-shaped, and includes two additional metal films of thickness h t. (b) Coupling length Lc as a function of w i (solid line). The metal film thicknesses are h i=400 nm, h t=50 nm. All other parameters are as in Fig. 3(b). Also shown are the asymptotic value of Lc for w i→∞ (dash-dotted line), and Lc for two coupled 2-D MDM plasmonic waveguides with the same w and D (dashed line). (c) Maximum transfer power p max as a function of w i (solid line). Also shown are the asymptotic value of p max for w i→∞ (dash-dotted line), and p max for two coupled 2-D MDM plasmonic waveguides with the same w and D (dashed line). All other parameters are as in (b).

Equations (11)

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

E ( x , y , z ) = c s ( z ) E s ( x , y ) + c a ( z ) E a ( x , y ) ,
E l ( x , y ) E s ( x , y ) 2 + E a ( x , y ) 2 ,
E r ( x , y ) E s ( x , y ) 2 - E a ( x , y ) 2 ,
E ( x , y , z ) = c l ( z ) E l ( x , y ) + c r ( z ) E r ( x , y ) .
[ c l ( z ) c r ( z ) ] = [ 1 2 1 2 1 2 1 2 ] [ c s ( z ) c a ( z ) ] ,
c r ( L ) 2 = 1 2 [ exp ( γ s L ) exp ( γ a L ) ] 2 .
L c π β s β a .
c r ( L ) 2 = exp ( 2 L L ̅ p ) 1 2 [ exp ( γ _ L ) exp ( γ _ L ) ] 2 ,
p max max L c r ( L ) 2 .
γ _ i ( β s β a ) 2 .
p max exp ( 2 x arctan ( x 1 ) ) 1 + x 2 , x = 2 L c ( π L ¯ p ) .

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