Abstract

Vertical directional coupling between a metal-insulator-metal (MIM) plasmonic waveguide and a conventional dielectric waveguide is investigated. The coupling length, extinction ratio, insertion loss and coupling efficiency of the hybrid coupler are analyzed. As an example, when the separation between the two waveguides is 250 nm, a maximum coupling efficiency of 73%, an insertion loss of −1.4 dB and an extinction ratio of 16 dB can be achieved at a coupling length of 4.5 µm at 1.55 µm wavelength. A particular feature of this hybrid coupler is that it is highly tolerant to the structural parameters of the plasmonic waveguide and the misalignment between the two waveguides. The performance of this hybrid coupler as a TM polarizer is also analyzed and a maximum extinction ratio of 44 dB and an insertion loss of −0.18 dB can be obtained. The application of this hybrid coupler includes the signal routing between plasmonic waveguides and dielectric waveguides in photonic integrated circuits and the polarization control between TE and TM modes. In addition, it provides an approach for efficiently exciting MIM plasmonic modes with conventional dielectric modes.

© 2010 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. 9, 21–25 (2010).
    [CrossRef]
  4. F. Liu, Y. Rao, Y. Huang, W. Zhang, and J. Peng, “Coupling between long range surface plasmon polariton mode and dielectric waveguide mode,” Appl. Phys. Lett. 90, 141101 (2007).
    [CrossRef]
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    [CrossRef]

2010

R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. 9, 21–25 (2010).
[CrossRef]

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

R. Yang, R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, “Efficient light coupling between dielectric slot waveguide and plasmonic slot waveguide,” Opt. Lett. 35, 649–651 (2010).
[CrossRef] [PubMed]

Z. Han, A. Y. Elezzabi, and V. Van, “Experimental realization of subwavelength plasmonic slot waveguides on a silicon platform,” Opt. Lett. 35, 502–504 (2010).
[CrossRef] [PubMed]

2009

J. Tian, S. Q. Yu, W. Yan, and M. Qiu, “Broadband high-efficiency surface-plasmon-polariton coupler with silicon-metal interface,” Appl. Phys. Lett. 95, 013504 (2009).
[CrossRef]

R. Yan, P. Pausauskie, J. Huang, and P. Yang, “Direct photonic-plasmonic coupling and routing in single nanowires,” Proc. Natl. Acad. Sci. U.S.A. 106, 21045–21050 (2009).
[CrossRef] [PubMed]

A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11, 015002 (2009).
[CrossRef]

2008

2007

2006

2005

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]

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]

1994

1984

K. L. Chen, and S. Wang, “Cross-talk problems in optical directional couplers,” Appl. Phys. Lett. 44, 166 (1984).
[CrossRef]

1973

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
[CrossRef]

Abushagur, M. A. G.

Baba, K.

Bozhevolnyi, S. I.

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

Brunets, I.

R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. 9, 21–25 (2010).
[CrossRef]

Chen, A.

A. L. Pyayt, B. Wiley, Y. Xia, A. Chen, and L. Dalton, “Integration of photonic and silver nanowire plasmonic waveguides,” Nat. Nanotechnol. 3, 660–665 (2008).
[CrossRef]

Chen, K. L.

K. L. Chen, and S. Wang, “Cross-talk problems in optical directional couplers,” Appl. Phys. Lett. 44, 166 (1984).
[CrossRef]

Chen, L.

Cho, S. Y.

A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11, 015002 (2009).
[CrossRef]

Dalton, L.

A. L. Pyayt, B. Wiley, Y. Xia, A. Chen, and L. Dalton, “Integration of photonic and silver nanowire plasmonic waveguides,” Nat. Nanotechnol. 3, 660–665 (2008).
[CrossRef]

Degiron, A.

A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11, 015002 (2009).
[CrossRef]

Elezzabi, A. Y.

Fan, S.

Feng, N. N.

Fukui, M.

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]

Gramotnev, D. K.

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

Han, Z.

Haraguchi, M.

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]

Hoffman, G. B.

Huang, J.

R. Yan, P. Pausauskie, J. Huang, and P. Yang, “Direct photonic-plasmonic coupling and routing in single nanowires,” Proc. Natl. Acad. Sci. U.S.A. 106, 21045–21050 (2009).
[CrossRef] [PubMed]

Huang, Y.

F. Liu, Y. Rao, Y. Huang, W. Zhang, and J. Peng, “Coupling between long range surface plasmon polariton mode and dielectric waveguide mode,” Appl. Phys. Lett. 90, 141101 (2007).
[CrossRef]

Jokerst, N. M.

A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11, 015002 (2009).
[CrossRef]

Lipson, M.

Liu, F.

F. Liu, Y. Rao, Y. Huang, W. Zhang, and J. Peng, “Coupling between long range surface plasmon polariton mode and dielectric waveguide mode,” Appl. Phys. Lett. 90, 141101 (2007).
[CrossRef]

Lu, Z.

Matsuzaki, Y.

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]

Miyagi, M.

Mortensen, N. A.

Nakano, T.

Negro, L. D.

Ogawa, T.

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]

Okamoto, T.

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]

Pausauskie, P.

R. Yan, P. Pausauskie, J. Huang, and P. Yang, “Direct photonic-plasmonic coupling and routing in single nanowires,” Proc. Natl. Acad. Sci. U.S.A. 106, 21045–21050 (2009).
[CrossRef] [PubMed]

Peng, J.

F. Liu, Y. Rao, Y. Huang, W. Zhang, and J. Peng, “Coupling between long range surface plasmon polariton mode and dielectric waveguide mode,” Appl. Phys. Lett. 90, 141101 (2007).
[CrossRef]

Pile, D. F. P.

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]

Polman, A.

R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. 9, 21–25 (2010).
[CrossRef]

Pyayt, A. L.

A. L. Pyayt, B. Wiley, Y. Xia, A. Chen, and L. Dalton, “Integration of photonic and silver nanowire plasmonic waveguides,” Nat. Nanotechnol. 3, 660–665 (2008).
[CrossRef]

Qiu, M.

J. Tian, S. Q. Yu, W. Yan, and M. Qiu, “Broadband high-efficiency surface-plasmon-polariton coupler with silicon-metal interface,” Appl. Phys. Lett. 95, 013504 (2009).
[CrossRef]

Rao, Y.

F. Liu, Y. Rao, Y. Huang, W. Zhang, and J. Peng, “Coupling between long range surface plasmon polariton mode and dielectric waveguide mode,” Appl. Phys. Lett. 90, 141101 (2007).
[CrossRef]

Reano, R. M.

Schmitz, J.

R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. 9, 21–25 (2010).
[CrossRef]

Shakya, J.

Smith, D. R.

A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11, 015002 (2009).
[CrossRef]

Tian, J.

J. Tian, S. Q. Yu, W. Yan, and M. Qiu, “Broadband high-efficiency surface-plasmon-polariton coupler with silicon-metal interface,” Appl. Phys. Lett. 95, 013504 (2009).
[CrossRef]

Tyler, T.

A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11, 015002 (2009).
[CrossRef]

Van, V.

van Loon, R. V. A.

R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. 9, 21–25 (2010).
[CrossRef]

Vernon, K. C.

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]

Veronis, G.

Wahsheh, R. A.

Walters, R. J.

R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. 9, 21–25 (2010).
[CrossRef]

Wang, S.

K. L. Chen, and S. Wang, “Cross-talk problems in optical directional couplers,” Appl. Phys. Lett. 44, 166 (1984).
[CrossRef]

Wiley, B.

A. L. Pyayt, B. Wiley, Y. Xia, A. Chen, and L. Dalton, “Integration of photonic and silver nanowire plasmonic waveguides,” Nat. Nanotechnol. 3, 660–665 (2008).
[CrossRef]

Xia, Y.

A. L. Pyayt, B. Wiley, Y. Xia, A. Chen, and L. Dalton, “Integration of photonic and silver nanowire plasmonic waveguides,” Nat. Nanotechnol. 3, 660–665 (2008).
[CrossRef]

Xiao, S.

Yamaguchi, K.

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]

Yan, R.

R. Yan, P. Pausauskie, J. Huang, and P. Yang, “Direct photonic-plasmonic coupling and routing in single nanowires,” Proc. Natl. Acad. Sci. U.S.A. 106, 21045–21050 (2009).
[CrossRef] [PubMed]

Yan, W.

J. Tian, S. Q. Yu, W. Yan, and M. Qiu, “Broadband high-efficiency surface-plasmon-polariton coupler with silicon-metal interface,” Appl. Phys. Lett. 95, 013504 (2009).
[CrossRef]

Yang, P.

R. Yan, P. Pausauskie, J. Huang, and P. Yang, “Direct photonic-plasmonic coupling and routing in single nanowires,” Proc. Natl. Acad. Sci. U.S.A. 106, 21045–21050 (2009).
[CrossRef] [PubMed]

Yang, R.

Yariv, A.

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
[CrossRef]

Yu, S. Q.

J. Tian, S. Q. Yu, W. Yan, and M. Qiu, “Broadband high-efficiency surface-plasmon-polariton coupler with silicon-metal interface,” Appl. Phys. Lett. 95, 013504 (2009).
[CrossRef]

Zhang, W.

F. Liu, Y. Rao, Y. Huang, W. Zhang, and J. Peng, “Coupling between long range surface plasmon polariton mode and dielectric waveguide mode,” Appl. Phys. Lett. 90, 141101 (2007).
[CrossRef]

Appl. Phys. Lett.

F. Liu, Y. Rao, Y. Huang, W. Zhang, and J. Peng, “Coupling between long range surface plasmon polariton mode and dielectric waveguide mode,” Appl. Phys. Lett. 90, 141101 (2007).
[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]

J. Tian, S. Q. Yu, W. Yan, and M. Qiu, “Broadband high-efficiency surface-plasmon-polariton coupler with silicon-metal interface,” Appl. Phys. Lett. 95, 013504 (2009).
[CrossRef]

K. L. Chen, and S. Wang, “Cross-talk problems in optical directional couplers,” Appl. Phys. Lett. 44, 166 (1984).
[CrossRef]

IEEE J. Quantum Electron.

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
[CrossRef]

J. Opt. Soc. Am. B

N. J. Phys.

A. Degiron, S. Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11, 015002 (2009).
[CrossRef]

Nat. Mater.

R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, “A silicon-based electrical source of surface plasmon polaritons,” Nat. Mater. 9, 21–25 (2010).
[CrossRef]

Nat. Nanotechnol.

A. L. Pyayt, B. Wiley, Y. Xia, A. Chen, and L. Dalton, “Integration of photonic and silver nanowire plasmonic waveguides,” Nat. Nanotechnol. 3, 660–665 (2008).
[CrossRef]

Nat. Photonics

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

Opt. Express

Opt. Lett.

Proc. Natl. Acad. Sci. U.S.A.

R. Yan, P. Pausauskie, J. Huang, and P. Yang, “Direct photonic-plasmonic coupling and routing in single nanowires,” Proc. Natl. Acad. Sci. U.S.A. 106, 21045–21050 (2009).
[CrossRef] [PubMed]

Other

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1998).

A. W. Snyder, and J. D. Love, Optical Waveguide Theory (Chapman &Hall, London, New York, 1983).

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Figures (12)

Fig. 1.
Fig. 1.

Schematic diagram of the hybrid directional coupler. The red region denotes Au and the green region denotes Si. z is he light propagation direction.

Fig. 2.
Fig. 2.

Electric field amplitudes (∣Ex ∣) of (a) the quasi-even and (c) the quasi-odd modes supported by the hybrid coupler. The arrows indicate electric field oscillation orientations in x-y plane. (b) and (d) are corresponding electric field (Ex ) profiles along x=0. The dashed lines in (b) and (d) indicate the boundaries of both arms.

Fig. 3.
Fig. 3.

Effective refractive indices (neff ) and losses of the two eigenmodes versus the arm separation (s).

Fig. 4.
Fig. 4.

(a) Electric field and (b) magnetic field intensities along x=0 in the coupler as functions of the position z when the fields are excited by the dielectric modes at z=0 (s=250nm), respectively. The green arrows indicate where the fields in the coupler are excited.

Fig. 5.
Fig. 5.

Output power from the two output arms versus the interaction length z at s=250 nm.

Fig. 6.
Fig. 6.

Coupling length (Lc ) versus the arm separation (s) when the fields are excited by the dielectric mode. Lc is normalized to the propagation length of the decoupled plasmonic waveguide L 0.

Fig. 7.
Fig. 7.

Extinction ratio (ER) and amplitude of the coupling coefficient ∣C∣ versus the arm separation (s) when the field is excited by the dielectric mode.

Fig. 8.
Fig. 8.

(a) Losses versus the arm separation (s). (b) Comparison of the input dielectric electric field intensity and the coupled electric field intensity along x=0 at z=0. (c) Comparison of the output plasmonic electric field intensity and the coupled electric field intensity along x=0 at z=Lc . The fields are excited by the dielectric modes at s=250 nm. The dashed lines in (b) and (c) indicate the boundaries of both arms.

Fig. 9.
Fig. 9.

Tolerance of the hybrid coupler to slot structural parameters. (a)–(c) are the coupling length, extinction ratio (ER) and insertion loss (IL) versus the slot height for different slot widths at s=250 nm, respectively.

Fig. 10.
Fig. 10.

(a) Effective refractive index and (b) loss of the decoupled MIM plasmonic waveguide versus the slot height for different slot widths.

Fig. 11.
Fig. 11.

(a) and (b) are electric field (Ex ) amplitudes of the quasi-even mode and quasi-odd mode in the hybrid coupler at Δx=200 nm (s=250 nm), respectively. All the parameters except Δx are the same as those in Fig. 2. (c) Coupling length and extinction ratio (ER) versus the misalignment Δx at s=250 nm. (d) Insertion loss (IL) versus the misalignment Δx at s=250 nm.

Fig. 12.
Fig. 12.

(a) and (b) are electric field (Ex ) amplitudes of TM modes in the hybrid coupler at s=250 nm and the decoupled dielectric waveguide, respectively. (c) Insertion loss (IL) and extinction ratio (ER) of the TM polarizer at s=250 nm.

Equations (5)

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

E ( x , y , z ) = C de E e ( x , y ) e i β e z + C do E o ( x , y ) e i β e z
C ij = 1 2 E i × H j · z ̂ dS = C ij e i θ i j
E d ( x , y , z ) = C de C ed e β ei z e i ( β er z + θ de + θ ed ) E e ( x , y ) + C do C od e β oi z e i ( β or z + θ do + θ od ) E o ( x , y )
E p ( x , y , z ) = C de C ep e β ei z e i ( β er z + θ de + θ ep ) E e ( x , y ) + C do C op e β oi z e i ( β or z + θ do + θ op ) E o ( x , y )
ER = 20 × lg C de C ep e β ei L c e i ( β er L c + θ de + θ ep ) + C do C op e β oi L c e i ( β or L c + θ do + θ op ) C de C ed e β ei L c e i ( β er L c + θ de + θ ed ) + C do C od e β oi L c e i ( β or L c + θ do + θ od )

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