Abstract

Inefficient coupling between dielectric guided mode and plasmon mode has been overlooked in the past. The coupling mechanism is essentially different from the conventional coupling between dielectric modes. Based on qualitative theoretical analysis, we proposed two methods to strengthen the coupling between dielectric waveguide modes and exterior plasmon whispering gallery modes. One is using a U-shaped bent waveguide to break the adiabatic mode conversion process, and the other is to utilize higher-order dielectric mode to reach phase matching with plasmon mode. Both the transmission spectrum of waveguide and the energy spectrum of cavity demonstrate that the coupling efficiency can be greatly improved. These simple configurations are potential for wide applications, for example, tunable integrated optical devices and sensors.

© 2013 Optical Society of America

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    [CrossRef]

2013 (5)

S. H. Kwon, “Ultrasmall plasmonic cavity for chemical sensing,” Plasmonics8, 963–967 (2013).
[CrossRef]

R. M. Ma, R. F. Oulton, V. J. Sorger, and X. Zhang, “Plasmon lasers: coherent light source at molecular scales,” Laser Photonics Rev.7, 1–21 (2013).
[CrossRef]

X. Xiong, C. L. Zou, X. F. Ren, A. P. Liu, Y. X. Ye, F. W. Sun, and G. C. Guo, “Silver nanowires for photonics applications,” Laser Photonics Rev.7, 901–919 (2013).
[CrossRef]

Y. L. Chen, C. L. Zou, Y. W. Hu, and Q. Gong, “High-Q plasmonic and dielectric mode in a metal-coated whispering-gallery microcavity,” Phys. Rev. A87, 023824 (2013).
[CrossRef]

X. Xiong, C. L. Zou, X. F. Ren, and G. C. Guo, “Integrated polarization rotator/converter by stimulated Raman adiabatic passage,” Opt. Express21, 17097–17107 (2013).
[CrossRef] [PubMed]

2012 (5)

T. P. H. Sidiropoulos, S. A. Maier, and R. F. Oulton, “Efficient low dispersion compact plasmonic-photonic coupler,” Opt. Express20, 12359–12365 (2012).
[CrossRef] [PubMed]

C. L. Zou, F. W. Sun, C. H. Dong, Y. F. Xiao, X. F. Ren, L. Lv, X. D. Chen, J. M. Cui, Z. F. Han, and G. C. Guo, “Movable fiber-integrated hybrid plasmonic waveguide on metal film,” IEEE Photonics Technol. Lett.24, 434–436 (2012).
[CrossRef]

M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature482, 204–207 (2012).
[CrossRef] [PubMed]

M. Mayy, G. Zhu, E. Mayy, A. Webb, and M. A. Noginov, “Low temperature studies of surface plasmon polaritons in silver films,” J. Appl. Phys.111, 094103 (2012).
[CrossRef]

F. B. Arango, A. Kwadrin, and A. F. Koenderink, “Plasmonic antennas hybrid with dielectric wavegudies,” ACS Nano6, 10156–10167 (2012).
[CrossRef]

2011 (2)

2010 (4)

D. K. Gramotenv and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4, 83–91 (2010).
[CrossRef]

L. Novotny, “Strong coupling, energy splitting, and level crossings: a classical perspective,” Am. J. Phys.78, 1199–1202 (2010).
[CrossRef]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9, 205–213 (2010).
[CrossRef] [PubMed]

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. H. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105, 153902 (2010).
[CrossRef]

2009 (5)

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature457, 455–458 (2009).
[CrossRef] [PubMed]

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature460, 1110–1113 (2009).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461, 629–632 (2009).
[CrossRef] [PubMed]

F. Liu, R. Y. Wan, Y. X. Li, Y. D. Huang, Y. Miura, D. Ohnishi, and J. D. Peng, “Extremely high efficient coupling between long range surface plasmon polariton and dielectric waveguide mode,” Appl. Phys. Lett.95, 091104 (2009).
[CrossRef]

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics Rev.3, 243–261 (2009).
[CrossRef]

2007 (2)

R. Kirchain and L. Kimerling, “A roadmap for nanophotonics,” Nat. Photonics1, 303–305 (2007).
[CrossRef]

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. C. Zhu, T. D. Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics1, 589–594 (2007).
[CrossRef]

2005 (1)

C. Wittig, “The Landau-Zener formula,” J. Phys. Chem. B109, 8428–8430 (2005).
[CrossRef]

2003 (3)

S. Khorasani and B. Rashidian, “Coupled mode theory of waveguides with conducting interfaces,” Scientia Iranica10, 426–435 (2003).

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett.91, 043902 (2003).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature424, 839–846 (2003).
[CrossRef] [PubMed]

2002 (2)

M. Skorobogatiy, S. Jacobs, S. Johnson, and Y. Fink, “Geometric variations in high index-contrast waveguides, coupled mode theory in curvilinear coordinates,” Opt. Express10, 1227–1243 (2002).
[CrossRef] [PubMed]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E66, 066608 (2002).
[CrossRef]

1991 (1)

H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE79, 1501–1518 (1991).

1975 (1)

1974 (1)

J. Nkoma, R. Loudon, and D. R. Tilley, “Elementary properties of surface polaritons,” J. Phys. C: Solid State Phys.7, 3547–3559 (1974).
[CrossRef]

Arango, F. B.

F. B. Arango, A. Kwadrin, and A. F. Koenderink, “Plasmonic antennas hybrid with dielectric wavegudies,” ACS Nano6, 10156–10167 (2012).
[CrossRef]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9, 205–213 (2010).
[CrossRef] [PubMed]

Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature460, 1110–1113 (2009).
[CrossRef] [PubMed]

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461, 629–632 (2009).
[CrossRef] [PubMed]

Belgrave, A. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature460, 1110–1113 (2009).
[CrossRef] [PubMed]

Bienstman, P.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E66, 066608 (2002).
[CrossRef]

Bozhevolnyi, S. I.

D. K. Gramotenv and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4, 83–91 (2010).
[CrossRef]

Chen, X. D.

C. L. Zou, F. W. Sun, C. H. Dong, Y. F. Xiao, X. F. Ren, L. Lv, X. D. Chen, J. M. Cui, Z. F. Han, and G. C. Guo, “Movable fiber-integrated hybrid plasmonic waveguide on metal film,” IEEE Photonics Technol. Lett.24, 434–436 (2012).
[CrossRef]

C. L. Zou, F. W. Sun, C. H. Dong, X. F. Ren, J. M. Cui, X. D. Chen, Z. F. Han, and G. C. Guo, “Broadband integrated polarization beam splitter with surface plasmon,” Opt. Lett.36, 3630–3632 (2011).
[CrossRef] [PubMed]

Chen, Y. L.

Y. L. Chen, C. L. Zou, Y. W. Hu, and Q. Gong, “High-Q plasmonic and dielectric mode in a metal-coated whispering-gallery microcavity,” Phys. Rev. A87, 023824 (2013).
[CrossRef]

Cui, J. M.

C. L. Zou, F. W. Sun, C. H. Dong, Y. F. Xiao, X. F. Ren, L. Lv, X. D. Chen, J. M. Cui, Z. F. Han, and G. C. Guo, “Movable fiber-integrated hybrid plasmonic waveguide on metal film,” IEEE Photonics Technol. Lett.24, 434–436 (2012).
[CrossRef]

C. L. Zou, F. W. Sun, C. H. Dong, X. F. Ren, J. M. Cui, X. D. Chen, Z. F. Han, and G. C. Guo, “Broadband integrated polarization beam splitter with surface plasmon,” Opt. Lett.36, 3630–3632 (2011).
[CrossRef] [PubMed]

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461, 629–632 (2009).
[CrossRef] [PubMed]

Dong, C. H.

C. L. Zou, F. W. Sun, C. H. Dong, Y. F. Xiao, X. F. Ren, L. Lv, X. D. Chen, J. M. Cui, Z. F. Han, and G. C. Guo, “Movable fiber-integrated hybrid plasmonic waveguide on metal film,” IEEE Photonics Technol. Lett.24, 434–436 (2012).
[CrossRef]

C. L. Zou, F. W. Sun, C. H. Dong, X. F. Ren, J. M. Cui, X. D. Chen, Z. F. Han, and G. C. Guo, “Broadband integrated polarization beam splitter with surface plasmon,” Opt. Lett.36, 3630–3632 (2011).
[CrossRef] [PubMed]

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. H. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105, 153902 (2010).
[CrossRef]

Eijkemans, T. J.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. C. Zhu, T. D. Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics1, 589–594 (2007).
[CrossRef]

Fainman, Y.

M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature482, 204–207 (2012).
[CrossRef] [PubMed]

Fink, Y.

Geluk, E. J.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. C. Zhu, T. D. Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics1, 589–594 (2007).
[CrossRef]

Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461, 629–632 (2009).
[CrossRef] [PubMed]

Gong, Q.

Y. L. Chen, C. L. Zou, Y. W. Hu, and Q. Gong, “High-Q plasmonic and dielectric mode in a metal-coated whispering-gallery microcavity,” Phys. Rev. A87, 023824 (2013).
[CrossRef]

Gong, Q. H.

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. H. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105, 153902 (2010).
[CrossRef]

Gramotenv, D. K.

D. K. Gramotenv and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4, 83–91 (2010).
[CrossRef]

Guo, G. C.

X. Xiong, C. L. Zou, X. F. Ren, A. P. Liu, Y. X. Ye, F. W. Sun, and G. C. Guo, “Silver nanowires for photonics applications,” Laser Photonics Rev.7, 901–919 (2013).
[CrossRef]

X. Xiong, C. L. Zou, X. F. Ren, and G. C. Guo, “Integrated polarization rotator/converter by stimulated Raman adiabatic passage,” Opt. Express21, 17097–17107 (2013).
[CrossRef] [PubMed]

C. L. Zou, F. W. Sun, C. H. Dong, Y. F. Xiao, X. F. Ren, L. Lv, X. D. Chen, J. M. Cui, Z. F. Han, and G. C. Guo, “Movable fiber-integrated hybrid plasmonic waveguide on metal film,” IEEE Photonics Technol. Lett.24, 434–436 (2012).
[CrossRef]

C. L. Zou, F. W. Sun, C. H. Dong, X. F. Ren, J. M. Cui, X. D. Chen, Z. F. Han, and G. C. Guo, “Broadband integrated polarization beam splitter with surface plasmon,” Opt. Lett.36, 3630–3632 (2011).
[CrossRef] [PubMed]

Han, Z. F.

C. L. Zou, F. W. Sun, C. H. Dong, Y. F. Xiao, X. F. Ren, L. Lv, X. D. Chen, J. M. Cui, Z. F. Han, and G. C. Guo, “Movable fiber-integrated hybrid plasmonic waveguide on metal film,” IEEE Photonics Technol. Lett.24, 434–436 (2012).
[CrossRef]

C. L. Zou, F. W. Sun, C. H. Dong, X. F. Ren, J. M. Cui, X. D. Chen, Z. F. Han, and G. C. Guo, “Broadband integrated polarization beam splitter with surface plasmon,” Opt. Lett.36, 3630–3632 (2011).
[CrossRef] [PubMed]

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. H. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105, 153902 (2010).
[CrossRef]

Hanfner, J. H.

K. M. Mayer and J. H. Hanfner, “Localized surface plasmon resonance sensors,” Chem. Rev.111, 3828–3857 (2011).
[CrossRef] [PubMed]

Haus, H. A.

H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE79, 1501–1518 (1991).

Herz, E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature460, 1110–1113 (2009).
[CrossRef] [PubMed]

Hill, M. T.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. C. Zhu, T. D. Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics1, 589–594 (2007).
[CrossRef]

Hu, Y. W.

Y. L. Chen, C. L. Zou, Y. W. Hu, and Q. Gong, “High-Q plasmonic and dielectric mode in a metal-coated whispering-gallery microcavity,” Phys. Rev. A87, 023824 (2013).
[CrossRef]

Huang, W.

H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE79, 1501–1518 (1991).

Huang, Y. D.

F. Liu, R. Y. Wan, Y. X. Li, Y. D. Huang, Y. Miura, D. Ohnishi, and J. D. Peng, “Extremely high efficient coupling between long range surface plasmon polariton and dielectric waveguide mode,” Appl. Phys. Lett.95, 091104 (2009).
[CrossRef]

Ibanescu, M.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E66, 066608 (2002).
[CrossRef]

Jacobs, S.

Joannopoulos, J. D.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E66, 066608 (2002).
[CrossRef]

Johnson, S.

Johnson, S. G.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E66, 066608 (2002).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(a) Coupling between dielectric waveguide and dielectric cavity, with waveguide width 0.26μm, cavity radius 3μm, minimum gap 100nm. (b) Transmission spectrum of waveguide and the spectrum of normalized energy inside the cavity, corresponding to the configuration in (a). (c) Coupling between dielectric waveguide and plasmonic cavity, with waveguide width 0.36μm, cavity radius 20μm, minimum gap 50nm. White dashed line indicates the outline of silver cavity. Inset: enlarged picture of the coupling region. (d) Transmission spectrum of waveguide and the spectrum of normalized energy, corresponding to the configuration in (c).

Fig. 2
Fig. 2

(a) Schematic illustration of the coupling between dielectric waveguide and metal microresonator, with waveguide tangent to the cavity. The origin is where the gap between waveguide and cavity is zero. (b) neff of eigenmodes, which is dependent on the gap between waveguide and cavity, at each point z. (c)–(d) For metal cavity coupling, the normalized electric field profiles of the eigen plasmon mode at z = −8 μm (c) and z = 0 (d), respectively. The green and gray regions represent dielectric waveguide and metal cavity, respectively. (e)–(f) For metal cavity coupling, the normalized electric field profiles of the eigen dielectric mode at z = −8 μm (e) and z = 0 (f), respectively. (g)–(h) For dielectric cavity coupling, the electric field profiles of the eigen dielectric mode at z = −8 μm (g) and z = 0 (h), respectively.

Fig. 3
Fig. 3

(a) Coupling between a U-shaped bent silica waveguide and silver cavity, with R = 20μm, r = 1.2μm, and waveguide width being 0.36μm. Inset: enlarged picture of the coupling region. (b) Transmission spectrum of waveguide and the spectrum of normalized energy |E|, with d0 = 50nm.

Fig. 4
Fig. 4

(a) Dependence of Q factor on 1/r. (b) Dependence of normalized energy |E| on 1/r. Red lines represent the smoothed curves of the data.

Fig. 5
Fig. 5

(a) Coupling with second-order guided mode between a straight silica waveguide and silver cavity, with R = 20μm, and waveguide width being 0.36μm. Inset: enlarged picture of the coupling region. (b) Transmission spectrum of waveguide and the spectrum of normalized energy |E|, with d0 = 0.36μm.

Fig. 6
Fig. 6

Dependence of Q factor (a) and dependence of normalized energy |E| (b) on d0. Red lines represent the smoothed curves of the data.

Equations (4)

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

E s = 2 κ 1 i ( ω ω c ) κ 0 κ 1 E i ,
E t = i ( ω ω c ) κ 0 + κ 1 i ( ω ω c ) κ 0 κ 1 E i ,
i z | φ ( z ) = H ( z ) | φ ( z ) ,
z a k ( z ) = φ k ( z ) | z | φ k ( z ) a k ( z ) m k g k m ( z ) e i ( β m ( z ) β k ( z ) ) d z a m ( z ) .

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