Abstract

We investigate a classic analog of electromagnetically induced transparency (EIT) in a metal–dielectric–metal (MDM) bus waveguide coupled to two stub resonators. A uniform theoretical model, for both direct and indirect couplings between the two stubs, is established to study spectral features in the plasmonic stub waveguide, and the theoretical results agree well with the finite difference time domain simulations. Adjusting phase difference and coupling strength of the interaction, one can realize the EIT-like phenomena and achieve the required slow light effect. The theoretical results may provide a guideline for the control of light in highly integrated optical circuits.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013 (3)

2012 (4)

A. Ishikawa, R. F. Oulton, T. Zentgra, and X. Zhang, Phys. Rev. B 85, 155108 (2012).
[CrossRef]

G. X. Wang, H. Lu, and X. M. Liu, Opt. Express 20, 20902 (2012).
[CrossRef]

H. Lu, X. M. Liu, and D. Mao, Phys. Rev. A 85, 053803 (2012).
[CrossRef]

Y. H. Guo, L. S. Yan, W. Pan, B. Luo, K. H. Wen, Z. Guo, and X. G. Luo, Opt. Express 20, 24348 (2012).
[CrossRef]

2011 (6)

2010 (3)

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
[CrossRef]

L. Yang, C. G. Min, and G. Veronis, Opt. Lett. 35, 4184 (2010).
[CrossRef]

R. D. Kekatpure, Phys. Rev. Lett. 104, 243902 (2010).
[CrossRef]

2009 (2)

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef]

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, Phys. Rev. B 80, 195415 (2009).
[CrossRef]

2008 (1)

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, Phys. Today 61(5), 44 (2008).
[CrossRef]

2007 (2)

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef]

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, Phys. Rev. A 75, 063833 (2007).
[CrossRef]

2006 (1)

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

2005 (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

1991 (2)

K. J. Boller, A. Imamolu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef]

H. A. Haus and W. P. Huang, Proc. IEEE 79, 1505 (1991).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

1969 (1)

E. N. Economou, Phys. Rev. 182, 539 (1969).
[CrossRef]

Boller, K. J.

K. J. Boller, A. Imamolu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef]

Bozhevolnyi, S. I.

Z. H. Han and S. I. Bozhevolnyi, Opt. Express 19, 3251 (2011).
[CrossRef]

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
[CrossRef]

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, Phys. Today 61(5), 44 (2008).
[CrossRef]

Cai, B.

Cao, G. T.

Chen, L.

Chen, Y. L.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Darmawan, S.

Ebbesen, T. W.

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, Phys. Today 61(5), 44 (2008).
[CrossRef]

Economou, E. N.

E. N. Economou, Phys. Rev. 182, 539 (1969).
[CrossRef]

Fan, S.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Gao, C. M.

Genet, C.

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, Phys. Today 61(5), 44 (2008).
[CrossRef]

Gong, Y. K.

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
[CrossRef]

Guo, G. C.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Guo, Y. H.

Guo, Z.

Hagness, S.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

Han, Z. H.

Harris, S. E.

K. J. Boller, A. Imamolu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef]

Haus, H. A.

H. A. Haus and W. P. Huang, Proc. IEEE 79, 1505 (1991).
[CrossRef]

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984), Chap. 7.

He, Z. H.

Huang, W. P.

H. A. Haus and W. P. Huang, Proc. IEEE 79, 1505 (1991).
[CrossRef]

Huang, Y.

Y. Huang, C. Min, and G. Veronis, Appl. Phys. Lett. 99, 143117 (2011).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Imamolu, A.

K. J. Boller, A. Imamolu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef]

Ishikawa, A.

A. Ishikawa, R. F. Oulton, T. Zentgra, and X. Zhang, Phys. Rev. B 85, 155108 (2012).
[CrossRef]

Jiang, W.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Kekatpure, R. D.

R. D. Kekatpure, Phys. Rev. Lett. 104, 243902 (2010).
[CrossRef]

Kobayashi, N.

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef]

Koo, S.

Kwong, D. L.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef]

Lee, K. H.

Li, H. J.

Lipson, M.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Liu, X. M.

Liu, Z. M.

Lu, H.

Luo, B.

Luo, X. G.

Mao, D.

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Mei, T.

Min, C.

Y. Huang, C. Min, and G. Veronis, Appl. Phys. Lett. 99, 143117 (2011).
[CrossRef]

Min, C. G.

Okada, T.

K. Ooi, T. Okada, and K. Tanaka, Phys. Rev. B 84, 115405 (2011).
[CrossRef]

Ooi, K.

K. Ooi, T. Okada, and K. Tanaka, Phys. Rev. B 84, 115405 (2011).
[CrossRef]

Oulton, R. F.

A. Ishikawa, R. F. Oulton, T. Zentgra, and X. Zhang, Phys. Rev. B 85, 155108 (2012).
[CrossRef]

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, Phys. Rev. B 80, 195415 (2009).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants in Solids (Academic, 1982).

Pan, W.

Park, N.

Piao, X. J.

Povinelli, M. L.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Sandhu, S.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Shakya, J.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Taflove, A.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

Tanaka, K.

K. Ooi, T. Okada, and K. Tanaka, Phys. Rev. B 84, 115405 (2011).
[CrossRef]

Tobing, L. Y. M.

Tomita, M.

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef]

Totsuka, K.

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef]

Veronis, G.

Y. Huang, C. Min, and G. Veronis, Appl. Phys. Lett. 99, 143117 (2011).
[CrossRef]

L. Yang, C. G. Min, and G. Veronis, Opt. Lett. 35, 4184 (2010).
[CrossRef]

Wang, G. X.

Wang, Y.

Wen, K. H.

Wong, C. W.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef]

Xiao, Y. F.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Xu, H. Q.

Xu, J. M.

Xu, Q.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

Yan, L. S.

Yang, L.

Yang, X.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef]

Yu, M.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef]

Yu, S.

Zang, X. F.

Zentgra, T.

A. Ishikawa, R. F. Oulton, T. Zentgra, and X. Zhang, Phys. Rev. B 85, 155108 (2012).
[CrossRef]

Zentgraf, T.

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, Phys. Rev. B 80, 195415 (2009).
[CrossRef]

Zhan, S. P.

Zhang, D. H.

Zhang, S.

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, Phys. Rev. B 80, 195415 (2009).
[CrossRef]

Zhang, X.

A. Ishikawa, R. F. Oulton, T. Zentgra, and X. Zhang, Phys. Rev. B 85, 155108 (2012).
[CrossRef]

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, Phys. Rev. B 80, 195415 (2009).
[CrossRef]

Zhang, Y.

Zhu, Y. M.

Zou, X. B.

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, Phys. Rev. A 75, 063833 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Huang, C. Min, and G. Veronis, Appl. Phys. Lett. 99, 143117 (2011).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nat. Photonics (1)

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
[CrossRef]

Opt. Express (5)

Opt. Lett. (4)

Phys. Rev. (1)

E. N. Economou, Phys. Rev. 182, 539 (1969).
[CrossRef]

Phys. Rev. A (2)

Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, Phys. Rev. A 75, 063833 (2007).
[CrossRef]

H. Lu, X. M. Liu, and D. Mao, Phys. Rev. A 85, 053803 (2012).
[CrossRef]

Phys. Rev. B (4)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

A. Ishikawa, R. F. Oulton, T. Zentgra, and X. Zhang, Phys. Rev. B 85, 155108 (2012).
[CrossRef]

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, Phys. Rev. B 80, 195415 (2009).
[CrossRef]

K. Ooi, T. Okada, and K. Tanaka, Phys. Rev. B 84, 115405 (2011).
[CrossRef]

Phys. Rev. Lett. (5)

R. D. Kekatpure, Phys. Rev. Lett. 104, 243902 (2010).
[CrossRef]

K. J. Boller, A. Imamolu, and S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991).
[CrossRef]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, Phys. Rev. Lett. 96, 123901 (2006).
[CrossRef]

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, Phys. Rev. Lett. 102, 173902 (2009).
[CrossRef]

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef]

Phys. Today (1)

T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, Phys. Today 61(5), 44 (2008).
[CrossRef]

Proc. IEEE (1)

H. A. Haus and W. P. Huang, Proc. IEEE 79, 1505 (1991).
[CrossRef]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Other (3)

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984), Chap. 7.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

E. D. Palik, Handbook of Optical Constants in Solids (Academic, 1982).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of MDM waveguide coupled to two stub resonators.

Fig. 2.
Fig. 2.

(a) and (c) Transmission spectra with different coupling distance L between the two stub resonators. (b) Coupling coefficient and coupling quality factor versus coupling distance L. (d) Evolution of the transmission spectra versus L and λ. The other geometrical parameters are w=100nm, d1=300nm, and d2=290nm. The circles are the simulation results and the solid curves are the analytical fits using the CMT.

Fig. 3.
Fig. 3.

Group index in the plasmonic stub waveguide for coupling distance (a) L=150nm, (b) L=100nm, (c) L=50nm, and (d) L=0nm. The other geometrical parameters are w=100nm, d1=300nm, and d2=290nm.

Fig. 4.
Fig. 4.

Evolution of transmission spectrum with coupling coefficient μ for coupling distance (a) L=0nm and (b) L=50nm. (c) and (d) are transmission phase shifts corresponding to (a) and (b), respectively. The other geometrical parameters are w=100nm and d1=d2=300nm.

Equations (11)

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

da1dt=(jω11τi11τw1)a1+S+,in(1)1τw1+S,in(1)1τw1jμ12a2,
da2dt=(jω21τi21τw2)a2+S+,in(2)1τw2+S,in(2)1τw2jμ21a1,
S,in(1)=S,out(2)ejφ,
S+,in(2)=S+,out(1)ejφ,
S+,out(1)=S+,in(1)1τw1a1,
S,out(2)=S,in(2)1τw2a2,
S+,out(2)=S+,in(2)1τw2a2,
t=S+,out(2)S+,in(1)=ejφ+(γ11τw2+γ21τw1+χ21τw1τw2ejφ+χ11τw1τw2ejφ)(γ1γ2χ1χ2)1ejφ,
t=ejφ+ejφγ11τw2+γ21τw1+2χ1τw1τw2cosφγ1γ2χ2,
ng=cvg=clτg=cldθdω,
t=ejφ+ejφ1τw2γ+2χcosφγ2χ2,

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