Abstract

We theoretically present the analysis and design of a nanoplasmonic bandpass filter with flat-top spectral characteristics by cascading a series of directly connected rectangular ring resonators based on metal–insulator–metal waveguides. Analyzed by the equivalent lumped circuit model of the transmission line to plasmonic waveguides, the transmission properties of a symmetric rectangular ring resonator with the directly connected input and output waveguides are approximately the same as that of a Fabry–Perot resonator. Then the thin-film design methodology is applied to realize a plasmonic bandpass filter with the squared passband. An example of cascaded two-rectangular ring resonator structure is numerically demonstrated by using the transmission line model and 2D finite difference time domain method.

© 2014 Optical Society of America

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2013 (1)

2012 (2)

H. Nejati and A. Beirami, Opt. Lett. 37, 1050 (2012).
[CrossRef]

J. X. Tan, Y. B. Xie, J. W. Dong, and H. Z. Wang, Plasmonics 7, 435 (2012).
[CrossRef]

2011 (1)

A. Setayesh, S. R. Mirnaziry, and M. S. Abrishamian, J. Opt. 13, 035004 (2011).
[CrossRef]

2010 (1)

R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, Nat. Mater. 9, 21 (2010).
[CrossRef]

2009 (2)

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, Nat. Photonics 3, 283 (2009).
[CrossRef]

T. B. Wang, X. W. Wen, C. P. Yin, and H. Z. Wang, Opt. Express 17, 24096 (2009).
[CrossRef]

2008 (1)

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, IEEE J. Sel. Top. Quantum Electron. 14, 1462 (2008).
[CrossRef]

2007 (2)

C.-H. Chen and Y. Fainman, IEEE J. Sel. Top. Quantum Electron. 13, 262 (2007).
[CrossRef]

A. Hosseini and Y. Massoud, Appl. Phys. Lett. 90, 181102 (2007).
[CrossRef]

2006 (1)

E. Ozbay, Science 311, 189 (2006).
[CrossRef]

2005 (3)

1998 (1)

1995 (1)

Abrishamian, M. S.

A. Setayesh, S. R. Mirnaziry, and M. S. Abrishamian, J. Opt. 13, 035004 (2011).
[CrossRef]

Beirami, A.

Borghs, G.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, Nat. Photonics 3, 283 (2009).
[CrossRef]

Brunets, I.

R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, Nat. Mater. 9, 21 (2010).
[CrossRef]

Chang, K.

K. Chang and L. H. Hsieh, Microwave Ring Circuits and Related Structures (Wiley, 2004).

Chen, C. H.

Chen, C.-H.

C.-H. Chen and Y. Fainman, IEEE J. Sel. Top. Quantum Electron. 13, 262 (2007).
[CrossRef]

C.-H. Chen, K. Tetz, W. Nakagawa, and Y. Fainman, Appl. Opt. 44, 1503 (2005).
[CrossRef]

De Vlaminck, I.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, Nat. Photonics 3, 283 (2009).
[CrossRef]

Djurisic, A. B.

Dong, J. W.

J. X. Tan, Y. B. Xie, J. W. Dong, and H. Z. Wang, Plasmonics 7, 435 (2012).
[CrossRef]

Elazar, J. M.

Fainman, Y.

C.-H. Chen and Y. Fainman, IEEE J. Sel. Top. Quantum Electron. 13, 262 (2007).
[CrossRef]

C.-H. Chen, K. Tetz, W. Nakagawa, and Y. Fainman, Appl. Opt. 44, 1503 (2005).
[CrossRef]

Fan, S.

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, IEEE J. Sel. Top. Quantum Electron. 14, 1462 (2008).
[CrossRef]

G. Veronis and S. Fan, Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

Gray, S.

Hosseini, A.

A. Hosseini and Y. Massoud, Appl. Phys. Lett. 90, 181102 (2007).
[CrossRef]

Hsieh, L. H.

K. Chang and L. H. Hsieh, Microwave Ring Circuits and Related Structures (Wiley, 2004).

Kocabas, S. E.

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, IEEE J. Sel. Top. Quantum Electron. 14, 1462 (2008).
[CrossRef]

Lagae, L.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, Nat. Photonics 3, 283 (2009).
[CrossRef]

Lee, T. W.

Liao, K. S.

Majewski, M. L.

Massoud, Y.

A. Hosseini and Y. Massoud, Appl. Phys. Lett. 90, 181102 (2007).
[CrossRef]

Miller, D. A. B.

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, IEEE J. Sel. Top. Quantum Electron. 14, 1462 (2008).
[CrossRef]

Mirnaziry, S. R.

A. Setayesh, S. R. Mirnaziry, and M. S. Abrishamian, J. Opt. 13, 035004 (2011).
[CrossRef]

Nakagawa, W.

Nejati, H.

Neutens, P.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, Nat. Photonics 3, 283 (2009).
[CrossRef]

Ozbay, E.

E. Ozbay, Science 311, 189 (2006).
[CrossRef]

Polman, A.

R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, Nat. Mater. 9, 21 (2010).
[CrossRef]

Rakic, A. D.

Schmitz, J.

R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, Nat. Mater. 9, 21 (2010).
[CrossRef]

Setayesh, A.

A. Setayesh, S. R. Mirnaziry, and M. S. Abrishamian, J. Opt. 13, 035004 (2011).
[CrossRef]

Tan, J. X.

J. X. Tan, Y. B. Xie, J. W. Dong, and H. Z. Wang, Plasmonics 7, 435 (2012).
[CrossRef]

Tetz, K.

Thelen, A.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, 1989).

Troitski, Y. V.

Van Dorpe, P.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, Nat. Photonics 3, 283 (2009).
[CrossRef]

van Loon, R. V. A.

R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, Nat. Mater. 9, 21 (2010).
[CrossRef]

Veronis, G.

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, IEEE J. Sel. Top. Quantum Electron. 14, 1462 (2008).
[CrossRef]

G. Veronis and S. Fan, Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

Walters, R. J.

R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, Nat. Mater. 9, 21 (2010).
[CrossRef]

Wang, H. Z.

J. X. Tan, Y. B. Xie, J. W. Dong, and H. Z. Wang, Plasmonics 7, 435 (2012).
[CrossRef]

T. B. Wang, X. W. Wen, C. P. Yin, and H. Z. Wang, Opt. Express 17, 24096 (2009).
[CrossRef]

Wang, T. B.

Wen, X. W.

Xie, Y. B.

J. X. Tan, Y. B. Xie, J. W. Dong, and H. Z. Wang, Plasmonics 7, 435 (2012).
[CrossRef]

Yin, C. P.

Appl. Opt. (3)

Appl. Phys. Lett. (2)

G. Veronis and S. Fan, Appl. Phys. Lett. 87, 131102 (2005).
[CrossRef]

A. Hosseini and Y. Massoud, Appl. Phys. Lett. 90, 181102 (2007).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, IEEE J. Sel. Top. Quantum Electron. 14, 1462 (2008).
[CrossRef]

C.-H. Chen and Y. Fainman, IEEE J. Sel. Top. Quantum Electron. 13, 262 (2007).
[CrossRef]

J. Opt. (1)

A. Setayesh, S. R. Mirnaziry, and M. S. Abrishamian, J. Opt. 13, 035004 (2011).
[CrossRef]

Nat. Mater. (1)

R. J. Walters, R. V. A. van Loon, I. Brunets, J. Schmitz, and A. Polman, Nat. Mater. 9, 21 (2010).
[CrossRef]

Nat. Photonics (1)

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, Nat. Photonics 3, 283 (2009).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Plasmonics (1)

J. X. Tan, Y. B. Xie, J. W. Dong, and H. Z. Wang, Plasmonics 7, 435 (2012).
[CrossRef]

Science (1)

E. Ozbay, Science 311, 189 (2006).
[CrossRef]

Other (2)

K. Chang and L. H. Hsieh, Microwave Ring Circuits and Related Structures (Wiley, 2004).

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, 1989).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic diagram of the directly connected rectangular ring resonator. (b) Corresponding equivalent lumped circuit.

Fig. 2.
Fig. 2.

Schematic illustration of a generalized cascaded rectangular ring resonator structure.

Fig. 3.
Fig. 3.

Reflectance spectra obtained by using FDTD method (black dashed curve) and using Eq. (5) (blue solid curve) and the reflectance phase by using Eq. (5) (green dotted curve) of the AD mirror with w 1 = 120 nm , w i = 20 nm , w o = 100 nm , and L 1 = 725.8 nm . The inset is the schematic structure of the one-cavity plasmonic AD mirror.

Fig. 4.
Fig. 4.

(a) Transmission spectra of the bandpass filter with the cavity’s length d of 362.1 nm simulated by FDTD method (dark dashed curve) and calculated by Eq. (6) (blue solid curve). Upper inset is the schematic of the simulated cascaded ring resonator structure. Lower inset is the transmission spectra in linear scale. (b) Calculated total phase shift inside the cavity C.

Fig. 5.
Fig. 5.

Transmission spectrum variations with (a) different deviation ratios ζ : ζ = 0.95 (red dotted curve), ζ = 1.00 (blue solid curve), and ζ = 1.05 (black dashed curve) and (b) different thicknesses of the metal film h: h = 400 nm (red dotted curve), h = 1000 nm (black dashed curve), h = 1500 nm (magenta dot-dashed curve), and 2D results (blue solid curve). Inset is the schematic of the 3D MIM waveguide structure.

Equations (8)

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ε ( ω ) = ε ω p 2 ω 2 + i γ ω n = 1 5 Δ ε n ω n 2 ω 2 ω n 2 + i γ n ω ,
Z a = j Z 1 tan ( β 1 L 1 / 2 )
Z b = j Z 1 csc ( β 1 L 1 ) ,
T = V 2 + V 1 + = ( 1 + r 2 ) ( 1 r 1 ) e j β 1 L 1 1 r 1 r 2 e 2 j β 1 L 1 ,
R = V 1 V 1 + = r 1 r 2 e 2 j β 1 L 1 1 r 1 r 2 e 2 j β 1 L 1 ,
t total = E out E in = t A t B e j φ 1 r A r B e j 2 φ ,
Φ = 2 Re { φ } ϕ A ϕ B = 2 m π ,
d Φ ( λ 0 ) d λ 0 ,

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