Abstract

An open waveguide cavity formed by a pair of planar waveguides, in which one guiding layer is a negative index medium and the other is a positive index medium, is theoretically demonstrated. For such a waveguide cavity the resonant frequency is independent of the total length of the waveguide system. With the coupled mode theory it is shown that energy flow circulation can be established through the special coupling between the waveguides at the resonant frequency, and thus the wave fields are localized. This phenomenon is further verified numerically with the finite-difference time-domain method. The quality factor of the open waveguide cavity is also discussed.

© 2008 Optical Society of America

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  1. V. Veselago, Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  2. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  3. R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
    [CrossRef] [PubMed]
  4. I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 67, 057602 (2003).
    [CrossRef]
  5. B.-l. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, J. Appl. Phys. 93, 9386 (2003).
    [CrossRef]
  6. Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, Appl. Phys. Lett. 88, 211903 (2006).
    [CrossRef]
  7. W. Yan, L. F. Shen, Y. Yuan, and T. J. Yang, http://www.arXiv:0808.3528 [physics. optics] (2008).
  8. S. D. Gedney, Electromagnetics 16, 399 (1996).
    [CrossRef]
  9. H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, J. Lightwave Technol. 5, 161987.
    [CrossRef]
  10. A. W. Snyder, A. Ankiewicz, and A. Altintas, Electron. Lett. 23, 1097 (1987).
    [CrossRef]
  11. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).
  12. A. Taflove and S. C. Hagness, Computational Electrodynamics--The Finite Difference Time-Domain Method (Artech House, 2000).

2008 (1)

W. Yan, L. F. Shen, Y. Yuan, and T. J. Yang, http://www.arXiv:0808.3528 [physics. optics] (2008).

2006 (1)

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, Appl. Phys. Lett. 88, 211903 (2006).
[CrossRef]

2003 (2)

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 67, 057602 (2003).
[CrossRef]

B.-l. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, J. Appl. Phys. 93, 9386 (2003).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

2000 (2)

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

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

1996 (1)

S. D. Gedney, Electromagnetics 16, 399 (1996).
[CrossRef]

1987 (2)

H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, J. Lightwave Technol. 5, 161987.
[CrossRef]

A. W. Snyder, A. Ankiewicz, and A. Altintas, Electron. Lett. 23, 1097 (1987).
[CrossRef]

1983 (1)

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

1968 (1)

V. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Altintas, A.

A. W. Snyder, A. Ankiewicz, and A. Altintas, Electron. Lett. 23, 1097 (1987).
[CrossRef]

Ankiewicz, A.

A. W. Snyder, A. Ankiewicz, and A. Altintas, Electron. Lett. 23, 1097 (1987).
[CrossRef]

Chen, H.

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, Appl. Phys. Lett. 88, 211903 (2006).
[CrossRef]

Gedney, S. D.

S. D. Gedney, Electromagnetics 16, 399 (1996).
[CrossRef]

Grzegorczyk, T. M.

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, Appl. Phys. Lett. 88, 211903 (2006).
[CrossRef]

B.-l. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, J. Appl. Phys. 93, 9386 (2003).
[CrossRef]

Hagness, S. C.

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

Haus, H. A.

H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, J. Lightwave Technol. 5, 161987.
[CrossRef]

Huang, W. P.

H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, J. Lightwave Technol. 5, 161987.
[CrossRef]

Huangfu, J.

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, Appl. Phys. Lett. 88, 211903 (2006).
[CrossRef]

Kawakami, S.

H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, J. Lightwave Technol. 5, 161987.
[CrossRef]

Kivshar, Y. S.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Kong, J. A.

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, Appl. Phys. Lett. 88, 211903 (2006).
[CrossRef]

B.-l. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, J. Appl. Phys. 93, 9386 (2003).
[CrossRef]

Love, J. D.

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

Pendry, J. B.

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Ran, L.

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, Appl. Phys. Lett. 88, 211903 (2006).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Shen, L. F.

W. Yan, L. F. Shen, Y. Yuan, and T. J. Yang, http://www.arXiv:0808.3528 [physics. optics] (2008).

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Snyder, A. W.

A. W. Snyder, A. Ankiewicz, and A. Altintas, Electron. Lett. 23, 1097 (1987).
[CrossRef]

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

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Taflove, A.

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

Veselago, V.

V. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Whitaker, N. A.

H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, J. Lightwave Technol. 5, 161987.
[CrossRef]

Wu, B.-l.

B.-l. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, J. Appl. Phys. 93, 9386 (2003).
[CrossRef]

Yan, W.

W. Yan, L. F. Shen, Y. Yuan, and T. J. Yang, http://www.arXiv:0808.3528 [physics. optics] (2008).

Yang, T. J.

W. Yan, L. F. Shen, Y. Yuan, and T. J. Yang, http://www.arXiv:0808.3528 [physics. optics] (2008).

Yuan, Y.

W. Yan, L. F. Shen, Y. Yuan, and T. J. Yang, http://www.arXiv:0808.3528 [physics. optics] (2008).

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, Appl. Phys. Lett. 88, 211903 (2006).
[CrossRef]

Zhang, Y.

B.-l. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, J. Appl. Phys. 93, 9386 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, Appl. Phys. Lett. 88, 211903 (2006).
[CrossRef]

Electromagnetics (1)

S. D. Gedney, Electromagnetics 16, 399 (1996).
[CrossRef]

Electron. Lett. (1)

A. W. Snyder, A. Ankiewicz, and A. Altintas, Electron. Lett. 23, 1097 (1987).
[CrossRef]

J. Appl. Phys. (1)

B.-l. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, J. Appl. Phys. 93, 9386 (2003).
[CrossRef]

J. Lightwave Technol. (1)

H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, J. Lightwave Technol. 5, 161987.
[CrossRef]

Phys. Rev. E (1)

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Other (3)

W. Yan, L. F. Shen, Y. Yuan, and T. J. Yang, http://www.arXiv:0808.3528 [physics. optics] (2008).

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

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

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Figures (3)

Fig. 1
Fig. 1

Geometry of open waveguide cavity.

Fig. 2
Fig. 2

(a) Spectrum for the FDTD simulated fields. (b) Spatial variation of the amplitude of E y at the resonant frequency ω r = 0 .4 ( 2 π c a ) . (c) Envelope of the distribution of E y amplitude along the PIM waveguide axis.

Fig. 3
Fig. 3

Quality factor versus the cavity length.

Equations (8)

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

d U d z = i β a U + i C a b V ,
d V d z = i β b V + i C b a U ,
C p q = 4 ω S p [ Δ ε q ( e p t e q t e p z e q z ) + Δ μ q ( h p t h q t h p z h q z ) ] d x ,
U 1 ( z ) = A 1 e i β ¯ z + α z , V 1 ( z ) = A 1 Δ β 2 i α 2 C a b e i β ¯ z + α z ,
U 3 ( z ) = A 3 e i β ¯ z α z , V 3 ( z ) = A 3 Δ β + 2 i α 2 C a b e i β ¯ z α z ,
U 3 ( L c 2 ) = U 1 ( L c 2 ) e i β a L c ,
V 3 ( L c 2 ) = V 1 ( L c 2 ) e i β c L c .
L c = 2 n π + 2 arctan ( Δ β 2 4 C a b C b a Δ β ) β c β a ,

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