Abstract

We propose a tunable directional coupler based on a two-dimensional photonic crystal made of dielectric elastomer rods embedded in air background. In the interaction region, the inclusions are a dielectric elastomer cylindrical actuator made of a hollow cylinder sandwiched between two compliant electrodes. By applying a voltage between the compliant electrodes, the radial strain of the silicon-made actuator and the coupling characteristics of the photonic crystal coupler are investigated. The coupling length of the photonic crystal coupler depends on the voltage applied between the electrodes, which is analyzed by the plane wave expansion method. Due to the radial strain of the dielectric elastomer under external voltage, the tunable photonic crystal coupler is realized. Numerical simulations obtained by the finite-difference time-domain method confirmed the feasibility of the tunable photonic crystal coupler.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489(1987).
    [CrossRef] [PubMed]
  3. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
    [CrossRef] [PubMed]
  4. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
    [CrossRef] [PubMed]
  5. S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162–165 (2001).
    [CrossRef]
  6. H. Takeda and K. Yoshino, “Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals composed of semiconductors depending on temperature,” Opt. Commun. 219, 177–182 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. W. P. Yang and L. W. Chen, “The tunable acoustic band gaps of two-dimensional phononic crystals with a dielectric elastomer cylindrical actuator,” Smart Mater. Struct. 17, 015011–015016(2008).
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  19. F. Xiang, H. Wang, and X. Yao, “Dielectric properties of SrTiO3/POE flexible composites for microwave applications,” J. Euro. Ceram. Soc. 27, 3093–3097 (2007).
    [CrossRef]

2009

2008

W. P. Yang and L. W. Chen, “The tunable acoustic band gaps of two-dimensional phononic crystals with a dielectric elastomer cylindrical actuator,” Smart Mater. Struct. 17, 015011–015016(2008).
[CrossRef]

2007

F. Xiang, H. Wang, and X. Yao, “Dielectric properties of SrTiO3/POE flexible composites for microwave applications,” J. Euro. Ceram. Soc. 27, 3093–3097 (2007).
[CrossRef]

2005

F. Carpi, A. Migliore, G. Serra, and D. De Rossi, “Helical dielectric elastomer actuators,” Smart Mater. Struct. 14, 1210–1216 (2005).
[CrossRef]

C. Y. Liu and L. W. Chen, “The analysis of interaction region of elliptical pillars of a directional photonic crystal waveguide coupler,” Physica E (Amsterdam) 28, 185–190(2005).
[CrossRef]

2004

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[CrossRef]

C. Y. Liu and L. W. Chen, “Tunable photonic crystal waveguide Mach–Zehnder interferometer achieved by nematic liquid crystal phase modulation,” Opt. Express 12, 2616–2624(2004).
[CrossRef] [PubMed]

F. Carpi and D. D. Rossi, “Dielectric elastomer cylindrical actuators: electromechanical modeling and experimental evaluation,” Mater. Sci. Eng. C 24, 555–562 (2004).
[CrossRef]

2003

H. Takeda and K. Yoshino, “Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals composed of semiconductors depending on temperature,” Opt. Commun. 219, 177–182 (2003).
[CrossRef]

2001

2000

R. E. Pelrine, R. D. Kornbluh, Q. Pei, and J. P. Joseph, “High-speed electrically actuated elastomers with strain greater than 100%,” Science 287, 836–839 (2000).
[CrossRef] [PubMed]

R. E. Pelrine, R. D. Kornbluh, and G. Kofod, “High-strain actuator material based on dielectric elastomers,” Adv. Mater. 12, 1223–1225 (2000).
[CrossRef]

1999

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

1998

R. E. Pelrine, R. D. Kornbluh, and J. P. Joseph, “Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation,” Sens. Actuators A, Phys. 64, 77–85(1998).
[CrossRef]

1996

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

1987

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062(1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489(1987).
[CrossRef] [PubMed]

Atalar, A.

Aydinli, A.

Beck, M.

Cao, J. R.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[CrossRef]

Carpi, F.

F. Carpi, A. Migliore, G. Serra, and D. De Rossi, “Helical dielectric elastomer actuators,” Smart Mater. Struct. 14, 1210–1216 (2005).
[CrossRef]

F. Carpi and D. D. Rossi, “Dielectric elastomer cylindrical actuators: electromechanical modeling and experimental evaluation,” Mater. Sci. Eng. C 24, 555–562 (2004).
[CrossRef]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Chen, L. W.

W. P. Yang and L. W. Chen, “The tunable acoustic band gaps of two-dimensional phononic crystals with a dielectric elastomer cylindrical actuator,” Smart Mater. Struct. 17, 015011–015016(2008).
[CrossRef]

C. Y. Liu and L. W. Chen, “The analysis of interaction region of elliptical pillars of a directional photonic crystal waveguide coupler,” Physica E (Amsterdam) 28, 185–190(2005).
[CrossRef]

C. Y. Liu and L. W. Chen, “Tunable photonic crystal waveguide Mach–Zehnder interferometer achieved by nematic liquid crystal phase modulation,” Opt. Express 12, 2616–2624(2004).
[CrossRef] [PubMed]

Choi, S. J.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[CrossRef]

Dapkus, P. D.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

De Rossi, D.

F. Carpi, A. Migliore, G. Serra, and D. De Rossi, “Helical dielectric elastomer actuators,” Smart Mater. Struct. 14, 1210–1216 (2005).
[CrossRef]

Ertas, G.

Fan, S.

S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162–165 (2001).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Haus, H. A.

Joannopoulos, J. D.

S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18, 162–165 (2001).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489(1987).
[CrossRef] [PubMed]

Johnson, S. G.

Joseph, J. P.

R. E. Pelrine, R. D. Kornbluh, Q. Pei, and J. P. Joseph, “High-speed electrically actuated elastomers with strain greater than 100%,” Science 287, 836–839 (2000).
[CrossRef] [PubMed]

R. E. Pelrine, R. D. Kornbluh, and J. P. Joseph, “Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation,” Sens. Actuators A, Phys. 64, 77–85(1998).
[CrossRef]

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Kim, W. J.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[CrossRef]

Kocabas, A.

Kofod, G.

R. E. Pelrine, R. D. Kornbluh, and G. Kofod, “High-strain actuator material based on dielectric elastomers,” Adv. Mater. 12, 1223–1225 (2000).
[CrossRef]

Kornbluh, R. D.

R. E. Pelrine, R. D. Kornbluh, Q. Pei, and J. P. Joseph, “High-speed electrically actuated elastomers with strain greater than 100%,” Science 287, 836–839 (2000).
[CrossRef] [PubMed]

R. E. Pelrine, R. D. Kornbluh, and G. Kofod, “High-strain actuator material based on dielectric elastomers,” Adv. Mater. 12, 1223–1225 (2000).
[CrossRef]

R. E. Pelrine, R. D. Kornbluh, and J. P. Joseph, “Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation,” Sens. Actuators A, Phys. 64, 77–85(1998).
[CrossRef]

Koshiba, M.

Kuang, W.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[CrossRef]

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Liu, C. Y.

C. Y. Liu and L. W. Chen, “The analysis of interaction region of elliptical pillars of a directional photonic crystal waveguide coupler,” Physica E (Amsterdam) 28, 185–190(2005).
[CrossRef]

C. Y. Liu and L. W. Chen, “Tunable photonic crystal waveguide Mach–Zehnder interferometer achieved by nematic liquid crystal phase modulation,” Opt. Express 12, 2616–2624(2004).
[CrossRef] [PubMed]

Manolatou, C.

Marshall, W. K.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[CrossRef]

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Migliore, A.

F. Carpi, A. Migliore, G. Serra, and D. De Rossi, “Helical dielectric elastomer actuators,” Smart Mater. Struct. 14, 1210–1216 (2005).
[CrossRef]

O’Brien, J. D.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Olcum, S.

Painter, O.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Pei, Q.

R. E. Pelrine, R. D. Kornbluh, Q. Pei, and J. P. Joseph, “High-speed electrically actuated elastomers with strain greater than 100%,” Science 287, 836–839 (2000).
[CrossRef] [PubMed]

Pelrine, R. E.

R. E. Pelrine, R. D. Kornbluh, Q. Pei, and J. P. Joseph, “High-speed electrically actuated elastomers with strain greater than 100%,” Science 287, 836–839 (2000).
[CrossRef] [PubMed]

R. E. Pelrine, R. D. Kornbluh, and G. Kofod, “High-strain actuator material based on dielectric elastomers,” Adv. Mater. 12, 1223–1225 (2000).
[CrossRef]

R. E. Pelrine, R. D. Kornbluh, and J. P. Joseph, “Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation,” Sens. Actuators A, Phys. 64, 77–85(1998).
[CrossRef]

Reto, F.

Rossi, D. D.

F. Carpi and D. D. Rossi, “Dielectric elastomer cylindrical actuators: electromechanical modeling and experimental evaluation,” Mater. Sci. Eng. C 24, 555–562 (2004).
[CrossRef]

Scherer, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Serra, G.

F. Carpi, A. Migliore, G. Serra, and D. De Rossi, “Helical dielectric elastomer actuators,” Smart Mater. Struct. 14, 1210–1216 (2005).
[CrossRef]

Shih, M. H.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[CrossRef]

Stemmer, A.

Takeda, H.

H. Takeda and K. Yoshino, “Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals composed of semiconductors depending on temperature,” Opt. Commun. 219, 177–182 (2003).
[CrossRef]

Villeneuve, P. R.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Wang, H.

F. Xiang, H. Wang, and X. Yao, “Dielectric properties of SrTiO3/POE flexible composites for microwave applications,” J. Euro. Ceram. Soc. 27, 3093–3097 (2007).
[CrossRef]

Xiang, F.

F. Xiang, H. Wang, and X. Yao, “Dielectric properties of SrTiO3/POE flexible composites for microwave applications,” J. Euro. Ceram. Soc. 27, 3093–3097 (2007).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062(1987).
[CrossRef] [PubMed]

Yang, W. P.

W. P. Yang and L. W. Chen, “The tunable acoustic band gaps of two-dimensional phononic crystals with a dielectric elastomer cylindrical actuator,” Smart Mater. Struct. 17, 015011–015016(2008).
[CrossRef]

Yao, X.

F. Xiang, H. Wang, and X. Yao, “Dielectric properties of SrTiO3/POE flexible composites for microwave applications,” J. Euro. Ceram. Soc. 27, 3093–3097 (2007).
[CrossRef]

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Yoshino, K.

H. Takeda and K. Yoshino, “Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals composed of semiconductors depending on temperature,” Opt. Commun. 219, 177–182 (2003).
[CrossRef]

Yukawa, H.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[CrossRef]

Adv. Mater.

R. E. Pelrine, R. D. Kornbluh, and G. Kofod, “High-strain actuator material based on dielectric elastomers,” Adv. Mater. 12, 1223–1225 (2000).
[CrossRef]

Appl. Phys. Lett.

M. H. Shih, W. J. Kim, W. Kuang, J. R. Cao, H. Yukawa, S. J. Choi, J. D. O’Brien, P. D. Dapkus, and W. K. Marshall, “Two-dimensional photonic crystal Mach–Zehnder interferometers,” Appl. Phys. Lett. 84, 460–462 (2004).
[CrossRef]

J. Euro. Ceram. Soc.

F. Xiang, H. Wang, and X. Yao, “Dielectric properties of SrTiO3/POE flexible composites for microwave applications,” J. Euro. Ceram. Soc. 27, 3093–3097 (2007).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Mater. Sci. Eng. C

F. Carpi and D. D. Rossi, “Dielectric elastomer cylindrical actuators: electromechanical modeling and experimental evaluation,” Mater. Sci. Eng. C 24, 555–562 (2004).
[CrossRef]

Opt. Commun.

H. Takeda and K. Yoshino, “Tunable light propagation in Y-shaped waveguides in two-dimensional photonic crystals composed of semiconductors depending on temperature,” Opt. Commun. 219, 177–182 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062(1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489(1987).
[CrossRef] [PubMed]

Physica E (Amsterdam)

C. Y. Liu and L. W. Chen, “The analysis of interaction region of elliptical pillars of a directional photonic crystal waveguide coupler,” Physica E (Amsterdam) 28, 185–190(2005).
[CrossRef]

Science

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

R. E. Pelrine, R. D. Kornbluh, Q. Pei, and J. P. Joseph, “High-speed electrically actuated elastomers with strain greater than 100%,” Science 287, 836–839 (2000).
[CrossRef] [PubMed]

Sens. Actuators A, Phys.

R. E. Pelrine, R. D. Kornbluh, and J. P. Joseph, “Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation,” Sens. Actuators A, Phys. 64, 77–85(1998).
[CrossRef]

Smart Mater. Struct.

F. Carpi, A. Migliore, G. Serra, and D. De Rossi, “Helical dielectric elastomer actuators,” Smart Mater. Struct. 14, 1210–1216 (2005).
[CrossRef]

W. P. Yang and L. W. Chen, “The tunable acoustic band gaps of two-dimensional phononic crystals with a dielectric elastomer cylindrical actuator,” Smart Mater. Struct. 17, 015011–015016(2008).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Cross section of the DE tubes with outer radius r o and inner radius r i . The uniform compression acts on the inner and outer surfaces.

Fig. 2
Fig. 2

Schematic diagram of PhC coupler structure with dielectric elastomer rods.

Fig. 3
Fig. 3

Band structure of the perfect 2D DE photonic crystal. The lower PBG ranges from 0.29 0.37 ( c / a ) . The inset shows the Brillouin zone of the PhC.

Fig. 4
Fig. 4

Outer and inner radii of the dielectric elastomer tubes versus applied voltage per unit wall thickness. The outer and inner radii at rest are 0.25 a and 0.10 a , respectively.

Fig. 5
Fig. 5

Dispersion relation of the PhC coupler. The solid line represents the situation when 2.5 ( kV / a ) voltage is applied, and the dashed line is the initial configuration.

Fig. 6
Fig. 6

Coupling length of a PhC coupler with different voltage applied.

Fig. 7
Fig. 7

Electric field distributions at normalized frequency 0.345 ( w a / 2 π c ) under different applied voltages: (a)  0 kV / a , (b)  2.5 kV / a , (c)  3.0 kV / a .

Fig. 8
Fig. 8

Schematic diagram of the tunable PhC coupler structure with dielectric elastomer inclusions. The coupling length is set to 10 a .

Fig. 9
Fig. 9

Normalized output power related to the power injected into the input port under varying external voltage applied. The input light wave frequency is 0.3462 ( w a / 2 π c ) .

Fig. 10
Fig. 10

Electric field distribution at normalized frequency 0.3462 ( w a / 2 π c ) under different applied voltages: (a)  0 kV / a and (b)  3.0 kV / a .

Equations (10)

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p = ε 0 ε r ( V d ) 2 ,
p i = D ε 0 ε r V 2 2 ln 2 ( r o r i ) r i 2 r o ( r o 2 r i 2 ) ,
p o = D ε 0 ε r V 2 2 ln 2 ( r o r i ) r i r o 2 ( r o 2 r i 2 ) ,
D = [ r i 6 + r o 6 r i 2 r o 4 r i 4 r o 2 + 8 ln 2 ( r o r i ) ( r o 2 r i 2 ) r i 2 r o 2 + 4 ln 2 ( r o r i ) ( r o 2 + r i 2 ) r i 2 r o 2 ] 1 / 2 .
u ( r ) = D ε 0 ε r r 2 ln 2 ( r o r i ) r i r o E ( r i r o ) ( r i + r o ) 2 × [ ( r i r o r 2 + 1 ) ( 1 + ν ) 2 ] ( V r o r i ) 2 ,
× [ 1 ε ( r ) × H ( r ) ] = ω 2 c 2 H ( r ) ,
ε 1 ( r ) = G η ( G ) e i G · r ,
H ( r ) = G λ = 1 , 2 h G , λ e ^ λ e i ( k + G ) · r ,
G | k + G | | k + G | η ( G G ) [ e ^ 2 · e ^ 2 e ^ 2 · e ^ 1 e ^ 1 · e ^ 2 e ^ 1 · e ^ 1 ] ( h G , 1 h G , 2 ) = ω 2 c 2 ( h G , 1 h G , 2 ) .
G | k + G | | k + G | η ( G G ) h G = ω 2 c 2 h G .

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