Abstract

Fractal multilayer structures based on one-dimensional photonic crystals are constructed to generate multiple defect modes. The proposed fractal photonic crystals can produce as many defect modes as desired by adjusting the number of the defect layers. The interaction effect between the defect states of such fractal structures is avoided. Therefore, the frequency, frequency interval, and number of the defect modes corresponding to different kinds of defects can be tuned separately. With perfect transmission and mode controllability, these structures provide an efficient way to fabricate multichannel filters with specific channels.

© 2009 Optical Society of America

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    [CrossRef] [PubMed]
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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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2008 (1)

2006 (1)

2004 (3)

S. V. Zhukovsky, A. V. Lavrinenko, and S. V. Gaponenko, “Spectral scalability as a result of geometrical self-similarity in fractal multilayers,” Europhys. Lett. 66, 455-461 (2004).
[CrossRef]

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

Z. S. Wang, L. Wang, Y. G. Wu, L. Y. Chen, X. S. Chen, and W. Lu, “Multiple channeled phenomena in heterostructures with defects mode,” Appl. Phys. Lett. 84, 1629-1631 (2004).
[CrossRef]

2003 (2)

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirskii, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: Scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2003).
[CrossRef]

H. Y. Lee and T. Yao, “Design and evaluation of omnidirectional one-dimensional photonic crystals,” J. Appl. Phys. 93, 819-830 (2003).
[CrossRef]

2002 (1)

H. Y. Lee, H. Makino, T. Yao, and A. Tanaka, “Si-based omnidirectional reflector and transmission filter optimized at a wavelength of 1.55μm,” Appl. Phys. Lett. 81, 4502-4504 (2002).
[CrossRef]

2000 (1)

F. Qiao, C. Zhang, J. Wan, and J. Zi, “Photonic quantum-well structures: Multiple channeled filtering phenomena,” Appl. Phys. Lett. 77, 3698-3700 (2000).
[CrossRef]

1997 (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic-bandgap microcavities in optical waveguides,” Nature 386, 143-145 (1997).
[CrossRef]

1987 (2)

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]

Chen, L. Y.

Z. S. Wang, L. Wang, Y. G. Wu, L. Y. Chen, X. S. Chen, and W. Lu, “Multiple channeled phenomena in heterostructures with defects mode,” Appl. Phys. Lett. 84, 1629-1631 (2004).
[CrossRef]

Chen, X. S.

Z. S. Wang, L. Wang, Y. G. Wu, L. Y. Chen, X. S. Chen, and W. Lu, “Multiple channeled phenomena in heterostructures with defects mode,” Appl. Phys. Lett. 84, 1629-1631 (2004).
[CrossRef]

Chen, Y. H.

Dong, J. W.

Fan, S.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic-bandgap microcavities in optical waveguides,” Nature 386, 143-145 (1997).
[CrossRef]

Floris van Driel, A.

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

Gaponenko, S. V.

S. V. Zhukovsky, A. V. Lavrinenko, and S. V. Gaponenko, “Spectral scalability as a result of geometrical self-similarity in fractal multilayers,” Europhys. Lett. 66, 455-461 (2004).
[CrossRef]

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirskii, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: Scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2003).
[CrossRef]

Irman, A.

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

Joannopoulos, J. D.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic-bandgap microcavities in optical waveguides,” Nature 386, 143-145 (1997).
[CrossRef]

John, S.

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

Lavrinenko, A. V.

S. V. Zhukovsky, A. V. Lavrinenko, and S. V. Gaponenko, “Spectral scalability as a result of geometrical self-similarity in fractal multilayers,” Europhys. Lett. 66, 455-461 (2004).
[CrossRef]

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirskii, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: Scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2003).
[CrossRef]

Lee, H. Y.

H. Y. Lee and T. Yao, “Design and evaluation of omnidirectional one-dimensional photonic crystals,” J. Appl. Phys. 93, 819-830 (2003).
[CrossRef]

H. Y. Lee, H. Makino, T. Yao, and A. Tanaka, “Si-based omnidirectional reflector and transmission filter optimized at a wavelength of 1.55μm,” Appl. Phys. Lett. 81, 4502-4504 (2002).
[CrossRef]

Lodahl, P.

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

Lu, W.

Z. S. Wang, L. Wang, Y. G. Wu, L. Y. Chen, X. S. Chen, and W. Lu, “Multiple channeled phenomena in heterostructures with defects mode,” Appl. Phys. Lett. 84, 1629-1631 (2004).
[CrossRef]

Makino, H.

H. Y. Lee, H. Makino, T. Yao, and A. Tanaka, “Si-based omnidirectional reflector and transmission filter optimized at a wavelength of 1.55μm,” Appl. Phys. Lett. 81, 4502-4504 (2002).
[CrossRef]

Nikolaev, I. S.

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

Overgaag, K.

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

Qiao, F.

F. Qiao, C. Zhang, J. Wan, and J. Zi, “Photonic quantum-well structures: Multiple channeled filtering phenomena,” Appl. Phys. Lett. 77, 3698-3700 (2000).
[CrossRef]

Sandomirskii, K. S.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirskii, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: Scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2003).
[CrossRef]

Tanaka, A.

H. Y. Lee, H. Makino, T. Yao, and A. Tanaka, “Si-based omnidirectional reflector and transmission filter optimized at a wavelength of 1.55μm,” Appl. Phys. Lett. 81, 4502-4504 (2002).
[CrossRef]

Vanmaekelbergh, D.

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic-bandgap microcavities in optical waveguides,” Nature 386, 143-145 (1997).
[CrossRef]

Vos, W. L.

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

Wan, J.

F. Qiao, C. Zhang, J. Wan, and J. Zi, “Photonic quantum-well structures: Multiple channeled filtering phenomena,” Appl. Phys. Lett. 77, 3698-3700 (2000).
[CrossRef]

Wang, H. Z.

Wang, L.

Z. S. Wang, L. Wang, Y. G. Wu, L. Y. Chen, X. S. Chen, and W. Lu, “Multiple channeled phenomena in heterostructures with defects mode,” Appl. Phys. Lett. 84, 1629-1631 (2004).
[CrossRef]

Wang, Z. S.

Z. S. Wang, L. Wang, Y. G. Wu, L. Y. Chen, X. S. Chen, and W. Lu, “Multiple channeled phenomena in heterostructures with defects mode,” Appl. Phys. Lett. 84, 1629-1631 (2004).
[CrossRef]

Wu, Y. G.

Z. S. Wang, L. Wang, Y. G. Wu, L. Y. Chen, X. S. Chen, and W. Lu, “Multiple channeled phenomena in heterostructures with defects mode,” Appl. Phys. Lett. 84, 1629-1631 (2004).
[CrossRef]

Yablonovitch, E.

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

Yao, T.

H. Y. Lee and T. Yao, “Design and evaluation of omnidirectional one-dimensional photonic crystals,” J. Appl. Phys. 93, 819-830 (2003).
[CrossRef]

H. Y. Lee, H. Makino, T. Yao, and A. Tanaka, “Si-based omnidirectional reflector and transmission filter optimized at a wavelength of 1.55μm,” Appl. Phys. Lett. 81, 4502-4504 (2002).
[CrossRef]

Zhang, C.

F. Qiao, C. Zhang, J. Wan, and J. Zi, “Photonic quantum-well structures: Multiple channeled filtering phenomena,” Appl. Phys. Lett. 77, 3698-3700 (2000).
[CrossRef]

Zhukovsky, S. V.

S. V. Zhukovsky, A. V. Lavrinenko, and S. V. Gaponenko, “Spectral scalability as a result of geometrical self-similarity in fractal multilayers,” Europhys. Lett. 66, 455-461 (2004).
[CrossRef]

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirskii, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: Scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2003).
[CrossRef]

Zi, J.

F. Qiao, C. Zhang, J. Wan, and J. Zi, “Photonic quantum-well structures: Multiple channeled filtering phenomena,” Appl. Phys. Lett. 77, 3698-3700 (2000).
[CrossRef]

Appl. Phys. Lett. (3)

H. Y. Lee, H. Makino, T. Yao, and A. Tanaka, “Si-based omnidirectional reflector and transmission filter optimized at a wavelength of 1.55μm,” Appl. Phys. Lett. 81, 4502-4504 (2002).
[CrossRef]

F. Qiao, C. Zhang, J. Wan, and J. Zi, “Photonic quantum-well structures: Multiple channeled filtering phenomena,” Appl. Phys. Lett. 77, 3698-3700 (2000).
[CrossRef]

Z. S. Wang, L. Wang, Y. G. Wu, L. Y. Chen, X. S. Chen, and W. Lu, “Multiple channeled phenomena in heterostructures with defects mode,” Appl. Phys. Lett. 84, 1629-1631 (2004).
[CrossRef]

Europhys. Lett. (1)

S. V. Zhukovsky, A. V. Lavrinenko, and S. V. Gaponenko, “Spectral scalability as a result of geometrical self-similarity in fractal multilayers,” Europhys. Lett. 66, 455-461 (2004).
[CrossRef]

J. Appl. Phys. (1)

H. Y. Lee and T. Yao, “Design and evaluation of omnidirectional one-dimensional photonic crystals,” J. Appl. Phys. 93, 819-830 (2003).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nature (2)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic-bandgap microcavities in optical waveguides,” Nature 386, 143-145 (1997).
[CrossRef]

P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos, “Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals,” Nature 430, 654-657 (2004).
[CrossRef] [PubMed]

Phys. Rev. E (1)

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirskii, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: Scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2003).
[CrossRef]

Phys. Rev. Lett. (2)

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]

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Figures (5)

Fig. 1
Fig. 1

Transmission spectra of fractal structures S 1 = ( H L ) 4 D H 1 ( LH ) 4 D H 1 for (a) D H 1 = α H and α = 2.0 , (b) D H 1 = α H ( L H ) 2 L α H and α = 2.0 , (c) D H 1 = α H ( L H ) 2 L α H ( L H ) 2 L α H and α = 2.0 , and (d) D H 1 = α H ( L H ) 2 L α H and α = 1.5 , 2.0 , 2.5 .

Fig. 2
Fig. 2

(a) to (e) are the transmission spectra of structure S 2 = [ ( H L ) 4 D H 1 ( L H ) 4 D L 2 ] 2 for D H 1 = α H ( L H ) 4 L α H and D L 2 = β L ( H L ) 6 H β L with different α and β. (f) is the transmittance of a symmetrical structure ( H L ) 4 D H 1 ( L H ) 4 D L 2 ( H L ) 4 D H 1 ( L H ) 4 with α = 2.0 and β = 2.7 .

Fig. 3
Fig. 3

Transmission spectra of the structure S 2 = [ ( H L ) 4 D H 1 ( L H ) 4 D L 2 ] 2 for D H 1 = α H ( L H ) l L α H and D L 2 = β L ( H L ) m H β L with α = 1.8 and β = 2.5 . The period numbers are (a) l = 4 and m = 6 , (b) l = 5 and m = 6 , (c) l = 6 and m = 6 , (d) l = 6 and m = 4 , and (e) l = 6 and m = 2 , respectively.

Fig. 4
Fig. 4

(a) to (e) are the transmission spectra of structure S 2 = [ ( H L ) 4 D H 1 ( L H ) 4 D L 2 ] 2 for D H 1 = α H and D L 2 = β L ( H L ) 2 H β L ( H L ) 2 H β L with different α and β. (f) is the transmittance of a symmetrical structure ( H L ) 4 D H 1 ( L H ) 4 D L 2 ( H L ) 4 D H 1 ( L H ) 4 with α = 2.0 and β = 2.8 .

Fig. 5
Fig. 5

Transmission spectra of structure S 3 = [ ( H L ) 4 D H 1 ( L H ) 4 D L 2 ( H L ) 4 D H 1 ( L H ) 4 D L 3 ] 2 for D H 1 = α H , D L 2 = β L ( H L ) 4 H β L , and D L 3 = γ L ( H L ) 4 H γ L with different α, β and γ.

Equations (6)

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S 0 ( H L ) s
S 1 ( H L ) s D H 1 ( L H ) s D H 1
S 2 [ ( H L ) s D H 1 ( L H ) s D L 2 ] 2
S 3 [ ( H L ) s D H 1 ( L H ) s D L 2 ( H L ) s D H 1 ( L H ) s D L 3 ] 2
S 4 [ ( H L ) s D H 1 ( L H ) s D L 2 ( H L ) s D H 1 ( L H ) s D L 3 ( H L ) s D H 1 ( L H ) s D L 2 ( H L ) s D H 1 ( L H ) s D L 4 ] 2

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