Abstract

In this paper, we investigate the influences of the mode, number, and sequence of unit cell on the production of photonic band gaps (PBGs) in one-dimensional (1D) optical waveguide networks (OWNs) and find that the sufficient condition for producing PBG is related to the mode and number of unit cell, but the sequence of unit cell does not affect the production of PBGs. Only when a 1D OWN contains enough evanescent-mode unit cells can it produce PBGs. Otherwise, no matter how the sequence of unit cell is, the 1D OWN can not produce any PBG. It may deepen people’s knowledge on the mechanism of the production of PBGs in 1D OWNs and may be useful for the designing of PBG materials/devices. On the other hand, according to the classification method of 1D lattices in solid state physics, we classify the unit cells of OWNs as two types: the simple and complex unit cells. This classification method may be useful for investigating OWNs strictly, deeply, and taxonomically.

© 2015 Optical Society of America

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2014 (1)

2013 (1)

B. Pal, P. Patra, J. P. Saha, and A. Chakrabarti, “Engineering wave localization in a fractal waveguide network,” Phys. Rev. A 87, 023814 (2013).
[Crossref]

2012 (2)

Q. Xiao, X. Yang, J. Lu, and C. Liu, “Huge photonic band gaps with strong attenuations resulted from quasi-one-dimensional waveguide networks composed of triangular fundamental loops,” Opt. Commun. 285, 3775–3780 (2012).
[Crossref]

J. Lu, X. Yang, and L. Cai, “Large photonic band gap and strong attenuation of multiconnected Peano network,” Opt. Commun. 285, 459–464 (2012).
[Crossref]

2011 (3)

J. Lu, X. Yang, G. Zhang, and L. Cai, “Large photonic band gaps and strong attenuations of two-segment-connected Peano derivative networks,” Phys. Lett. A 375, 3904–3909 (2011).
[Crossref]

L. Cai, X. Yang, and J. Lu, “Large photonic band gap and strong attenuation of multiconnected sierpinski network,” J. Electromagnet. Wave. 25, 147–160 (2011).
[Crossref]

K. Rivoire, S. Buckley, and J. Vučković, “Multiply resonant photonic crystal nanocavities for nonlinear frequency conversion,” Opt. Express 19, 22198–22207 (2011).
[Crossref] [PubMed]

2010 (1)

H. H. Song and X. B. Yang, “Photonic band structures of quadrangular multiconnected networks,” Chinese Phys. B 19, 074213 (2010).
[Crossref]

2007 (2)

Z. Y. Wang and X. Yang, “Strong attenuation within the photonic band gaps of multiconnected networks,” Phys. Rev. B 76, 235104 (2007).
[Crossref]

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90, 121133 (2007).
[Crossref]

2005 (2)

A. G. Barriuso, J. J. Monzón, and L. L. Sánchez-Soto, “Comparing omnidirectional reflection from periodic and quasiperiodic one-dimensional photonic crystals,” Opt. Express 13, 3913–3920 (2005).
[Crossref] [PubMed]

M. Beruete, M. Sorolla, S. Member, IEEE I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced Millimeter Wave Transmission Through Quasioptical Subwavelength Perforated Plates,” IEEE T. Antenn. Propag. 53, 1897–1903 (2005).
[Crossref]

2004 (3)

D. Felbacq and R. Smaâli, “Bloch Modes Dressed by Evanescent Waves and the Generalized Goos-Hänchen Effect in Photonic Crystals,” Phys. Rev. Lett. 92, 193902 (2004).
[Crossref]

L. Wang, H. Chen, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70, 245102 (2004).
[Crossref]

S. K. Cheung, T. L. Chan, Z. Q. Zhang, and C. T. Chan, “Large photonic band gaps in certain periodic and quasiperiodic networks in two and three dimensions,” Phys. Rev. B 70, 125104 (2004).
[Crossref]

2003 (2)

A. D’Orazio, M. De Sario, V. Petruzzelli, and F. Prudenzano, “Photonic band gap filter forwavelength division multiplexer,” Opt. Express 11, 230–239 (2003).
[Crossref]

A. Mir, A. Akjouj, J. O. Vasseur, B. Djafari-Rouhani, N. Fettouhi, E. H. E. Boudouti, L. Dobrzynski, and J. Zemmouri, “Observation of large photonic band gaps and defect modes in one-dimensional networked waveguides,” J. Phys.: Condens. Mat. 15, 1593–1598 (2003).

2000 (2)

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, “Robust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[Crossref] [PubMed]

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
[Crossref] [PubMed]

1999 (1)

Y. Liu, Z. Hou, P. M. Hui, and W. Sritrakoo, “Electronic transport properties of Sierpinski lattices,” Phys. Rev. B 60, 13444–13452 (1999).
[Crossref]

1998 (3)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A Dielectric Omnidirectional Reflector,” Science 282, 1679–1682 (1998).
[Crossref] [PubMed]

Z. Q. Zhang, C. C. Wong, K. K. Fung, Y. L. Ho, W. L. Chan, S. C. Kan, T. L. Chan, and N. Cheung, “Observation of localized electromagnetic waves in three-dimensional networks of waveguides,” Phys. Rev. Lett. 81, 5540–5543 (1998).
[Crossref]

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, and J. O. Vasseur, “Giant gaps in photonic band structures,” Phys. Rev. B 57, R9388–R9391 (1998).
[Crossref]

1997 (1)

J. O. Vasseur, P. A. Deymier, L. Dobrzynski, B. Djafari-Rouhani, and A. Akjouj, “Absolute band gaps and electromagnetic transmission in quasi-one-dimensional comb structures,” Phys. Rev. B 55, 10434–10442 (1997).
[Crossref]

1994 (1)

Z. Q. Zhang and P. Sheng, “Wave localization in random networks,” Phys. Rev. B 49, 83–89 (1994).
[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]

1887 (1)

L. Rayleigh, “On the maintenance of vibrations by forces of double frequency, and on the propagation of waves through a medium endowed with a periodic structure,” Phil. Mag. J. Sci. 24, 145–159 (1887).
[Crossref]

Akjouj, A.

A. Mir, A. Akjouj, J. O. Vasseur, B. Djafari-Rouhani, N. Fettouhi, E. H. E. Boudouti, L. Dobrzynski, and J. Zemmouri, “Observation of large photonic band gaps and defect modes in one-dimensional networked waveguides,” J. Phys.: Condens. Mat. 15, 1593–1598 (2003).

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, and J. O. Vasseur, “Giant gaps in photonic band structures,” Phys. Rev. B 57, R9388–R9391 (1998).
[Crossref]

J. O. Vasseur, P. A. Deymier, L. Dobrzynski, B. Djafari-Rouhani, and A. Akjouj, “Absolute band gaps and electromagnetic transmission in quasi-one-dimensional comb structures,” Phys. Rev. B 55, 10434–10442 (1997).
[Crossref]

Barriuso, A. G.

Beruete, M.

M. Beruete, M. Sorolla, S. Member, IEEE I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced Millimeter Wave Transmission Through Quasioptical Subwavelength Perforated Plates,” IEEE T. Antenn. Propag. 53, 1897–1903 (2005).
[Crossref]

Boudouti, E. H. E.

A. Mir, A. Akjouj, J. O. Vasseur, B. Djafari-Rouhani, N. Fettouhi, E. H. E. Boudouti, L. Dobrzynski, and J. Zemmouri, “Observation of large photonic band gaps and defect modes in one-dimensional networked waveguides,” J. Phys.: Condens. Mat. 15, 1593–1598 (2003).

Bravo-Abad, J.

M. Beruete, M. Sorolla, S. Member, IEEE I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced Millimeter Wave Transmission Through Quasioptical Subwavelength Perforated Plates,” IEEE T. Antenn. Propag. 53, 1897–1903 (2005).
[Crossref]

Buckley, S.

Cai, L.

J. Lu, X. Yang, and L. Cai, “Large photonic band gap and strong attenuation of multiconnected Peano network,” Opt. Commun. 285, 459–464 (2012).
[Crossref]

J. Lu, X. Yang, G. Zhang, and L. Cai, “Large photonic band gaps and strong attenuations of two-segment-connected Peano derivative networks,” Phys. Lett. A 375, 3904–3909 (2011).
[Crossref]

L. Cai, X. Yang, and J. Lu, “Large photonic band gap and strong attenuation of multiconnected sierpinski network,” J. Electromagnet. Wave. 25, 147–160 (2011).
[Crossref]

Campbell, M.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
[Crossref] [PubMed]

Campillo, I.

M. Beruete, M. Sorolla, S. Member, IEEE I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced Millimeter Wave Transmission Through Quasioptical Subwavelength Perforated Plates,” IEEE T. Antenn. Propag. 53, 1897–1903 (2005).
[Crossref]

Chakrabarti, A.

B. Pal, P. Patra, J. P. Saha, and A. Chakrabarti, “Engineering wave localization in a fractal waveguide network,” Phys. Rev. A 87, 023814 (2013).
[Crossref]

Chan, C. T.

S. K. Cheung, T. L. Chan, Z. Q. Zhang, and C. T. Chan, “Large photonic band gaps in certain periodic and quasiperiodic networks in two and three dimensions,” Phys. Rev. B 70, 125104 (2004).
[Crossref]

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, “Robust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[Crossref] [PubMed]

Chan, T. L.

S. K. Cheung, T. L. Chan, Z. Q. Zhang, and C. T. Chan, “Large photonic band gaps in certain periodic and quasiperiodic networks in two and three dimensions,” Phys. Rev. B 70, 125104 (2004).
[Crossref]

Z. Q. Zhang, C. C. Wong, K. K. Fung, Y. L. Ho, W. L. Chan, S. C. Kan, T. L. Chan, and N. Cheung, “Observation of localized electromagnetic waves in three-dimensional networks of waveguides,” Phys. Rev. Lett. 81, 5540–5543 (1998).
[Crossref]

Chan, W. L.

Z. Q. Zhang, C. C. Wong, K. K. Fung, Y. L. Ho, W. L. Chan, S. C. Kan, T. L. Chan, and N. Cheung, “Observation of localized electromagnetic waves in three-dimensional networks of waveguides,” Phys. Rev. Lett. 81, 5540–5543 (1998).
[Crossref]

Chen, C.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A Dielectric Omnidirectional Reflector,” Science 282, 1679–1682 (1998).
[Crossref] [PubMed]

Chen, H.

L. Wang, H. Chen, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70, 245102 (2004).
[Crossref]

Cheung, N.

Z. Q. Zhang, C. C. Wong, K. K. Fung, Y. L. Ho, W. L. Chan, S. C. Kan, T. L. Chan, and N. Cheung, “Observation of localized electromagnetic waves in three-dimensional networks of waveguides,” Phys. Rev. Lett. 81, 5540–5543 (1998).
[Crossref]

Cheung, S. K.

S. K. Cheung, T. L. Chan, Z. Q. Zhang, and C. T. Chan, “Large photonic band gaps in certain periodic and quasiperiodic networks in two and three dimensions,” Phys. Rev. B 70, 125104 (2004).
[Crossref]

D’Orazio, A.

De Sario, M.

Denning, R. G.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
[Crossref] [PubMed]

Deymier, P. A.

J. O. Vasseur, P. A. Deymier, L. Dobrzynski, B. Djafari-Rouhani, and A. Akjouj, “Absolute band gaps and electromagnetic transmission in quasi-one-dimensional comb structures,” Phys. Rev. B 55, 10434–10442 (1997).
[Crossref]

Djafari-Rouhani, B.

A. Mir, A. Akjouj, J. O. Vasseur, B. Djafari-Rouhani, N. Fettouhi, E. H. E. Boudouti, L. Dobrzynski, and J. Zemmouri, “Observation of large photonic band gaps and defect modes in one-dimensional networked waveguides,” J. Phys.: Condens. Mat. 15, 1593–1598 (2003).

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, and J. O. Vasseur, “Giant gaps in photonic band structures,” Phys. Rev. B 57, R9388–R9391 (1998).
[Crossref]

J. O. Vasseur, P. A. Deymier, L. Dobrzynski, B. Djafari-Rouhani, and A. Akjouj, “Absolute band gaps and electromagnetic transmission in quasi-one-dimensional comb structures,” Phys. Rev. B 55, 10434–10442 (1997).
[Crossref]

Dobrzynski, L.

A. Mir, A. Akjouj, J. O. Vasseur, B. Djafari-Rouhani, N. Fettouhi, E. H. E. Boudouti, L. Dobrzynski, and J. Zemmouri, “Observation of large photonic band gaps and defect modes in one-dimensional networked waveguides,” J. Phys.: Condens. Mat. 15, 1593–1598 (2003).

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, and J. O. Vasseur, “Giant gaps in photonic band structures,” Phys. Rev. B 57, R9388–R9391 (1998).
[Crossref]

J. O. Vasseur, P. A. Deymier, L. Dobrzynski, B. Djafari-Rouhani, and A. Akjouj, “Absolute band gaps and electromagnetic transmission in quasi-one-dimensional comb structures,” Phys. Rev. B 55, 10434–10442 (1997).
[Crossref]

Dolado, J. S.

M. Beruete, M. Sorolla, S. Member, IEEE I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced Millimeter Wave Transmission Through Quasioptical Subwavelength Perforated Plates,” IEEE T. Antenn. Propag. 53, 1897–1903 (2005).
[Crossref]

Fan, S.

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90, 121133 (2007).
[Crossref]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A Dielectric Omnidirectional Reflector,” Science 282, 1679–1682 (1998).
[Crossref] [PubMed]

Fang, J. X.

J. X. Fang and D. Lu, Solid State Physics (Shanghai Science and Technology Press, 1980) pp 13 (in Chinese).

Felbacq, D.

D. Felbacq and R. Smaâli, “Bloch Modes Dressed by Evanescent Waves and the Generalized Goos-Hänchen Effect in Photonic Crystals,” Phys. Rev. Lett. 92, 193902 (2004).
[Crossref]

Fettouhi, N.

A. Mir, A. Akjouj, J. O. Vasseur, B. Djafari-Rouhani, N. Fettouhi, E. H. E. Boudouti, L. Dobrzynski, and J. Zemmouri, “Observation of large photonic band gaps and defect modes in one-dimensional networked waveguides,” J. Phys.: Condens. Mat. 15, 1593–1598 (2003).

Fink, Y.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A Dielectric Omnidirectional Reflector,” Science 282, 1679–1682 (1998).
[Crossref] [PubMed]

Fung, K. K.

Z. Q. Zhang, C. C. Wong, K. K. Fung, Y. L. Ho, W. L. Chan, S. C. Kan, T. L. Chan, and N. Cheung, “Observation of localized electromagnetic waves in three-dimensional networks of waveguides,” Phys. Rev. Lett. 81, 5540–5543 (1998).
[Crossref]

García-Vidal, F. J.

M. Beruete, M. Sorolla, S. Member, IEEE I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced Millimeter Wave Transmission Through Quasioptical Subwavelength Perforated Plates,” IEEE T. Antenn. Propag. 53, 1897–1903 (2005).
[Crossref]

Harrison, M. T.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
[Crossref] [PubMed]

Ho, Y. L.

Z. Q. Zhang, C. C. Wong, K. K. Fung, Y. L. Ho, W. L. Chan, S. C. Kan, T. L. Chan, and N. Cheung, “Observation of localized electromagnetic waves in three-dimensional networks of waveguides,” Phys. Rev. Lett. 81, 5540–5543 (1998).
[Crossref]

Hou, Z.

Y. Liu, Z. Hou, P. M. Hui, and W. Sritrakoo, “Electronic transport properties of Sierpinski lattices,” Phys. Rev. B 60, 13444–13452 (1999).
[Crossref]

Hui, P. M.

Y. Liu, Z. Hou, P. M. Hui, and W. Sritrakoo, “Electronic transport properties of Sierpinski lattices,” Phys. Rev. B 60, 13444–13452 (1999).
[Crossref]

Jiang, P.

D. Lu, P. Jiang, and Z. Z. Xu, Solid State Physics (Shanghai Science and Technology Press, 2010) pp 2 (in Chinese).

Joannopoulos, J. D.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A Dielectric Omnidirectional Reflector,” Science 282, 1679–1682 (1998).
[Crossref] [PubMed]

John, S.

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

Kan, S. C.

Z. Q. Zhang, C. C. Wong, K. K. Fung, Y. L. Ho, W. L. Chan, S. C. Kan, T. L. Chan, and N. Cheung, “Observation of localized electromagnetic waves in three-dimensional networks of waveguides,” Phys. Rev. Lett. 81, 5540–5543 (1998).
[Crossref]

Lei, X. Y.

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, “Robust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[Crossref] [PubMed]

Liu, C.

Q. Xiao, X. Yang, J. Lu, and C. Liu, “Huge photonic band gaps with strong attenuations resulted from quasi-one-dimensional waveguide networks composed of triangular fundamental loops,” Opt. Commun. 285, 3775–3780 (2012).
[Crossref]

Liu, Y.

Y. Liu, Z. Hou, P. M. Hui, and W. Sritrakoo, “Electronic transport properties of Sierpinski lattices,” Phys. Rev. B 60, 13444–13452 (1999).
[Crossref]

Lu, D.

J. X. Fang and D. Lu, Solid State Physics (Shanghai Science and Technology Press, 1980) pp 13 (in Chinese).

D. Lu, P. Jiang, and Z. Z. Xu, Solid State Physics (Shanghai Science and Technology Press, 2010) pp 2 (in Chinese).

Lu, J.

J. Lu, X. Yang, and L. Cai, “Large photonic band gap and strong attenuation of multiconnected Peano network,” Opt. Commun. 285, 459–464 (2012).
[Crossref]

Q. Xiao, X. Yang, J. Lu, and C. Liu, “Huge photonic band gaps with strong attenuations resulted from quasi-one-dimensional waveguide networks composed of triangular fundamental loops,” Opt. Commun. 285, 3775–3780 (2012).
[Crossref]

L. Cai, X. Yang, and J. Lu, “Large photonic band gap and strong attenuation of multiconnected sierpinski network,” J. Electromagnet. Wave. 25, 147–160 (2011).
[Crossref]

J. Lu, X. Yang, G. Zhang, and L. Cai, “Large photonic band gaps and strong attenuations of two-segment-connected Peano derivative networks,” Phys. Lett. A 375, 3904–3909 (2011).
[Crossref]

Martín-Moreno, L.

M. Beruete, M. Sorolla, S. Member, IEEE I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced Millimeter Wave Transmission Through Quasioptical Subwavelength Perforated Plates,” IEEE T. Antenn. Propag. 53, 1897–1903 (2005).
[Crossref]

Member, S.

M. Beruete, M. Sorolla, S. Member, IEEE I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced Millimeter Wave Transmission Through Quasioptical Subwavelength Perforated Plates,” IEEE T. Antenn. Propag. 53, 1897–1903 (2005).
[Crossref]

Michel, J.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A Dielectric Omnidirectional Reflector,” Science 282, 1679–1682 (1998).
[Crossref] [PubMed]

Mir, A.

A. Mir, A. Akjouj, J. O. Vasseur, B. Djafari-Rouhani, N. Fettouhi, E. H. E. Boudouti, L. Dobrzynski, and J. Zemmouri, “Observation of large photonic band gaps and defect modes in one-dimensional networked waveguides,” J. Phys.: Condens. Mat. 15, 1593–1598 (2003).

Monzón, J. J.

Pal, B.

B. Pal, P. Patra, J. P. Saha, and A. Chakrabarti, “Engineering wave localization in a fractal waveguide network,” Phys. Rev. A 87, 023814 (2013).
[Crossref]

Patra, P.

B. Pal, P. Patra, J. P. Saha, and A. Chakrabarti, “Engineering wave localization in a fractal waveguide network,” Phys. Rev. A 87, 023814 (2013).
[Crossref]

Petruzzelli, V.

Premaratne, M.

Prudenzano, F.

Rayleigh, L.

L. Rayleigh, “On the maintenance of vibrations by forces of double frequency, and on the propagation of waves through a medium endowed with a periodic structure,” Phil. Mag. J. Sci. 24, 145–159 (1887).
[Crossref]

Reddy, M. S.

Rivoire, K.

Rukhlenko, I. D.

Saha, J. P.

B. Pal, P. Patra, J. P. Saha, and A. Chakrabarti, “Engineering wave localization in a fractal waveguide network,” Phys. Rev. A 87, 023814 (2013).
[Crossref]

Sánchez-Soto, L. L.

Sharp, D. N.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
[Crossref] [PubMed]

Sheng, P.

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, “Robust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[Crossref] [PubMed]

Z. Q. Zhang and P. Sheng, “Wave localization in random networks,” Phys. Rev. B 49, 83–89 (1994).
[Crossref]

Smaâli, R.

D. Felbacq and R. Smaâli, “Bloch Modes Dressed by Evanescent Waves and the Generalized Goos-Hänchen Effect in Photonic Crystals,” Phys. Rev. Lett. 92, 193902 (2004).
[Crossref]

Song, H. H.

H. H. Song and X. B. Yang, “Photonic band structures of quadrangular multiconnected networks,” Chinese Phys. B 19, 074213 (2010).
[Crossref]

Sorolla, M.

M. Beruete, M. Sorolla, S. Member, IEEE I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced Millimeter Wave Transmission Through Quasioptical Subwavelength Perforated Plates,” IEEE T. Antenn. Propag. 53, 1897–1903 (2005).
[Crossref]

Sritrakoo, W.

Y. Liu, Z. Hou, P. M. Hui, and W. Sritrakoo, “Electronic transport properties of Sierpinski lattices,” Phys. Rev. B 60, 13444–13452 (1999).
[Crossref]

Tam, W. Y.

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, “Robust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[Crossref] [PubMed]

Thomas, E. L.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A Dielectric Omnidirectional Reflector,” Science 282, 1679–1682 (1998).
[Crossref] [PubMed]

Turberfield, A. J.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
[Crossref] [PubMed]

Vasseur, J. O.

A. Mir, A. Akjouj, J. O. Vasseur, B. Djafari-Rouhani, N. Fettouhi, E. H. E. Boudouti, L. Dobrzynski, and J. Zemmouri, “Observation of large photonic band gaps and defect modes in one-dimensional networked waveguides,” J. Phys.: Condens. Mat. 15, 1593–1598 (2003).

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, and J. O. Vasseur, “Giant gaps in photonic band structures,” Phys. Rev. B 57, R9388–R9391 (1998).
[Crossref]

J. O. Vasseur, P. A. Deymier, L. Dobrzynski, B. Djafari-Rouhani, and A. Akjouj, “Absolute band gaps and electromagnetic transmission in quasi-one-dimensional comb structures,” Phys. Rev. B 55, 10434–10442 (1997).
[Crossref]

Vijaya, R.

Vuckovic, J.

Wang, L.

L. Wang, H. Chen, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70, 245102 (2004).
[Crossref]

Wang, Z.

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90, 121133 (2007).
[Crossref]

Wang, Z. L.

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, “Robust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[Crossref] [PubMed]

Wang, Z. Y.

Z. Y. Wang and X. Yang, “Strong attenuation within the photonic band gaps of multiconnected networks,” Phys. Rev. B 76, 235104 (2007).
[Crossref]

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A Dielectric Omnidirectional Reflector,” Science 282, 1679–1682 (1998).
[Crossref] [PubMed]

Wong, C. C.

Z. Q. Zhang, C. C. Wong, K. K. Fung, Y. L. Ho, W. L. Chan, S. C. Kan, T. L. Chan, and N. Cheung, “Observation of localized electromagnetic waves in three-dimensional networks of waveguides,” Phys. Rev. Lett. 81, 5540–5543 (1998).
[Crossref]

Xiao, Q.

Q. Xiao, X. Yang, J. Lu, and C. Liu, “Huge photonic band gaps with strong attenuations resulted from quasi-one-dimensional waveguide networks composed of triangular fundamental loops,” Opt. Commun. 285, 3775–3780 (2012).
[Crossref]

Xu, Z. Z.

D. Lu, P. Jiang, and Z. Z. Xu, Solid State Physics (Shanghai Science and Technology Press, 2010) pp 2 (in Chinese).

Yablonovitch, E.

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

Yang, X.

Q. Xiao, X. Yang, J. Lu, and C. Liu, “Huge photonic band gaps with strong attenuations resulted from quasi-one-dimensional waveguide networks composed of triangular fundamental loops,” Opt. Commun. 285, 3775–3780 (2012).
[Crossref]

J. Lu, X. Yang, and L. Cai, “Large photonic band gap and strong attenuation of multiconnected Peano network,” Opt. Commun. 285, 459–464 (2012).
[Crossref]

J. Lu, X. Yang, G. Zhang, and L. Cai, “Large photonic band gaps and strong attenuations of two-segment-connected Peano derivative networks,” Phys. Lett. A 375, 3904–3909 (2011).
[Crossref]

L. Cai, X. Yang, and J. Lu, “Large photonic band gap and strong attenuation of multiconnected sierpinski network,” J. Electromagnet. Wave. 25, 147–160 (2011).
[Crossref]

Z. Y. Wang and X. Yang, “Strong attenuation within the photonic band gaps of multiconnected networks,” Phys. Rev. B 76, 235104 (2007).
[Crossref]

Yang, X. B.

H. H. Song and X. B. Yang, “Photonic band structures of quadrangular multiconnected networks,” Chinese Phys. B 19, 074213 (2010).
[Crossref]

Yu, Z.

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90, 121133 (2007).
[Crossref]

Zemmouri, J.

A. Mir, A. Akjouj, J. O. Vasseur, B. Djafari-Rouhani, N. Fettouhi, E. H. E. Boudouti, L. Dobrzynski, and J. Zemmouri, “Observation of large photonic band gaps and defect modes in one-dimensional networked waveguides,” J. Phys.: Condens. Mat. 15, 1593–1598 (2003).

Zhang, G.

J. Lu, X. Yang, G. Zhang, and L. Cai, “Large photonic band gaps and strong attenuations of two-segment-connected Peano derivative networks,” Phys. Lett. A 375, 3904–3909 (2011).
[Crossref]

Zhang, W. Y.

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, “Robust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[Crossref] [PubMed]

Zhang, Z. Q.

S. K. Cheung, T. L. Chan, Z. Q. Zhang, and C. T. Chan, “Large photonic band gaps in certain periodic and quasiperiodic networks in two and three dimensions,” Phys. Rev. B 70, 125104 (2004).
[Crossref]

Z. Q. Zhang, C. C. Wong, K. K. Fung, Y. L. Ho, W. L. Chan, S. C. Kan, T. L. Chan, and N. Cheung, “Observation of localized electromagnetic waves in three-dimensional networks of waveguides,” Phys. Rev. Lett. 81, 5540–5543 (1998).
[Crossref]

Z. Q. Zhang and P. Sheng, “Wave localization in random networks,” Phys. Rev. B 49, 83–89 (1994).
[Crossref]

Zheng, D. G.

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, “Robust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[Crossref] [PubMed]

Zhu, S.

L. Wang, H. Chen, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70, 245102 (2004).
[Crossref]

Appl. Phys. Lett. (1)

Z. Yu, Z. Wang, and S. Fan, “One-way total reflection with one-dimensional magneto-optical photonic crystals,” Appl. Phys. Lett. 90, 121133 (2007).
[Crossref]

Chinese Phys. B (1)

H. H. Song and X. B. Yang, “Photonic band structures of quadrangular multiconnected networks,” Chinese Phys. B 19, 074213 (2010).
[Crossref]

IEEE T. Antenn. Propag. (1)

M. Beruete, M. Sorolla, S. Member, IEEE I. Campillo, J. S. Dolado, L. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced Millimeter Wave Transmission Through Quasioptical Subwavelength Perforated Plates,” IEEE T. Antenn. Propag. 53, 1897–1903 (2005).
[Crossref]

J. Electromagnet. Wave. (1)

L. Cai, X. Yang, and J. Lu, “Large photonic band gap and strong attenuation of multiconnected sierpinski network,” J. Electromagnet. Wave. 25, 147–160 (2011).
[Crossref]

J. Phys.: Condens. Mat. (1)

A. Mir, A. Akjouj, J. O. Vasseur, B. Djafari-Rouhani, N. Fettouhi, E. H. E. Boudouti, L. Dobrzynski, and J. Zemmouri, “Observation of large photonic band gaps and defect modes in one-dimensional networked waveguides,” J. Phys.: Condens. Mat. 15, 1593–1598 (2003).

Nature (1)

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
[Crossref] [PubMed]

Opt. Commun. (2)

Q. Xiao, X. Yang, J. Lu, and C. Liu, “Huge photonic band gaps with strong attenuations resulted from quasi-one-dimensional waveguide networks composed of triangular fundamental loops,” Opt. Commun. 285, 3775–3780 (2012).
[Crossref]

J. Lu, X. Yang, and L. Cai, “Large photonic band gap and strong attenuation of multiconnected Peano network,” Opt. Commun. 285, 459–464 (2012).
[Crossref]

Opt. Express (4)

Phil. Mag. J. Sci. (1)

L. Rayleigh, “On the maintenance of vibrations by forces of double frequency, and on the propagation of waves through a medium endowed with a periodic structure,” Phil. Mag. J. Sci. 24, 145–159 (1887).
[Crossref]

Phys. Lett. A (1)

J. Lu, X. Yang, G. Zhang, and L. Cai, “Large photonic band gaps and strong attenuations of two-segment-connected Peano derivative networks,” Phys. Lett. A 375, 3904–3909 (2011).
[Crossref]

Phys. Rev. A (1)

B. Pal, P. Patra, J. P. Saha, and A. Chakrabarti, “Engineering wave localization in a fractal waveguide network,” Phys. Rev. A 87, 023814 (2013).
[Crossref]

Phys. Rev. B (7)

S. K. Cheung, T. L. Chan, Z. Q. Zhang, and C. T. Chan, “Large photonic band gaps in certain periodic and quasiperiodic networks in two and three dimensions,” Phys. Rev. B 70, 125104 (2004).
[Crossref]

Z. Y. Wang and X. Yang, “Strong attenuation within the photonic band gaps of multiconnected networks,” Phys. Rev. B 76, 235104 (2007).
[Crossref]

J. O. Vasseur, P. A. Deymier, L. Dobrzynski, B. Djafari-Rouhani, and A. Akjouj, “Absolute band gaps and electromagnetic transmission in quasi-one-dimensional comb structures,” Phys. Rev. B 55, 10434–10442 (1997).
[Crossref]

L. Dobrzynski, A. Akjouj, B. Djafari-Rouhani, and J. O. Vasseur, “Giant gaps in photonic band structures,” Phys. Rev. B 57, R9388–R9391 (1998).
[Crossref]

Z. Q. Zhang and P. Sheng, “Wave localization in random networks,” Phys. Rev. B 49, 83–89 (1994).
[Crossref]

Y. Liu, Z. Hou, P. M. Hui, and W. Sritrakoo, “Electronic transport properties of Sierpinski lattices,” Phys. Rev. B 60, 13444–13452 (1999).
[Crossref]

L. Wang, H. Chen, and S. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70, 245102 (2004).
[Crossref]

Phys. Rev. Lett. (5)

D. Felbacq and R. Smaâli, “Bloch Modes Dressed by Evanescent Waves and the Generalized Goos-Hänchen Effect in Photonic Crystals,” Phys. Rev. Lett. 92, 193902 (2004).
[Crossref]

Z. Q. Zhang, C. C. Wong, K. K. Fung, Y. L. Ho, W. L. Chan, S. C. Kan, T. L. Chan, and N. Cheung, “Observation of localized electromagnetic waves in three-dimensional networks of waveguides,” Phys. Rev. Lett. 81, 5540–5543 (1998).
[Crossref]

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]

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, “Robust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000).
[Crossref] [PubMed]

Science (1)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A Dielectric Omnidirectional Reflector,” Science 282, 1679–1682 (1998).
[Crossref] [PubMed]

Other (2)

J. X. Fang and D. Lu, Solid State Physics (Shanghai Science and Technology Press, 1980) pp 13 (in Chinese).

D. Lu, P. Jiang, and Z. Z. Xu, Solid State Physics (Shanghai Science and Technology Press, 2010) pp 2 (in Chinese).

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Figures (7)

Fig. 1
Fig. 1 Schematic diagram of a 1D OWN with the waveguide length ratio of d 1 : d 2 = 1 : 2 and containing three unit cells, where EI , ER , and EO represent the incident, reflected, and transmitted EM waves, respectively.
Fig. 2
Fig. 2 Intensity map of EM waves propagating in the OWN shown in Fig. 3, where mdi n (m=1,2,3, i=1,2, and n=2,3,4) represents the waveguide segment between nodes m and n and the length of the segment is di .
Fig. 3
Fig. 3 Schematic diagram of a 1D periodic OWN composed of simple unit cells, where d 1, d 2, ..., and dn are the lengths of the n waveguide segments, respectively.
Fig. 4
Fig. 4 Schematic diagram of a 1D periodic OWN composed of the complex unit cells of equilateral decagon, where each dashed line denotes a simple unit cell with equal waveguide length ratio and each waveguide length equals d 1. (a) Symmetrical mixed connection with q up = q low = 5. (b) Asymmetrical mixed connection with q up = 4 and q low = 6.
Fig. 5
Fig. 5 Schematic diagram of a 1D periodic OWN composed of the complex unit cells, which consist of series connection of the simplest and sub-simplest unit cells, where d 1, d 2, and d 3 are, respectively, the lengths of the three kinds of waveguide segments.
Fig. 6
Fig. 6 Transmission spectra of 1D OWNs, where the red solid and black dotted lines are the results for the OWNs containing 8 and 32 unit cells, respectively. (a) OWNs with the sequence of AO···O. (b) OWNs with the sequence of OA···A.
Fig. 7
Fig. 7 Transmission spectra of three kinds of 1D OWNs, where the red solid and black dotted lines are the results of the smaller and larger networks, respectively. (a) TM OWNs. (b) FC OWNs. (c) DS OWNs.

Equations (14)

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

cos K = 2 cos 2 π ν d 1 c 1 ,
ψ i j ( x ) = ψ i sin 2 π ν l i j c sin [ 2 π ν c ( l i j x ) ] + ψ j sin 2 π ν l i j c sin 2 π ν x c ,
cos K = i = 1 n cot 2 π ν d i c i = 1 n csc 2 π ν d i c ,
2 ψ 2 i = 1 n cot 2 π ν d i c + ( ψ 1 + ψ 3 ) i = 1 n csc 2 π ν d i c = 0 .
ψ 1 = e ι K ψ 2 ψ 3 = e ι K ψ 2 .
cos K = cos 2 π ν d 1 c .
2 ψ q up + 1 cos 2 π ν q up d 1 c + ( ψ 1 + ψ 3 q up ) = 0 .
ψ 1 = e ι K ψ q up + 1 ψ 3 q up = e ι K ψ q up + 1 .
cos K = cos 2 π ν q up d 1 c = cos 2 π ν q low d 1 c .
cos K = cos ( q up + q low 2 2 π ν d 1 c ) cos ( q up q low 2 2 π ν d 1 c ) .
cos K = 1 2 sin π ν L c cos π ν Δ L c × [ cos 2 π ν d 1 c sin 2 π ν L c + + sin 2 π ν d 1 c ( 5 4 cos 2 π ν L c 1 4 cos 2 π ν Δ L c 1 ) ] ,
TM G 4 = TM 8 = O 1 O 2 O 2 O 1 O 2 O 1 O 1 O 2 , TM G 6 = TM 32 = O 1 O 2 O 2 O 1 O 2 O 1 O 1 O 2 O 2 O 1 O 1 O 2 O 1 O 2 O 2 O 1 O 2 O 1 O 1 O 2 O 1 O 2 O 2 O 1 O 1 O 2 O 2 O 1 O 2 O 1 O 1 O 2 .
FC G 6 = FC 8 = O 2 O 1 O 2 O 2 O 1 O 2 O 1 O 2 , FC G 9 = FC 34 = O 2 O 1 O 2 O 2 O 1 O 2 O 1 O 2 O 2 O 1 O 2 O 2 O 1 O 2 O 1 O 2 O 2 O 1 O 2 O 1 O 2 O 2 O 1 O 2 O 2 O 1 O 2 O 1 O 2 O 2 O 1 O 2 O 2 O 1 .
DS 8 = O 2 O 1 O 2 O 1 O 2 O 2 O 1 O 1 , DS 32 = O 2 O 1 O 2 O 1 O 2 O 2 O 1 O 1 O 2 O 1 O 2 O 2 O 2 O 2 O 1 O 1 O 2 O 2 O 1 O 2 O 1 O 1 O 2 O 1 O 1 O 1 O 1 O 2 O 1 O 1 O 1 O 2 .

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