Abstract

In this paper, a fractal structure is introduced into a one-dimensional (1D) photonic crystal to design a new structure of photonic crystal. We create three typical fractal photonic crystals: the Cantor-like fractal photonic crystal (CLFPC), golden-section fractal photonic crystal (GSFPC), and Fibonacci fractal photonic crystal (FFPC). The transmission spectra of CLFPCs, GSFPCs, and FFPCs are simulated and analyzed. The calculation result shows that the transmission spectrum and the group velocity of a CLFPC are self-similar and in accord with the self-similarity in structure, and the peak numbers in the transmission spectra of the GSFPC and FFPC also follow the principals of special fractal structures.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  4. Y. Kanamori, N. Matsuyama, and K. Hane, “Resonant-wavelength tuning of a pitch-variable 1-D photonic crystal filter at telecom frequencies,” IEEE Photon. Technol. Lett. 20, 1136-1138 (2008).
    [CrossRef]
  5. H. Nemec, L. Duvillaret, and F. Garet, “Thermally tunable filter for terahertz range based on a one-dimensional photonic crystal with a defect,” J. Appl. Phys. 96, 4072-4075 (2004).
    [CrossRef]
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    [CrossRef]
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2009 (1)

2008 (5)

H. Zou, G.-Q. Liang, and H.-Z. Wang, “Efficient all-optical dual-channel switches, logic gates, half-adder, and half-subtracter in a one-dimensional photonic hetero-structure,” J. Opt. Soc. Am. B 25, 351-360 (2008).
[CrossRef]

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2, 465-473 (2008).
[CrossRef]

A. Di Falco, L. O'Faolain, and T. F. Krauss, “Dispersion control and slow light in slotted photonic crystal waveguides,” Appl. Phys. Lett. 92, 083501 (2008).
[CrossRef]

Y. Kanamori, N. Matsuyama, and K. Hane, “Resonant-wavelength tuning of a pitch-variable 1-D photonic crystal filter at telecom frequencies,” IEEE Photon. Technol. Lett. 20, 1136-1138 (2008).
[CrossRef]

V. Ya. Zyryanov, V. A. Gunyakov, S. A. Myslivets, V. G. Arkhipkin, and V. F. Shabanov, “Electro-optical switching in a one-dimensional photonic crystal,” Mol. Cryst. Liq. Cryst. 488, 1563-5287 (2008).
[CrossRef]

2007 (2)

F. Villa-Villa, J. A. Gaspar-Armenta, and A. Mendoza-Suárez, “Surface modes in one-dimensional photonic crystals that include left-handed materials,” J. Electromagn. Waves Appl. 21, 485-499 (2007).
[CrossRef]

C. Zheng, H. Tian, C. Li, and Y. Ji, “Tunable frequency and angular photonic crystal filter,” Proc. SPIE 6781, 678117 (2007).
[CrossRef]

2006 (1)

S. Corviser and M. Rams, “IFS attractors and Cantor sets,” Topol. Appl. 153, 1849-1859 (2006).
[CrossRef]

2005 (2)

M. Dai and L. Tian, “The structure of a Cantor-like set with overlap,” Chaos, Solitons Fractals 26, 295-301 (2005).
[CrossRef]

M. P. Jiang, X. F. Jiang, X. M. Shen, D. W. Xu, and D. F. Shi, “Study on the polarization property of 1-D photonic crystal,” Chinese J. Quantum Electron. 22, 612-616 (2005).

2004 (1)

H. Nemec, L. Duvillaret, and F. Garet, “Thermally tunable filter for terahertz range based on a one-dimensional photonic crystal with a defect,” J. Appl. Phys. 96, 4072-4075 (2004).
[CrossRef]

2002 (2)

N. H. Liu, S. Y. Zhu, H. Chen, and X. Wu, “Superluminal pulse propagation through one-dimensional photonic crystals with a dispersive defect,” Phys. Rev. E 65, 046607 (2002).
[CrossRef]

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
[CrossRef]

2000 (1)

R. Puppin, “Surface polaritons of a left-handed medium,” Phys. Lett. A 277, 61-64 (2000).
[CrossRef]

1998 (1)

J. Zi, J. Wan, and C. Zhang, “Large frequency range of negligible transmission in one-dimensional photonic quantum well structures,” Appl. Phys. Lett. 73, 2084-2086 (1998).
[CrossRef]

1997 (1)

D. J. Feng, H. Rao, and J. Wu, “The net measure properties for symmetric Cantor sets and their applications,” Prog. Nat. Sci. 7, 172-178 (1997).

1992 (2)

A. Arneodo, F. Argoul, E. Bacry, J. F. Muzy, and M. Tabard, “Golden mean arithmetic in the fractal branching of diffusion-limited aggregates,” Phys. Rev. Lett. 68, 3456-3459 (1992).
[CrossRef] [PubMed]

T. P. Srinivasan, “Fibonacci sequence, golden ratio, and a network of resistors,” Am. J. Phys. Vol. 60, 461-462 (1992).
[CrossRef]

1990 (1)

Andalib, P.

Argoul, F.

A. Arneodo, F. Argoul, E. Bacry, J. F. Muzy, and M. Tabard, “Golden mean arithmetic in the fractal branching of diffusion-limited aggregates,” Phys. Rev. Lett. 68, 3456-3459 (1992).
[CrossRef] [PubMed]

Arkhipkin, V. G.

V. Ya. Zyryanov, V. A. Gunyakov, S. A. Myslivets, V. G. Arkhipkin, and V. F. Shabanov, “Electro-optical switching in a one-dimensional photonic crystal,” Mol. Cryst. Liq. Cryst. 488, 1563-5287 (2008).
[CrossRef]

V. A. Gunyakov, V. Ya. Zyryanov, S. A. Myslivets, V. G. Arkhipkin, and V. F. Shabanov, “Electrically controllable optical switch based on one-dimensional photonic crystal,” in Proceedings of IEEE Fourth International Conference on Advanced Optoelectronics and Lasers (IEEE, 2009), pp.186-188.
[CrossRef]

Arneodo, A.

A. Arneodo, F. Argoul, E. Bacry, J. F. Muzy, and M. Tabard, “Golden mean arithmetic in the fractal branching of diffusion-limited aggregates,” Phys. Rev. Lett. 68, 3456-3459 (1992).
[CrossRef] [PubMed]

Baba, T.

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2, 465-473 (2008).
[CrossRef]

Bacry, E.

A. Arneodo, F. Argoul, E. Bacry, J. F. Muzy, and M. Tabard, “Golden mean arithmetic in the fractal branching of diffusion-limited aggregates,” Phys. Rev. Lett. 68, 3456-3459 (1992).
[CrossRef] [PubMed]

Chen, H.

N. H. Liu, S. Y. Zhu, H. Chen, and X. Wu, “Superluminal pulse propagation through one-dimensional photonic crystals with a dispersive defect,” Phys. Rev. E 65, 046607 (2002).
[CrossRef]

Corviser, S.

S. Corviser and M. Rams, “IFS attractors and Cantor sets,” Topol. Appl. 153, 1849-1859 (2006).
[CrossRef]

Dai, M.

M. Dai and L. Tian, “The structure of a Cantor-like set with overlap,” Chaos, Solitons Fractals 26, 295-301 (2005).
[CrossRef]

Di Falco, A.

A. Di Falco, L. O'Faolain, and T. F. Krauss, “Dispersion control and slow light in slotted photonic crystal waveguides,” Appl. Phys. Lett. 92, 083501 (2008).
[CrossRef]

Dunlap, R. A.

R. A. Dunlap, The golden ratio and Fibonacci numbers (World Scientific, 1997).
[CrossRef]

Duvillaret, L.

H. Nemec, L. Duvillaret, and F. Garet, “Thermally tunable filter for terahertz range based on a one-dimensional photonic crystal with a defect,” J. Appl. Phys. 96, 4072-4075 (2004).
[CrossRef]

Feng, D. J.

D. J. Feng, H. Rao, and J. Wu, “The net measure properties for symmetric Cantor sets and their applications,” Prog. Nat. Sci. 7, 172-178 (1997).

Gaponenko, S. V.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
[CrossRef]

Garet, F.

H. Nemec, L. Duvillaret, and F. Garet, “Thermally tunable filter for terahertz range based on a one-dimensional photonic crystal with a defect,” J. Appl. Phys. 96, 4072-4075 (2004).
[CrossRef]

Gaspar-Armenta, J. A.

F. Villa-Villa, J. A. Gaspar-Armenta, and A. Mendoza-Suárez, “Surface modes in one-dimensional photonic crystals that include left-handed materials,” J. Electromagn. Waves Appl. 21, 485-499 (2007).
[CrossRef]

Granpayeh, N.

Gunyakov, V. A.

V. Ya. Zyryanov, V. A. Gunyakov, S. A. Myslivets, V. G. Arkhipkin, and V. F. Shabanov, “Electro-optical switching in a one-dimensional photonic crystal,” Mol. Cryst. Liq. Cryst. 488, 1563-5287 (2008).
[CrossRef]

V. A. Gunyakov, V. Ya. Zyryanov, S. A. Myslivets, V. G. Arkhipkin, and V. F. Shabanov, “Electrically controllable optical switch based on one-dimensional photonic crystal,” in Proceedings of IEEE Fourth International Conference on Advanced Optoelectronics and Lasers (IEEE, 2009), pp.186-188.
[CrossRef]

Hane, K.

Y. Kanamori, N. Matsuyama, and K. Hane, “Resonant-wavelength tuning of a pitch-variable 1-D photonic crystal filter at telecom frequencies,” IEEE Photon. Technol. Lett. 20, 1136-1138 (2008).
[CrossRef]

Hilton, P.

H. Walser and P. Hilton, The golden section (Mathematical Association of America, 2001).

Jaggard, D. L.

Ji, Y.

C. Zheng, H. Tian, C. Li, and Y. Ji, “Tunable frequency and angular photonic crystal filter,” Proc. SPIE 6781, 678117 (2007).
[CrossRef]

Jiang, M. P.

M. P. Jiang, X. F. Jiang, X. M. Shen, D. W. Xu, and D. F. Shi, “Study on the polarization property of 1-D photonic crystal,” Chinese J. Quantum Electron. 22, 612-616 (2005).

Jiang, X. F.

M. P. Jiang, X. F. Jiang, X. M. Shen, D. W. Xu, and D. F. Shi, “Study on the polarization property of 1-D photonic crystal,” Chinese J. Quantum Electron. 22, 612-616 (2005).

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: molding the flow of light (Princeton Univ. Press, 2007).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: molding the flow of light (Princeton Univ. Press, 2007).

Kanamori, Y.

Y. Kanamori, N. Matsuyama, and K. Hane, “Resonant-wavelength tuning of a pitch-variable 1-D photonic crystal filter at telecom frequencies,” IEEE Photon. Technol. Lett. 20, 1136-1138 (2008).
[CrossRef]

Krauss, T.

T. Krauss, “Ultracompact optical switch based on photonic crystal waveguides,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OWC2.

Krauss, T. F.

A. Di Falco, L. O'Faolain, and T. F. Krauss, “Dispersion control and slow light in slotted photonic crystal waveguides,” Appl. Phys. Lett. 92, 083501 (2008).
[CrossRef]

Lavrinenko, A. V.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
[CrossRef]

Li, C.

C. Zheng, H. Tian, C. Li, and Y. Ji, “Tunable frequency and angular photonic crystal filter,” Proc. SPIE 6781, 678117 (2007).
[CrossRef]

Liang, G.-Q.

Liu, N. H.

N. H. Liu, S. Y. Zhu, H. Chen, and X. Wu, “Superluminal pulse propagation through one-dimensional photonic crystals with a dispersive defect,” Phys. Rev. E 65, 046607 (2002).
[CrossRef]

Matsuyama, N.

Y. Kanamori, N. Matsuyama, and K. Hane, “Resonant-wavelength tuning of a pitch-variable 1-D photonic crystal filter at telecom frequencies,” IEEE Photon. Technol. Lett. 20, 1136-1138 (2008).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: molding the flow of light (Princeton Univ. Press, 2007).

Mendoza-Suárez, A.

F. Villa-Villa, J. A. Gaspar-Armenta, and A. Mendoza-Suárez, “Surface modes in one-dimensional photonic crystals that include left-handed materials,” J. Electromagn. Waves Appl. 21, 485-499 (2007).
[CrossRef]

Muzy, J. F.

A. Arneodo, F. Argoul, E. Bacry, J. F. Muzy, and M. Tabard, “Golden mean arithmetic in the fractal branching of diffusion-limited aggregates,” Phys. Rev. Lett. 68, 3456-3459 (1992).
[CrossRef] [PubMed]

Myslivets, S. A.

V. Ya. Zyryanov, V. A. Gunyakov, S. A. Myslivets, V. G. Arkhipkin, and V. F. Shabanov, “Electro-optical switching in a one-dimensional photonic crystal,” Mol. Cryst. Liq. Cryst. 488, 1563-5287 (2008).
[CrossRef]

V. A. Gunyakov, V. Ya. Zyryanov, S. A. Myslivets, V. G. Arkhipkin, and V. F. Shabanov, “Electrically controllable optical switch based on one-dimensional photonic crystal,” in Proceedings of IEEE Fourth International Conference on Advanced Optoelectronics and Lasers (IEEE, 2009), pp.186-188.
[CrossRef]

Nemec, H.

H. Nemec, L. Duvillaret, and F. Garet, “Thermally tunable filter for terahertz range based on a one-dimensional photonic crystal with a defect,” J. Appl. Phys. 96, 4072-4075 (2004).
[CrossRef]

O'Faolain, L.

A. Di Falco, L. O'Faolain, and T. F. Krauss, “Dispersion control and slow light in slotted photonic crystal waveguides,” Appl. Phys. Lett. 92, 083501 (2008).
[CrossRef]

Puppin, R.

R. Puppin, “Surface polaritons of a left-handed medium,” Phys. Lett. A 277, 61-64 (2000).
[CrossRef]

Rams, M.

S. Corviser and M. Rams, “IFS attractors and Cantor sets,” Topol. Appl. 153, 1849-1859 (2006).
[CrossRef]

Rao, H.

D. J. Feng, H. Rao, and J. Wu, “The net measure properties for symmetric Cantor sets and their applications,” Prog. Nat. Sci. 7, 172-178 (1997).

Sandomirski, K. S.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
[CrossRef]

Shabanov, V. F.

V. Ya. Zyryanov, V. A. Gunyakov, S. A. Myslivets, V. G. Arkhipkin, and V. F. Shabanov, “Electro-optical switching in a one-dimensional photonic crystal,” Mol. Cryst. Liq. Cryst. 488, 1563-5287 (2008).
[CrossRef]

V. A. Gunyakov, V. Ya. Zyryanov, S. A. Myslivets, V. G. Arkhipkin, and V. F. Shabanov, “Electrically controllable optical switch based on one-dimensional photonic crystal,” in Proceedings of IEEE Fourth International Conference on Advanced Optoelectronics and Lasers (IEEE, 2009), pp.186-188.
[CrossRef]

Shen, X. M.

M. P. Jiang, X. F. Jiang, X. M. Shen, D. W. Xu, and D. F. Shi, “Study on the polarization property of 1-D photonic crystal,” Chinese J. Quantum Electron. 22, 612-616 (2005).

Shi, D. F.

M. P. Jiang, X. F. Jiang, X. M. Shen, D. W. Xu, and D. F. Shi, “Study on the polarization property of 1-D photonic crystal,” Chinese J. Quantum Electron. 22, 612-616 (2005).

Srinivasan, T. P.

T. P. Srinivasan, “Fibonacci sequence, golden ratio, and a network of resistors,” Am. J. Phys. Vol. 60, 461-462 (1992).
[CrossRef]

Sun, X.

Tabard, M.

A. Arneodo, F. Argoul, E. Bacry, J. F. Muzy, and M. Tabard, “Golden mean arithmetic in the fractal branching of diffusion-limited aggregates,” Phys. Rev. Lett. 68, 3456-3459 (1992).
[CrossRef] [PubMed]

Tian, H.

C. Zheng, H. Tian, C. Li, and Y. Ji, “Tunable frequency and angular photonic crystal filter,” Proc. SPIE 6781, 678117 (2007).
[CrossRef]

Tian, L.

M. Dai and L. Tian, “The structure of a Cantor-like set with overlap,” Chaos, Solitons Fractals 26, 295-301 (2005).
[CrossRef]

Villa-Villa, F.

F. Villa-Villa, J. A. Gaspar-Armenta, and A. Mendoza-Suárez, “Surface modes in one-dimensional photonic crystals that include left-handed materials,” J. Electromagn. Waves Appl. 21, 485-499 (2007).
[CrossRef]

Walser, H.

H. Walser and P. Hilton, The golden section (Mathematical Association of America, 2001).

Wan, J.

J. Zi, J. Wan, and C. Zhang, “Large frequency range of negligible transmission in one-dimensional photonic quantum well structures,” Appl. Phys. Lett. 73, 2084-2086 (1998).
[CrossRef]

Wang, H.-Z.

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: molding the flow of light (Princeton Univ. Press, 2007).

Wu, J.

D. J. Feng, H. Rao, and J. Wu, “The net measure properties for symmetric Cantor sets and their applications,” Prog. Nat. Sci. 7, 172-178 (1997).

Wu, X.

N. H. Liu, S. Y. Zhu, H. Chen, and X. Wu, “Superluminal pulse propagation through one-dimensional photonic crystals with a dispersive defect,” Phys. Rev. E 65, 046607 (2002).
[CrossRef]

Xu, D. W.

M. P. Jiang, X. F. Jiang, X. M. Shen, D. W. Xu, and D. F. Shi, “Study on the polarization property of 1-D photonic crystal,” Chinese J. Quantum Electron. 22, 612-616 (2005).

Zhang, C.

J. Zi, J. Wan, and C. Zhang, “Large frequency range of negligible transmission in one-dimensional photonic quantum well structures,” Appl. Phys. Lett. 73, 2084-2086 (1998).
[CrossRef]

Zheng, C.

C. Zheng, H. Tian, C. Li, and Y. Ji, “Tunable frequency and angular photonic crystal filter,” Proc. SPIE 6781, 678117 (2007).
[CrossRef]

Zhu, S. Y.

N. H. Liu, S. Y. Zhu, H. Chen, and X. Wu, “Superluminal pulse propagation through one-dimensional photonic crystals with a dispersive defect,” Phys. Rev. E 65, 046607 (2002).
[CrossRef]

Zhukovsky, S. V.

A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
[CrossRef]

Zi, J.

J. Zi, J. Wan, and C. Zhang, “Large frequency range of negligible transmission in one-dimensional photonic quantum well structures,” Appl. Phys. Lett. 73, 2084-2086 (1998).
[CrossRef]

Zou, H.

Zyryanov, V. Ya.

V. Ya. Zyryanov, V. A. Gunyakov, S. A. Myslivets, V. G. Arkhipkin, and V. F. Shabanov, “Electro-optical switching in a one-dimensional photonic crystal,” Mol. Cryst. Liq. Cryst. 488, 1563-5287 (2008).
[CrossRef]

V. A. Gunyakov, V. Ya. Zyryanov, S. A. Myslivets, V. G. Arkhipkin, and V. F. Shabanov, “Electrically controllable optical switch based on one-dimensional photonic crystal,” in Proceedings of IEEE Fourth International Conference on Advanced Optoelectronics and Lasers (IEEE, 2009), pp.186-188.
[CrossRef]

Am. J. Phys. (1)

T. P. Srinivasan, “Fibonacci sequence, golden ratio, and a network of resistors,” Am. J. Phys. Vol. 60, 461-462 (1992).
[CrossRef]

Appl. Phys. Lett. (2)

A. Di Falco, L. O'Faolain, and T. F. Krauss, “Dispersion control and slow light in slotted photonic crystal waveguides,” Appl. Phys. Lett. 92, 083501 (2008).
[CrossRef]

J. Zi, J. Wan, and C. Zhang, “Large frequency range of negligible transmission in one-dimensional photonic quantum well structures,” Appl. Phys. Lett. 73, 2084-2086 (1998).
[CrossRef]

Chaos, Solitons Fractals (1)

M. Dai and L. Tian, “The structure of a Cantor-like set with overlap,” Chaos, Solitons Fractals 26, 295-301 (2005).
[CrossRef]

Chinese J. Quantum Electron. (1)

M. P. Jiang, X. F. Jiang, X. M. Shen, D. W. Xu, and D. F. Shi, “Study on the polarization property of 1-D photonic crystal,” Chinese J. Quantum Electron. 22, 612-616 (2005).

IEEE Photon. Technol. Lett. (1)

Y. Kanamori, N. Matsuyama, and K. Hane, “Resonant-wavelength tuning of a pitch-variable 1-D photonic crystal filter at telecom frequencies,” IEEE Photon. Technol. Lett. 20, 1136-1138 (2008).
[CrossRef]

J. Appl. Phys. (1)

H. Nemec, L. Duvillaret, and F. Garet, “Thermally tunable filter for terahertz range based on a one-dimensional photonic crystal with a defect,” J. Appl. Phys. 96, 4072-4075 (2004).
[CrossRef]

J. Electromagn. Waves Appl. (1)

F. Villa-Villa, J. A. Gaspar-Armenta, and A. Mendoza-Suárez, “Surface modes in one-dimensional photonic crystals that include left-handed materials,” J. Electromagn. Waves Appl. 21, 485-499 (2007).
[CrossRef]

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

Mol. Cryst. Liq. Cryst. (1)

V. Ya. Zyryanov, V. A. Gunyakov, S. A. Myslivets, V. G. Arkhipkin, and V. F. Shabanov, “Electro-optical switching in a one-dimensional photonic crystal,” Mol. Cryst. Liq. Cryst. 488, 1563-5287 (2008).
[CrossRef]

Nat. Photonics (1)

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A. V. Lavrinenko, S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, “Propagation of classical waves in nonperiodic media: scaling properties of an optical Cantor filter,” Phys. Rev. E 65, 036621 (2002).
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Figures (10)

Fig. 1
Fig. 1

Structures of Cantor-like fractal photonic crystal (CLFPC) with generators G = BAAB and G = BAAAAB .

Fig. 2
Fig. 2

Transmission spectrum of CLFPC with generator G = BAAB and series S ranging from 2 to 4.

Fig. 3
Fig. 3

Group velocity of CLFPC with generator G = BAAAAB and series S ranging from 1 to 3.

Fig. 4
Fig. 4

Structure of golden section fractal PC.

Fig. 5
Fig. 5

Transmission spectrum of GSFPC with series S ranging from 2 to 4.

Fig. 6
Fig. 6

Structure of Fibonacci fractal photonic crystal (FFPC).

Fig. 7
Fig. 7

Transmission spectrum of two-period FFPC with series ranging from 5 to 8.

Fig. 8
Fig. 8

Transmission spectrum of fifth series FFPC with period ranging from 2 to 5.

Fig. 9
Fig. 9

Field distribution of fifth series FFPC with period from 2 to 5.

Fig. 10
Fig. 10

Number of transmission peaks of FFPC with different series and periods.

Equations (16)

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M j = [ cos δ j i η j sin δ j i η j sin δ j cos δ j ] .
{ δ j = ω c ε j h j cos θ j η j = ε 0 μ 0 ε j cos 2 θ j } . .
[ E I H I ] = M 1 M 2 M N [ E N + 1 H N + 1 ] = M a M b M a M b M a [ E N + 1 H N + 1 ] = M [ E N + 1 H N + 1 ] = [ A B C D ] [ E N + 1 H N + 1 ] .
t = E t , N + 1 E i , 1 = 2 η 0 A η 0 + B η 0 η N + 1 + C + D η N + 1 ,
r = E r , 1 E i , 1 = A η 0 + B η 0 η N + 1 C D η N + 1 A η 0 + B η 0 η N + 1 + C + D η N + 1 .
T = t t * ,
R = r r * .
n eff ( ω ) = n ( ω ) + i k ( ω ) ,
t ( ω ) = | t ( ω ) | e i ϕ ( ω ) ,
n ( ω ) = c ϕ ( ω ) L ω ,
k ( ω ) = c L ω ln | t ( ω ) | ,
n g ( ω ) = n ( ω ) + ω d n ( ω ) d ω .
v g = c n + ω d n d ω .
C n 1 3 ( 2 3 + C n 1 3 ) .
D = log ( N ) log ( r ) .
M = ( 1 + S ) × S 2 + 1.

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