Abstract

In this paper, the equations for the transfer matrix method of one-dimensional cylindrical magnetized plasma photonic crystals are proposed, and its nonreciprocal properties based on the Thue–Morse sequence are also studied. By adding the influence of the magnetic field into Maxwell’s equations in the cylindrical coordinate system, the transmission matrix equation of cylindrical wave propagation in the cylindrical medium is obtained and a quasi-periodic structure with the Thue–Morse sequence is designed to study its nonreciprocal features. By considering Maxwell’s equations and the equations of motion of charged particles, the relative dielectric function of plasma under the $z$-axis magnetic field is achieved. Considering the influences of this dielectric function in the cylindrical coordinate system, the transmission matrix equations of cylindrical wave propagation in the cylindrical medium are derived, and those equations are used to design a cylindrical structure with two layers of ordinary medium and one layer of plasma satisfying the Thue–Morse sequence. It is concluded that the nonreciprocal phenomenon becomes more and more obvious with the increase of the plasma frequency, the relative dielectric constant of the medium, and the incident angle. But with the increase of ${\omega _c}$, the nonreciprocal propagation is attenuated, and there is no significant change when the collision frequency is enlarging.

© 2021 Optical Society of America

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    [Crossref]
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  17. H. F. Zhang, S. B. Liu, X. K. Kong, B. R. Bian, and Y. Dai, “Omnidirectional photonic band gap enlarged by one-dimensional ternary unmagnetized plasma photonic crystals based on a new Fibonacci quasiperiodic structure,” Phys. Plasmas 19, 112102 (2012).
    [Crossref]
  18. X. K. Kong, H. W. Yang, and S. B. Liu, “Anomalous dispersion in one-dimensional plasma photonic crystals,” Optik 121, 1873–1876 (2010).
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    [Crossref]
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    [Crossref]
  21. L. M. Qi, Z. Q. Yang, F. Lan, G. Xi, and Z. J. Shi, “Properties of obliquely incident electromagnetic wave in one-dimensional magnetized plasma photonic crystals,” Phys. Plasmas 17, 042501 (2010).
    [Crossref]
  22. C. A. Hu, C. J. Wu, T. J. Yang, and S. L. Yang, “Analysis of optical properties in cylindrical dielectric photonic crystal,” Opt. Commun. 291, 424–434 (2013).
    [Crossref]
  23. Y. L. Wang, S. Y. Chen, P. P. Wen, S. Liu, and S. Y. Zhong, “Omnidirectional absorption properties of a terahertz one-dimensional ternary magnetized plasma photonic crystal based on a tunable structure,” Results Phys. 18, 103298 (2020).
    [Crossref]
  24. Y. Ma, H. Zhang, H. F. Zhang, T. Liu, and W. Y. Li, “Nonreciprocal properties of one-dimensional magnetized plasma photonic crystals with Fibonacci sequence,” Plasma Sci. Technol. 21, 015001 (2018).
    [Crossref]
  25. M. Bicknell, “A primer on the Thue-Morse sequence and related sequences,” Fibonacci Quart. 13, 345–349 (1975).
  26. J. Ercolano, “Matrix generators of Thue-Morse sequences,” Fibonacci. Quart. 17, 474–476 (1979).
  27. M. Drmota and J. F. Morgenbesser, “Generalized Thue-Morse sequences of squares,” Isr. J. Math. 190, 157–193 (2012).
    [Crossref]
  28. A. Barb and F. von Haeseler, “Correlation and spectral properties of multidimensional Thue–Morse sequences,” Int. J. Bifurcat. Chaos. 17, 1265–1303 (2011).
    [Crossref]
  29. E. H. E. Abdalaoui, S. Kasjan, and M. Lemańczyk, “0-1 sequences of the Thue-Morse type and Sarnak’s conjecture,” Proc. Am. Math. Soc. 144, 161–176 (2015).
    [Crossref]
  30. B. K. Singh and P. C. Pandey, “Effect of temperature on terahertz photonic and omnidirectional band gaps in one-dimensional quasi-periodic photonic crystals composed of semiconductor InSb,” Appl. Opt. 55, 1684–1692 (2016).
    [Crossref]
  31. B. K. Singh and P. C. Pandey, “Influence of graded index materials on the photonic localization in one-dimensional quasiperiodic (Thue–Morse and double-periodic) photonic crystals,” Opt. Commun. 333, 84–91 (2014).
    [Crossref]
  32. B. K. Singh and P. C. Pandey, “A study of optical reflectance and localization modes of 1-D Fibonacci photonic quasicrystals using different graded dielectric materials,” J. Mod. Opt. 61, 887–897 (2014).
    [Crossref]
  33. M. A. Kaliteevski, R. A. Abram, V. V. Nikolaev, G. S. Sokolovski, and J. Mod, “Bragg reflectors for cylindrical waves,” J. Mod. Opt. 46, 875–890 (1999).
    [Crossref]

2021 (1)

D. H. Ge, H. Chen, P. F. Jin, L. Q. Zhang, W. Li, and J. W. Jiao, “Magnetic field sensor based on evanescent wave coupling effect of photonic crystal slab microcavity,” J. Magn. Magn. Mater. 527, 167696 (2021).
[Crossref]

2020 (1)

Y. L. Wang, S. Y. Chen, P. P. Wen, S. Liu, and S. Y. Zhong, “Omnidirectional absorption properties of a terahertz one-dimensional ternary magnetized plasma photonic crystal based on a tunable structure,” Results Phys. 18, 103298 (2020).
[Crossref]

2019 (1)

Z. Rahmani and N. Rezaee, “The reflection and absorption characteristics of one-dimensional ternary plasma photonic crystals irradiated by TE and TM waves,” Optik 184, 134–141 (2019).
[Crossref]

2018 (2)

M. Zamani, M. Amanollahi, and A. Hocini, “Photonic band gap spectra in Octonacci all superconducting aperiodic photonic crystals,” Phys. B 556, 151–157 (2018).
[Crossref]

Y. Ma, H. Zhang, H. F. Zhang, T. Liu, and W. Y. Li, “Nonreciprocal properties of one-dimensional magnetized plasma photonic crystals with Fibonacci sequence,” Plasma Sci. Technol. 21, 015001 (2018).
[Crossref]

2016 (2)

B. K. Singh and P. C. Pandey, “Effect of temperature on terahertz photonic and omnidirectional band gaps in one-dimensional quasi-periodic photonic crystals composed of semiconductor InSb,” Appl. Opt. 55, 1684–1692 (2016).
[Crossref]

B. K. Singh, M. K. Chaudhari, and P. C. Pandey, “Photonic and omnidirectional band gap engineering in one-dimensional photonic crystals consisting of linearly graded index material,” J. Lightwave Technol. 34, 2431–2438 (2016).
[Crossref]

2015 (1)

E. H. E. Abdalaoui, S. Kasjan, and M. Lemańczyk, “0-1 sequences of the Thue-Morse type and Sarnak’s conjecture,” Proc. Am. Math. Soc. 144, 161–176 (2015).
[Crossref]

2014 (2)

B. K. Singh and P. C. Pandey, “Influence of graded index materials on the photonic localization in one-dimensional quasiperiodic (Thue–Morse and double-periodic) photonic crystals,” Opt. Commun. 333, 84–91 (2014).
[Crossref]

B. K. Singh and P. C. Pandey, “A study of optical reflectance and localization modes of 1-D Fibonacci photonic quasicrystals using different graded dielectric materials,” J. Mod. Opt. 61, 887–897 (2014).
[Crossref]

2013 (1)

C. A. Hu, C. J. Wu, T. J. Yang, and S. L. Yang, “Analysis of optical properties in cylindrical dielectric photonic crystal,” Opt. Commun. 291, 424–434 (2013).
[Crossref]

2012 (2)

M. Drmota and J. F. Morgenbesser, “Generalized Thue-Morse sequences of squares,” Isr. J. Math. 190, 157–193 (2012).
[Crossref]

H. F. Zhang, S. B. Liu, X. K. Kong, B. R. Bian, and Y. Dai, “Omnidirectional photonic band gap enlarged by one-dimensional ternary unmagnetized plasma photonic crystals based on a new Fibonacci quasiperiodic structure,” Phys. Plasmas 19, 112102 (2012).
[Crossref]

2011 (1)

A. Barb and F. von Haeseler, “Correlation and spectral properties of multidimensional Thue–Morse sequences,” Int. J. Bifurcat. Chaos. 17, 1265–1303 (2011).
[Crossref]

2010 (2)

L. M. Qi, Z. Q. Yang, F. Lan, G. Xi, and Z. J. Shi, “Properties of obliquely incident electromagnetic wave in one-dimensional magnetized plasma photonic crystals,” Phys. Plasmas 17, 042501 (2010).
[Crossref]

X. K. Kong, H. W. Yang, and S. B. Liu, “Anomalous dispersion in one-dimensional plasma photonic crystals,” Optik 121, 1873–1876 (2010).
[Crossref]

2006 (1)

O. L. Berman, Y. E. Lozovik, S. L. Eiderman, and R. D. Coalson, “Superconducting photonic crystals: numerical calculations of the band structure,” Phys. Rev. B 74, 092505 (2006).
[Crossref]

2003 (1)

M. F. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[Crossref]

2000 (2)

C. H. R. Ooi, T. C. A. Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920 (2000).
[Crossref]

M. Born, E. Wolf, and E. Hecht, “Principles of optics electromagnetic theory of propagation, interference and diffraction of light,” Phys. Today 53, 77–78 (2000).
[Crossref]

1999 (2)

C. H. R. Ooi and T. C. A. Yeung, “Polariton gap in a superconductor–dielectric superlattice,” Phys. Lett. A 259, 413–419 (1999).
[Crossref]

M. A. Kaliteevski, R. A. Abram, V. V. Nikolaev, G. S. Sokolovski, and J. Mod, “Bragg reflectors for cylindrical waves,” J. Mod. Opt. 46, 875–890 (1999).
[Crossref]

1998 (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]

1991 (2)

S. Mccall, P. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).
[Crossref]

P. R. Villeneuve and M. Piché, “Photonic band gaps of transverse-electric modes in two-dimensionally periodic media,” J. Opt. Soc. Am. A 8, 1296–1305 (1991).
[Crossref]

1990 (3)

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646–2649 (1990).
[Crossref]

Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[Crossref]

K. M. Ho, C. T. Chan, and A. C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref]

1987 (1)

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

1979 (1)

J. Ercolano, “Matrix generators of Thue-Morse sequences,” Fibonacci. Quart. 17, 474–476 (1979).

1975 (1)

M. Bicknell, “A primer on the Thue-Morse sequence and related sequences,” Fibonacci Quart. 13, 345–349 (1975).

Abdalaoui, E. H. E.

E. H. E. Abdalaoui, S. Kasjan, and M. Lemańczyk, “0-1 sequences of the Thue-Morse type and Sarnak’s conjecture,” Proc. Am. Math. Soc. 144, 161–176 (2015).
[Crossref]

Abram, R. A.

M. A. Kaliteevski, R. A. Abram, V. V. Nikolaev, G. S. Sokolovski, and J. Mod, “Bragg reflectors for cylindrical waves,” J. Mod. Opt. 46, 875–890 (1999).
[Crossref]

Akimoto, K.

H. Hojo, K. Akimoto, and A. Mase, “Enhanced wave transmission in one-dimensional plasma photonic crystals,” in Conference Digest on the 28th International Conference on Infrared and Millimeter Waves, Otsu, Japan (2003), pp. 347–348.

Amanollahi, M.

M. Zamani, M. Amanollahi, and A. Hocini, “Photonic band gap spectra in Octonacci all superconducting aperiodic photonic crystals,” Phys. B 556, 151–157 (2018).
[Crossref]

Barb, A.

A. Barb and F. von Haeseler, “Correlation and spectral properties of multidimensional Thue–Morse sequences,” Int. J. Bifurcat. Chaos. 17, 1265–1303 (2011).
[Crossref]

Berman, O. L.

O. L. Berman, Y. E. Lozovik, S. L. Eiderman, and R. D. Coalson, “Superconducting photonic crystals: numerical calculations of the band structure,” Phys. Rev. B 74, 092505 (2006).
[Crossref]

Bian, B. R.

H. F. Zhang, S. B. Liu, X. K. Kong, B. R. Bian, and Y. Dai, “Omnidirectional photonic band gap enlarged by one-dimensional ternary unmagnetized plasma photonic crystals based on a new Fibonacci quasiperiodic structure,” Phys. Plasmas 19, 112102 (2012).
[Crossref]

Bicknell, M.

M. Bicknell, “A primer on the Thue-Morse sequence and related sequences,” Fibonacci Quart. 13, 345–349 (1975).

Born, M.

M. Born, E. Wolf, and E. Hecht, “Principles of optics electromagnetic theory of propagation, interference and diffraction of light,” Phys. Today 53, 77–78 (2000).
[Crossref]

Chan, C. T.

K. M. Ho, C. T. Chan, and A. C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref]

Chaudhari, M. K.

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]

Chen, H.

D. H. Ge, H. Chen, P. F. Jin, L. Q. Zhang, W. Li, and J. W. Jiao, “Magnetic field sensor based on evanescent wave coupling effect of photonic crystal slab microcavity,” J. Magn. Magn. Mater. 527, 167696 (2021).
[Crossref]

Chen, S. Y.

Y. L. Wang, S. Y. Chen, P. P. Wen, S. Liu, and S. Y. Zhong, “Omnidirectional absorption properties of a terahertz one-dimensional ternary magnetized plasma photonic crystal based on a tunable structure,” Results Phys. 18, 103298 (2020).
[Crossref]

Coalson, R. D.

O. L. Berman, Y. E. Lozovik, S. L. Eiderman, and R. D. Coalson, “Superconducting photonic crystals: numerical calculations of the band structure,” Phys. Rev. B 74, 092505 (2006).
[Crossref]

Dai, Y.

H. F. Zhang, S. B. Liu, X. K. Kong, B. R. Bian, and Y. Dai, “Omnidirectional photonic band gap enlarged by one-dimensional ternary unmagnetized plasma photonic crystals based on a new Fibonacci quasiperiodic structure,” Phys. Plasmas 19, 112102 (2012).
[Crossref]

Dalichaouch, R.

S. Mccall, P. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).
[Crossref]

Drmota, M.

M. Drmota and J. F. Morgenbesser, “Generalized Thue-Morse sequences of squares,” Isr. J. Math. 190, 157–193 (2012).
[Crossref]

Eiderman, S. L.

O. L. Berman, Y. E. Lozovik, S. L. Eiderman, and R. D. Coalson, “Superconducting photonic crystals: numerical calculations of the band structure,” Phys. Rev. B 74, 092505 (2006).
[Crossref]

Ercolano, J.

J. Ercolano, “Matrix generators of Thue-Morse sequences,” Fibonacci. Quart. 17, 474–476 (1979).

Fan, S.

M. F. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[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]

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]

Ge, D. H.

D. H. Ge, H. Chen, P. F. Jin, L. Q. Zhang, W. Li, and J. W. Jiao, “Magnetic field sensor based on evanescent wave coupling effect of photonic crystal slab microcavity,” J. Magn. Magn. Mater. 527, 167696 (2021).
[Crossref]

Hecht, E.

M. Born, E. Wolf, and E. Hecht, “Principles of optics electromagnetic theory of propagation, interference and diffraction of light,” Phys. Today 53, 77–78 (2000).
[Crossref]

Ho, K. M.

K. M. Ho, C. T. Chan, and A. C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref]

Hocini, A.

M. Zamani, M. Amanollahi, and A. Hocini, “Photonic band gap spectra in Octonacci all superconducting aperiodic photonic crystals,” Phys. B 556, 151–157 (2018).
[Crossref]

Hojo, H.

H. Hojo, K. Akimoto, and A. Mase, “Enhanced wave transmission in one-dimensional plasma photonic crystals,” in Conference Digest on the 28th International Conference on Infrared and Millimeter Waves, Otsu, Japan (2003), pp. 347–348.

Hu, C. A.

C. A. Hu, C. J. Wu, T. J. Yang, and S. L. Yang, “Analysis of optical properties in cylindrical dielectric photonic crystal,” Opt. Commun. 291, 424–434 (2013).
[Crossref]

Jiao, J. W.

D. H. Ge, H. Chen, P. F. Jin, L. Q. Zhang, W. Li, and J. W. Jiao, “Magnetic field sensor based on evanescent wave coupling effect of photonic crystal slab microcavity,” J. Magn. Magn. Mater. 527, 167696 (2021).
[Crossref]

Jin, P. F.

D. H. Ge, H. Chen, P. F. Jin, L. Q. Zhang, W. Li, and J. W. Jiao, “Magnetic field sensor based on evanescent wave coupling effect of photonic crystal slab microcavity,” J. Magn. Magn. Mater. 527, 167696 (2021).
[Crossref]

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]

Kaliteevski, M. A.

M. A. Kaliteevski, R. A. Abram, V. V. Nikolaev, G. S. Sokolovski, and J. Mod, “Bragg reflectors for cylindrical waves,” J. Mod. Opt. 46, 875–890 (1999).
[Crossref]

Kam, C. H.

C. H. R. Ooi, T. C. A. Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920 (2000).
[Crossref]

Kasjan, S.

E. H. E. Abdalaoui, S. Kasjan, and M. Lemańczyk, “0-1 sequences of the Thue-Morse type and Sarnak’s conjecture,” Proc. Am. Math. Soc. 144, 161–176 (2015).
[Crossref]

Kong, X. K.

H. F. Zhang, S. B. Liu, X. K. Kong, B. R. Bian, and Y. Dai, “Omnidirectional photonic band gap enlarged by one-dimensional ternary unmagnetized plasma photonic crystals based on a new Fibonacci quasiperiodic structure,” Phys. Plasmas 19, 112102 (2012).
[Crossref]

X. K. Kong, H. W. Yang, and S. B. Liu, “Anomalous dispersion in one-dimensional plasma photonic crystals,” Optik 121, 1873–1876 (2010).
[Crossref]

Lan, F.

L. M. Qi, Z. Q. Yang, F. Lan, G. Xi, and Z. J. Shi, “Properties of obliquely incident electromagnetic wave in one-dimensional magnetized plasma photonic crystals,” Phys. Plasmas 17, 042501 (2010).
[Crossref]

Lemanczyk, M.

E. H. E. Abdalaoui, S. Kasjan, and M. Lemańczyk, “0-1 sequences of the Thue-Morse type and Sarnak’s conjecture,” Proc. Am. Math. Soc. 144, 161–176 (2015).
[Crossref]

Leung, K. M.

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646–2649 (1990).
[Crossref]

Li, W.

D. H. Ge, H. Chen, P. F. Jin, L. Q. Zhang, W. Li, and J. W. Jiao, “Magnetic field sensor based on evanescent wave coupling effect of photonic crystal slab microcavity,” J. Magn. Magn. Mater. 527, 167696 (2021).
[Crossref]

Li, W. Y.

Y. Ma, H. Zhang, H. F. Zhang, T. Liu, and W. Y. Li, “Nonreciprocal properties of one-dimensional magnetized plasma photonic crystals with Fibonacci sequence,” Plasma Sci. Technol. 21, 015001 (2018).
[Crossref]

Lim, T. K.

C. H. R. Ooi, T. C. A. Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920 (2000).
[Crossref]

Liu, S.

Y. L. Wang, S. Y. Chen, P. P. Wen, S. Liu, and S. Y. Zhong, “Omnidirectional absorption properties of a terahertz one-dimensional ternary magnetized plasma photonic crystal based on a tunable structure,” Results Phys. 18, 103298 (2020).
[Crossref]

Liu, S. B.

H. F. Zhang, S. B. Liu, X. K. Kong, B. R. Bian, and Y. Dai, “Omnidirectional photonic band gap enlarged by one-dimensional ternary unmagnetized plasma photonic crystals based on a new Fibonacci quasiperiodic structure,” Phys. Plasmas 19, 112102 (2012).
[Crossref]

X. K. Kong, H. W. Yang, and S. B. Liu, “Anomalous dispersion in one-dimensional plasma photonic crystals,” Optik 121, 1873–1876 (2010).
[Crossref]

Liu, T.

Y. Ma, H. Zhang, H. F. Zhang, T. Liu, and W. Y. Li, “Nonreciprocal properties of one-dimensional magnetized plasma photonic crystals with Fibonacci sequence,” Plasma Sci. Technol. 21, 015001 (2018).
[Crossref]

Liu, Y. F.

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646–2649 (1990).
[Crossref]

Lozovik, Y. E.

O. L. Berman, Y. E. Lozovik, S. L. Eiderman, and R. D. Coalson, “Superconducting photonic crystals: numerical calculations of the band structure,” Phys. Rev. B 74, 092505 (2006).
[Crossref]

Ma, Y.

Y. Ma, H. Zhang, H. F. Zhang, T. Liu, and W. Y. Li, “Nonreciprocal properties of one-dimensional magnetized plasma photonic crystals with Fibonacci sequence,” Plasma Sci. Technol. 21, 015001 (2018).
[Crossref]

Mase, A.

H. Hojo, K. Akimoto, and A. Mase, “Enhanced wave transmission in one-dimensional plasma photonic crystals,” in Conference Digest on the 28th International Conference on Infrared and Millimeter Waves, Otsu, Japan (2003), pp. 347–348.

Mccall, S.

S. Mccall, P. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).
[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]

Mod, J.

M. A. Kaliteevski, R. A. Abram, V. V. Nikolaev, G. S. Sokolovski, and J. Mod, “Bragg reflectors for cylindrical waves,” J. Mod. Opt. 46, 875–890 (1999).
[Crossref]

Morgenbesser, J. F.

M. Drmota and J. F. Morgenbesser, “Generalized Thue-Morse sequences of squares,” Isr. J. Math. 190, 157–193 (2012).
[Crossref]

Narayan, P. G.

P. G. Narayan and B. Suthar, “Transmittance properties of superconductor-dielectric photonic crystal,” Mater. Today Proc. (to be published).
[Crossref]

Nikolaev, V. V.

M. A. Kaliteevski, R. A. Abram, V. V. Nikolaev, G. S. Sokolovski, and J. Mod, “Bragg reflectors for cylindrical waves,” J. Mod. Opt. 46, 875–890 (1999).
[Crossref]

Ooi, C. H. R.

C. H. R. Ooi, T. C. A. Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920 (2000).
[Crossref]

C. H. R. Ooi and T. C. A. Yeung, “Polariton gap in a superconductor–dielectric superlattice,” Phys. Lett. A 259, 413–419 (1999).
[Crossref]

Pandey, P. C.

B. K. Singh, M. K. Chaudhari, and P. C. Pandey, “Photonic and omnidirectional band gap engineering in one-dimensional photonic crystals consisting of linearly graded index material,” J. Lightwave Technol. 34, 2431–2438 (2016).
[Crossref]

B. K. Singh and P. C. Pandey, “Effect of temperature on terahertz photonic and omnidirectional band gaps in one-dimensional quasi-periodic photonic crystals composed of semiconductor InSb,” Appl. Opt. 55, 1684–1692 (2016).
[Crossref]

B. K. Singh and P. C. Pandey, “A study of optical reflectance and localization modes of 1-D Fibonacci photonic quasicrystals using different graded dielectric materials,” J. Mod. Opt. 61, 887–897 (2014).
[Crossref]

B. K. Singh and P. C. Pandey, “Influence of graded index materials on the photonic localization in one-dimensional quasiperiodic (Thue–Morse and double-periodic) photonic crystals,” Opt. Commun. 333, 84–91 (2014).
[Crossref]

Piché, M.

Platzman, P.

S. Mccall, P. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).
[Crossref]

Qi, L. M.

L. M. Qi, Z. Q. Yang, F. Lan, G. Xi, and Z. J. Shi, “Properties of obliquely incident electromagnetic wave in one-dimensional magnetized plasma photonic crystals,” Phys. Plasmas 17, 042501 (2010).
[Crossref]

Rahmani, Z.

Z. Rahmani and N. Rezaee, “The reflection and absorption characteristics of one-dimensional ternary plasma photonic crystals irradiated by TE and TM waves,” Optik 184, 134–141 (2019).
[Crossref]

Rezaee, N.

Z. Rahmani and N. Rezaee, “The reflection and absorption characteristics of one-dimensional ternary plasma photonic crystals irradiated by TE and TM waves,” Optik 184, 134–141 (2019).
[Crossref]

Satpathy, S.

Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[Crossref]

Schultz, S.

S. Mccall, P. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).
[Crossref]

Shi, Z. J.

L. M. Qi, Z. Q. Yang, F. Lan, G. Xi, and Z. J. Shi, “Properties of obliquely incident electromagnetic wave in one-dimensional magnetized plasma photonic crystals,” Phys. Plasmas 17, 042501 (2010).
[Crossref]

Singh, B. K.

B. K. Singh, M. K. Chaudhari, and P. C. Pandey, “Photonic and omnidirectional band gap engineering in one-dimensional photonic crystals consisting of linearly graded index material,” J. Lightwave Technol. 34, 2431–2438 (2016).
[Crossref]

B. K. Singh and P. C. Pandey, “Effect of temperature on terahertz photonic and omnidirectional band gaps in one-dimensional quasi-periodic photonic crystals composed of semiconductor InSb,” Appl. Opt. 55, 1684–1692 (2016).
[Crossref]

B. K. Singh and P. C. Pandey, “Influence of graded index materials on the photonic localization in one-dimensional quasiperiodic (Thue–Morse and double-periodic) photonic crystals,” Opt. Commun. 333, 84–91 (2014).
[Crossref]

B. K. Singh and P. C. Pandey, “A study of optical reflectance and localization modes of 1-D Fibonacci photonic quasicrystals using different graded dielectric materials,” J. Mod. Opt. 61, 887–897 (2014).
[Crossref]

Smith, D.

S. Mccall, P. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).
[Crossref]

Sokolovski, G. S.

M. A. Kaliteevski, R. A. Abram, V. V. Nikolaev, G. S. Sokolovski, and J. Mod, “Bragg reflectors for cylindrical waves,” J. Mod. Opt. 46, 875–890 (1999).
[Crossref]

Soljacic, M.

M. F. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[Crossref]

Soukoulis, A. C. M.

K. M. Ho, C. T. Chan, and A. C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref]

Suthar, B.

P. G. Narayan and B. Suthar, “Transmittance properties of superconductor-dielectric photonic crystal,” Mater. Today Proc. (to be published).
[Crossref]

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]

Villeneuve, P. R.

von Haeseler, F.

A. Barb and F. von Haeseler, “Correlation and spectral properties of multidimensional Thue–Morse sequences,” Int. J. Bifurcat. Chaos. 17, 1265–1303 (2011).
[Crossref]

Wang, Y. L.

Y. L. Wang, S. Y. Chen, P. P. Wen, S. Liu, and S. Y. Zhong, “Omnidirectional absorption properties of a terahertz one-dimensional ternary magnetized plasma photonic crystal based on a tunable structure,” Results Phys. 18, 103298 (2020).
[Crossref]

Wen, P. P.

Y. L. Wang, S. Y. Chen, P. P. Wen, S. Liu, and S. Y. Zhong, “Omnidirectional absorption properties of a terahertz one-dimensional ternary magnetized plasma photonic crystal based on a tunable structure,” Results Phys. 18, 103298 (2020).
[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]

Wolf, E.

M. Born, E. Wolf, and E. Hecht, “Principles of optics electromagnetic theory of propagation, interference and diffraction of light,” Phys. Today 53, 77–78 (2000).
[Crossref]

Wu, C. J.

C. A. Hu, C. J. Wu, T. J. Yang, and S. L. Yang, “Analysis of optical properties in cylindrical dielectric photonic crystal,” Opt. Commun. 291, 424–434 (2013).
[Crossref]

Xi, G.

L. M. Qi, Z. Q. Yang, F. Lan, G. Xi, and Z. J. Shi, “Properties of obliquely incident electromagnetic wave in one-dimensional magnetized plasma photonic crystals,” Phys. Plasmas 17, 042501 (2010).
[Crossref]

Yablonovitch, E.

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

Yang, H. W.

X. K. Kong, H. W. Yang, and S. B. Liu, “Anomalous dispersion in one-dimensional plasma photonic crystals,” Optik 121, 1873–1876 (2010).
[Crossref]

Yang, S. L.

C. A. Hu, C. J. Wu, T. J. Yang, and S. L. Yang, “Analysis of optical properties in cylindrical dielectric photonic crystal,” Opt. Commun. 291, 424–434 (2013).
[Crossref]

Yang, T. J.

C. A. Hu, C. J. Wu, T. J. Yang, and S. L. Yang, “Analysis of optical properties in cylindrical dielectric photonic crystal,” Opt. Commun. 291, 424–434 (2013).
[Crossref]

Yang, Z. Q.

L. M. Qi, Z. Q. Yang, F. Lan, G. Xi, and Z. J. Shi, “Properties of obliquely incident electromagnetic wave in one-dimensional magnetized plasma photonic crystals,” Phys. Plasmas 17, 042501 (2010).
[Crossref]

Yanik, M. F.

M. F. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[Crossref]

Yeung, T. C. A.

C. H. R. Ooi, T. C. A. Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920 (2000).
[Crossref]

C. H. R. Ooi and T. C. A. Yeung, “Polariton gap in a superconductor–dielectric superlattice,” Phys. Lett. A 259, 413–419 (1999).
[Crossref]

Zamani, M.

M. Zamani, M. Amanollahi, and A. Hocini, “Photonic band gap spectra in Octonacci all superconducting aperiodic photonic crystals,” Phys. B 556, 151–157 (2018).
[Crossref]

Zhang, H.

Y. Ma, H. Zhang, H. F. Zhang, T. Liu, and W. Y. Li, “Nonreciprocal properties of one-dimensional magnetized plasma photonic crystals with Fibonacci sequence,” Plasma Sci. Technol. 21, 015001 (2018).
[Crossref]

Zhang, H. F.

Y. Ma, H. Zhang, H. F. Zhang, T. Liu, and W. Y. Li, “Nonreciprocal properties of one-dimensional magnetized plasma photonic crystals with Fibonacci sequence,” Plasma Sci. Technol. 21, 015001 (2018).
[Crossref]

H. F. Zhang, S. B. Liu, X. K. Kong, B. R. Bian, and Y. Dai, “Omnidirectional photonic band gap enlarged by one-dimensional ternary unmagnetized plasma photonic crystals based on a new Fibonacci quasiperiodic structure,” Phys. Plasmas 19, 112102 (2012).
[Crossref]

Zhang, L. Q.

D. H. Ge, H. Chen, P. F. Jin, L. Q. Zhang, W. Li, and J. W. Jiao, “Magnetic field sensor based on evanescent wave coupling effect of photonic crystal slab microcavity,” J. Magn. Magn. Mater. 527, 167696 (2021).
[Crossref]

Zhang, Z.

Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[Crossref]

Zhong, S. Y.

Y. L. Wang, S. Y. Chen, P. P. Wen, S. Liu, and S. Y. Zhong, “Omnidirectional absorption properties of a terahertz one-dimensional ternary magnetized plasma photonic crystal based on a tunable structure,” Results Phys. 18, 103298 (2020).
[Crossref]

Appl. Opt. (1)

B. K. Singh and P. C. Pandey, “Effect of temperature on terahertz photonic and omnidirectional band gaps in one-dimensional quasi-periodic photonic crystals composed of semiconductor InSb,” Appl. Opt. 55, 1684–1692 (2016).
[Crossref]

Appl. Phys. Lett. (1)

M. F. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[Crossref]

Fibonacci Quart. (1)

M. Bicknell, “A primer on the Thue-Morse sequence and related sequences,” Fibonacci Quart. 13, 345–349 (1975).

Fibonacci. Quart. (1)

J. Ercolano, “Matrix generators of Thue-Morse sequences,” Fibonacci. Quart. 17, 474–476 (1979).

Int. J. Bifurcat. Chaos. (1)

A. Barb and F. von Haeseler, “Correlation and spectral properties of multidimensional Thue–Morse sequences,” Int. J. Bifurcat. Chaos. 17, 1265–1303 (2011).
[Crossref]

Isr. J. Math. (1)

M. Drmota and J. F. Morgenbesser, “Generalized Thue-Morse sequences of squares,” Isr. J. Math. 190, 157–193 (2012).
[Crossref]

J. Lightwave Technol. (1)

J. Magn. Magn. Mater. (1)

D. H. Ge, H. Chen, P. F. Jin, L. Q. Zhang, W. Li, and J. W. Jiao, “Magnetic field sensor based on evanescent wave coupling effect of photonic crystal slab microcavity,” J. Magn. Magn. Mater. 527, 167696 (2021).
[Crossref]

J. Mod. Opt. (2)

B. K. Singh and P. C. Pandey, “A study of optical reflectance and localization modes of 1-D Fibonacci photonic quasicrystals using different graded dielectric materials,” J. Mod. Opt. 61, 887–897 (2014).
[Crossref]

M. A. Kaliteevski, R. A. Abram, V. V. Nikolaev, G. S. Sokolovski, and J. Mod, “Bragg reflectors for cylindrical waves,” J. Mod. Opt. 46, 875–890 (1999).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

B. K. Singh and P. C. Pandey, “Influence of graded index materials on the photonic localization in one-dimensional quasiperiodic (Thue–Morse and double-periodic) photonic crystals,” Opt. Commun. 333, 84–91 (2014).
[Crossref]

C. A. Hu, C. J. Wu, T. J. Yang, and S. L. Yang, “Analysis of optical properties in cylindrical dielectric photonic crystal,” Opt. Commun. 291, 424–434 (2013).
[Crossref]

Optik (2)

X. K. Kong, H. W. Yang, and S. B. Liu, “Anomalous dispersion in one-dimensional plasma photonic crystals,” Optik 121, 1873–1876 (2010).
[Crossref]

Z. Rahmani and N. Rezaee, “The reflection and absorption characteristics of one-dimensional ternary plasma photonic crystals irradiated by TE and TM waves,” Optik 184, 134–141 (2019).
[Crossref]

Phys. B (1)

M. Zamani, M. Amanollahi, and A. Hocini, “Photonic band gap spectra in Octonacci all superconducting aperiodic photonic crystals,” Phys. B 556, 151–157 (2018).
[Crossref]

Phys. Lett. A (1)

C. H. R. Ooi and T. C. A. Yeung, “Polariton gap in a superconductor–dielectric superlattice,” Phys. Lett. A 259, 413–419 (1999).
[Crossref]

Phys. Plasmas (2)

H. F. Zhang, S. B. Liu, X. K. Kong, B. R. Bian, and Y. Dai, “Omnidirectional photonic band gap enlarged by one-dimensional ternary unmagnetized plasma photonic crystals based on a new Fibonacci quasiperiodic structure,” Phys. Plasmas 19, 112102 (2012).
[Crossref]

L. M. Qi, Z. Q. Yang, F. Lan, G. Xi, and Z. J. Shi, “Properties of obliquely incident electromagnetic wave in one-dimensional magnetized plasma photonic crystals,” Phys. Plasmas 17, 042501 (2010).
[Crossref]

Phys. Rev. B (2)

C. H. R. Ooi, T. C. A. Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920 (2000).
[Crossref]

O. L. Berman, Y. E. Lozovik, S. L. Eiderman, and R. D. Coalson, “Superconducting photonic crystals: numerical calculations of the band structure,” Phys. Rev. B 74, 092505 (2006).
[Crossref]

Phys. Rev. Lett. (5)

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65, 2646–2649 (1990).
[Crossref]

Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[Crossref]

K. M. Ho, C. T. Chan, and A. C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152–3155 (1990).
[Crossref]

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

S. Mccall, P. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, “Microwave propagation in two-dimensional dielectric lattices,” Phys. Rev. Lett. 67, 2017–2020 (1991).
[Crossref]

Phys. Today (1)

M. Born, E. Wolf, and E. Hecht, “Principles of optics electromagnetic theory of propagation, interference and diffraction of light,” Phys. Today 53, 77–78 (2000).
[Crossref]

Plasma Sci. Technol. (1)

Y. Ma, H. Zhang, H. F. Zhang, T. Liu, and W. Y. Li, “Nonreciprocal properties of one-dimensional magnetized plasma photonic crystals with Fibonacci sequence,” Plasma Sci. Technol. 21, 015001 (2018).
[Crossref]

Proc. Am. Math. Soc. (1)

E. H. E. Abdalaoui, S. Kasjan, and M. Lemańczyk, “0-1 sequences of the Thue-Morse type and Sarnak’s conjecture,” Proc. Am. Math. Soc. 144, 161–176 (2015).
[Crossref]

Results Phys. (1)

Y. L. Wang, S. Y. Chen, P. P. Wen, S. Liu, and S. Y. Zhong, “Omnidirectional absorption properties of a terahertz one-dimensional ternary magnetized plasma photonic crystal based on a tunable structure,” Results Phys. 18, 103298 (2020).
[Crossref]

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]

Other (2)

H. Hojo, K. Akimoto, and A. Mase, “Enhanced wave transmission in one-dimensional plasma photonic crystals,” in Conference Digest on the 28th International Conference on Infrared and Millimeter Waves, Otsu, Japan (2003), pp. 347–348.

P. G. Narayan and B. Suthar, “Transmittance properties of superconductor-dielectric photonic crystal,” Mater. Today Proc. (to be published).
[Crossref]

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (10)

Fig. 1.
Fig. 1. Simple structure of researched CMPPCs.
Fig. 2.
Fig. 2. Schematic view of the designed quasi-periodic sequence structure. (a) Top view of the structure and (b) a reference to each layer of media in the structure.
Fig. 3.
Fig. 3. Diagrams of IOS of CMPPCs. ${\omega _c} = 5{\omega _p}$ , $\nu = 0.001{\omega _p}$ , ${\varepsilon _{{\rm Br}}} = 5$ , ${\varepsilon _{{\rm Ar}}} = 18$ , ${d_1} = 0.2d$ , ${d_2} = 0.1d$ , ${d_3} = 0.7d$ , ${\rho _0} = 40 {d_3}$ , $m = 1$ . (a)  $\theta = 80^{\circ}$ and (b)  $\theta = 30^{\circ}$ .
Fig. 4.
Fig. 4. Transmittance of the forward and backward propagation of CMPPCs. $\nu = 0.001{\omega _p}$ , ${\omega _c} = 5{\omega _p}$ , ${\varepsilon _{{\rm Br}}} = 5$ , ${\varepsilon _{{\rm Ar}}} = 18$ , ${d_1} = 0.2d$ , ${d_2} = 0.1d$ , ${d_3} = 0.7d$ , ${\rho _0} = 40 {d_3}$ , $\theta = 70^{\circ}$ . (a)  $m = 1$ , (b)  $m = 3$ , (c)  $m = 5$ , and (d)  $m = 7$ .
Fig. 5.
Fig. 5. Transmittance of the forward and backward propagation of CMPPCs. $\nu = 0.001{\omega _p}$ , ${\omega _c} = 5{\omega _p}$ , ${\varepsilon _{{\rm Br}}} = 5$ , ${\varepsilon _{{\rm Ar}}} = 18$ , ${d_1} = 0.2 d$ , ${d_2} = 0.1 d$ , ${d_3} = 0.7 d$ , ${\rho _0} = 40{d_3}$ , $m = 1$ . (a)  $\theta = 40^{\circ}$ , (b)  $\theta = 60^{\circ}$ , (c)  $\theta = 80^{\circ}$ , and (d) diagram of the relationship between IOS and $\theta$ .
Fig. 6.
Fig. 6. Transmittance of the forward and backward propagation of CMPPCs. ${\omega _c} = 5{\omega _p}$ , ${\varepsilon _{{\rm Br}}} = 5$ , ${\varepsilon _{{\rm Ar}}} = 18$ , ${d_1} = 0.2 d$ , ${d_2} = 0.1 d$ , ${d_3} = 0.7 d$ , ${\rho _0} = 40{d_3}$ , $\theta = 70^{\circ}$ , $m = 1$ . (a)  $\nu =$ ${0.005}{\omega _p}$ , (b)  $\nu = 0.01{\omega _p}$ , (c)  $\nu = 0.02{\omega _p}$ , and (d) diagram of the relationship between IOS and $\nu$ .
Fig. 7.
Fig. 7. Transmittance of the forward and backward propagation of CMPPCs. $\nu = 0.001{\omega _p}$ , ${\omega _c} = 5{\omega _p}$ , ${\varepsilon _{{\rm Br}}} = 5$ , ${\varepsilon _{{\rm Ar}}} = 18$ , ${d_1} = 0.2 d$ , ${d_2} = 0.1 d$ , ${d_3} = 0.7 d$ , ${\rho _0} = 40{d_3}$ , $\theta = 70^{\circ}$ , $m = 1$ . (a)  ${\varepsilon _{{\rm Ar}}} = 8$ , (b)  ${\varepsilon _{{\rm Ar}}} = 15$ , (c)  ${\varepsilon _{{\rm Ar}}} = 25$ , and (d) plot of the relationship between IOS and ${\varepsilon _{{\rm Ar}}}$ .
Fig. 8.
Fig. 8. Transmittance of the forward and backward propagation of CMPPCs. $\nu = 0.001{\omega _p}$ , ${\omega _c} = 5{\omega _p}$ , ${\varepsilon _{{\rm Br}}} = 5$ , ${\varepsilon _{{\rm Ar}}} = 18$ , ${d_1} = 0.2 d$ , ${d_2} = 0.1 d$ , ${d_3} = 0.7 d$ , ${\rho _0} = 40{d_3}$ , $\theta = 70^{\circ}$ , $m = 1$ . (a)  ${\omega _p} = 0.06 \times {2}\pi {\rm c/}d$ , (b)  ${\omega _p} = 0.1 \times {2}\pi {\rm c/}d$ , (c)  ${\omega _p} = 0.15 \times {2}\pi {\rm c/}d$ , and (d) diagram of the relationship between IOS and ${\omega _p}$ .
Fig. 9.
Fig. 9. Transmittance of the forward and backward propagation of CMPPCs. $\nu = 0.001{\omega _p}$ , ${\omega _c} = 5{\omega _p}$ , ${\varepsilon _{{\rm Br}}} = 5$ , ${\varepsilon _{{\rm Ar}}} = 18$ , ${d_1} = 0.2 d$ , ${d_2} = 0.1 d$ , ${d_3} = 0.7 d$ , ${\rho _0} = 40{d_3}$ , $\theta = 70^{\circ}$ , ${\omega _p} = 0.12 \times {2}\pi {\rm c/}d$ , $m = 1$ . (a)  ${\omega _c} = 5.2{\omega _p}$ , (b)  ${\omega _c} = 6{\omega _p}$ , and (c) diagram of the relationship between IOS and  ${\omega _c}$ .
Fig. 10.
Fig. 10. (a) Transmittance of the forward and backward propagation of conventional PCs, (b) the transmittance of the forward and backward propagation of conventional PC structures with the Thue–Morse sequence, and (c) the transmittance of the forward and backward propagation of CMPPCs.

Equations (42)

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

× E = μ a H t ,
× H = ε a E t + J ,
d J d t + ν J = ω c × J + ε 0 ω p 2 E .
{ j ω J ρ + ν J ρ = ε a ω p 2 E ρ J ϕ ω c j ω J z + ν J z = ε a ω p 2 E z j ω J ϕ + ν J ϕ = ε a ω p 2 E ϕ + J ρ ω c .
( J ρ J ϕ J z ) = ε a ( j ω p 2 ( ω + j ν ) ω c + ( ω + j ν ) 2 ω p 2 ω c ω c + ( ω + j ν ) 2 0 ω p 2 ω c ( ω + j ν ) 2 + ω c j ω p 2 ( ω + j ν ) ω c ( ω + j ν ) 2 0 0 0 j ω p 2 ω + j ν ) ( E ρ E ϕ E z ) .
× H = ε a ε k E t ,
ε k = ( ε 1 j ε 2 0 j ε 2 ε 1 0 0 0 ε 3 ) ,
ε 1 = 1 + ω p 2 ( ω + j v ) ω [ ω c 2 ( ω + j v ) 2 ] ,
ε 2 = ω p 2 ω c ω [ ω c 2 ( ω + j v c ) 2 ] ,
ε 3 = 1 + ω p 2 ω ( ω + j v ) .
1 ρ ( E ρ ϕ ( ρ E ϕ ) ρ ) = j ω μ a H z ,
1 ρ H z ϕ + H ϕ z = j ω ε a ( ε 1 E ρ + j ε 2 E ϕ ) ,
H ρ z + H ϕ ρ = j ω ε a ε 1 E ϕ ω ε a ε 2 E ρ .
1 ρ H z ϕ = j ω ε a ( ε 1 E ρ + j ε 2 E ϕ ) ,
H z ρ = j ω ε a ε 1 E ϕ ω ε a ε 2 E ρ .
1 ρ 1 ω ε a ( ε 2 2 ε 1 2 ) [ ε 2 ρ ( H z ϕ ) j ε 1 ρ ( ρ H z ρ ) j ε 1 1 ρ ϕ ( H z ϕ ) + ε 2 ϕ ( H z ρ ) ] = j ω μ a H z .
d 2 Φ d ϕ 2 + m 2 Φ = 0 ,
1 ρ 1 ω ε a ( ε 2 2 ε 1 2 ) [ ε 2 d Φ d ϕ d V d ρ + j ε 1 Φ d d ρ ( ρ d V d ρ ) + j ε 1 1 ρ V ( m 2 Φ ) ε 2 d Φ d ϕ d V d ρ ] = j ω μ 0 H z ,
1 ρ j ε 1 ω ε a ( ε 2 2 ε 1 2 ) [ d d ρ ( ρ d V d ρ ) + 1 ρ m 2 V ] = j ω μ a V .
ρ d d ρ ( ρ d V d ρ ) = m 2 V ε a ω 2 μ a ε 1 ( ε 1 ε 2 2 ε 1 ) .
ε m = ε 1 ε 2 2 ε 1 .
ρ d d ρ ( ρ d V d ρ ) = m 2 V k 2 ρ 2 V ,
V ( ρ ) = A J m ( k ρ ) + B Y m ( k ρ ) .
H z ( ρ , ϕ ) = A J m ( k ρ ) e ( j m ϕ ) + B Y m ( k ρ ) e ( j m ϕ ) .
m ω ε a 1 ρ V ( ρ ) e ( j m ϕ ) = ε 1 E ρ + j ε 2 E ϕ ,
1 j ω ε a V ρ e ( j m ϕ ) = j ε 2 E ρ + ε 1 E ϕ .
1 j ω ε a V ρ e ( j m ϕ ) = U ( ρ ) e ( j m ϕ ) ,
d V d ρ = j ω ε a U ( ρ ) .
U ( ρ ) = j p A J m ( k ρ ) + j p B Y m ( k ρ ) ,
( V ( ρ ) U ( ρ ) ) = ( M 1 M 2 M 3 M 4 ) ( V ( ρ 0 ) U ( ρ 0 ) ) .
M 1 = V ( ρ ) , M 3 = U ( ρ ) .
A = Y m ( k ρ 0 ) 2 / ( π k ρ 0 ) , B = J m ( k ρ 0 ) 2 / ( π k ρ 0 ) .
M 1 = π 2 k ρ 0 [ Y m ( k ρ 0 ) J m ( k ρ ) + J m ( k ρ 0 ) Y m ( k ρ ) ] ,
M 3 = j π 2 k p ρ 0 [ Y m ( k ρ 0 ) J m ( k ρ 1 ) + J m ( k ρ 0 ) Y m ( k ρ 1 ) ] ,
M 2 = j π 2 k p 1 ρ 0 [ J m ( k ρ 0 ) Y m ( k ρ 1 ) + Y m ( k ρ 0 ) J m ( k ρ 1 ) ] ,
M 4 = π 2 k ρ 0 [ J m ( k ρ 0 ) Y m ( k ρ 1 ) + Y m ( k ρ 0 ) J m ( k ρ 1 ) ] .
r d = ( M 2 + j p a C ma 2 M 1 ) j p f C mf 2 ( M 4 + j p a C ma 2 M 2 ) ( j p a C ma 1 M 1 + M 3 ) + j p f C mf 2 ( j p a C ma 1 M 2 + M 4 ) ,
t d = 4 ε a / μ a π K ρ 0 H m 2 ( k a ρ 0 ) H m 1 ( k a ρ 0 ) [ ( j p a C ma 1 M 1 + M 3 ) + j p f C mf 2 ( j p a C ma 2 M 2 + M 4 ) ] ,
C mr ( 1 , 2 ) = H m ( 1 , 2 ) ( k r ρ r ) / H m ( 1 , 2 ) ( k r ρ r ) , r = a , f ,
M k = M k 1 M ¯ k 1 ( k 1 ) ,
M ¯ 0 = { H I I H } , M 0 = { I H H I } .
I O S = | l g ( T b T f ) | × 10 ,