Abstract

We present the structuring of different graded-index materials in the form of one-dimensional (1D) photonic crystals (PCs) for highly efficient light trapping and controlling photonic devices in terms of tuned and controlled photonic bandgap (PBG) performance. We consider hyperbolic, exponential, and linear refractive index variation in the graded-index layer. We systematically study the influence of structural and grading parameters on the bandgap performance for two different graded photonic crystal (GPC) structures formed by stacking different graded-index layers. Compared with conventional PCs, the GPC bandgaps can be changed and tuned by the refractive index profile of the graded-index layer. We show that the number of bandgaps increases with the graded-index layer thickness and the bandgap frequencies can be tuned by the grading profiles. We observe the sequential increment in bandwidth for the complete PBGs in the GPC structures with linear, exponential, and hyperbolic graded-index materials. We also study the influence of the stacking pattern and grading profiles on the bandgap, phase shift, group velocity, delay time, and field distribution. The proposed GPC configurations facilitate the design of reflectors, multi-channel filters, detectors, and other photonic devices. The study may also provide the basis of understanding of the influence of graded-index materials on the PBG characteristics in the GPCs.

© 2020 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Analysis of one-dimensional high-index guiding photonic bandgap waveguides

Jie Li and Kin Seng Chiang
J. Opt. Soc. Am. B 26(11) 2007-2015 (2009)

Controlling electromagnetic fields with graded photonic crystals in metamaterial regime

Borislav Vasić, Goran Isić, Radoš Gajić, and Kurt Hingerl
Opt. Express 18(19) 20321-20333 (2010)

References

  • View by:
  • |
  • |
  • |

  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [Crossref]
  2. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–159 (1997).
    [Crossref]
  3. R. H. Lipson and C. Lu, “Photonic crystals: a unique partnership between light and matter,” Eur. J. Phys. 30, S33–S48 (2009).
    [Crossref]
  4. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding Flow of Light (Princeton University, 2008).
  5. V. A. Tolmachev, T. S. Perova, J. Ruttle, and E. V. Khokhlova, “Design of one-dimensional photonic crystals using combination of band diagram and photonic gap map approaches,” J. Appl. Phys. 104, 033536 (2008).
    [Crossref]
  6. L. D. Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, “Spectrally enhanced light emission from aperiodic photonic structures,” Appl. Phys. Lett. 86, 261905 (2005).
    [Crossref]
  7. L. Zhou, Z. Song, X. Huang, and C. T. Chan, “Physics of the zero-n photonic gap: fundamentals and latest developments,” Nanophotonics 1, 181–198 (2012).
    [Crossref]
  8. M. S. Vasconcelos, P. W. Mauriz, F. F. de Medeiros, and E. L. Albuquerque, “Photonic band gaps in quasiperiodic photonic crystals with negative refractive index,” Phys. Rev. B 76, 165117 (2007).
    [Crossref]
  9. 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]
  10. E. Macia, “Exploiting aperiodic designs in nanophotonic devices,” Rep. Prog. Phys. 75, 036502 (2012).
    [Crossref]
  11. B. K. Singh and P. C. Pandey, “Influence of graded index materials on the photonic localization in one-dimensional quasiperiodic (Thue-Mosre and double-periodic) photonic crystals,” Opt. Commun. 333, 84–91 (2014).
    [Crossref]
  12. E. Centeno and D. Cassagne, “Graded photonic crystals,” Opt. Lett. 30, 2278–2280 (2005).
    [Crossref]
  13. H. Kurt and D. S. Citrin, “Graded index photonic crystals,” Opt. Express 15, 1240–1253 (2007).
    [Crossref]
  14. S. C. S. Lin, T. J. Huang, J. H. Sun, and T. T. Wu, “Gradient index photonic crystals,” Phys. Rev. B 79, 094302 (2009).
    [Crossref]
  15. M. Lu, B. K. Juluri, S. C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108, 103505 (2010).
    [Crossref]
  16. H. W. Wang and L. W. Chen, “High transmission efficiency of arbitrary waveguide bends formed by graded index photonic crystals,” J. Opt. Soc. Am. B 28, 2098–2104 (2011).
    [Crossref]
  17. A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105, 103708 (2009).
    [Crossref]
  18. B. Vasic and R. Gajic, “Self-focusing media using graded photonic crystals, Fourier transforming and imaging, directive emission, and directional cloaking,” J. Appl. Phys. 110, 053103 (2011).
    [Crossref]
  19. H. W. Wang and L. W. Chen, “A cylindrical optical black hole using graded index photonic crystals,” J. Appl. Phys. 109, 103104 (2011).
    [Crossref]
  20. S. Ji, M. Ponting, R. S. Lepkowicz, A. Rosenberg, R. Flynn, G. Beadie, and E. Baer, “A bio-inspired polymeric gradient refractive index (GRIN) human eye lens,” Opt. Express 20, 26746–26754 (2012).
    [Crossref]
  21. E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92, 133501 (2008).
    [Crossref]
  22. A. Zukauskas, I. Matulaitien, D. Paipulas, G. Niaura, M. Malinauskas, and R. Gadonas, “Tuning the refractive index in 3D direct laser writing lithography: towards GRIN microoptics,” Laser Photon. Rev. 9, 706–712 (2015).
    [Crossref]
  23. Q. Zhu and Y. Fu, “Graded index photonic crystals: a review,” Ann. Phys. 527, 205–218 (2015).
    [Crossref]
  24. J. H. Park, W. S. Choi, H. Y. Koo, and D. Y. Kim, “Colloidal photonic crystal with graded refractive index distribution,” Adv. Mater. 17, 879–885 (2005).
    [Crossref]
  25. F. Gaufillet and E. Akmansoy, “Design and experimental evidence of a flat graded-index photonic crystal lens,” J. Appl. Phys. 114, 083105 (2013).
    [Crossref]
  26. H. Rauh, G. I. Yampolskaya, and S. V. Yampolskii, “Optical transmittance of photonic structures with linearly graded dielectric constituents,” New J. Phys. 12, 073033 (2010).
    [Crossref]
  27. Z. F. Sang and Z. Y. Li, “Optical properties of one-dimensional photonic crystals containing graded materials,” Opt. Commun. 259, 174–178 (2006).
    [Crossref]
  28. H. Rauh, G. I. Yampolskaya, and S. V. Yampolskii, “Optical transmittance of photonic structures with logarithmically similar dielectric constituents,” J. Opt. 14, 015101 (2012).
    [Crossref]
  29. B. K. Singh and P. C. Pandey, “Tunable temperature-dependent THz photonic band gaps and localization mode engineering in 1-D periodic and quasi-periodic structures with graded-index materials and InSb,” Appl. Opt. 57, 8171–8181 (2018).
    [Crossref]
  30. P. Yeh, Optical Wave in Layered Media (Wiley, 1988).
  31. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University, 2007).

2018 (1)

2015 (2)

A. Zukauskas, I. Matulaitien, D. Paipulas, G. Niaura, M. Malinauskas, and R. Gadonas, “Tuning the refractive index in 3D direct laser writing lithography: towards GRIN microoptics,” Laser Photon. Rev. 9, 706–712 (2015).
[Crossref]

Q. Zhu and Y. Fu, “Graded index photonic crystals: a review,” Ann. Phys. 527, 205–218 (2015).
[Crossref]

2014 (1)

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

2013 (1)

F. Gaufillet and E. Akmansoy, “Design and experimental evidence of a flat graded-index photonic crystal lens,” J. Appl. Phys. 114, 083105 (2013).
[Crossref]

2012 (4)

H. Rauh, G. I. Yampolskaya, and S. V. Yampolskii, “Optical transmittance of photonic structures with logarithmically similar dielectric constituents,” J. Opt. 14, 015101 (2012).
[Crossref]

S. Ji, M. Ponting, R. S. Lepkowicz, A. Rosenberg, R. Flynn, G. Beadie, and E. Baer, “A bio-inspired polymeric gradient refractive index (GRIN) human eye lens,” Opt. Express 20, 26746–26754 (2012).
[Crossref]

L. Zhou, Z. Song, X. Huang, and C. T. Chan, “Physics of the zero-n photonic gap: fundamentals and latest developments,” Nanophotonics 1, 181–198 (2012).
[Crossref]

E. Macia, “Exploiting aperiodic designs in nanophotonic devices,” Rep. Prog. Phys. 75, 036502 (2012).
[Crossref]

2011 (3)

H. W. Wang and L. W. Chen, “High transmission efficiency of arbitrary waveguide bends formed by graded index photonic crystals,” J. Opt. Soc. Am. B 28, 2098–2104 (2011).
[Crossref]

B. Vasic and R. Gajic, “Self-focusing media using graded photonic crystals, Fourier transforming and imaging, directive emission, and directional cloaking,” J. Appl. Phys. 110, 053103 (2011).
[Crossref]

H. W. Wang and L. W. Chen, “A cylindrical optical black hole using graded index photonic crystals,” J. Appl. Phys. 109, 103104 (2011).
[Crossref]

2010 (2)

M. Lu, B. K. Juluri, S. C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108, 103505 (2010).
[Crossref]

H. Rauh, G. I. Yampolskaya, and S. V. Yampolskii, “Optical transmittance of photonic structures with linearly graded dielectric constituents,” New J. Phys. 12, 073033 (2010).
[Crossref]

2009 (3)

S. C. S. Lin, T. J. Huang, J. H. Sun, and T. T. Wu, “Gradient index photonic crystals,” Phys. Rev. B 79, 094302 (2009).
[Crossref]

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105, 103708 (2009).
[Crossref]

R. H. Lipson and C. Lu, “Photonic crystals: a unique partnership between light and matter,” Eur. J. Phys. 30, S33–S48 (2009).
[Crossref]

2008 (2)

V. A. Tolmachev, T. S. Perova, J. Ruttle, and E. V. Khokhlova, “Design of one-dimensional photonic crystals using combination of band diagram and photonic gap map approaches,” J. Appl. Phys. 104, 033536 (2008).
[Crossref]

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92, 133501 (2008).
[Crossref]

2007 (3)

M. S. Vasconcelos, P. W. Mauriz, F. F. de Medeiros, and E. L. Albuquerque, “Photonic band gaps in quasiperiodic photonic crystals with negative refractive index,” Phys. Rev. B 76, 165117 (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]

H. Kurt and D. S. Citrin, “Graded index photonic crystals,” Opt. Express 15, 1240–1253 (2007).
[Crossref]

2006 (1)

Z. F. Sang and Z. Y. Li, “Optical properties of one-dimensional photonic crystals containing graded materials,” Opt. Commun. 259, 174–178 (2006).
[Crossref]

2005 (3)

J. H. Park, W. S. Choi, H. Y. Koo, and D. Y. Kim, “Colloidal photonic crystal with graded refractive index distribution,” Adv. Mater. 17, 879–885 (2005).
[Crossref]

E. Centeno and D. Cassagne, “Graded photonic crystals,” Opt. Lett. 30, 2278–2280 (2005).
[Crossref]

L. D. Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, “Spectrally enhanced light emission from aperiodic photonic structures,” Appl. Phys. Lett. 86, 261905 (2005).
[Crossref]

1997 (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–159 (1997).
[Crossref]

1987 (1)

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

Akmansoy, E.

F. Gaufillet and E. Akmansoy, “Design and experimental evidence of a flat graded-index photonic crystal lens,” J. Appl. Phys. 114, 083105 (2013).
[Crossref]

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92, 133501 (2008).
[Crossref]

Albuquerque, E. L.

M. S. Vasconcelos, P. W. Mauriz, F. F. de Medeiros, and E. L. Albuquerque, “Photonic band gaps in quasiperiodic photonic crystals with negative refractive index,” Phys. Rev. B 76, 165117 (2007).
[Crossref]

Baer, E.

Beadie, G.

Caglayan, H.

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105, 103708 (2009).
[Crossref]

Cakmak, A. O.

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105, 103708 (2009).
[Crossref]

Cassagne, D.

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92, 133501 (2008).
[Crossref]

E. Centeno and D. Cassagne, “Graded photonic crystals,” Opt. Lett. 30, 2278–2280 (2005).
[Crossref]

Centeno, E.

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92, 133501 (2008).
[Crossref]

E. Centeno and D. Cassagne, “Graded photonic crystals,” Opt. Lett. 30, 2278–2280 (2005).
[Crossref]

Chan, C. T.

L. Zhou, Z. Song, X. Huang, and C. T. Chan, “Physics of the zero-n photonic gap: fundamentals and latest developments,” Nanophotonics 1, 181–198 (2012).
[Crossref]

Chen, L. W.

H. W. Wang and L. W. Chen, “High transmission efficiency of arbitrary waveguide bends formed by graded index photonic crystals,” J. Opt. Soc. Am. B 28, 2098–2104 (2011).
[Crossref]

H. W. Wang and L. W. Chen, “A cylindrical optical black hole using graded index photonic crystals,” J. Appl. Phys. 109, 103104 (2011).
[Crossref]

Choi, W. S.

J. H. Park, W. S. Choi, H. Y. Koo, and D. Y. Kim, “Colloidal photonic crystal with graded refractive index distribution,” Adv. Mater. 17, 879–885 (2005).
[Crossref]

Citrin, D. S.

Colak, E.

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105, 103708 (2009).
[Crossref]

de Medeiros, F. F.

M. S. Vasconcelos, P. W. Mauriz, F. F. de Medeiros, and E. L. Albuquerque, “Photonic band gaps in quasiperiodic photonic crystals with negative refractive index,” Phys. Rev. B 76, 165117 (2007).
[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]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–159 (1997).
[Crossref]

Flynn, R.

Fu, Y.

Q. Zhu and Y. Fu, “Graded index photonic crystals: a review,” Ann. Phys. 527, 205–218 (2015).
[Crossref]

Gadonas, R.

A. Zukauskas, I. Matulaitien, D. Paipulas, G. Niaura, M. Malinauskas, and R. Gadonas, “Tuning the refractive index in 3D direct laser writing lithography: towards GRIN microoptics,” Laser Photon. Rev. 9, 706–712 (2015).
[Crossref]

Gajic, R.

B. Vasic and R. Gajic, “Self-focusing media using graded photonic crystals, Fourier transforming and imaging, directive emission, and directional cloaking,” J. Appl. Phys. 110, 053103 (2011).
[Crossref]

Gao, T.

M. Lu, B. K. Juluri, S. C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108, 103505 (2010).
[Crossref]

Gaufillet, F.

F. Gaufillet and E. Akmansoy, “Design and experimental evidence of a flat graded-index photonic crystal lens,” J. Appl. Phys. 114, 083105 (2013).
[Crossref]

Huang, T. J.

M. Lu, B. K. Juluri, S. C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108, 103505 (2010).
[Crossref]

S. C. S. Lin, T. J. Huang, J. H. Sun, and T. T. Wu, “Gradient index photonic crystals,” Phys. Rev. B 79, 094302 (2009).
[Crossref]

Huang, X.

L. Zhou, Z. Song, X. Huang, and C. T. Chan, “Physics of the zero-n photonic gap: fundamentals and latest developments,” Nanophotonics 1, 181–198 (2012).
[Crossref]

Ji, S.

Joannopoulos, J. D.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–159 (1997).
[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding Flow of Light (Princeton University, 2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding Flow of Light (Princeton University, 2008).

Juluri, B. K.

M. Lu, B. K. Juluri, S. C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108, 103505 (2010).
[Crossref]

Khokhlova, E. V.

V. A. Tolmachev, T. S. Perova, J. Ruttle, and E. V. Khokhlova, “Design of one-dimensional photonic crystals using combination of band diagram and photonic gap map approaches,” J. Appl. Phys. 104, 033536 (2008).
[Crossref]

Kim, D. Y.

J. H. Park, W. S. Choi, H. Y. Koo, and D. Y. Kim, “Colloidal photonic crystal with graded refractive index distribution,” Adv. Mater. 17, 879–885 (2005).
[Crossref]

Kimerling, L. C.

L. D. Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, “Spectrally enhanced light emission from aperiodic photonic structures,” Appl. Phys. Lett. 86, 261905 (2005).
[Crossref]

Kiraly, B.

M. Lu, B. K. Juluri, S. C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108, 103505 (2010).
[Crossref]

Koo, H. Y.

J. H. Park, W. S. Choi, H. Y. Koo, and D. Y. Kim, “Colloidal photonic crystal with graded refractive index distribution,” Adv. Mater. 17, 879–885 (2005).
[Crossref]

Kurt, H.

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105, 103708 (2009).
[Crossref]

H. Kurt and D. S. Citrin, “Graded index photonic crystals,” Opt. Express 15, 1240–1253 (2007).
[Crossref]

Lepkowicz, R. S.

Li, Z. Y.

Z. F. Sang and Z. Y. Li, “Optical properties of one-dimensional photonic crystals containing graded materials,” Opt. Commun. 259, 174–178 (2006).
[Crossref]

Lin, S. C. S.

M. Lu, B. K. Juluri, S. C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108, 103505 (2010).
[Crossref]

S. C. S. Lin, T. J. Huang, J. H. Sun, and T. T. Wu, “Gradient index photonic crystals,” Phys. Rev. B 79, 094302 (2009).
[Crossref]

Lipson, R. H.

R. H. Lipson and C. Lu, “Photonic crystals: a unique partnership between light and matter,” Eur. J. Phys. 30, S33–S48 (2009).
[Crossref]

Lourtioz, J. M.

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92, 133501 (2008).
[Crossref]

Lu, C.

R. H. Lipson and C. Lu, “Photonic crystals: a unique partnership between light and matter,” Eur. J. Phys. 30, S33–S48 (2009).
[Crossref]

Lu, M.

M. Lu, B. K. Juluri, S. C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108, 103505 (2010).
[Crossref]

Macia, E.

E. Macia, “Exploiting aperiodic designs in nanophotonic devices,” Rep. Prog. Phys. 75, 036502 (2012).
[Crossref]

Malinauskas, M.

A. Zukauskas, I. Matulaitien, D. Paipulas, G. Niaura, M. Malinauskas, and R. Gadonas, “Tuning the refractive index in 3D direct laser writing lithography: towards GRIN microoptics,” Laser Photon. Rev. 9, 706–712 (2015).
[Crossref]

Matulaitien, I.

A. Zukauskas, I. Matulaitien, D. Paipulas, G. Niaura, M. Malinauskas, and R. Gadonas, “Tuning the refractive index in 3D direct laser writing lithography: towards GRIN microoptics,” Laser Photon. Rev. 9, 706–712 (2015).
[Crossref]

Mauriz, P. W.

M. S. Vasconcelos, P. W. Mauriz, F. F. de Medeiros, and E. L. Albuquerque, “Photonic band gaps in quasiperiodic photonic crystals with negative refractive index,” Phys. Rev. B 76, 165117 (2007).
[Crossref]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding Flow of Light (Princeton University, 2008).

Michel, J.

L. D. Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, “Spectrally enhanced light emission from aperiodic photonic structures,” Appl. Phys. Lett. 86, 261905 (2005).
[Crossref]

Negro, L. D.

L. D. Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, “Spectrally enhanced light emission from aperiodic photonic structures,” Appl. Phys. Lett. 86, 261905 (2005).
[Crossref]

Nguyen, V.

L. D. Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, “Spectrally enhanced light emission from aperiodic photonic structures,” Appl. Phys. Lett. 86, 261905 (2005).
[Crossref]

Niaura, G.

A. Zukauskas, I. Matulaitien, D. Paipulas, G. Niaura, M. Malinauskas, and R. Gadonas, “Tuning the refractive index in 3D direct laser writing lithography: towards GRIN microoptics,” Laser Photon. Rev. 9, 706–712 (2015).
[Crossref]

Ozbay, E.

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105, 103708 (2009).
[Crossref]

Paipulas, D.

A. Zukauskas, I. Matulaitien, D. Paipulas, G. Niaura, M. Malinauskas, and R. Gadonas, “Tuning the refractive index in 3D direct laser writing lithography: towards GRIN microoptics,” Laser Photon. Rev. 9, 706–712 (2015).
[Crossref]

Pandey, P. C.

B. K. Singh and P. C. Pandey, “Tunable temperature-dependent THz photonic band gaps and localization mode engineering in 1-D periodic and quasi-periodic structures with graded-index materials and InSb,” Appl. Opt. 57, 8171–8181 (2018).
[Crossref]

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

Park, J. H.

J. H. Park, W. S. Choi, H. Y. Koo, and D. Y. Kim, “Colloidal photonic crystal with graded refractive index distribution,” Adv. Mater. 17, 879–885 (2005).
[Crossref]

Perova, T. S.

V. A. Tolmachev, T. S. Perova, J. Ruttle, and E. V. Khokhlova, “Design of one-dimensional photonic crystals using combination of band diagram and photonic gap map approaches,” J. Appl. Phys. 104, 033536 (2008).
[Crossref]

Ponting, M.

Rauh, H.

H. Rauh, G. I. Yampolskaya, and S. V. Yampolskii, “Optical transmittance of photonic structures with logarithmically similar dielectric constituents,” J. Opt. 14, 015101 (2012).
[Crossref]

H. Rauh, G. I. Yampolskaya, and S. V. Yampolskii, “Optical transmittance of photonic structures with linearly graded dielectric constituents,” New J. Phys. 12, 073033 (2010).
[Crossref]

Rosenberg, A.

Ruttle, J.

V. A. Tolmachev, T. S. Perova, J. Ruttle, and E. V. Khokhlova, “Design of one-dimensional photonic crystals using combination of band diagram and photonic gap map approaches,” J. Appl. Phys. 104, 033536 (2008).
[Crossref]

Sang, Z. F.

Z. F. Sang and Z. Y. Li, “Optical properties of one-dimensional photonic crystals containing graded materials,” Opt. Commun. 259, 174–178 (2006).
[Crossref]

Singh, B. K.

B. K. Singh and P. C. Pandey, “Tunable temperature-dependent THz photonic band gaps and localization mode engineering in 1-D periodic and quasi-periodic structures with graded-index materials and InSb,” Appl. Opt. 57, 8171–8181 (2018).
[Crossref]

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

Song, Z.

L. Zhou, Z. Song, X. Huang, and C. T. Chan, “Physics of the zero-n photonic gap: fundamentals and latest developments,” Nanophotonics 1, 181–198 (2012).
[Crossref]

Sun, J. H.

S. C. S. Lin, T. J. Huang, J. H. Sun, and T. T. Wu, “Gradient index photonic crystals,” Phys. Rev. B 79, 094302 (2009).
[Crossref]

Tolmachev, V. A.

V. A. Tolmachev, T. S. Perova, J. Ruttle, and E. V. Khokhlova, “Design of one-dimensional photonic crystals using combination of band diagram and photonic gap map approaches,” J. Appl. Phys. 104, 033536 (2008).
[Crossref]

Vasconcelos, M. S.

M. S. Vasconcelos, P. W. Mauriz, F. F. de Medeiros, and E. L. Albuquerque, “Photonic band gaps in quasiperiodic photonic crystals with negative refractive index,” Phys. Rev. B 76, 165117 (2007).
[Crossref]

Vasic, B.

B. Vasic and R. Gajic, “Self-focusing media using graded photonic crystals, Fourier transforming and imaging, directive emission, and directional cloaking,” J. Appl. Phys. 110, 053103 (2011).
[Crossref]

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–159 (1997).
[Crossref]

Vynck, K.

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92, 133501 (2008).
[Crossref]

Wang, H. W.

H. W. Wang and L. W. Chen, “A cylindrical optical black hole using graded index photonic crystals,” J. Appl. Phys. 109, 103104 (2011).
[Crossref]

H. W. Wang and L. W. Chen, “High transmission efficiency of arbitrary waveguide bends formed by graded index photonic crystals,” J. Opt. Soc. Am. B 28, 2098–2104 (2011).
[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]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding Flow of Light (Princeton University, 2008).

Wu, T. T.

S. C. S. Lin, T. J. Huang, J. H. Sun, and T. T. Wu, “Gradient index photonic crystals,” Phys. Rev. B 79, 094302 (2009).
[Crossref]

Yablonovitch, E.

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

Yampolskaya, G. I.

H. Rauh, G. I. Yampolskaya, and S. V. Yampolskii, “Optical transmittance of photonic structures with logarithmically similar dielectric constituents,” J. Opt. 14, 015101 (2012).
[Crossref]

H. Rauh, G. I. Yampolskaya, and S. V. Yampolskii, “Optical transmittance of photonic structures with linearly graded dielectric constituents,” New J. Phys. 12, 073033 (2010).
[Crossref]

Yampolskii, S. V.

H. Rauh, G. I. Yampolskaya, and S. V. Yampolskii, “Optical transmittance of photonic structures with logarithmically similar dielectric constituents,” J. Opt. 14, 015101 (2012).
[Crossref]

H. Rauh, G. I. Yampolskaya, and S. V. Yampolskii, “Optical transmittance of photonic structures with linearly graded dielectric constituents,” New J. Phys. 12, 073033 (2010).
[Crossref]

Yariv, A.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University, 2007).

Yeh, P.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University, 2007).

P. Yeh, Optical Wave in Layered Media (Wiley, 1988).

Yi, J. H.

L. D. Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, “Spectrally enhanced light emission from aperiodic photonic structures,” Appl. Phys. Lett. 86, 261905 (2005).
[Crossref]

Yi, Y.

L. D. Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, “Spectrally enhanced light emission from aperiodic photonic structures,” Appl. Phys. Lett. 86, 261905 (2005).
[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]

Zhou, L.

L. Zhou, Z. Song, X. Huang, and C. T. Chan, “Physics of the zero-n photonic gap: fundamentals and latest developments,” Nanophotonics 1, 181–198 (2012).
[Crossref]

Zhu, Q.

Q. Zhu and Y. Fu, “Graded index photonic crystals: a review,” Ann. Phys. 527, 205–218 (2015).
[Crossref]

Zukauskas, A.

A. Zukauskas, I. Matulaitien, D. Paipulas, G. Niaura, M. Malinauskas, and R. Gadonas, “Tuning the refractive index in 3D direct laser writing lithography: towards GRIN microoptics,” Laser Photon. Rev. 9, 706–712 (2015).
[Crossref]

Adv. Mater. (1)

J. H. Park, W. S. Choi, H. Y. Koo, and D. Y. Kim, “Colloidal photonic crystal with graded refractive index distribution,” Adv. Mater. 17, 879–885 (2005).
[Crossref]

Ann. Phys. (1)

Q. Zhu and Y. Fu, “Graded index photonic crystals: a review,” Ann. Phys. 527, 205–218 (2015).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

L. D. Negro, J. H. Yi, V. Nguyen, Y. Yi, J. Michel, and L. C. Kimerling, “Spectrally enhanced light emission from aperiodic photonic structures,” Appl. Phys. Lett. 86, 261905 (2005).
[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]

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92, 133501 (2008).
[Crossref]

Eur. J. Phys. (1)

R. H. Lipson and C. Lu, “Photonic crystals: a unique partnership between light and matter,” Eur. J. Phys. 30, S33–S48 (2009).
[Crossref]

J. Appl. Phys. (6)

M. Lu, B. K. Juluri, S. C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108, 103505 (2010).
[Crossref]

A. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105, 103708 (2009).
[Crossref]

B. Vasic and R. Gajic, “Self-focusing media using graded photonic crystals, Fourier transforming and imaging, directive emission, and directional cloaking,” J. Appl. Phys. 110, 053103 (2011).
[Crossref]

H. W. Wang and L. W. Chen, “A cylindrical optical black hole using graded index photonic crystals,” J. Appl. Phys. 109, 103104 (2011).
[Crossref]

V. A. Tolmachev, T. S. Perova, J. Ruttle, and E. V. Khokhlova, “Design of one-dimensional photonic crystals using combination of band diagram and photonic gap map approaches,” J. Appl. Phys. 104, 033536 (2008).
[Crossref]

F. Gaufillet and E. Akmansoy, “Design and experimental evidence of a flat graded-index photonic crystal lens,” J. Appl. Phys. 114, 083105 (2013).
[Crossref]

J. Opt. (1)

H. Rauh, G. I. Yampolskaya, and S. V. Yampolskii, “Optical transmittance of photonic structures with logarithmically similar dielectric constituents,” J. Opt. 14, 015101 (2012).
[Crossref]

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

Laser Photon. Rev. (1)

A. Zukauskas, I. Matulaitien, D. Paipulas, G. Niaura, M. Malinauskas, and R. Gadonas, “Tuning the refractive index in 3D direct laser writing lithography: towards GRIN microoptics,” Laser Photon. Rev. 9, 706–712 (2015).
[Crossref]

Nanophotonics (1)

L. Zhou, Z. Song, X. Huang, and C. T. Chan, “Physics of the zero-n photonic gap: fundamentals and latest developments,” Nanophotonics 1, 181–198 (2012).
[Crossref]

Nature (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–159 (1997).
[Crossref]

New J. Phys. (1)

H. Rauh, G. I. Yampolskaya, and S. V. Yampolskii, “Optical transmittance of photonic structures with linearly graded dielectric constituents,” New J. Phys. 12, 073033 (2010).
[Crossref]

Opt. Commun. (2)

Z. F. Sang and Z. Y. Li, “Optical properties of one-dimensional photonic crystals containing graded materials,” Opt. Commun. 259, 174–178 (2006).
[Crossref]

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

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (2)

S. C. S. Lin, T. J. Huang, J. H. Sun, and T. T. Wu, “Gradient index photonic crystals,” Phys. Rev. B 79, 094302 (2009).
[Crossref]

M. S. Vasconcelos, P. W. Mauriz, F. F. de Medeiros, and E. L. Albuquerque, “Photonic band gaps in quasiperiodic photonic crystals with negative refractive index,” Phys. Rev. B 76, 165117 (2007).
[Crossref]

Phys. Rev. Lett. (1)

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

Rep. Prog. Phys. (1)

E. Macia, “Exploiting aperiodic designs in nanophotonic devices,” Rep. Prog. Phys. 75, 036502 (2012).
[Crossref]

Other (3)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding Flow of Light (Princeton University, 2008).

P. Yeh, Optical Wave in Layered Media (Wiley, 1988).

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University, 2007).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1. Variations of refractive indices as a function of layer thickness in hyperbolic, exponential, and linear graded-index systems in (a) increasing and (b) decreasing fashion.
Fig. 2.
Fig. 2. Schematics of periodic (exponential, linear, and hyperbolic) GPC structures with (a) increasing and (b) decreasing refractive index profiles.
Fig. 3.
Fig. 3. Reflectance spectra of GPC structures of (a) hyperbolic, (b) exponential, and (c) linear graded-index layers for different layer thicknesses.
Fig. 4.
Fig. 4. Panel (i) shows the dispersion spectra of the GPC structures with (a) hyperbolic, (b) exponential, and (c) linear graded-index systems, while panels (ii) and (iii) illustrate the reflection shift for the structures with increasing and decreasing gradation profiles, and the layer thickness $d = 100\;{\rm nm}$.
Fig. 5.
Fig. 5. Distributions of PBG (black region) as a function of the layer thickness, $d$, for the periodic (a) hyperbolic, (b) exponential, and (c) linear graded-index structures.
Fig. 6.
Fig. 6. Variations of group velocity $({v_g}/c)$, group effective index $({n_{{g_{\rm eff}}}})$, and group delay $(\tau )$ in GPCs for layer thickness $d = 100\;{\rm nm}$.
Fig. 7.
Fig. 7. Variations of group velocity $({v_g}/c)$ and group delay time $(\tau )$ in GPCs for layer thickness $d = 150\;{\rm nm}$.
Fig. 8.
Fig. 8. Distributions of electric field intensity in the periodic system of (a) hyperbolic, (b) exponential, and (c) linear graded-index media with (i) increasing and (ii) decreasing gradation profiles at the layer thickness $d = 200\;{\rm nm}$.
Fig. 9.
Fig. 9. Reflection spectra at the different values of $| {{n_f} - {n_i}} |$ for the GPC structures of (a) hyperbolic, (b) exponential, and (c) linear graded-index media.
Fig. 10.
Fig. 10. Distribution of PBGs as a function of the refractive indices (i) ${n_i}$ with ${n_f} = 4.5$ and (ii) ${n_f}$ with ${n_i} = 1.5$ for the structures with (a) hyperbolic, (b) exponential, and (c) linear graded-index media, and $d = 100\;{\rm nm}$.

Tables (1)

Tables Icon

Table 1. Band Region and Bandwidth of PBGs Falling in the Considered Frequency Range for 1D GPC Structures with Different Graded-Index Layers

Equations (14)

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

n H ( x ) = n i 1 α x ,
E H ( x ) = A H ξ H cos ( m log ξ H ) + B H ξ H sin ( m log ξ H ) ,
n E ( x ) = n i e x p ( γ x ) ,
E E ( x ) = A E J 0 ( ξ E γ ) + B E Y 0 ( ξ E γ ) ,
n L ( x ) = n i + ( ( n f n i ) d ) x .
E L ( x ) = ξ L [ A L J 1 / 4 ( ξ L 2 2 β ) + B L Y 1 / 4 ( ξ L 2 2 β ) ] ,
( A 0 B 0 ) = M 0 1 ( M G or M G ) N M 0 ( A N + 1 0 ) ,
M i = ( 1 0 α / 2 α m ) , M f = ( n i n f cos ( z H ) n i n f sin ( z H ) α 2 n i n f [ 2 m sin ( z H ) cos ( z H ) ] α 2 n i n f [ 2 m sin ( z H ) + cos ( z H ) ] ) ,
M i = ( J 0 ( ξ i γ ) Y 0 ( ξ i γ ) ξ i J 1 ( ξ i γ ) ξ i Y 1 ( ξ i γ ) ) a n d M f = ( J 0 ( ξ f γ ) Y 0 ( ξ f γ ) ξ f J 1 ( ξ f γ ) ξ f Y 1 ( ξ f γ ) ) ,
M i = ( ξ 0 J 1 4 ( ξ 0 2 2 β ) ξ 0 Y 1 4 ( ξ 0 2 2 β ) ( β 2 ξ 0 3 / 2 J 1 4 ( ξ 0 2 2 β ) + ξ 0 3 / 2 J 1 4 ( ξ 0 2 2 β ) ) ( β 2 ξ 0 3 / 2 Y 1 4 ( ξ 0 2 2 β ) + ξ 0 3 / 2 Y 1 4 ( ξ 0 2 2 β ) ) ) M f = ( ξ 1 J 1 4 ( ξ 1 2 2 β ) ξ 1 Y 1 4 ( ξ 1 2 2 β ) ( β 2 ξ 1 3 / 2 J 1 4 ( ξ 1 2 2 β ) + ξ 1 3 / 2 J 1 4 ( ξ 1 2 2 β ) ) ( β 2 ξ 1 3 / 2 Y 1 4 ( ξ 1 2 2 β ) + ξ 1 3 / 2 Y 1 4 ( ξ 1 2 2 β ) ) ) ,
M 0 = ( 1 1 i k 0 i k 0 ) ,
R = | r | 2 = | B 0 A 0 | 2 a n d T = | t | 2 = | A N + 1 A 0 | 2 r = | r | e x p ( i Ψ ) } .
K ( ω ) = 1 d cos 1 { 1 2 ( M 11 + M 22 ) } ,
v g = d ω d K = [ d K d ω ] 1 , n g e f f = c v g = c . d K d ω , a n d τ = d v g ,