Abstract

A method of photonic band gap extension using mixing of periodic structures with two or more consecutively placed photonic crystals with different lattice constants is proposed. For the design of the structures with maximal photonic band gap extension the gap map imposition method is utilised. Optimal structures have been established and the gap map of photonic band gaps has been calculated at normal incidence of light for both small and large optical contrast and at oblique incidence of light for small optical contrast.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. E. Yablonovitch, �??Inhibited spontaneous emission in solid-state physics and electronics,�?? Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Singapore, 1995).
  3. Y. Fink, J. N. Winn, F. Shanhui, C. Chiping, J. Michel, J. D. Joannopoulos, and E. L. Thomas,�??A dielectric omnidirectional reflector,�?? Science 282, 1679-1682 (1998).
    [CrossRef] [PubMed]
  4. D.N. Chigrin, A.V. Lavrinenko, D.A. Yarotsky, S.V. Gaponenko, �??Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,�?? Appl.Phys. A 68, 25-28 (1999).
    [CrossRef]
  5. P.St.J. Russell, S. Tredwell, P.J. Roberts, �??Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,�?? Opt.Commun. 160, 66-71 (1999).
    [CrossRef]
  6. P. Yeh, A. Yariv, Optical waves in crystals (Wiley, USA, 1984, pp.589).
  7. D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko,�??All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control,�?? J Lightwave Techn. 17, 2018-2024 (1999).
    [CrossRef]
  8. C. Jamois, R.B. Wehrspohn, L.C. Andreani, C. Hermannd, O. Hess, and U. Gosele, �??Silicon-based twodimensional photonic crystal waveguides,�?? Photonics and Nanostructures �?? Fundamentals and Applications 1, 1-13 (2003).
    [CrossRef]
  9. L.F. Marsal, T. Trifonov, A. Rodriguez, J. Pallares, and R. Alcubilla, �??Larger absolute photonic band gap in two-dimensional air�??silicon structures,�?? Physica E 16, 580-585 (2003).
    [CrossRef]
  10. V.A. Tolmachev, T.S. Perova, E.V. Astrova, J.A. Pilyugina and R.A. Moore, �??Optical characteristics of ordinary and tunable 1D Si photonic crystals in the mid infrared range,�?? Proc. SPIE 5825 (to be published).
  11. M. Born, and E. Wolf, Principles of Optics (sixth ed., Pergamon Press, 1980, p. 381); R.M.A. Azzam, and N.M. Bashara, Ellipsometry and polarized light (North-Holland, Amsterdam, Netherlands, 1977).
  12. V.A. Tolmachev, T.S. Perova and K. Berwick, �??Design criteria and optical characteristics of 1D photonic crystals based on periodically grooved silicon,�?? Appl. Opt. 42, 5679- 5683 (2003).
    [CrossRef] [PubMed]
  13. Optical Interference Coatings, eds.N. Kaiser, H.K.Pulker (Springer, Germany, 2003, pp.503).
  14. D. Zhang, W. Hu, Y. Zhang, Z. Li, B. Cheng, and G. Yang, �??Experimental verification of light localization for disordered multilayers in the visible-infrared spectrum,�?? Phys.Rev. B50, 9810-9814 (1994).
  15. D. Zhang, Z. Li, W. Hu and B. Cheng, �??Broadband optical reflector�??an application of light localization in one dimension,�?? Appl.Phys.Lett. 67, 2431-2432 (1995).
    [CrossRef]
  16. H. Li, H. Cheng and X. Qiu, �??Band-gap extension of disordered 1D binary photonic crystals,�?? Physica B 279, 164-167 (2000).
    [CrossRef]
  17. V.A. Tolmachev , T.S. Perova, J. Pilyugina, and R.A. Moore, �??Experimental verification of photonic band gap extension for disordered 1D photonic crystal based on Si�??, Opt.Commun. (to be published).
  18. W.H. Southwell, �??Omnidirectional mirror design with quarter-wave dielectric stacks,�?? Appl.Opt. 38, 5464-5467 (1999).
    [CrossRef]
  19. X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zia, �??Enlagment of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,�?? Appl. Phys. Lett. 80, 4291-4293 (2002)
    [CrossRef]
  20. V.A. Tolmachev, T.S. Perova, and K. Berwick, �??Design of 1D composite photonic crystals with an extended photonic band gap,�?? J.App.Phys. (paper submitted).

Appl. Opt.

Appl. Phys. Lett.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zia, �??Enlagment of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,�?? Appl. Phys. Lett. 80, 4291-4293 (2002)
[CrossRef]

Appl.Opt.

W.H. Southwell, �??Omnidirectional mirror design with quarter-wave dielectric stacks,�?? Appl.Opt. 38, 5464-5467 (1999).
[CrossRef]

Appl.Phys. A

D.N. Chigrin, A.V. Lavrinenko, D.A. Yarotsky, S.V. Gaponenko, �??Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,�?? Appl.Phys. A 68, 25-28 (1999).
[CrossRef]

Appl.Phys.Lett.

D. Zhang, Z. Li, W. Hu and B. Cheng, �??Broadband optical reflector�??an application of light localization in one dimension,�?? Appl.Phys.Lett. 67, 2431-2432 (1995).
[CrossRef]

J Lightwave Techn.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko,�??All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control,�?? J Lightwave Techn. 17, 2018-2024 (1999).
[CrossRef]

J.App.Phys.

V.A. Tolmachev, T.S. Perova, and K. Berwick, �??Design of 1D composite photonic crystals with an extended photonic band gap,�?? J.App.Phys. (paper submitted).

Opt.Commun.

P.St.J. Russell, S. Tredwell, P.J. Roberts, �??Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,�?? Opt.Commun. 160, 66-71 (1999).
[CrossRef]

V.A. Tolmachev , T.S. Perova, J. Pilyugina, and R.A. Moore, �??Experimental verification of photonic band gap extension for disordered 1D photonic crystal based on Si�??, Opt.Commun. (to be published).

Photonics and Nanostructures

C. Jamois, R.B. Wehrspohn, L.C. Andreani, C. Hermannd, O. Hess, and U. Gosele, �??Silicon-based twodimensional photonic crystal waveguides,�?? Photonics and Nanostructures �?? Fundamentals and Applications 1, 1-13 (2003).
[CrossRef]

Phys. Rev. Lett.

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

Phys.Rev. B

D. Zhang, W. Hu, Y. Zhang, Z. Li, B. Cheng, and G. Yang, �??Experimental verification of light localization for disordered multilayers in the visible-infrared spectrum,�?? Phys.Rev. B50, 9810-9814 (1994).

Physica B

H. Li, H. Cheng and X. Qiu, �??Band-gap extension of disordered 1D binary photonic crystals,�?? Physica B 279, 164-167 (2000).
[CrossRef]

Physica E

L.F. Marsal, T. Trifonov, A. Rodriguez, J. Pallares, and R. Alcubilla, �??Larger absolute photonic band gap in two-dimensional air�??silicon structures,�?? Physica E 16, 580-585 (2003).
[CrossRef]

Proc. SPIE

V.A. Tolmachev, T.S. Perova, E.V. Astrova, J.A. Pilyugina and R.A. Moore, �??Optical characteristics of ordinary and tunable 1D Si photonic crystals in the mid infrared range,�?? Proc. SPIE 5825 (to be published).

Science

Y. Fink, J. N. Winn, F. Shanhui, C. Chiping, J. Michel, J. D. Joannopoulos, and E. L. Thomas,�??A dielectric omnidirectional reflector,�?? Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Other

Optical Interference Coatings, eds.N. Kaiser, H.K.Pulker (Springer, Germany, 2003, pp.503).

M. Born, and E. Wolf, Principles of Optics (sixth ed., Pergamon Press, 1980, p. 381); R.M.A. Azzam, and N.M. Bashara, Ellipsometry and polarized light (North-Holland, Amsterdam, Netherlands, 1977).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Singapore, 1995).

P. Yeh, A. Yariv, Optical waves in crystals (Wiley, USA, 1984, pp.589).

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 (3)

Fig 1.
Fig 1.

(a) The region of the lowest PBG for PC with A=0.21 μm (thin line) and imposition of the gap maps for ID PCs with different A shown beside the regions of the corresponding PBGs (thick lines). The calculations are performed at normal incidence of light using the optical contrast ∆n=2.3/1.45, m=l0 and criterion R PBG=0.999. The PBG regions of higher order are not shown. The predicted region of v (or λ), due to the overlapping of PBGs of four PCs, is ∆λ≈0.4μm for the filling factor f =0.3. (b) The gap map of composite ID PC with the extended PBG (grey region) obtained for the sequence of PCs with A=0.21-0.185-0.156-0.13 μm (marked as a ‘comb’). The gap map for A=0.21 μm and m=40 (shown by dash-dotted line) and m=10 (shown by dark region) are presented for comparison. Insert - the dependence of the relative width of PBG, (∆λ/λ) versus f.

Fig. 2.
Fig. 2.

(a) Overlapping of two PBG gap maps from two conventional PCs with lattice constants A1=3 (white regions) and A2=0.71×A1=2.13 μm (grey regions) at m=10 and optical contrast ∆n=3.42/1 and the regions of the extended PBG (dark regions). (b) The gap map of a CPC obtained for values of m=7 (thin line) and m=10 (dotted line) with extended PBG for m=7 (dark region) and m=10 (grey regions).

Fig. 3.
Fig. 3.

The PBG maps (a) for PC1 with lattice constants A1=0.21 μm (contours drawn by thick line) and PC2 with A2=0.18 μm (contours drawn by thin line) calculated at number of periods m1,2=20, optical contrast (∆n =2.35/1.45) and angles of incidence φ=0° (dash contours) and 85° (light grey regions for TE polarisation and dark grey regions for TM polarisation). (b) The PBG maps for composite PC with wide omni-directional region (crosshatched region) shown in the range of f=0.28-0.4 (the relative width of ∆λ/λ=11.8% for f=0.35).

Metrics