Abstract

The vector wave multiple scattering method is a reliable and efficient technique in treating the photonic band gap problem for photonic crystals composed of spherically scattering objects with metallic components. In this paper, we describe the formalism and its application to the photonic band structures of systems comprising of metallo-dielectric spheres. We show that the photonic band gaps are essentially determined by local short-range order rather than by the translational symmetry if the volume fraction of the metallic core is high.

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References

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  1. See, e.g., K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152 (1990).
    [CrossRef] [PubMed]
  2. See, e.g., A. J. Ward and J. B. Pendry, "Calculating photonic Green's function using a nonorthogonal finite-difference time-domain method," Phys. Rev. B58, 7252 (1998).
  3. S. Fan, P. R. Villeneuve, and Joannopoulos, "Large omnidirectional band gaps in metallodielectric photonic crystals," Phys. Rev. B54, 11245 (1996).
  4. J. Korringa, Physica 13, 392 (1947).
    [CrossRef]
  5. W. Kohn and N. Rostoker, "Solution of Schrodinger equation in periodic lattice with an application to metallic lithium," Phys. Rev. 94, 1111 (1954).
    [CrossRef]
  6. J. L. Beeby, "The electronic structures of disordered systems," Proc. R. Soc. A279, 82 (1964).
  7. See, e.g., K. Ohtaka, "Energy band of photons and low-energy photon diffraction," Phys. Rev. B19, 5057 (1979).
  8. X. D. Wang, X.-G. Zhang, Q. L. Yu, and B. N. Harmon, "Multiple scattering theory for electro-magnetic waves," Phys. Rev. B47, 4161 (1993).
  9. N. Stefanou, V. Yannopapas, and A. Modinos, "Heterostructures of photonic crystals: frequency bands and transmission coefficients," Computer Phys. Commun. 113, 49 (1998).
    [CrossRef]
  10. W.Y. Zhang, X.Y. Lei, Z.L. Wang, D.G. Zheng, W.Y. Tam, C.T. Chan, and P. Sheng, "Robust photonic band gap from tunable scatterers," Phys. Rev. Lett. 84, 2853 (2000).
    [CrossRef] [PubMed]

Other

See, e.g., K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152 (1990).
[CrossRef] [PubMed]

See, e.g., A. J. Ward and J. B. Pendry, "Calculating photonic Green's function using a nonorthogonal finite-difference time-domain method," Phys. Rev. B58, 7252 (1998).

S. Fan, P. R. Villeneuve, and Joannopoulos, "Large omnidirectional band gaps in metallodielectric photonic crystals," Phys. Rev. B54, 11245 (1996).

J. Korringa, Physica 13, 392 (1947).
[CrossRef]

W. Kohn and N. Rostoker, "Solution of Schrodinger equation in periodic lattice with an application to metallic lithium," Phys. Rev. 94, 1111 (1954).
[CrossRef]

J. L. Beeby, "The electronic structures of disordered systems," Proc. R. Soc. A279, 82 (1964).

See, e.g., K. Ohtaka, "Energy band of photons and low-energy photon diffraction," Phys. Rev. B19, 5057 (1979).

X. D. Wang, X.-G. Zhang, Q. L. Yu, and B. N. Harmon, "Multiple scattering theory for electro-magnetic waves," Phys. Rev. B47, 4161 (1993).

N. Stefanou, V. Yannopapas, and A. Modinos, "Heterostructures of photonic crystals: frequency bands and transmission coefficients," Computer Phys. Commun. 113, 49 (1998).
[CrossRef]

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

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Figures (4)

Fig. 1.
Fig. 1.

The photonic band structures of metallo-dielectric spheres in air, the filling ratio is f=0.74, the metal core is modeled by ε=-200, and coating layer is 5% in radius with a dielectric constant ε=12. (a) HCP crystal; (b) FCC crystal.

Fig. 2.
Fig. 2.

The photonic band structures of touching metallo-dielectric spheres in air for (a) hexagonal diamond; (b) cubic diamond structure.

Fig. 3.
Fig. 3.

The gap/mid-gap ratio as a function of the filling ratio f for the photonic crystals made of metal spheres in air for (a) HCP crystal; (b) FCC crystal.

Fig. 4.
Fig. 4.

The gap/mid-gap ratio ratio as a function of the filling ratio f for the photonic crystals made of metal spheres in air for (a) hexagonal diamond crystal; (b) cubic diamond crystal.

Equations (7)

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× × E ( r , ω ) k 2 ( r , ω ) E ( r , ω ) = 0 ,
E 0 ( r , ω ) = d S · { d 0 ( r r ) × [ × E ( r , ω ) ] + [ × d 0 ( r r ) ] × E ( r , ω ) } .
E 0 ( r , ω ) = i d S i × { d 0 ( r r ¯ ) × [ × E ( r ¯ , ω ) ] + [ × d 0 ( r r ¯ ) ] × E ( r , ω ) } .
E 0 ( R i + r ) = l m σ b i l m σ J i l m σ ( r ) ;
E ( R i + r ) = l m σ a i l m σ P i l m σ ( r ) ;
[ δ s s δ l l δ m m δ σσ l " m " σ " G l m σ ; l " m " σ " s s ( k ) t l " m " σ " ; l m σ s ] a s l m σ = b s l m σ .
G l m σ ; l m σ i j ( R ) = { μ C ( l 1 l ; m μ μ ) for σ = σ g l m μ ; l m μ C ( l 1 l ; m μ μ ) 2 l + 1 l + 1 for σ = e 1 and σ = e 2 μ C ( l 1 l ; m μ μ ) g l m μ ; l 1 m μ C ( l 11 l ; m μ μ ) 2 l + 1 l + 1 μ C ( l 1 l ; m μ μ ) g l m μ ; l 1 m μ C ( l 11 l ; m μ μ ) for σ = e 2 and σ = e 1 .

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