Abstract

Using an available program package based on the transfer-matrix method, we calculated the photonic band structure for two different structures: a quasi-three-dimensional crystal of square air rods in a high-index matrix and an opal structure of high-index spheres in a matrix of low index, ε = 1.5. The high index used is representative of gallium arsenide in the thermal infrared range. The geometric parameters of the rod dimension, sphere radius, and lattice constants were chosen to give total reflectance for normal incidence, i.e., minimum thermal emittance, in either one of the two infrared atmospheric windows. For these four photonic crystals, the bulk reflectance spectra and the wavelength-averaged thermal emittance as a function of crystal thickness were calculated. The results reveal that potentially useful thermal signature suppression is obtained for crystals as thin as 20–50 µm, i.e., comparable with that of a paint layer.

© 2002 Optical Society of America

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  1. See, e.g., “Focus issue: photonic bandgap calculations,” Opt. Exp. 8 (3) (2001) and references therein, www.opticsexpress.org/issue.cfm?issue_id=101 .
  2. E. Yablonovitch, “Inhibited spontaneous emission in solid state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef] [PubMed]
  3. S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53, 2169–2173 (1984).
    [CrossRef]
  4. J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals (Princeton University, Princeton, N.J., 1995), Chap. 2.
  5. E. Yablonovitch, “Photonic crystals,” J. Mod. Opt. 41, 173–194 (1994).
    [CrossRef]
  6. J. D. Joannopoulos, P. R. Villeneuve, S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386, 143–149 (1997).
    [CrossRef]
  7. See, e.g., C. Kittel, Introduction to Solid State Physics, 7th ed. (Wiley, New York, 1996), Chap. 7.
  8. S. John, T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
    [CrossRef] [PubMed]
  9. G. Tayeb, D. Maystre, “Rigorous theoretical study of finite-size two-dimensional photonic crystals doped by microcavities,” J. Opt. Soc. Am. A 14, 3323–3332 (1997).
    [CrossRef]
  10. A. J. LaRocca, “Atmospheric absorption,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, eds. (Environmental Research Institute of Michrgan, Ann Arbor, Mich., 1989), Sect. 5.9.
  11. S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature (London) 394, 251–253 (1998).
    [CrossRef]
  12. See A. L. Reynolds, “Photonic band gap materials,” Photonic Band Gap Materials Research Group, Optoelectronics Research Group, Department of Electronics and Electrical Engineering, University of Glasgow, Glasgow, Scotland, http://www.elec.gla.ac.uk/∼areynolds .
  13. P. M. Bell, J. B. Pendry, L. M. Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
    [CrossRef]
  14. E. D. Palik, “Gallium arsenide,” in Handbook of Optical Constants of Solids I, E. D. Palik, ed. (Academic, New York, 1985), pp. 429–443.

2001

See, e.g., “Focus issue: photonic bandgap calculations,” Opt. Exp. 8 (3) (2001) and references therein, www.opticsexpress.org/issue.cfm?issue_id=101 .

1998

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature (London) 394, 251–253 (1998).
[CrossRef]

1997

G. Tayeb, D. Maystre, “Rigorous theoretical study of finite-size two-dimensional photonic crystals doped by microcavities,” J. Opt. Soc. Am. A 14, 3323–3332 (1997).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386, 143–149 (1997).
[CrossRef]

1995

P. M. Bell, J. B. Pendry, L. M. Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

1994

E. Yablonovitch, “Photonic crystals,” J. Mod. Opt. 41, 173–194 (1994).
[CrossRef]

S. John, T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[CrossRef] [PubMed]

1987

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

1984

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53, 2169–2173 (1984).
[CrossRef]

Bell, P. M.

P. M. Bell, J. B. Pendry, L. M. Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

Biswas, R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature (London) 394, 251–253 (1998).
[CrossRef]

Bur, J.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature (London) 394, 251–253 (1998).
[CrossRef]

Fan, S.

J. D. Joannopoulos, P. R. Villeneuve, S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386, 143–149 (1997).
[CrossRef]

Fleming, J. G.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature (London) 394, 251–253 (1998).
[CrossRef]

Hetherington, D. L.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature (London) 394, 251–253 (1998).
[CrossRef]

Ho, K. M.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature (London) 394, 251–253 (1998).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, P. R. Villeneuve, S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386, 143–149 (1997).
[CrossRef]

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals (Princeton University, Princeton, N.J., 1995), Chap. 2.

John, S.

S. John, T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[CrossRef] [PubMed]

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53, 2169–2173 (1984).
[CrossRef]

Kittel, C.

See, e.g., C. Kittel, Introduction to Solid State Physics, 7th ed. (Wiley, New York, 1996), Chap. 7.

Kurtz, S. R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature (London) 394, 251–253 (1998).
[CrossRef]

LaRocca, A. J.

A. J. LaRocca, “Atmospheric absorption,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, eds. (Environmental Research Institute of Michrgan, Ann Arbor, Mich., 1989), Sect. 5.9.

Lin, S. Y.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature (London) 394, 251–253 (1998).
[CrossRef]

Maystre, D.

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals (Princeton University, Princeton, N.J., 1995), Chap. 2.

Moreno, L. M.

P. M. Bell, J. B. Pendry, L. M. Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

Palik, E. D.

E. D. Palik, “Gallium arsenide,” in Handbook of Optical Constants of Solids I, E. D. Palik, ed. (Academic, New York, 1985), pp. 429–443.

Pendry, J. B.

P. M. Bell, J. B. Pendry, L. M. Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

Quang, T.

S. John, T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[CrossRef] [PubMed]

Sigalas, M. M.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature (London) 394, 251–253 (1998).
[CrossRef]

Smith, B. K.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature (London) 394, 251–253 (1998).
[CrossRef]

Tayeb, G.

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386, 143–149 (1997).
[CrossRef]

Ward, A. J.

P. M. Bell, J. B. Pendry, L. M. Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals (Princeton University, Princeton, N.J., 1995), Chap. 2.

Yablonovitch, E.

E. Yablonovitch, “Photonic crystals,” J. Mod. Opt. 41, 173–194 (1994).
[CrossRef]

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

Zubrzycki, W.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature (London) 394, 251–253 (1998).
[CrossRef]

Comput. Phys. Commun.

P. M. Bell, J. B. Pendry, L. M. Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun. 85, 306–322 (1995).
[CrossRef]

J. Mod. Opt.

E. Yablonovitch, “Photonic crystals,” J. Mod. Opt. 41, 173–194 (1994).
[CrossRef]

J. Opt. Soc. Am. A

Nature (London)

J. D. Joannopoulos, P. R. Villeneuve, S. Fan, “Photonic crystals: putting a new twist on light,” Nature (London) 386, 143–149 (1997).
[CrossRef]

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature (London) 394, 251–253 (1998).
[CrossRef]

Opt. Exp.

See, e.g., “Focus issue: photonic bandgap calculations,” Opt. Exp. 8 (3) (2001) and references therein, www.opticsexpress.org/issue.cfm?issue_id=101 .

Phys. Rev. A

S. John, T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett.

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

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53, 2169–2173 (1984).
[CrossRef]

Other

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals (Princeton University, Princeton, N.J., 1995), Chap. 2.

See, e.g., C. Kittel, Introduction to Solid State Physics, 7th ed. (Wiley, New York, 1996), Chap. 7.

A. J. LaRocca, “Atmospheric absorption,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, eds. (Environmental Research Institute of Michrgan, Ann Arbor, Mich., 1989), Sect. 5.9.

See A. L. Reynolds, “Photonic band gap materials,” Photonic Band Gap Materials Research Group, Optoelectronics Research Group, Department of Electronics and Electrical Engineering, University of Glasgow, Glasgow, Scotland, http://www.elec.gla.ac.uk/∼areynolds .

E. D. Palik, “Gallium arsenide,” in Handbook of Optical Constants of Solids I, E. D. Palik, ed. (Academic, New York, 1985), pp. 429–443.

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Figures (9)

Fig. 1
Fig. 1

Two-dimensional unit cell is a square lattice of quadratic air wells in a dielectric matrix.

Fig. 2
Fig. 2

Three-dimensional opal structure with the [111]- direction as indicated. It corresponds to a face-centered cubic structure of nontouching dielectric spheres in a low-index polymer matrix.

Fig. 3
Fig. 3

Band diagram for the infinite rod structure. Energy units are normalized frequency f* a/ c.

Fig. 4
Fig. 4

Band structure for the 3-D material, sphere radii r = 1.3 µm. Energy units are normalized frequency f* a/ c.

Fig. 5
Fig. 5

Reflectance spectrum for 32 layers of the 2-D structure. The wavelength scale is normalized with the unit cell constant.

Fig. 6
Fig. 6

Reflectance spectrum for 64 layers of the 3-D structure. a = 1.55 µm.

Fig. 7
Fig. 7

Reflectance spectrum for 64 layers of the 3-D structure. a = 4.0 µm.

Fig. 8
Fig. 8

Average thermal emittance in the two atmospheric windows for the rod structure as a function of photonic crystal thickness.

Fig. 9
Fig. 9

Average thermal emittance in both atmospheric windows for the opal structure as a function of photonic crystal thickness.

Equations (1)

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ε¯T, d=ab1-Rλ, dLbbλ, ddλab Lbbλ, ddλ,

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