Abstract

During high-velocity atmospheric entries, space vehicles can be exposed to strong electromagnetic radiation from ionized gas in the shock layer. Glassy carbon (GC) and silicon carbide (SiC) are candidate thermal protection materials due to their high melting point and also their good thermal and mechanical properties. Based on data from shock tube experiments, a significant fraction of radiation at hypersonic entry conditions is in the frequency range from 215 to 415 THz. We propose and analyze SiC and GC photonic structures to increase the reflection of radiation in that range. For this purpose, we performed numerical optimizations of various structures using an evolutionary strategy. Among the considered structures are layered, porous, woodpile, inverse opal and guided-mode resonance structures. In order to estimate the impact of fabrication inaccuracies, the sensitivity of the reflectivity to structural imperfections is analyzed. We estimate that the reflectivity of GC photonic structures is limited to 38% in the aforementioned range, due to material absorption. However, GC material can be effective for photonic reflection of individual, strong spectral line. SiC on the other hand can be used to design a good reflector for the entire frequency range.

© 2012 OSA

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References

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  1. J. Joannopoulos, S. Johnson, J. Winn, and R. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008).
  2. V. Shklover, L. Braginsky, G. Witz, M. Mishrikey, and C. Hafner, “High-temperature photonic structures. Thermal barrier coatings, infrared sources and other applications,” J. Comput. Theor. Nanosci. 5, 862–893 (2008).
  3. J. Grinstead, M. Wilder, J. Olejniczak, D. Bogdanoff, G. Allen, K. Dang, and M. Forrest, “Shock-heated air radiation measurements at Lunar return conditions,” AIAA Pap. 1244, 092407 (2008).
  4. C. Park, “Stagnation-region heating environment of the Galileo probe,” J. Thermophys. Heat Transfer 23, 417–424 (2009).
    [CrossRef]
  5. N. Komarevskiy, L. Braginsky, V. Shklover, C. Hafner, and J. Lawson, “Fast numerical methods for the design of layered photonic structures with rough interfaces,” Opt. Express 19, 5489–5499 (2011).
    [CrossRef] [PubMed]
  6. N. Komarevskiy, V. Shklover, L. Braginsky, C. Hafner, O. Fabrichnaya, S. White, and J. Lawson, “Design of reflective, photonic shields for atmospheric reentry,” J. Electromagn. Anal. Appl. 3, 228–237 (2011).
  7. A. Brandis, C. Johnston, B. Cruden, D. Prabhu, and D. Bose, “Uncertainty analysis of Neqair and Hara predictions of air radiation measurements obtained in the East facility,” in 42nd AIAA Thermophysics Conference, (American Institute of Aeronautics & Astronautics (AIAA), 2011), pp. 1–14.
  8. Directionality can be obtained from simulation sets that are calibrated against shock tube data.
  9. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996).
    [CrossRef]
  10. D. Whittaker and I. Culshaw, “Scattering-matrix treatment of patterned multilayer photonic structures,” Phys. Rev. B 60, 2610–2618 (1999).
    [CrossRef]
  11. J. Fröhlich, “Evolutionary Optimization for Computational Electromagnetics,” Ph.D. thesis (ETH Zurich, IFH Laboratory, 1997).
  12. [Online]. Available: http://www.sopra-sa.com/
  13. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).
  14. M. Williams and E. Arakawa, “Optical properties of glassy carbon from 0 to 82 eV,” J. Appl. Phys. 43, 3460–3463 (1972).
    [CrossRef]
  15. J. Shor, I. Grimberg, B. Weiss, and A. Kurtz, “Direct observation of porous SiC formed by anodization in HF,” Appl. Phys. Lett. 62, 2836–2838 (1993).
    [CrossRef]
  16. There is no mathematical proof for this observation, but it seems reasonable from the physical point of view, since no scattering occurs at planar interfaces.
  17. A. Zakhidov, R. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. Dantas, J. Marti, and V. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
    [CrossRef] [PubMed]
  18. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606–2613 (1993).
    [CrossRef] [PubMed]
  19. M. Gale, K. Knop, and R. Morf, “Zero-order diffractive microstructures for security applications,” Proc. SPIE 1210, 83–89 (1990).
    [CrossRef]
  20. Z. Liu, S. Tibuleac, D. Shin, P. Young, and R. Magnusson, “High-efficiency guided-mode resonance filter,” Opt. Lett. 23, 1556–1558 (1998).
    [CrossRef]
  21. S. Tikhodeev, A. Yablonskii, E. Muljarov, N. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
    [CrossRef]
  22. L. Braginsky and V. Shklover, “Light propagation in an imperfect photonic crystal,” Phys. Rev. B 73, 085107 (2006).
    [CrossRef]

2011 (2)

N. Komarevskiy, L. Braginsky, V. Shklover, C. Hafner, and J. Lawson, “Fast numerical methods for the design of layered photonic structures with rough interfaces,” Opt. Express 19, 5489–5499 (2011).
[CrossRef] [PubMed]

N. Komarevskiy, V. Shklover, L. Braginsky, C. Hafner, O. Fabrichnaya, S. White, and J. Lawson, “Design of reflective, photonic shields for atmospheric reentry,” J. Electromagn. Anal. Appl. 3, 228–237 (2011).

2009 (1)

C. Park, “Stagnation-region heating environment of the Galileo probe,” J. Thermophys. Heat Transfer 23, 417–424 (2009).
[CrossRef]

2008 (2)

V. Shklover, L. Braginsky, G. Witz, M. Mishrikey, and C. Hafner, “High-temperature photonic structures. Thermal barrier coatings, infrared sources and other applications,” J. Comput. Theor. Nanosci. 5, 862–893 (2008).

J. Grinstead, M. Wilder, J. Olejniczak, D. Bogdanoff, G. Allen, K. Dang, and M. Forrest, “Shock-heated air radiation measurements at Lunar return conditions,” AIAA Pap. 1244, 092407 (2008).

2006 (1)

L. Braginsky and V. Shklover, “Light propagation in an imperfect photonic crystal,” Phys. Rev. B 73, 085107 (2006).
[CrossRef]

2002 (1)

S. Tikhodeev, A. Yablonskii, E. Muljarov, N. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
[CrossRef]

1999 (1)

D. Whittaker and I. Culshaw, “Scattering-matrix treatment of patterned multilayer photonic structures,” Phys. Rev. B 60, 2610–2618 (1999).
[CrossRef]

1998 (2)

Z. Liu, S. Tibuleac, D. Shin, P. Young, and R. Magnusson, “High-efficiency guided-mode resonance filter,” Opt. Lett. 23, 1556–1558 (1998).
[CrossRef]

A. Zakhidov, R. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. Dantas, J. Marti, and V. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

1996 (1)

1993 (2)

J. Shor, I. Grimberg, B. Weiss, and A. Kurtz, “Direct observation of porous SiC formed by anodization in HF,” Appl. Phys. Lett. 62, 2836–2838 (1993).
[CrossRef]

S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32, 2606–2613 (1993).
[CrossRef] [PubMed]

1990 (1)

M. Gale, K. Knop, and R. Morf, “Zero-order diffractive microstructures for security applications,” Proc. SPIE 1210, 83–89 (1990).
[CrossRef]

1972 (1)

M. Williams and E. Arakawa, “Optical properties of glassy carbon from 0 to 82 eV,” J. Appl. Phys. 43, 3460–3463 (1972).
[CrossRef]

Allen, G.

J. Grinstead, M. Wilder, J. Olejniczak, D. Bogdanoff, G. Allen, K. Dang, and M. Forrest, “Shock-heated air radiation measurements at Lunar return conditions,” AIAA Pap. 1244, 092407 (2008).

Arakawa, E.

M. Williams and E. Arakawa, “Optical properties of glassy carbon from 0 to 82 eV,” J. Appl. Phys. 43, 3460–3463 (1972).
[CrossRef]

Baughman, R.

A. Zakhidov, R. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. Dantas, J. Marti, and V. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

Bogdanoff, D.

J. Grinstead, M. Wilder, J. Olejniczak, D. Bogdanoff, G. Allen, K. Dang, and M. Forrest, “Shock-heated air radiation measurements at Lunar return conditions,” AIAA Pap. 1244, 092407 (2008).

Bose, D.

A. Brandis, C. Johnston, B. Cruden, D. Prabhu, and D. Bose, “Uncertainty analysis of Neqair and Hara predictions of air radiation measurements obtained in the East facility,” in 42nd AIAA Thermophysics Conference, (American Institute of Aeronautics & Astronautics (AIAA), 2011), pp. 1–14.

Braginsky, L.

N. Komarevskiy, L. Braginsky, V. Shklover, C. Hafner, and J. Lawson, “Fast numerical methods for the design of layered photonic structures with rough interfaces,” Opt. Express 19, 5489–5499 (2011).
[CrossRef] [PubMed]

N. Komarevskiy, V. Shklover, L. Braginsky, C. Hafner, O. Fabrichnaya, S. White, and J. Lawson, “Design of reflective, photonic shields for atmospheric reentry,” J. Electromagn. Anal. Appl. 3, 228–237 (2011).

V. Shklover, L. Braginsky, G. Witz, M. Mishrikey, and C. Hafner, “High-temperature photonic structures. Thermal barrier coatings, infrared sources and other applications,” J. Comput. Theor. Nanosci. 5, 862–893 (2008).

L. Braginsky and V. Shklover, “Light propagation in an imperfect photonic crystal,” Phys. Rev. B 73, 085107 (2006).
[CrossRef]

Brandis, A.

A. Brandis, C. Johnston, B. Cruden, D. Prabhu, and D. Bose, “Uncertainty analysis of Neqair and Hara predictions of air radiation measurements obtained in the East facility,” in 42nd AIAA Thermophysics Conference, (American Institute of Aeronautics & Astronautics (AIAA), 2011), pp. 1–14.

Cruden, B.

A. Brandis, C. Johnston, B. Cruden, D. Prabhu, and D. Bose, “Uncertainty analysis of Neqair and Hara predictions of air radiation measurements obtained in the East facility,” in 42nd AIAA Thermophysics Conference, (American Institute of Aeronautics & Astronautics (AIAA), 2011), pp. 1–14.

Cui, C.

A. Zakhidov, R. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. Dantas, J. Marti, and V. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

Culshaw, I.

D. Whittaker and I. Culshaw, “Scattering-matrix treatment of patterned multilayer photonic structures,” Phys. Rev. B 60, 2610–2618 (1999).
[CrossRef]

Dang, K.

J. Grinstead, M. Wilder, J. Olejniczak, D. Bogdanoff, G. Allen, K. Dang, and M. Forrest, “Shock-heated air radiation measurements at Lunar return conditions,” AIAA Pap. 1244, 092407 (2008).

Dantas, S.

A. Zakhidov, R. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. Dantas, J. Marti, and V. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

Fabrichnaya, O.

N. Komarevskiy, V. Shklover, L. Braginsky, C. Hafner, O. Fabrichnaya, S. White, and J. Lawson, “Design of reflective, photonic shields for atmospheric reentry,” J. Electromagn. Anal. Appl. 3, 228–237 (2011).

Forrest, M.

J. Grinstead, M. Wilder, J. Olejniczak, D. Bogdanoff, G. Allen, K. Dang, and M. Forrest, “Shock-heated air radiation measurements at Lunar return conditions,” AIAA Pap. 1244, 092407 (2008).

Fröhlich, J.

J. Fröhlich, “Evolutionary Optimization for Computational Electromagnetics,” Ph.D. thesis (ETH Zurich, IFH Laboratory, 1997).

Gale, M.

M. Gale, K. Knop, and R. Morf, “Zero-order diffractive microstructures for security applications,” Proc. SPIE 1210, 83–89 (1990).
[CrossRef]

Gippius, N.

S. Tikhodeev, A. Yablonskii, E. Muljarov, N. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Grimberg, I.

J. Shor, I. Grimberg, B. Weiss, and A. Kurtz, “Direct observation of porous SiC formed by anodization in HF,” Appl. Phys. Lett. 62, 2836–2838 (1993).
[CrossRef]

Grinstead, J.

J. Grinstead, M. Wilder, J. Olejniczak, D. Bogdanoff, G. Allen, K. Dang, and M. Forrest, “Shock-heated air radiation measurements at Lunar return conditions,” AIAA Pap. 1244, 092407 (2008).

Hafner, C.

N. Komarevskiy, V. Shklover, L. Braginsky, C. Hafner, O. Fabrichnaya, S. White, and J. Lawson, “Design of reflective, photonic shields for atmospheric reentry,” J. Electromagn. Anal. Appl. 3, 228–237 (2011).

N. Komarevskiy, L. Braginsky, V. Shklover, C. Hafner, and J. Lawson, “Fast numerical methods for the design of layered photonic structures with rough interfaces,” Opt. Express 19, 5489–5499 (2011).
[CrossRef] [PubMed]

V. Shklover, L. Braginsky, G. Witz, M. Mishrikey, and C. Hafner, “High-temperature photonic structures. Thermal barrier coatings, infrared sources and other applications,” J. Comput. Theor. Nanosci. 5, 862–893 (2008).

Iqbal, Z.

A. Zakhidov, R. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. Dantas, J. Marti, and V. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

Ishihara, T.

S. Tikhodeev, A. Yablonskii, E. Muljarov, N. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Joannopoulos, J.

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

Johnson, S.

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

Johnston, C.

A. Brandis, C. Johnston, B. Cruden, D. Prabhu, and D. Bose, “Uncertainty analysis of Neqair and Hara predictions of air radiation measurements obtained in the East facility,” in 42nd AIAA Thermophysics Conference, (American Institute of Aeronautics & Astronautics (AIAA), 2011), pp. 1–14.

Khayrullin, I.

A. Zakhidov, R. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. Dantas, J. Marti, and V. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

Knop, K.

M. Gale, K. Knop, and R. Morf, “Zero-order diffractive microstructures for security applications,” Proc. SPIE 1210, 83–89 (1990).
[CrossRef]

Komarevskiy, N.

N. Komarevskiy, L. Braginsky, V. Shklover, C. Hafner, and J. Lawson, “Fast numerical methods for the design of layered photonic structures with rough interfaces,” Opt. Express 19, 5489–5499 (2011).
[CrossRef] [PubMed]

N. Komarevskiy, V. Shklover, L. Braginsky, C. Hafner, O. Fabrichnaya, S. White, and J. Lawson, “Design of reflective, photonic shields for atmospheric reentry,” J. Electromagn. Anal. Appl. 3, 228–237 (2011).

Kurtz, A.

J. Shor, I. Grimberg, B. Weiss, and A. Kurtz, “Direct observation of porous SiC formed by anodization in HF,” Appl. Phys. Lett. 62, 2836–2838 (1993).
[CrossRef]

Lawson, J.

N. Komarevskiy, L. Braginsky, V. Shklover, C. Hafner, and J. Lawson, “Fast numerical methods for the design of layered photonic structures with rough interfaces,” Opt. Express 19, 5489–5499 (2011).
[CrossRef] [PubMed]

N. Komarevskiy, V. Shklover, L. Braginsky, C. Hafner, O. Fabrichnaya, S. White, and J. Lawson, “Design of reflective, photonic shields for atmospheric reentry,” J. Electromagn. Anal. Appl. 3, 228–237 (2011).

Li, L.

Liu, Z.

Magnusson, R.

Marti, J.

A. Zakhidov, R. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. Dantas, J. Marti, and V. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

Meade, R.

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

Mishrikey, M.

V. Shklover, L. Braginsky, G. Witz, M. Mishrikey, and C. Hafner, “High-temperature photonic structures. Thermal barrier coatings, infrared sources and other applications,” J. Comput. Theor. Nanosci. 5, 862–893 (2008).

Morf, R.

M. Gale, K. Knop, and R. Morf, “Zero-order diffractive microstructures for security applications,” Proc. SPIE 1210, 83–89 (1990).
[CrossRef]

Muljarov, E.

S. Tikhodeev, A. Yablonskii, E. Muljarov, N. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Olejniczak, J.

J. Grinstead, M. Wilder, J. Olejniczak, D. Bogdanoff, G. Allen, K. Dang, and M. Forrest, “Shock-heated air radiation measurements at Lunar return conditions,” AIAA Pap. 1244, 092407 (2008).

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).

Park, C.

C. Park, “Stagnation-region heating environment of the Galileo probe,” J. Thermophys. Heat Transfer 23, 417–424 (2009).
[CrossRef]

Prabhu, D.

A. Brandis, C. Johnston, B. Cruden, D. Prabhu, and D. Bose, “Uncertainty analysis of Neqair and Hara predictions of air radiation measurements obtained in the East facility,” in 42nd AIAA Thermophysics Conference, (American Institute of Aeronautics & Astronautics (AIAA), 2011), pp. 1–14.

Ralchenko, V.

A. Zakhidov, R. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. Dantas, J. Marti, and V. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

Shin, D.

Shklover, V.

N. Komarevskiy, L. Braginsky, V. Shklover, C. Hafner, and J. Lawson, “Fast numerical methods for the design of layered photonic structures with rough interfaces,” Opt. Express 19, 5489–5499 (2011).
[CrossRef] [PubMed]

N. Komarevskiy, V. Shklover, L. Braginsky, C. Hafner, O. Fabrichnaya, S. White, and J. Lawson, “Design of reflective, photonic shields for atmospheric reentry,” J. Electromagn. Anal. Appl. 3, 228–237 (2011).

V. Shklover, L. Braginsky, G. Witz, M. Mishrikey, and C. Hafner, “High-temperature photonic structures. Thermal barrier coatings, infrared sources and other applications,” J. Comput. Theor. Nanosci. 5, 862–893 (2008).

L. Braginsky and V. Shklover, “Light propagation in an imperfect photonic crystal,” Phys. Rev. B 73, 085107 (2006).
[CrossRef]

Shor, J.

J. Shor, I. Grimberg, B. Weiss, and A. Kurtz, “Direct observation of porous SiC formed by anodization in HF,” Appl. Phys. Lett. 62, 2836–2838 (1993).
[CrossRef]

Tibuleac, S.

Tikhodeev, S.

S. Tikhodeev, A. Yablonskii, E. Muljarov, N. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Wang, S.

Weiss, B.

J. Shor, I. Grimberg, B. Weiss, and A. Kurtz, “Direct observation of porous SiC formed by anodization in HF,” Appl. Phys. Lett. 62, 2836–2838 (1993).
[CrossRef]

White, S.

N. Komarevskiy, V. Shklover, L. Braginsky, C. Hafner, O. Fabrichnaya, S. White, and J. Lawson, “Design of reflective, photonic shields for atmospheric reentry,” J. Electromagn. Anal. Appl. 3, 228–237 (2011).

Whittaker, D.

D. Whittaker and I. Culshaw, “Scattering-matrix treatment of patterned multilayer photonic structures,” Phys. Rev. B 60, 2610–2618 (1999).
[CrossRef]

Wilder, M.

J. Grinstead, M. Wilder, J. Olejniczak, D. Bogdanoff, G. Allen, K. Dang, and M. Forrest, “Shock-heated air radiation measurements at Lunar return conditions,” AIAA Pap. 1244, 092407 (2008).

Williams, M.

M. Williams and E. Arakawa, “Optical properties of glassy carbon from 0 to 82 eV,” J. Appl. Phys. 43, 3460–3463 (1972).
[CrossRef]

Winn, J.

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

Witz, G.

V. Shklover, L. Braginsky, G. Witz, M. Mishrikey, and C. Hafner, “High-temperature photonic structures. Thermal barrier coatings, infrared sources and other applications,” J. Comput. Theor. Nanosci. 5, 862–893 (2008).

Yablonskii, A.

S. Tikhodeev, A. Yablonskii, E. Muljarov, N. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Young, P.

Zakhidov, A.

A. Zakhidov, R. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. Dantas, J. Marti, and V. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

AIAA Pap. (1)

J. Grinstead, M. Wilder, J. Olejniczak, D. Bogdanoff, G. Allen, K. Dang, and M. Forrest, “Shock-heated air radiation measurements at Lunar return conditions,” AIAA Pap. 1244, 092407 (2008).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. Shor, I. Grimberg, B. Weiss, and A. Kurtz, “Direct observation of porous SiC formed by anodization in HF,” Appl. Phys. Lett. 62, 2836–2838 (1993).
[CrossRef]

J. Appl. Phys. (1)

M. Williams and E. Arakawa, “Optical properties of glassy carbon from 0 to 82 eV,” J. Appl. Phys. 43, 3460–3463 (1972).
[CrossRef]

J. Comput. Theor. Nanosci. (1)

V. Shklover, L. Braginsky, G. Witz, M. Mishrikey, and C. Hafner, “High-temperature photonic structures. Thermal barrier coatings, infrared sources and other applications,” J. Comput. Theor. Nanosci. 5, 862–893 (2008).

J. Electromagn. Anal. Appl. (1)

N. Komarevskiy, V. Shklover, L. Braginsky, C. Hafner, O. Fabrichnaya, S. White, and J. Lawson, “Design of reflective, photonic shields for atmospheric reentry,” J. Electromagn. Anal. Appl. 3, 228–237 (2011).

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

J. Thermophys. Heat Transfer (1)

C. Park, “Stagnation-region heating environment of the Galileo probe,” J. Thermophys. Heat Transfer 23, 417–424 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (3)

S. Tikhodeev, A. Yablonskii, E. Muljarov, N. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
[CrossRef]

L. Braginsky and V. Shklover, “Light propagation in an imperfect photonic crystal,” Phys. Rev. B 73, 085107 (2006).
[CrossRef]

D. Whittaker and I. Culshaw, “Scattering-matrix treatment of patterned multilayer photonic structures,” Phys. Rev. B 60, 2610–2618 (1999).
[CrossRef]

Proc. SPIE (1)

M. Gale, K. Knop, and R. Morf, “Zero-order diffractive microstructures for security applications,” Proc. SPIE 1210, 83–89 (1990).
[CrossRef]

Science (1)

A. Zakhidov, R. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. Dantas, J. Marti, and V. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998).
[CrossRef] [PubMed]

Other (7)

A. Brandis, C. Johnston, B. Cruden, D. Prabhu, and D. Bose, “Uncertainty analysis of Neqair and Hara predictions of air radiation measurements obtained in the East facility,” in 42nd AIAA Thermophysics Conference, (American Institute of Aeronautics & Astronautics (AIAA), 2011), pp. 1–14.

Directionality can be obtained from simulation sets that are calibrated against shock tube data.

There is no mathematical proof for this observation, but it seems reasonable from the physical point of view, since no scattering occurs at planar interfaces.

J. Fröhlich, “Evolutionary Optimization for Computational Electromagnetics,” Ph.D. thesis (ETH Zurich, IFH Laboratory, 1997).

[Online]. Available: http://www.sopra-sa.com/

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).

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

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Figures (10)

Fig. 1
Fig. 1

(a)–(c) Experimental data of spectral radiation distribution, obtained at atmospheric re-entry relevant conditions [7] (a) red - experimental radiative spectrum in the range B=215–415 THz, blue dashed curve - spectrum smoothed with Gaussian window function of full width Δf = 10 THz.

Fig. 2
Fig. 2

Permittivity of (a) SiC taken from [12, 13] (b) GC taken from [14].

Fig. 3
Fig. 3

1D structures optimized with ES for reflection of radiation uν (a) SiC/air (b) GC/air (c) reflection spectra of the structures.

Fig. 4
Fig. 4

(a) 1D-periodic GC/air structure optimized for reflection at 345 THz. Two parameters d1 and d2 (GC and air thicknesses respectively) were optimized with ES (b) red solid curve - reflectivity of the optimal GC/air structure containing N=12 periods; blue dashed and green dotted curves - reflectivity of 3D GC/air structure (shown in the right inset), with different brick dimensions, w = 100 nm and w = 200 nm respectively; black solid curve -reflection of the inverse opal with the optimal period dx and sphere radii r.

Fig. 5
Fig. 5

(a) unit cell of GC inverse opal, formed by the fcc arrangement of spheres (b) reflectivity of GC inverse opal at f=345 THz, as a function of period dx and sphere radius r.

Fig. 6
Fig. 6

(a) Silicon carbide GMR structure, optimized for reflection of external radiation uν. Ambient material is air. Four parameters, marked with arrows were optimized with ES (b) reflection spectrum of the obtained optimal structure. The radiative spectrum uν is depicted above to show the correlation with RΣ.

Fig. 7
Fig. 7

(a) Silicon carbide GMR structure, optimized for reflection of external radiation uν. Ambient material is air. Four parameters, marked with arrows were optimized with ES (b) reflection spectrum of the obtained optimal structure. The radiative spectrum uν is depicted above to show the correlation with RΣ.

Fig. 8
Fig. 8

(a) 8-layered SiC woodpile structure (b) reflection spectrum of woodpile optimized for external radiation uν. Dips between 300–415 THz are the result of the excitation of the leaky modes.

Fig. 9
Fig. 9

Dispersion diagrams of the waveguide modes (of the woodpiles, presented in Table 1) in the empty lattice approximation (a) 4-layered woodpile, slab thickness 0.8 μm, 〈ε〉 = 2.46 (b) 8-layered woodpile, slab thickness 1.4 μm, 〈ε〉 = 2.39. Resonances in the Γ point between 215–415 THz are marked with numbers.

Fig. 10
Fig. 10

(a) SiC porous-reflector. Etched spheres are located in the center and corners of a rectangular unit cell (b) reflection spectrum of the porous-reflector with different number of porous layers, optimized for external radiation uν. Parameters are listed in Table 2. Black dashed curve - spectra of an inverse opal with r = dx/2 = 190 nm, center of PBG coincides with the central frequency f = 315 THz.

Tables (2)

Tables Icon

Table 1 Optimal parameters of woodpile obtained with the ES optimizer for reflectivity in B=215–415 THz and sensitivity of the structures to geometrical imperfections

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Table 2 Optimal parameters of a porous-reflector obtained with the ES optimizer for re-flectivity in B=215–415 THz and sensitivity of the structures to geometrical imperfections

Equations (9)

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R u ν = R Σ u ν d ν u tot , u tot = u ν d ν ,
R Σ = 0.5 ( R s + R p ) ,
R s , p = R 0 s , p + D i s , p , i = ± 1 , ± 2 ,
R = R Σ d ν Δ ν .
Par = Par opt ( 2 η ζ η + 1 ) ,
δ i = R u ν R u ν i , i = 1 , , M
δ ¯ = δ i M = R u ν R u ν i M ,
δ max = max [ δ 1 , δ 2 , , δ M ] .
T ~ exp ( 4 Δ / S d ( 1 β δ V ¯ 2 ) ) ,

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