Abstract

Wavelength-selective infrared (IR) absorptance of modified complex gratings of heavily doped silicon with nanoscale features is studied by a finite-difference time-domain numerical scheme. The purpose of this work is to demonstrate the possibility of using complex gratings and nanoscale surface features to modify far-field radiative properties. By properly choosing the carrier concentration and geometry, silicon complex gratings exhibit a broadband absorptance peak resulting from the excitation of surface plasmon polaritons. Meanwhile, the absorptance of four modified complex gratings with attached features has been numerically investigated for their impact. First, the first peaks of the absorptance spectra of gratings due to Wood’s anomaly remain unchanged; the second peaks shift toward longer wavelengths in modified complex gratings, as compared with complex gratings without attached features. The modified complex gratings with attached features on both sides of the ridges have the most obvious effect on the absorptance spectral shift. Second, the spectral absorptance curves of complex gratings with square features in three sizes (100, 200, and 300nm) are compared and show that the peak wavelength shifts toward longer wavelengths with enlarged feature size. These combined effects of doped silicon, complex gratings, and the addition of submicrometer-sized features to grating side walls can be used for further tailoring thermal radiative properties, which may be very useful for enhancing the performance of IR detectors.

© 2011 Optical Society of America

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References

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  1. Z. M. Zhang, Nano/Microscale Heat Transfer (McGraw-Hill, 2007).
  2. P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324, 549–551 (1986).
    [CrossRef]
  3. P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. I. Doped silicon: the normal direction,” Phys. Rev. B 37, 10795–10802(1988).
    [CrossRef]
  4. J. Le Gall, M. Olivier, and J. J. Greffet, “Experimental and theoretical study of reflection and coherent thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55, 10105–10114 (1997).
    [CrossRef]
  5. J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
    [CrossRef] [PubMed]
  6. Y. B. Chen and Z. M. Zhang, “Heavily doped silicon complex gratings as wavelength-selective absorbing surfaces,” J. Phys. D 41, 095406 (2008).
    [CrossRef]
  7. W. C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134–11138 (2000).
    [CrossRef]
  8. A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Excitation of remarkably nondispersive surface plasmons on a nondiffracting, dual-pitch metal grating,” Appl. Phys. Lett. 80, 2410–2412 (2002).
    [CrossRef]
  9. M. Laroche, F. Marquier, R. Carminati, and J. J. Greffet, “Tailoring silicon radiative properties,” Opt. Commun. 250, 316–320(2005).
    [CrossRef]
  10. Y.-B. Chen, J.-S. Chen, and P.-F. Hsu, “Impacts of geometric modifications on infrared optical responses of metallic slit arrays,” Opt. Express 17, 9789–9803 (2009).
    [CrossRef] [PubMed]
  11. K. Park, B. J. Lee, C. Fu, and Z. M. Zhang, “Study of the surface and bulk polaritons with a negative index metamaterial,” J. Opt. Soc. Am. B 22, 1016–1023 (2005).
    [CrossRef]
  12. F. Marquier, K. Joulain, J. P. Mulet, R. Carminati, and J. J. Greffet, “Engineering infrared emission properties of silicon in the near field and the far field,” Opt. Commun. 237, 379–388 (2004).
    [CrossRef]
  13. S. Basu, B. J. Lee, and Z. M. Zhang, “Infrared radiative properties of heavily doped silicon at room temperature,” J. Heat Transfer 132, 023301 (2010).
    [CrossRef]
  14. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).
  15. K. Fu and P.-F. Hsu, “Modeling the radiative properties of microscale random roughness surfaces,” J. Heat Transfer 129, 71–78(2007).
    [CrossRef]
  16. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
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  17. K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Eletromagnetics (CRC Press, 1993).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010 (1)

S. Basu, B. J. Lee, and Z. M. Zhang, “Infrared radiative properties of heavily doped silicon at room temperature,” J. Heat Transfer 132, 023301 (2010).
[CrossRef]

2009 (1)

2008 (1)

Y. B. Chen and Z. M. Zhang, “Heavily doped silicon complex gratings as wavelength-selective absorbing surfaces,” J. Phys. D 41, 095406 (2008).
[CrossRef]

2007 (3)

K. Fu and P.-F. Hsu, “Modeling the radiative properties of microscale random roughness surfaces,” J. Heat Transfer 129, 71–78(2007).
[CrossRef]

K. Fu and P.-F. Hsu, “Radiative properties of gold surfaces with one-dimensional microscale Gaussian random roughness,” Int. J. Thermophys. 28, 598–615 (2007).
[CrossRef]

Y. B. Chen, Z. M. Zhang, and P. J. Timans, “Radiative properties of patterned wafers with nanoscale linewidth,” J. Heat Transfer 129, 79–90 (2007).
[CrossRef]

2005 (2)

M. Laroche, F. Marquier, R. Carminati, and J. J. Greffet, “Tailoring silicon radiative properties,” Opt. Commun. 250, 316–320(2005).
[CrossRef]

K. Park, B. J. Lee, C. Fu, and Z. M. Zhang, “Study of the surface and bulk polaritons with a negative index metamaterial,” J. Opt. Soc. Am. B 22, 1016–1023 (2005).
[CrossRef]

2004 (1)

F. Marquier, K. Joulain, J. P. Mulet, R. Carminati, and J. J. Greffet, “Engineering infrared emission properties of silicon in the near field and the far field,” Opt. Commun. 237, 379–388 (2004).
[CrossRef]

2002 (2)

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
[CrossRef] [PubMed]

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Excitation of remarkably nondispersive surface plasmons on a nondiffracting, dual-pitch metal grating,” Appl. Phys. Lett. 80, 2410–2412 (2002).
[CrossRef]

2000 (1)

W. C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134–11138 (2000).
[CrossRef]

1997 (1)

J. Le Gall, M. Olivier, and J. J. Greffet, “Experimental and theoretical study of reflection and coherent thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55, 10105–10114 (1997).
[CrossRef]

1996 (1)

1994 (1)

1988 (1)

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. I. Doped silicon: the normal direction,” Phys. Rev. B 37, 10795–10802(1988).
[CrossRef]

1986 (1)

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324, 549–551 (1986).
[CrossRef]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

1965 (1)

Basu, S.

S. Basu, B. J. Lee, and Z. M. Zhang, “Infrared radiative properties of heavily doped silicon at room temperature,” J. Heat Transfer 132, 023301 (2010).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1998).
[CrossRef]

Carminati, R.

M. Laroche, F. Marquier, R. Carminati, and J. J. Greffet, “Tailoring silicon radiative properties,” Opt. Commun. 250, 316–320(2005).
[CrossRef]

F. Marquier, K. Joulain, J. P. Mulet, R. Carminati, and J. J. Greffet, “Engineering infrared emission properties of silicon in the near field and the far field,” Opt. Commun. 237, 379–388 (2004).
[CrossRef]

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
[CrossRef] [PubMed]

Chateau, N.

Chen, J.-S.

Chen, Y.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
[CrossRef] [PubMed]

Chen, Y. B.

Y. B. Chen and Z. M. Zhang, “Heavily doped silicon complex gratings as wavelength-selective absorbing surfaces,” J. Phys. D 41, 095406 (2008).
[CrossRef]

Y. B. Chen, Z. M. Zhang, and P. J. Timans, “Radiative properties of patterned wafers with nanoscale linewidth,” J. Heat Transfer 129, 79–90 (2007).
[CrossRef]

Chen, Y.-B.

Fu, C.

Fu, K.

K. Fu and P.-F. Hsu, “Radiative properties of gold surfaces with one-dimensional microscale Gaussian random roughness,” Int. J. Thermophys. 28, 598–615 (2007).
[CrossRef]

K. Fu and P.-F. Hsu, “Modeling the radiative properties of microscale random roughness surfaces,” J. Heat Transfer 129, 71–78(2007).
[CrossRef]

Gebhart, B.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. I. Doped silicon: the normal direction,” Phys. Rev. B 37, 10795–10802(1988).
[CrossRef]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324, 549–551 (1986).
[CrossRef]

Greffet, J. J.

M. Laroche, F. Marquier, R. Carminati, and J. J. Greffet, “Tailoring silicon radiative properties,” Opt. Commun. 250, 316–320(2005).
[CrossRef]

F. Marquier, K. Joulain, J. P. Mulet, R. Carminati, and J. J. Greffet, “Engineering infrared emission properties of silicon in the near field and the far field,” Opt. Commun. 237, 379–388 (2004).
[CrossRef]

J. Le Gall, M. Olivier, and J. J. Greffet, “Experimental and theoretical study of reflection and coherent thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55, 10105–10114 (1997).
[CrossRef]

Greffet, J.-J.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
[CrossRef] [PubMed]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

Hesketh, P. J.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. I. Doped silicon: the normal direction,” Phys. Rev. B 37, 10795–10802(1988).
[CrossRef]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324, 549–551 (1986).
[CrossRef]

Hessel, A.

Hibbins, A. P.

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Excitation of remarkably nondispersive surface plasmons on a nondiffracting, dual-pitch metal grating,” Appl. Phys. Lett. 80, 2410–2412 (2002).
[CrossRef]

Hsu, P.-F.

Y.-B. Chen, J.-S. Chen, and P.-F. Hsu, “Impacts of geometric modifications on infrared optical responses of metallic slit arrays,” Opt. Express 17, 9789–9803 (2009).
[CrossRef] [PubMed]

K. Fu and P.-F. Hsu, “Modeling the radiative properties of microscale random roughness surfaces,” J. Heat Transfer 129, 71–78(2007).
[CrossRef]

K. Fu and P.-F. Hsu, “Radiative properties of gold surfaces with one-dimensional microscale Gaussian random roughness,” Int. J. Thermophys. 28, 598–615 (2007).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1998).
[CrossRef]

Hugonin, J.-P.

Joulain, K.

F. Marquier, K. Joulain, J. P. Mulet, R. Carminati, and J. J. Greffet, “Engineering infrared emission properties of silicon in the near field and the far field,” Opt. Commun. 237, 379–388 (2004).
[CrossRef]

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
[CrossRef] [PubMed]

Kunz, K. S.

K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Eletromagnetics (CRC Press, 1993).

Laroche, M.

M. Laroche, F. Marquier, R. Carminati, and J. J. Greffet, “Tailoring silicon radiative properties,” Opt. Commun. 250, 316–320(2005).
[CrossRef]

Lawrence, C. R.

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Excitation of remarkably nondispersive surface plasmons on a nondiffracting, dual-pitch metal grating,” Appl. Phys. Lett. 80, 2410–2412 (2002).
[CrossRef]

Le Gall, J.

J. Le Gall, M. Olivier, and J. J. Greffet, “Experimental and theoretical study of reflection and coherent thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55, 10105–10114 (1997).
[CrossRef]

Lee, B. J.

S. Basu, B. J. Lee, and Z. M. Zhang, “Infrared radiative properties of heavily doped silicon at room temperature,” J. Heat Transfer 132, 023301 (2010).
[CrossRef]

K. Park, B. J. Lee, C. Fu, and Z. M. Zhang, “Study of the surface and bulk polaritons with a negative index metamaterial,” J. Opt. Soc. Am. B 22, 1016–1023 (2005).
[CrossRef]

Li, L.

Luebbers, R. J.

K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Eletromagnetics (CRC Press, 1993).

Mainguy, S.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
[CrossRef] [PubMed]

Marquier, F.

M. Laroche, F. Marquier, R. Carminati, and J. J. Greffet, “Tailoring silicon radiative properties,” Opt. Commun. 250, 316–320(2005).
[CrossRef]

F. Marquier, K. Joulain, J. P. Mulet, R. Carminati, and J. J. Greffet, “Engineering infrared emission properties of silicon in the near field and the far field,” Opt. Commun. 237, 379–388 (2004).
[CrossRef]

Mulet, J. P.

F. Marquier, K. Joulain, J. P. Mulet, R. Carminati, and J. J. Greffet, “Engineering infrared emission properties of silicon in the near field and the far field,” Opt. Commun. 237, 379–388 (2004).
[CrossRef]

Mulet, J.-P.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
[CrossRef] [PubMed]

Oliner, A. A.

Olivier, M.

J. Le Gall, M. Olivier, and J. J. Greffet, “Experimental and theoretical study of reflection and coherent thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55, 10105–10114 (1997).
[CrossRef]

Park, K.

Preist, T. W.

W. C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134–11138 (2000).
[CrossRef]

Sambles, J. R.

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Excitation of remarkably nondispersive surface plasmons on a nondiffracting, dual-pitch metal grating,” Appl. Phys. Lett. 80, 2410–2412 (2002).
[CrossRef]

Sambles, R. J.

W. C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134–11138 (2000).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

Tan, W. C.

W. C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134–11138 (2000).
[CrossRef]

Timans, P. J.

Y. B. Chen, Z. M. Zhang, and P. J. Timans, “Radiative properties of patterned wafers with nanoscale linewidth,” J. Heat Transfer 129, 79–90 (2007).
[CrossRef]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

Zemel, J. N.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. I. Doped silicon: the normal direction,” Phys. Rev. B 37, 10795–10802(1988).
[CrossRef]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324, 549–551 (1986).
[CrossRef]

Zhang, Z. M.

S. Basu, B. J. Lee, and Z. M. Zhang, “Infrared radiative properties of heavily doped silicon at room temperature,” J. Heat Transfer 132, 023301 (2010).
[CrossRef]

Y. B. Chen and Z. M. Zhang, “Heavily doped silicon complex gratings as wavelength-selective absorbing surfaces,” J. Phys. D 41, 095406 (2008).
[CrossRef]

Y. B. Chen, Z. M. Zhang, and P. J. Timans, “Radiative properties of patterned wafers with nanoscale linewidth,” J. Heat Transfer 129, 79–90 (2007).
[CrossRef]

K. Park, B. J. Lee, C. Fu, and Z. M. Zhang, “Study of the surface and bulk polaritons with a negative index metamaterial,” J. Opt. Soc. Am. B 22, 1016–1023 (2005).
[CrossRef]

Z. M. Zhang, Nano/Microscale Heat Transfer (McGraw-Hill, 2007).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Excitation of remarkably nondispersive surface plasmons on a nondiffracting, dual-pitch metal grating,” Appl. Phys. Lett. 80, 2410–2412 (2002).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

Int. J. Thermophys. (1)

K. Fu and P.-F. Hsu, “Radiative properties of gold surfaces with one-dimensional microscale Gaussian random roughness,” Int. J. Thermophys. 28, 598–615 (2007).
[CrossRef]

J. Heat Transfer (3)

Y. B. Chen, Z. M. Zhang, and P. J. Timans, “Radiative properties of patterned wafers with nanoscale linewidth,” J. Heat Transfer 129, 79–90 (2007).
[CrossRef]

S. Basu, B. J. Lee, and Z. M. Zhang, “Infrared radiative properties of heavily doped silicon at room temperature,” J. Heat Transfer 132, 023301 (2010).
[CrossRef]

K. Fu and P.-F. Hsu, “Modeling the radiative properties of microscale random roughness surfaces,” J. Heat Transfer 129, 71–78(2007).
[CrossRef]

J. Opt. Soc. Am. A (2)

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

J. Phys. D (1)

Y. B. Chen and Z. M. Zhang, “Heavily doped silicon complex gratings as wavelength-selective absorbing surfaces,” J. Phys. D 41, 095406 (2008).
[CrossRef]

Nature (2)

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324, 549–551 (1986).
[CrossRef]

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
[CrossRef] [PubMed]

Opt. Commun. (2)

M. Laroche, F. Marquier, R. Carminati, and J. J. Greffet, “Tailoring silicon radiative properties,” Opt. Commun. 250, 316–320(2005).
[CrossRef]

F. Marquier, K. Joulain, J. P. Mulet, R. Carminati, and J. J. Greffet, “Engineering infrared emission properties of silicon in the near field and the far field,” Opt. Commun. 237, 379–388 (2004).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (3)

W. C. Tan, T. W. Preist, and R. J. Sambles, “Resonant tunneling of light through thin metal films via strongly localized surface plasmons,” Phys. Rev. B 62, 11134–11138 (2000).
[CrossRef]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. I. Doped silicon: the normal direction,” Phys. Rev. B 37, 10795–10802(1988).
[CrossRef]

J. Le Gall, M. Olivier, and J. J. Greffet, “Experimental and theoretical study of reflection and coherent thermal emission by a SiC grating supporting a surface-phonon polariton,” Phys. Rev. B 55, 10105–10114 (1997).
[CrossRef]

Other (4)

Z. M. Zhang, Nano/Microscale Heat Transfer (McGraw-Hill, 2007).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, 1998).
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000).

K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Eletromagnetics (CRC Press, 1993).

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Figures (11)

Fig. 1
Fig. 1

Schematics of simple and the complex gratings, where Λ is the grating period, and f, g, and h are the widths of the ridges and grooves, height of the ridges, respectively. (a) TM wave incidence on a simple grating; (b) complex grating I; (c) complex grating II.

Fig. 2
Fig. 2

Schematics of four modified complex gratings, where a represents the square feature size. (a) Modified complex grating I-a; (b) modified complex grating I-b; (c) modified complex grating I-c; (d) modified complex gratings I-d and I-e.

Fig. 3
Fig. 3

Spectral absorptance of plain heavily doped silicon at normal incidence. (a) Boron-doped silicon (p-type); (b) phosphorous-doped silicon (n-type).

Fig. 4
Fig. 4

Spectral absorptance of simple gratings made of p-type heavily doped silicon.

Fig. 5
Fig. 5

Spectral absorptance of n-type silicon complex grating I and complex grating II (complex grating I with h = 5.2 μm , complex grating II with h = 5.2 , 4.5 μm ).

Fig. 6
Fig. 6

Spectral absorptance of n-type silicon complex grating I with different periods.

Fig. 7
Fig. 7

Comparisons of spectral absorptance between complex grating I and five modified complex gratings. (a) Complex grating I and modified complex gratings I-a and I-b; (b) complex grating I and modified complex gratings I-c, I-d ( f 2 = Λ / 6 , g 1 = g 2 = Λ / 6 ), and I-e ( f 2 = Λ / 18 , g 1 = g 2 = 4 Λ / 18 ).

Fig. 8
Fig. 8

Spectral absorptance of modified complex grating I-d with different square feature sizes (in which case a = 0 is complex grating I).

Fig. 9
Fig. 9

Poynting vectors for modified complex grating I-d at λ = 10.3 μm .

Fig. 10
Fig. 10

Magnitude square of the complex magnetic field for modified complex grating I-d at λ = 10.3 μm . (a) Peak position of a wave period; (b)  1 / 4 wave period after the peak position; (c)  1 / 2 wave period after the peak position.

Fig. 11
Fig. 11

Magnitude square of the complex magnetic field for modified complex grating I-e at λ = 9.8 μm .

Equations (9)

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

ς ( ω ) = ( n + i κ ) 2 = ς ω p 2 ω ( ω + i γ c ) ,
α λ = 4 n Si ( n Si + 1 ) 2 + κ Si 2 .
ε E t = × H σ E J S ,
μ H t = × E σ * H M S ,
H y n ( i , j ) = μ σ * Δ t / 2 μ + σ * Δ t / 2 H y n 1 ( i , j ) + Δ t μ + σ * Δ t / 2 × { 1 Δ x [ E z n 1 / 2 ( i + 1 / 2 , j ) E z n 1 / 2 ( i 1 / 2 , j ) ] 1 Δ z [ E x n 1 / 2 ( i , j + 1 / 2 ) E x n 1 / 2 ( i , j 1 / 2 ) ] } ,
E x n + 1 / 2 ( i , j + 1 / 2 ) = ε σ Δ t / 2 ε + σ Δ t / 2 E x n 1 / 2 ( i , j + 1 / 2 ) Δ t ( ε + σ Δ t / 2 ) Δ z [ H y n ( i , j + 1 ) H y n ( i , j ) ] ,
E z n + 1 / 2 ( i + 1 / 2 , j ) = ε σ Δ t / 2 ε + σ Δ t / 2 E z n 1 / 2 ( i + 1 / 2 , j ) + Δ t ( ε + σ Δ t / 2 ) Δ x [ H y n ( i + 1 , j ) H y n ( i , j ) ] ,
E z n + 1 ( i ) = ε σ Δ t / 2 ε o ε + σ Δ t / 2 ε o + χ 0 E z n ( i ) + 1 ε + σ Δ t / 2 ε o + χ 0 m = 0 n 1 E z n m ( i ) Δ χ m Δ t ε + σ Δ t / 2 ε o + χ 0 [ H y n 1 / 2 ( i + 1 / 2 ) H y n 1 / 2 ( i 1 / 2 ) ] 1 ε o Δ x ,
S = 0.5 Re ( E × H * ) ,

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