Abstract

The Rayleigh-Modal method is used to calculate the electromagnetic field within the grooves of a perfectly conducting, rectangular-shaped one-dimensional diffraction grating. An enhancement coefficient (η) is introduced in order to quantify such an energy concentration. Accordingly, η>1 means that the amount of electromagnetic energy present within the grooves is larger than that one will have, over the same volume, if the diffraction grating is replaced by a perfectly reflecting mirror. The results in this paper show that η can be as large as several decades at certain, often narrow, ranges of wavelengths. However, it reduces to approximately 20% under sunlight illumination. In this latter case, such values are achieved when the optical spacing between the grooves dn is greater than 500 nm, where d is the groove spacing and n is the refractive index of the substance within the grooves. For dn smaller than 500 nm the enhancement coefficient turns negligibly small.

© 2011 Optical Society of America

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  1. N. E. Glass and A. A. Maradudin, “Diffraction of light by a bigrating: surface polarization resonances and electric field enhancements,” Phys. Rev. B27, 5150–5153 (1983).
  2. A. Wirgin and A. A. Maradudin, “Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light,” Phys. Rev. B31, 5573–5576 (1985).
  3. H. Lochbihler and R. A. Depine, “Highly conducting wire gratings in the resonance region,” Appl. Opt. 32, 3459–3465 (1993).
    [CrossRef]
  4. R. A. Depine and D. C. Skigin, “Scattering from metallic surfaces having a finite number of rectangular grooves,” J. Opt. Soc. Am. A11, 2844–2850 (1993).
  5. D. Crouse, “Numerical modeling and electromagnetic resonance modes in complex grating structures and optoelectronic device applications,” IEEE Trans. Electron Devices 52, 2365–2373 (2005).
    [CrossRef]
  6. Y.-C. Lee, C.-F. Huang, J.-Y. Chang, and M. L. Wu, “Enhanced light trapping based on guided mode resonance effect for thin-film silicon solar cells with two filling factor gratings,” Opt. Express 16, 7969–7975 (2008).
    [CrossRef]
  7. F. Llopis, I. Tobías, and M. M. Jakas, “Light intensity enhancement inside the grooves of metallic gratings,” J. Opt. Soc. Am. B27, 1198–2006 (2010).
  8. W. Wang, S. Wu, K. Reinhardt, Y. Lu, and S. Chen, “Broadband light absorption enhancement in thin-film silicon solar cells,” Nano Lett. 10, 2012–2018 (2010).
    [CrossRef]
  9. M. M. Jakas and F. Llopis, “Light trapping within the grooves of diffraction gratings,” Paper presented at 29th Progress in Electromagnetics Research Symposium, Marrakesh, Morocco, 20–23 March 2011.
  10. J. A. Kong, Electromagnetic Wave Theory (John Wiley & Sons, 1986).
  11. J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, 1962).
  12. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computation (Cambridge University, 1992).
  13. H. R. Philipp and E. A. Taft, “Optical constants of silicon in the region 1 to 10 ev,” Phys. Rev. 120, 37–38 (1960).
    [CrossRef]
  14. The solar spectral irradiance are obtained by fitting an analytical expression to data for Air Mass 1.5, available from: http://rredc.nrel.gov/solar/spectra/am1.5/

2010 (2)

F. Llopis, I. Tobías, and M. M. Jakas, “Light intensity enhancement inside the grooves of metallic gratings,” J. Opt. Soc. Am. B27, 1198–2006 (2010).

W. Wang, S. Wu, K. Reinhardt, Y. Lu, and S. Chen, “Broadband light absorption enhancement in thin-film silicon solar cells,” Nano Lett. 10, 2012–2018 (2010).
[CrossRef]

2008 (1)

2005 (1)

D. Crouse, “Numerical modeling and electromagnetic resonance modes in complex grating structures and optoelectronic device applications,” IEEE Trans. Electron Devices 52, 2365–2373 (2005).
[CrossRef]

1993 (2)

R. A. Depine and D. C. Skigin, “Scattering from metallic surfaces having a finite number of rectangular grooves,” J. Opt. Soc. Am. A11, 2844–2850 (1993).

H. Lochbihler and R. A. Depine, “Highly conducting wire gratings in the resonance region,” Appl. Opt. 32, 3459–3465 (1993).
[CrossRef]

1992 (1)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computation (Cambridge University, 1992).

1986 (1)

J. A. Kong, Electromagnetic Wave Theory (John Wiley & Sons, 1986).

1985 (1)

A. Wirgin and A. A. Maradudin, “Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light,” Phys. Rev. B31, 5573–5576 (1985).

1983 (1)

N. E. Glass and A. A. Maradudin, “Diffraction of light by a bigrating: surface polarization resonances and electric field enhancements,” Phys. Rev. B27, 5150–5153 (1983).

1962 (1)

J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, 1962).

1960 (1)

H. R. Philipp and E. A. Taft, “Optical constants of silicon in the region 1 to 10 ev,” Phys. Rev. 120, 37–38 (1960).
[CrossRef]

Chang, J.-Y.

Chen, S.

W. Wang, S. Wu, K. Reinhardt, Y. Lu, and S. Chen, “Broadband light absorption enhancement in thin-film silicon solar cells,” Nano Lett. 10, 2012–2018 (2010).
[CrossRef]

Crouse, D.

D. Crouse, “Numerical modeling and electromagnetic resonance modes in complex grating structures and optoelectronic device applications,” IEEE Trans. Electron Devices 52, 2365–2373 (2005).
[CrossRef]

Depine, R. A.

R. A. Depine and D. C. Skigin, “Scattering from metallic surfaces having a finite number of rectangular grooves,” J. Opt. Soc. Am. A11, 2844–2850 (1993).

H. Lochbihler and R. A. Depine, “Highly conducting wire gratings in the resonance region,” Appl. Opt. 32, 3459–3465 (1993).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computation (Cambridge University, 1992).

Glass, N. E.

N. E. Glass and A. A. Maradudin, “Diffraction of light by a bigrating: surface polarization resonances and electric field enhancements,” Phys. Rev. B27, 5150–5153 (1983).

Huang, C.-F.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, 1962).

Jakas, M. M.

M. M. Jakas and F. Llopis, “Light trapping within the grooves of diffraction gratings,” Paper presented at 29th Progress in Electromagnetics Research Symposium, Marrakesh, Morocco, 20–23 March 2011.

F. Llopis, I. Tobías, and M. M. Jakas, “Light intensity enhancement inside the grooves of metallic gratings,” J. Opt. Soc. Am. B27, 1198–2006 (2010).

Kong, J. A.

J. A. Kong, Electromagnetic Wave Theory (John Wiley & Sons, 1986).

Lee, Y.-C.

Llopis, F.

M. M. Jakas and F. Llopis, “Light trapping within the grooves of diffraction gratings,” Paper presented at 29th Progress in Electromagnetics Research Symposium, Marrakesh, Morocco, 20–23 March 2011.

F. Llopis, I. Tobías, and M. M. Jakas, “Light intensity enhancement inside the grooves of metallic gratings,” J. Opt. Soc. Am. B27, 1198–2006 (2010).

Lochbihler, H.

Lu, Y.

W. Wang, S. Wu, K. Reinhardt, Y. Lu, and S. Chen, “Broadband light absorption enhancement in thin-film silicon solar cells,” Nano Lett. 10, 2012–2018 (2010).
[CrossRef]

Maradudin, A. A.

A. Wirgin and A. A. Maradudin, “Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light,” Phys. Rev. B31, 5573–5576 (1985).

N. E. Glass and A. A. Maradudin, “Diffraction of light by a bigrating: surface polarization resonances and electric field enhancements,” Phys. Rev. B27, 5150–5153 (1983).

Philipp, H. R.

H. R. Philipp and E. A. Taft, “Optical constants of silicon in the region 1 to 10 ev,” Phys. Rev. 120, 37–38 (1960).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computation (Cambridge University, 1992).

Reinhardt, K.

W. Wang, S. Wu, K. Reinhardt, Y. Lu, and S. Chen, “Broadband light absorption enhancement in thin-film silicon solar cells,” Nano Lett. 10, 2012–2018 (2010).
[CrossRef]

Skigin, D. C.

R. A. Depine and D. C. Skigin, “Scattering from metallic surfaces having a finite number of rectangular grooves,” J. Opt. Soc. Am. A11, 2844–2850 (1993).

Taft, E. A.

H. R. Philipp and E. A. Taft, “Optical constants of silicon in the region 1 to 10 ev,” Phys. Rev. 120, 37–38 (1960).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computation (Cambridge University, 1992).

Tobías, I.

F. Llopis, I. Tobías, and M. M. Jakas, “Light intensity enhancement inside the grooves of metallic gratings,” J. Opt. Soc. Am. B27, 1198–2006 (2010).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computation (Cambridge University, 1992).

Wang, W.

W. Wang, S. Wu, K. Reinhardt, Y. Lu, and S. Chen, “Broadband light absorption enhancement in thin-film silicon solar cells,” Nano Lett. 10, 2012–2018 (2010).
[CrossRef]

Wirgin, A.

A. Wirgin and A. A. Maradudin, “Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light,” Phys. Rev. B31, 5573–5576 (1985).

Wu, M. L.

Wu, S.

W. Wang, S. Wu, K. Reinhardt, Y. Lu, and S. Chen, “Broadband light absorption enhancement in thin-film silicon solar cells,” Nano Lett. 10, 2012–2018 (2010).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Electron Devices (1)

D. Crouse, “Numerical modeling and electromagnetic resonance modes in complex grating structures and optoelectronic device applications,” IEEE Trans. Electron Devices 52, 2365–2373 (2005).
[CrossRef]

J. Opt. Soc. Am. (2)

R. A. Depine and D. C. Skigin, “Scattering from metallic surfaces having a finite number of rectangular grooves,” J. Opt. Soc. Am. A11, 2844–2850 (1993).

F. Llopis, I. Tobías, and M. M. Jakas, “Light intensity enhancement inside the grooves of metallic gratings,” J. Opt. Soc. Am. B27, 1198–2006 (2010).

Nano Lett. (1)

W. Wang, S. Wu, K. Reinhardt, Y. Lu, and S. Chen, “Broadband light absorption enhancement in thin-film silicon solar cells,” Nano Lett. 10, 2012–2018 (2010).
[CrossRef]

Opt. Express (1)

Phys. Rev. (3)

H. R. Philipp and E. A. Taft, “Optical constants of silicon in the region 1 to 10 ev,” Phys. Rev. 120, 37–38 (1960).
[CrossRef]

N. E. Glass and A. A. Maradudin, “Diffraction of light by a bigrating: surface polarization resonances and electric field enhancements,” Phys. Rev. B27, 5150–5153 (1983).

A. Wirgin and A. A. Maradudin, “Resonant enhancement of the electric field in the grooves of bare metallic gratings exposed to S-polarized light,” Phys. Rev. B31, 5573–5576 (1985).

Other (5)

The solar spectral irradiance are obtained by fitting an analytical expression to data for Air Mass 1.5, available from: http://rredc.nrel.gov/solar/spectra/am1.5/

M. M. Jakas and F. Llopis, “Light trapping within the grooves of diffraction gratings,” Paper presented at 29th Progress in Electromagnetics Research Symposium, Marrakesh, Morocco, 20–23 March 2011.

J. A. Kong, Electromagnetic Wave Theory (John Wiley & Sons, 1986).

J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, 1962).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computation (Cambridge University, 1992).

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