Abstract

A detailed study of light absorption by silver gratings having two-dimensional periodicity is presented for structures constructed either of channels or of holes with subwavelength dimensions. Rigorous numerical modelling shows a systematic difference between the two structures: hole (cavity) gratings can strongly absorb light provided the cavity is sufficiently deep, when compared to the wavelength, whereas very thin channel gratings can induce total absorption. A detailed analysis is given in the limit when the period tends towards zero, and an explanation of the differences in behavior is presented using the properties of effective optical index of the metamaterial layer that substitutes the periodical structure in the limit when the period tend to zero.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Phylos. Mag.4, 396–402 (1902).
  2. U. Fano, “The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld’s waves),” J. Opt. Soc. Am.31(3), 213–222 (1941).
    [CrossRef]
  3. M. C. Hutley and D. Maystre, “Total absorption of light by a diffraction grating,” Opt. Commun.19(3), 431–436 (1976).
    [CrossRef]
  4. D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten, “Anomalous low-frequency Raman scattering from rough metal surfaces and the origin of the surface-enhanced Raman scattering,” Phys. Rev. Lett.45(5), 355–358 (1980).
    [CrossRef]
  5. R. Reinisch and M. Nevière, “Electromagnetic theory of diffraction in nonlinear optics and surface enhanced nonlinear optical effects,” Phys. Rev. B28(4), 1870–1885 (1983).
    [CrossRef]
  6. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature391(6668), 667–669 (1998).
    [CrossRef]
  7. J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett.100(6), 066408 (2008).
    [CrossRef] [PubMed]
  8. E. Popov, S. Enoch, and N. Bonod, “Absorption of light by extremely shallow metallic gratings: metamaterial behavior,” Opt. Express17(8), 6770–6781 (2009).
    [CrossRef] [PubMed]
  9. R.-L. Chern, Y.-T. Chen, and H.-Y. Lin, “Anomalous optical absorption in metallic gratings with subwavelength slits,” Opt. Express18(19), 19510–19521 (2010).
    [CrossRef] [PubMed]
  10. R. C. McPhedran, G. H. Derrick, and L. C. Botten, “Theory of crossed gratings,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer, Berlin, 1980).
  11. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A13, 1870–1876 (1996).
    [CrossRef]
  12. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A14(10), 2758–2767 (1997).
    [CrossRef]
  13. M. Nevière and E. Popov, “Crossed gratings,” in Light Propagation in Periodic Media, Differential Theory and Design (Marcel Dekker, New York, 2003) Chap. 9.
  14. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am.72, 1780–1787 (1986).
    [CrossRef]
  15. P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A13(4), 779–784 (1996).
    [CrossRef]
  16. G. Granet and B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A13(5), 1019–1023 (1996).
    [CrossRef]
  17. J. C. Maxwell-Garnett, “Colors in metal glasses and in. metallic films,” Philos. Trans. R. Soc. London Ser. A203(359-371), 385–420 (1904).
    [CrossRef]
  18. D. Yaghjian, “Electric dyadic Green's functions in the source region,” Proc. IEEE68(2), 248–263 (1980).
    [CrossRef]
  19. G. W. Milton, The Theory of Composites (Cambridge Univ. Press, 2002).
  20. G. W. Milton and K. Golden, “Representations for the Conductivity Functions of Multicomponent Composites,” Commun. Pure Appl. Math.43(5), 647–671 (1990).
    [CrossRef]

2010

2009

2008

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett.100(6), 066408 (2008).
[CrossRef] [PubMed]

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

1997

1996

1990

G. W. Milton and K. Golden, “Representations for the Conductivity Functions of Multicomponent Composites,” Commun. Pure Appl. Math.43(5), 647–671 (1990).
[CrossRef]

1986

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am.72, 1780–1787 (1986).
[CrossRef]

1983

R. Reinisch and M. Nevière, “Electromagnetic theory of diffraction in nonlinear optics and surface enhanced nonlinear optical effects,” Phys. Rev. B28(4), 1870–1885 (1983).
[CrossRef]

1980

D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten, “Anomalous low-frequency Raman scattering from rough metal surfaces and the origin of the surface-enhanced Raman scattering,” Phys. Rev. Lett.45(5), 355–358 (1980).
[CrossRef]

D. Yaghjian, “Electric dyadic Green's functions in the source region,” Proc. IEEE68(2), 248–263 (1980).
[CrossRef]

1976

M. C. Hutley and D. Maystre, “Total absorption of light by a diffraction grating,” Opt. Commun.19(3), 431–436 (1976).
[CrossRef]

1941

1904

J. C. Maxwell-Garnett, “Colors in metal glasses and in. metallic films,” Philos. Trans. R. Soc. London Ser. A203(359-371), 385–420 (1904).
[CrossRef]

1902

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Phylos. Mag.4, 396–402 (1902).

Barbara, A.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett.100(6), 066408 (2008).
[CrossRef] [PubMed]

Bonod, N.

Chen, Y.-T.

Chern, R.-L.

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Enoch, S.

Fano, U.

Gaylord, T. K.

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am.72, 1780–1787 (1986).
[CrossRef]

Genack, A. Z.

D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten, “Anomalous low-frequency Raman scattering from rough metal surfaces and the origin of the surface-enhanced Raman scattering,” Phys. Rev. Lett.45(5), 355–358 (1980).
[CrossRef]

Gersten, J. I.

D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten, “Anomalous low-frequency Raman scattering from rough metal surfaces and the origin of the surface-enhanced Raman scattering,” Phys. Rev. Lett.45(5), 355–358 (1980).
[CrossRef]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Golden, K.

G. W. Milton and K. Golden, “Representations for the Conductivity Functions of Multicomponent Composites,” Commun. Pure Appl. Math.43(5), 647–671 (1990).
[CrossRef]

Gramila, T. J.

D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten, “Anomalous low-frequency Raman scattering from rough metal surfaces and the origin of the surface-enhanced Raman scattering,” Phys. Rev. Lett.45(5), 355–358 (1980).
[CrossRef]

Granet, G.

Guizal, B.

Hutley, M. C.

M. C. Hutley and D. Maystre, “Total absorption of light by a diffraction grating,” Opt. Commun.19(3), 431–436 (1976).
[CrossRef]

Lalanne, P.

Le Perchec, J.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett.100(6), 066408 (2008).
[CrossRef] [PubMed]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Li, L.

Lin, H.-Y.

López-Ríos, T.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett.100(6), 066408 (2008).
[CrossRef] [PubMed]

Maxwell-Garnett, J. C.

J. C. Maxwell-Garnett, “Colors in metal glasses and in. metallic films,” Philos. Trans. R. Soc. London Ser. A203(359-371), 385–420 (1904).
[CrossRef]

Maystre, D.

M. C. Hutley and D. Maystre, “Total absorption of light by a diffraction grating,” Opt. Commun.19(3), 431–436 (1976).
[CrossRef]

Milton, G. W.

G. W. Milton and K. Golden, “Representations for the Conductivity Functions of Multicomponent Composites,” Commun. Pure Appl. Math.43(5), 647–671 (1990).
[CrossRef]

Moharam, M. G.

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am.72, 1780–1787 (1986).
[CrossRef]

Morris, G. M.

Nevière, M.

R. Reinisch and M. Nevière, “Electromagnetic theory of diffraction in nonlinear optics and surface enhanced nonlinear optical effects,” Phys. Rev. B28(4), 1870–1885 (1983).
[CrossRef]

Popov, E.

Quémerais, P.

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett.100(6), 066408 (2008).
[CrossRef] [PubMed]

Reinisch, R.

R. Reinisch and M. Nevière, “Electromagnetic theory of diffraction in nonlinear optics and surface enhanced nonlinear optical effects,” Phys. Rev. B28(4), 1870–1885 (1983).
[CrossRef]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Weitz, D. A.

D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten, “Anomalous low-frequency Raman scattering from rough metal surfaces and the origin of the surface-enhanced Raman scattering,” Phys. Rev. Lett.45(5), 355–358 (1980).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Wood, R. W.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Phylos. Mag.4, 396–402 (1902).

Yaghjian, D.

D. Yaghjian, “Electric dyadic Green's functions in the source region,” Proc. IEEE68(2), 248–263 (1980).
[CrossRef]

Commun. Pure Appl. Math.

G. W. Milton and K. Golden, “Representations for the Conductivity Functions of Multicomponent Composites,” Commun. Pure Appl. Math.43(5), 647–671 (1990).
[CrossRef]

J. Opt. Soc. Am.

U. Fano, “The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld’s waves),” J. Opt. Soc. Am.31(3), 213–222 (1941).
[CrossRef]

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am.72, 1780–1787 (1986).
[CrossRef]

J. Opt. Soc. Am. A

Nature

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through subwavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Opt. Commun.

M. C. Hutley and D. Maystre, “Total absorption of light by a diffraction grating,” Opt. Commun.19(3), 431–436 (1976).
[CrossRef]

Opt. Express

Philos. Trans. R. Soc. London Ser. A

J. C. Maxwell-Garnett, “Colors in metal glasses and in. metallic films,” Philos. Trans. R. Soc. London Ser. A203(359-371), 385–420 (1904).
[CrossRef]

Phylos. Mag.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Phylos. Mag.4, 396–402 (1902).

Phys. Rev. B

R. Reinisch and M. Nevière, “Electromagnetic theory of diffraction in nonlinear optics and surface enhanced nonlinear optical effects,” Phys. Rev. B28(4), 1870–1885 (1983).
[CrossRef]

Phys. Rev. Lett.

D. A. Weitz, T. J. Gramila, A. Z. Genack, and J. I. Gersten, “Anomalous low-frequency Raman scattering from rough metal surfaces and the origin of the surface-enhanced Raman scattering,” Phys. Rev. Lett.45(5), 355–358 (1980).
[CrossRef]

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett.100(6), 066408 (2008).
[CrossRef] [PubMed]

Proc. IEEE

D. Yaghjian, “Electric dyadic Green's functions in the source region,” Proc. IEEE68(2), 248–263 (1980).
[CrossRef]

Other

G. W. Milton, The Theory of Composites (Cambridge Univ. Press, 2002).

R. C. McPhedran, G. H. Derrick, and L. C. Botten, “Theory of crossed gratings,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer, Berlin, 1980).

M. Nevière and E. Popov, “Crossed gratings,” in Light Propagation in Periodic Media, Differential Theory and Design (Marcel Dekker, New York, 2003) Chap. 9.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Schematic representation of two types of gratings having two-dimensional periodicity: (a) channel (capacitive) grating, (b) hole (inductive) grating

Fig. 2
Fig. 2

Reflection of the gratings presented in Figs. 1(a) and 1(b), respectively, as a function of the filing factor f and the channel (hole) depth h (given in µm). Period in x- and y-direction is equal to 250 nm. Wavelength 457 nm in normal incidence.

Fig. 3
Fig. 3

Real and imaginary parts of the eigenvalues γ of the diffraction matrix, corresponding to Fig. 2(a), as a function of the filling factor. (a) the basic mode with minimum imaginary part; (b) three higher modes.

Fig. 4
Fig. 4

Real and imaginary parts of the eigenvalues γ of the diffraction matrix, corresponding to Fig. 2(b), as a function of the filling factor.

Fig. 5
Fig. 5

As in Fig. 2 but for the period of the structures equal to 3 nm (h is again given in µm).

Fig. 6
Fig. 6

Reflectivity as a function of the filling factor for the channel grating of Fig. 2(a) for two different periods (10 and 3 nm) and for two different forms of the pillars, square and circuler, as described in the legend. Blue curve, the results of Eqs. (23) and (24), cyan line, Eqs. (25) and (26). (a) h = 15 nm, (b) h = 415 nm.

Fig. 7
Fig. 7

Reflectivity as a function of the filling factor for the square hole grating of Fig. 2(b) for two different periods (10 and 3 nm), as described in the legend. Blue curve, the results of Eqs. (23) and (24). (a) h = 15 nm, (b) h = 900 nm.

Fig. 8
Fig. 8

Reflectivity as a function of f and h of metamaterial layers on silver substrate, corresponding to the limit of structures given in Fig. 2 when the period of the structures tends to zero. (a) channel grating, (b) hole array.

Fig. 9
Fig. 9

Dependence on the filling factor f of the real and imaginary parts of the normalized propagation constant of the wave propagating in direction of z, equal to n eff,xx = ε eff,xx / ε 0 . (a) channel grating, (b) hole array.

Equations (25)

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

f= c 2 d 2
E ( r )= m,n,p= E m,n,p ± exp[ i k 0 ( α m x+ β n y± γ p z ) ]
α m =m λ d x β n =n λ d y
D h = λ 2Re(γ)
E ( r )= E i ( r )+ scatterers G ( r r )( ε 2 ε 1 1 ) E ( r )d r
G( r r )=Lδ( r r )+ P v G( r r )
E ( r ) [ 1 L( ε 2 ε 1 1 ) ] 1 E i ( r )
Trace(L)=1
L= ( 1/3 0 0 0 1/3 0 0 0 1/3 )
L=( 1/2 0 0 0 1/2 0 0 0 0 )
E ( r ) 3 ε 1 2 ε 1 + ε 2 E i ( r )
E ( r )( 2 ε 1 ε 1 + ε 2 0 0 0 2 ε 1 ε 1 + ε 2 0 0 0 1 ) E i ( r )
L=( 0 0 0 0 0 0 0 0 1 )
E ( r )( 1 0 0 0 1 0 0 0 ε 1 ε 2 ) E i ( r )
D = ε eff E
E =f E ( r )+(1f) E i ( r )
D =f D ( r )+(1f) D i ( r )
D ( r )= ε 2 E ( r ) D i ( r )= ε 1 E i ( r )
f( ε eff ε 2 ) E ( r )=(1f)( ε eff ε 1 ) E i ( r )
ε eff =[ (1f) ε 1 +fQ ε 2 ] [ 1f(1Q) ] 1
ε eff,ii = (1f) ε 1 +f Q ii ε 2 1f(1 Q ii ) ,i=x,y,z
ε eff,xx = ε eff,yy = ε eff,o = ε 1 (1+f) ε 2 +(1f) ε 1 (1f) ε 2 +(1+f) ε 1
ε eff,zz = ε eff,e =f ε 2 +(1f) ε 1
ε eff,xx = ε eff,yy = ε eff,o =f ε 2 +(1f) ε 1
ε eff,zz = ε eff,e = ε 1 ε 2 f ε 1 +(1f) ε 2

Metrics