Abstract

Antireflective properties of pyramidally textured surfaces at normal light incidence are studied by the finite-difference time-domain (FDTD) method. Optimal parameters for the period of the texture and the pyramid height are found. The asymptotic behavior of the reflection coefficient with an increasing height-to-base size ratio for the pyramids is also estimated for two limiting approximations: the effective medium theory (EMT) and geometric optics. For calculations in the geometric optics limit the ray tracing method was applied. The FDTD results for these limits are in agreement with the EMT and with the ray tracing calculations. It was found that the key factor influencing the optimal scatterer size is the character of the substrate tiling by the pyramid bases.

© 2010 Optical Society of America

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References

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2009 (1)

2008 (1)

2007 (2)

2006 (1)

F. Llopis and I. Tobias, J. Appl. Phys. 100, 124504 (2006).
[CrossRef]

2002 (1)

A. A. Abouelsaood, S. A. El-Naggar, and M. Y. Ghannam, Prog. Photovoltaics 10, 513 (2002).
[CrossRef]

2001 (1)

F. Wu and K. W. Whites, Electromagnetics 21, 97 (2001).
[CrossRef]

1994 (1)

1993 (1)

1991 (1)

1983 (1)

B. L. Sopori and R. A. Pryor, Sol. Cells 8, 249 (1983).
[CrossRef]

1971 (1)

O. Bucci and G. Franceschetti, IEEE Trans. Antennas Propag. 19, 96 (1971).
[CrossRef]

Abouelsaood, A. A.

A. A. Abouelsaood, S. A. El-Naggar, and M. Y. Ghannam, Prog. Photovoltaics 10, 513 (2002).
[CrossRef]

Bae, S. Y.

Belousov, S.

Bräuer, R.

Bryngdahl, O.

Bucci, O.

O. Bucci and G. Franceschetti, IEEE Trans. Antennas Propag. 19, 96 (1971).
[CrossRef]

Chen, H. L.

Chuang, S. Y.

Deinega, A.

El-Naggar, S. A.

A. A. Abouelsaood, S. A. El-Naggar, and M. Y. Ghannam, Prog. Photovoltaics 10, 513 (2002).
[CrossRef]

Franceschetti, G.

O. Bucci and G. Franceschetti, IEEE Trans. Antennas Propag. 19, 96 (1971).
[CrossRef]

Ghannam, M. Y.

A. A. Abouelsaood, S. A. El-Naggar, and M. Y. Ghannam, Prog. Photovoltaics 10, 513 (2002).
[CrossRef]

Hagness, S. H.

A. Taflove and S. H. Hagness, Computational Electrodynamics: the Finite Difference Time-Domain Method (Artech House, 2005).

Lee, Y. T.

Lin, C. H.

Lin, Y. H.

Llopis, F.

F. Llopis and I. Tobias, J. Appl. Phys. 100, 124504 (2006).
[CrossRef]

Morris, G. M.

Pryor, R. A.

B. L. Sopori and R. A. Pryor, Sol. Cells 8, 249 (1983).
[CrossRef]

Raguin, D. H.

Song, Y. M.

Sopori, B. L.

B. L. Sopori and R. A. Pryor, Sol. Cells 8, 249 (1983).
[CrossRef]

Southwell, W. H.

Taflove, A.

A. Taflove and S. H. Hagness, Computational Electrodynamics: the Finite Difference Time-Domain Method (Artech House, 2005).

Tobias, I.

F. Llopis and I. Tobias, J. Appl. Phys. 100, 124504 (2006).
[CrossRef]

Valuev, I.

Whites, K. W.

F. Wu and K. W. Whites, Electromagnetics 21, 97 (2001).
[CrossRef]

Wu, F.

F. Wu and K. W. Whites, Electromagnetics 21, 97 (2001).
[CrossRef]

Yu, J. S.

Appl. Opt. (2)

Electromagnetics (1)

F. Wu and K. W. Whites, Electromagnetics 21, 97 (2001).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

O. Bucci and G. Franceschetti, IEEE Trans. Antennas Propag. 19, 96 (1971).
[CrossRef]

J. Appl. Phys. (1)

F. Llopis and I. Tobias, J. Appl. Phys. 100, 124504 (2006).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (3)

Prog. Photovoltaics (1)

A. A. Abouelsaood, S. A. El-Naggar, and M. Y. Ghannam, Prog. Photovoltaics 10, 513 (2002).
[CrossRef]

Sol. Cells (1)

B. L. Sopori and R. A. Pryor, Sol. Cells 8, 249 (1983).
[CrossRef]

Other (1)

A. Taflove and S. H. Hagness, Computational Electrodynamics: the Finite Difference Time-Domain Method (Artech House, 2005).

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Figures (4)

Fig. 1
Fig. 1

Curves are reflectance from a graded-index film with the optical properties corresponding to (open circles) grating with the integral profile f ( z ) = C o z e ζ 1 ( d ζ ) 1 d ζ , f ( d ) = 1 , TE case; square pyramids with (squares) linear and (crosses) quintic profiles closely packed in the square lattice; (filled circles) cones closely packed in the triangular lattice. Approximate expressions for the effective dielectric permittivity of square pyramids and cones were taken from [10, 11]. The FDTD calculations (symbols) are performed for the corresponding textures with Λ = 1 , d = 16 , 4 < λ < , mesh step δ x = 0.01 .

Fig. 2
Fig. 2

Left, curves are reflectance from different closely packed structures in the geometric optics limit. The FDTD calculations (symbols) are performed for Λ λ = 15 . Right, illustration of the ray tracing simulation and the substrate reflection by an incomplete tiling.

Fig. 3
Fig. 3

Reflectance from closely packed pyramids with square bases as a function of Λ λ and d Λ (FDTD results).

Fig. 4
Fig. 4

Reflectance from cones closely packed in the triangular lattice as a function of Λ λ and d Λ (FDTD results).

Equations (2)

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ρ = 0 d 1 2 n ̃ d n ̃ d z exp [ i 4 π λ 0 z n ̃ ( z ) d z ] d z .
ρ = 0 g ( d ) h e i g λ d g = | k = 1 ( i ) k λ k h ( k 1 ) e i g λ | 0 g ( d ) .

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