Abstract

We propose a class of antireflecting structures that can effectively suppress reflections for binary diffractive optics. In this structure, multiple periodic thin films with gradually varying refractive indices are used to shift all reflected diffraction to the transmitted orders. The structure is optimized to operate over broad bands and wide angles using rigorous coupled-wave analysis and genetic algorithms. We validated the structure numerically using finite-difference time-domain methods. The proposed structure may lead to more efficient diffractive devices for applications in thin-film photovoltaic, waveguide coupler, and holographic optical elements.

© 2010 Optical Society of America

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2008 (1)

2007 (2)

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, Nature Photon. 1, 176 (2007).

Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, Nature Nanotechnol. 2, 770 (2007).
[CrossRef]

2006 (1)

H. Stiebig, N. Senoussaoui, C. Zahren, C. Haase, and J. Müller, Prog. Photovoltaics 14, 13 (2006).
[CrossRef]

2005 (1)

2004 (2)

2001 (1)

C. Eisele, C. E. Nebel, and M. Stutzmann, J. Appl. Phys. 89, 7722 (2001).
[CrossRef]

1999 (1)

1997 (1)

P. Lalanne and G. M. Morris, Nanotechnology 8, 53 (1997).
[CrossRef]

1995 (3)

1983 (1)

Baets, R.

Bienstman, P.

Chang, Y.-H.

Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, Nature Nanotechnol. 2, 770 (2007).
[CrossRef]

Chattopadhyay, S.

Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, Nature Nanotechnol. 2, 770 (2007).
[CrossRef]

Chen, K.-H.

Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, Nature Nanotechnol. 2, 770 (2007).
[CrossRef]

Chen, L.-C.

Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, Nature Nanotechnol. 2, 770 (2007).
[CrossRef]

Chen, M.

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, Nature Photon. 1, 176 (2007).

Clausnitzer, T.

Eisele, C.

C. Eisele, C. E. Nebel, and M. Stutzmann, J. Appl. Phys. 89, 7722 (2001).
[CrossRef]

Elfström, H.

Gaylord, T. K.

Grann, E. B.

Haase, C.

H. Stiebig, N. Senoussaoui, C. Zahren, C. Haase, and J. Müller, Prog. Photovoltaics 14, 13 (2006).
[CrossRef]

Hane, K.

Hsu, C.-H.

Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, Nature Nanotechnol. 2, 770 (2007).
[CrossRef]

Hsu, Y.-K.

Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, Nature Nanotechnol. 2, 770 (2007).
[CrossRef]

Huang, Y.-F.

Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, Nature Nanotechnol. 2, 770 (2007).
[CrossRef]

Jen, Y.-J.

Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, Nature Nanotechnol. 2, 770 (2007).
[CrossRef]

Kanamori, Y.

Kim, J. K.

M.-L. Kuo, D. J. Poxson, Y. S. Kim, F. W. Mont, J. K. Kim, E. F. Schubert, and S.-Y. Lin, Opt. Lett. 33, 2527 (2008).
[CrossRef] [PubMed]

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, Nature Photon. 1, 176 (2007).

Kim, Y. S.

Kley, E.-B.

Kuittinen, M.

Kuo, M.-L.

Lalanne, P.

P. Lalanne and G. M. Morris, Nanotechnology 8, 53 (1997).
[CrossRef]

Lee, C.-S.

Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, Nature Nanotechnol. 2, 770 (2007).
[CrossRef]

Lin, S.-Y.

M.-L. Kuo, D. J. Poxson, Y. S. Kim, F. W. Mont, J. K. Kim, E. F. Schubert, and S.-Y. Lin, Opt. Lett. 33, 2527 (2008).
[CrossRef] [PubMed]

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, Nature Photon. 1, 176 (2007).

Liu, T.-A.

Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, Nature Nanotechnol. 2, 770 (2007).
[CrossRef]

Liu, W.

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, Nature Photon. 1, 176 (2007).

Lo, H.-C.

Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, Nature Nanotechnol. 2, 770 (2007).
[CrossRef]

Mao, G.

Moharam, M. G.

Mont, F. W.

Morris, G. M.

P. Lalanne and G. M. Morris, Nanotechnology 8, 53 (1997).
[CrossRef]

Müller, J.

H. Stiebig, N. Senoussaoui, C. Zahren, C. Haase, and J. Müller, Prog. Photovoltaics 14, 13 (2006).
[CrossRef]

Nebel, C. E.

C. Eisele, C. E. Nebel, and M. Stutzmann, J. Appl. Phys. 89, 7722 (2001).
[CrossRef]

Pan, C.-L.

Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, Nature Nanotechnol. 2, 770 (2007).
[CrossRef]

Peng, C.-Y.

Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, Nature Nanotechnol. 2, 770 (2007).
[CrossRef]

Pommet, D. A.

Poxson, D. J.

Sasaki, M.

Schubert, E. F.

M.-L. Kuo, D. J. Poxson, Y. S. Kim, F. W. Mont, J. K. Kim, E. F. Schubert, and S.-Y. Lin, Opt. Lett. 33, 2527 (2008).
[CrossRef] [PubMed]

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, Nature Photon. 1, 176 (2007).

Schubert, M. F.

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, Nature Photon. 1, 176 (2007).

Senoussaoui, N.

H. Stiebig, N. Senoussaoui, C. Zahren, C. Haase, and J. Müller, Prog. Photovoltaics 14, 13 (2006).
[CrossRef]

Smart, J. A.

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, Nature Photon. 1, 176 (2007).

Southwell, W. H.

Stiebig, H.

H. Stiebig, N. Senoussaoui, C. Zahren, C. Haase, and J. Müller, Prog. Photovoltaics 14, 13 (2006).
[CrossRef]

Stutzmann, M.

C. Eisele, C. E. Nebel, and M. Stutzmann, J. Appl. Phys. 89, 7722 (2001).
[CrossRef]

Taillaert, D.

Turunen, J.

Vallius, T.

Wang, J.

Xi, J.-Q.

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, Nature Photon. 1, 176 (2007).

Zahren, C.

H. Stiebig, N. Senoussaoui, C. Zahren, C. Haase, and J. Müller, Prog. Photovoltaics 14, 13 (2006).
[CrossRef]

Zhao, Y.

J. Appl. Phys. (1)

C. Eisele, C. E. Nebel, and M. Stutzmann, J. Appl. Phys. 89, 7722 (2001).
[CrossRef]

J. Opt. Soc. Am. A (3)

Nanotechnology (1)

P. Lalanne and G. M. Morris, Nanotechnology 8, 53 (1997).
[CrossRef]

Nature Nanotechnol. (1)

Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, Nature Nanotechnol. 2, 770 (2007).
[CrossRef]

Nature Photon. (1)

J.-Q. Xi, M. F. Schubert, J. K. Kim, E. F. Schubert, M. Chen, S.-Y. Lin, W. Liu, and J. A. Smart, Nature Photon. 1, 176 (2007).

Opt. Express (1)

Opt. Lett. (5)

Prog. Photovoltaics (1)

H. Stiebig, N. Senoussaoui, C. Zahren, C. Haase, and J. Müller, Prog. Photovoltaics 14, 13 (2006).
[CrossRef]

Supplementary Material (2)

» Media 1: MPG (2285 KB)     
» Media 2: MPG (2029 KB)     

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic of the proposed AR structure for a binary grating. (b) The structure consists of multilayers of periodic thin films with gradually varying refractive index on both the ridge and the groove of the grating.

Fig. 2
Fig. 2

Simulated (a) reflected and (b) transmitted diffraction efficiencies for varying individual film thickness d o in an N = 7 AR structure.

Fig. 3
Fig. 3

Optimized total reflection for varying the number of layers N in the AR structure.

Fig. 4
Fig. 4

Reflection of a normal incident plane wave with λ = 633 nm from a binary diffraction grating (a) without (Media 1) and (b) with (Media 2) the optimized AR structure simulated using FDTD. The scale denotes normalized E y fields.

Fig. 5
Fig. 5

Simulated reflected diffraction efficiencies using RCWA for the optimized broadband wide-angle AR structure as functions of (a) wavelength for normal incidence and (b) incident angle for λ = 633 nm . Higher-order diffraction efficiencies are not shown.

Equations (3)

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f ( d i ) = j R j ( d i ) ,
n i = n air + ( n s n air ) [ 10 ( d i N + 1 ) 3 15 ( d i N + 1 ) 4 + 6 ( d i N + 1 ) 5 ] ,
f ( d i ) = l k j R j k l ( d i ) ,

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