Abstract

We demonstrate that the phase of light transmitted through double-layer subwavelength metallic slit arrays can be controlled through lateral shift of the two layers. Our samples consist of two aluminum layers, each of which contains an array of subwavelength slits. The two layers are placed in sufficient proximity to allow coupling of the evanescent fields at resonance. By changing the lateral shift between the layers from zero to half the period, the phase of the transmitted electromagnetic field is increased by π, while the transmitted intensity remains high. Such a controllable phase delay could open new capabilities for nanophotonic devices that cannot be achieved with single-layer structures.

© 2008 Optical Society of America

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2007

C. Cheng, J. Chen, Q.-Y. Wu, F.-F. Ren, J. Xu, Y.-X. Fan, and H.-T. Wang, Appl. Phys. Lett. 91, 111111 (2007).
[CrossRef]

A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, Phys. Rev. B 76, 235430 (2007).
[CrossRef]

Y. Poujet, J. Salvi, and F. I. Baida, Opt. Lett. 32, 2942 (2007).
[CrossRef] [PubMed]

2006

2005

Q. Li, X. Jiao, P. Wang, H. Ming, and J. Xie, Appl. Phys. B 81, 787 (2005).
[CrossRef]

J. H. Ye and J. Y. Zhang, Opt. Lett. 30, 1521 (2005).
[CrossRef] [PubMed]

2004

H. J. Lezec and T. Thio, Opt. Express 12, 3629 (2004).
[CrossRef] [PubMed]

R. M. Bakker, V. P. Drachev, H. K. Yuan, and V. M. Shalaev, Opt. Express 12, 3701 (2004).
[CrossRef] [PubMed]

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, Phys. Rev. Lett. 92, 143904 (2004).
[CrossRef] [PubMed]

J. T. Shen and P. M. Platzman, Phys. Rev. B 70, 035101 (2004).
[CrossRef]

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

2002

F. J. García-Vidal and L. Martín-Moreno, Phys. Rev. B 66, 155412 (2002).
[CrossRef]

M. Kreiter, S. Mittler, W. Knoll, and J. R. Sambles, Phys. Rev. B 65, 125415 (2002).
[CrossRef]

2001

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

2000

Z. N. Yu, P. Deshpande, W. Wu, J. Wang, and S. Y. Chou, Appl. Phys. Lett. 77, 927 (2000).
[CrossRef]

1999

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

1995

Baida, F. I.

Bakker, R. M.

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Bower, J. E.

Brown, J. R.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, Phys. Rev. Lett. 92, 143904 (2004).
[CrossRef] [PubMed]

Carr, D. W.

Chan, H. B.

Chen, J.

C. Cheng, J. Chen, Q.-Y. Wu, F.-F. Ren, J. Xu, Y.-X. Fan, and H.-T. Wang, Appl. Phys. Lett. 91, 111111 (2007).
[CrossRef]

Cheng, C.

C. Cheng, J. Chen, Q.-Y. Wu, F.-F. Ren, J. Xu, Y.-X. Fan, and H.-T. Wang, Appl. Phys. Lett. 91, 111111 (2007).
[CrossRef]

Chou, S. Y.

Z. N. Yu, P. Deshpande, W. Wu, J. Wang, and S. Y. Chou, Appl. Phys. Lett. 77, 927 (2000).
[CrossRef]

Cirelli, R. A.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Deshpande, P.

Z. N. Yu, P. Deshpande, W. Wu, J. Wang, and S. Y. Chou, Appl. Phys. Lett. 77, 927 (2000).
[CrossRef]

Drachev, V. P.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Fan, Y.-X.

C. Cheng, J. Chen, Q.-Y. Wu, F.-F. Ren, J. Xu, Y.-X. Fan, and H.-T. Wang, Appl. Phys. Lett. 91, 111111 (2007).
[CrossRef]

Fernández-Domínguez, A. I.

A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, Phys. Rev. B 76, 235430 (2007).
[CrossRef]

Ferry, E.

Garcia-Vidal, F. J.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

García-Vidal, F. J.

A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, Phys. Rev. B 76, 235430 (2007).
[CrossRef]

F. J. García-Vidal and L. Martín-Moreno, Phys. Rev. B 66, 155412 (2002).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Gaylord, T. K.

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Grann, E. B.

Hibbins, A. P.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, Phys. Rev. Lett. 92, 143904 (2004).
[CrossRef] [PubMed]

Jiao, X.

Q. Li, X. Jiao, P. Wang, H. Ming, and J. Xie, Appl. Phys. B 81, 787 (2005).
[CrossRef]

Klemens, F.

Knoll, W.

M. Kreiter, S. Mittler, W. Knoll, and J. R. Sambles, Phys. Rev. B 65, 125415 (2002).
[CrossRef]

Kreiter, M.

M. Kreiter, S. Mittler, W. Knoll, and J. R. Sambles, Phys. Rev. B 65, 125415 (2002).
[CrossRef]

Lawrence, C. R.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, Phys. Rev. Lett. 92, 143904 (2004).
[CrossRef] [PubMed]

Lezec, H. J.

H. J. Lezec and T. Thio, Opt. Express 12, 3629 (2004).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Li, Q.

Q. Li, X. Jiao, P. Wang, H. Ming, and J. Xie, Appl. Phys. B 81, 787 (2005).
[CrossRef]

Marcet, Z.

Martín-Moreno, L.

A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, Phys. Rev. B 76, 235430 (2007).
[CrossRef]

F. J. García-Vidal and L. Martín-Moreno, Phys. Rev. B 66, 155412 (2002).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Miner, J.

Ming, H.

Q. Li, X. Jiao, P. Wang, H. Ming, and J. Xie, Appl. Phys. B 81, 787 (2005).
[CrossRef]

Mittler, S.

M. Kreiter, S. Mittler, W. Knoll, and J. R. Sambles, Phys. Rev. B 65, 125415 (2002).
[CrossRef]

Moharam, M. G.

Pai, C. S.

Palik, E. D.

E. D. Palik, ed., Handbook of Optical Constants of Solids (McGraw-Hill, 1950).

Pellerin, K. M.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Pendry, J. B.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

Platzman, P. M.

J. T. Shen and P. M. Platzman, Phys. Rev. B 70, 035101 (2004).
[CrossRef]

Pommet, D. A.

Porto, J. A.

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

Poujet, Y.

Ren, F.-F.

C. Cheng, J. Chen, Q.-Y. Wu, F.-F. Ren, J. Xu, Y.-X. Fan, and H.-T. Wang, Appl. Phys. Lett. 91, 111111 (2007).
[CrossRef]

Salvi, J.

Sambles, J. R.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, Phys. Rev. Lett. 92, 143904 (2004).
[CrossRef] [PubMed]

M. Kreiter, S. Mittler, W. Knoll, and J. R. Sambles, Phys. Rev. B 65, 125415 (2002).
[CrossRef]

Shalaev, V. M.

Shen, J. T.

J. T. Shen and P. M. Platzman, Phys. Rev. B 70, 035101 (2004).
[CrossRef]

Tanner, D. B.

Taylor, J. A.

Thio, T.

H. J. Lezec and T. Thio, Opt. Express 12, 3629 (2004).
[CrossRef] [PubMed]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Wang, H.-T.

C. Cheng, J. Chen, Q.-Y. Wu, F.-F. Ren, J. Xu, Y.-X. Fan, and H.-T. Wang, Appl. Phys. Lett. 91, 111111 (2007).
[CrossRef]

Wang, J.

Z. N. Yu, P. Deshpande, W. Wu, J. Wang, and S. Y. Chou, Appl. Phys. Lett. 77, 927 (2000).
[CrossRef]

Wang, P.

Q. Li, X. Jiao, P. Wang, H. Ming, and J. Xie, Appl. Phys. B 81, 787 (2005).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Woo, K.

Wu, Q.-Y.

C. Cheng, J. Chen, Q.-Y. Wu, F.-F. Ren, J. Xu, Y.-X. Fan, and H.-T. Wang, Appl. Phys. Lett. 91, 111111 (2007).
[CrossRef]

Wu, W.

Z. N. Yu, P. Deshpande, W. Wu, J. Wang, and S. Y. Chou, Appl. Phys. Lett. 77, 927 (2000).
[CrossRef]

Xie, J.

Q. Li, X. Jiao, P. Wang, H. Ming, and J. Xie, Appl. Phys. B 81, 787 (2005).
[CrossRef]

Xu, J.

C. Cheng, J. Chen, Q.-Y. Wu, F.-F. Ren, J. Xu, Y.-X. Fan, and H.-T. Wang, Appl. Phys. Lett. 91, 111111 (2007).
[CrossRef]

Ye, J. H.

Yu, Z. N.

Z. N. Yu, P. Deshpande, W. Wu, J. Wang, and S. Y. Chou, Appl. Phys. Lett. 77, 927 (2000).
[CrossRef]

Yuan, H. K.

Zhang, J. Y.

Appl. Phys. B

Q. Li, X. Jiao, P. Wang, H. Ming, and J. Xie, Appl. Phys. B 81, 787 (2005).
[CrossRef]

Appl. Phys. Lett.

C. Cheng, J. Chen, Q.-Y. Wu, F.-F. Ren, J. Xu, Y.-X. Fan, and H.-T. Wang, Appl. Phys. Lett. 91, 111111 (2007).
[CrossRef]

Z. N. Yu, P. Deshpande, W. Wu, J. Wang, and S. Y. Chou, Appl. Phys. Lett. 77, 927 (2000).
[CrossRef]

J. Opt. Soc. Am. A

Nature

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. B

J. T. Shen and P. M. Platzman, Phys. Rev. B 70, 035101 (2004).
[CrossRef]

A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, Phys. Rev. B 76, 235430 (2007).
[CrossRef]

F. J. García-Vidal and L. Martín-Moreno, Phys. Rev. B 66, 155412 (2002).
[CrossRef]

M. Kreiter, S. Mittler, W. Knoll, and J. R. Sambles, Phys. Rev. B 65, 125415 (2002).
[CrossRef]

Phys. Rev. Lett.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, Phys. Rev. Lett. 92, 143904 (2004).
[CrossRef] [PubMed]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Other

E. D. Palik, ed., Handbook of Optical Constants of Solids (McGraw-Hill, 1950).

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Figures (3)

Fig. 1
Fig. 1

a, measured transmission through sample I with aligned double layers (dashed curve) and sample II with offset double layers (solid curve). Insets: The cross-sectional side view of structures fabricated on a silicon wafer with similar dimensions to samples I and II with the two layers aligned (right) and offset by 0.9 μ m (left). Light is incident from the top. b, transmission calculation using RCWA. Inset: Cross-sectional schematic of the structure used in RCWA calculations.

Fig. 2
Fig. 2

a, RCWA calculation of the phase of the transmitted light as a function of lateral shift between the two layers. Electromagnetic field distribution around b, single layer; c, aligned double layer; and d, offset double layer. The incoming wave is incident from the bottom with unit amplitude. The magnetic field is directed in and out of the page with the color bar representing its magnitude and direction. The arrows represent the electric field. For simplicity, the silicon oxide layers are assumed to extend through all space.

Fig. 3
Fig. 3

a, Solid curve shows the measured transmission of sample III with 10 μ m squares of aligned and offset regions in a checkerboard pattern (top view shown in left inset with light incident into the page). After covering the offset pixels with aluminum (right inset), the transmission peak increases in magnitude (dotted curve). b, Pixel size is increased to 50 μ m squares in sample IV.

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