Abstract

A quasi-transverse electric (TE) surface wave mode exists at a metal surface coated with an ultrathin high-index dielectric layer. As the coating is in dielectric stripe arrays, nearly perfect absorption of TE-polarized incidence light is observed in simulations, due to resonances of the quasi-surface waves at each segment of the dielectric-coated metal surfaces. In analysis, the Fabry–Perot-like nature of the resonances is clarified, and effects of symmetry on different behaviors of the odd- and even-order resonance modes are discussed. While the absorption peak is tunable, perfect absorption appears near cut-off wavelength of the surface mode.

© 2014 Optical Society of America

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2014 (1)

2013 (1)

A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, Sci. Rep. 3, 2155 (2013).
[CrossRef]

2012 (3)

M. A. Green and S. Pillai, Nat. Photonics 6, 130 (2012).
[CrossRef]

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, Nature 492, 86 (2012).
[CrossRef]

J. Hendrickson, J. Guo, B. Zhang, W. Buchwald, and R. Soref, Opt. Lett. 37, 371 (2012).
[CrossRef]

2011 (3)

B. Zhang, Y. Zhao, Q. Hao, B. Kiraly, I. Khoo, S. Chen, and T. J. Huang, Opt. Express 19, 15221 (2011).
[CrossRef]

Z. Sun and X. Zuo, Plasmonics 6, 83 (2011).
[CrossRef]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

2010 (2)

S. Xiao, J. Zhang, L. Peng, C. Jeppesen, R. Malureanu, A. Kristensen, and N. A. Mortensen, Appl. Phys. Lett. 97, 071116 (2010).
[CrossRef]

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[CrossRef]

2009 (1)

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

2008 (1)

2006 (2)

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, Appl. Phys. Lett. 88, 161102 (2006).
[CrossRef]

Y. S. Jung, Z. Sun, J. Wuenschell, and H. K. Kim, Appl. Phys. Lett. 88, 243105 (2006).
[CrossRef]

2005 (1)

T. V. Teperik, V. V. Popov, and F. J. G. de Abajo, Phys. Rev. B 71, 085408 (2005).
[CrossRef]

2004 (2)

A. G. Brolo, R. Gordon, B. Leathem, and K. L. Kavanagh, Langmuir 20, 4813 (2004).
[CrossRef]

Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
[CrossRef]

2003 (1)

Z. Sun, Y. S. Jung, and H. K. Kim, Appl. Phys. Lett. 83, 3021 (2003).
[CrossRef]

2002 (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef]

1998 (1)

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

1974 (1)

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Albrektsen, O.

A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, Sci. Rep. 3, 2155 (2013).
[CrossRef]

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

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Bozhevolnyi, S. I.

A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, Sci. Rep. 3, 2155 (2013).
[CrossRef]

Brolo, A. G.

A. G. Brolo, R. Gordon, B. Leathem, and K. L. Kavanagh, Langmuir 20, 4813 (2004).
[CrossRef]

Buchwald, W.

Capasso, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Catchpole, K. R.

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, Appl. Phys. Lett. 88, 161102 (2006).
[CrossRef]

Chen, S.

Chen, W.

Chilkoti, A.

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, Nature 492, 86 (2012).
[CrossRef]

Ciracì, C.

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, Nature 492, 86 (2012).
[CrossRef]

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

de Abajo, F. J. G.

T. V. Teperik, V. V. Popov, and F. J. G. de Abajo, Phys. Rev. B 71, 085408 (2005).
[CrossRef]

Degiron, A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef]

Devaux, E.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef]

Ebbesen, T. W.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef]

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

Enoch, S.

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Garcia-Vidal, F. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef]

Genevet, P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Ghaemi, H. F.

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

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
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Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Gordon, R.

A. G. Brolo, R. Gordon, B. Leathem, and K. L. Kavanagh, Langmuir 20, 4813 (2004).
[CrossRef]

Green, M. A.

M. A. Green and S. Pillai, Nat. Photonics 6, 130 (2012).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, Appl. Phys. Lett. 88, 161102 (2006).
[CrossRef]

Guan, T.

Guo, J.

Hao, Q.

Hendrickson, J.

Hentschel, M.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[CrossRef]

Hill, R. T.

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, Nature 492, 86 (2012).
[CrossRef]

Huang, T. J.

Jeppesen, C.

S. Xiao, J. Zhang, L. Peng, C. Jeppesen, R. Malureanu, A. Kristensen, and N. A. Mortensen, Appl. Phys. Lett. 97, 071116 (2010).
[CrossRef]

Joanopoulos, J. D.

J. D. Joanopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Johnson, S. G.

J. D. Joanopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Jung, Y. S.

Y. S. Jung, Z. Sun, J. Wuenschell, and H. K. Kim, Appl. Phys. Lett. 88, 243105 (2006).
[CrossRef]

Z. Sun, Y. S. Jung, and H. K. Kim, Appl. Phys. Lett. 83, 3021 (2003).
[CrossRef]

Kaminow, I. P.

Kats, M. A.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Kavanagh, K. L.

A. G. Brolo, R. Gordon, B. Leathem, and K. L. Kavanagh, Langmuir 20, 4813 (2004).
[CrossRef]

Khoo, I.

Kim, H. K.

Y. S. Jung, Z. Sun, J. Wuenschell, and H. K. Kim, Appl. Phys. Lett. 88, 243105 (2006).
[CrossRef]

Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
[CrossRef]

Z. Sun, Y. S. Jung, and H. K. Kim, Appl. Phys. Lett. 83, 3021 (2003).
[CrossRef]

Kiraly, B.

Kristensen, A.

S. Xiao, J. Zhang, L. Peng, C. Jeppesen, R. Malureanu, A. Kristensen, and N. A. Mortensen, Appl. Phys. Lett. 97, 071116 (2010).
[CrossRef]

Leathem, B.

A. G. Brolo, R. Gordon, B. Leathem, and K. L. Kavanagh, Langmuir 20, 4813 (2004).
[CrossRef]

Lezec, H. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef]

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

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef]

Liu, N.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[CrossRef]

Ma, R.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Malureanu, R.

S. Xiao, J. Zhang, L. Peng, C. Jeppesen, R. Malureanu, A. Kristensen, and N. A. Mortensen, Appl. Phys. Lett. 97, 071116 (2010).
[CrossRef]

Mammal, W. L.

Martin-Moreno, L.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef]

Maystre, D.

Meade, R. D.

J. D. Joanopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Mesch, M.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[CrossRef]

Mock, J. J.

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, Nature 492, 86 (2012).
[CrossRef]

Moreau, A.

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, Nature 492, 86 (2012).
[CrossRef]

Mortensen, N. A.

S. Xiao, J. Zhang, L. Peng, C. Jeppesen, R. Malureanu, A. Kristensen, and N. A. Mortensen, Appl. Phys. Lett. 97, 071116 (2010).
[CrossRef]

Oulton, R. F.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Peng, L.

S. Xiao, J. Zhang, L. Peng, C. Jeppesen, R. Malureanu, A. Kristensen, and N. A. Mortensen, Appl. Phys. Lett. 97, 071116 (2010).
[CrossRef]

Pillai, S.

M. A. Green and S. Pillai, Nat. Photonics 6, 130 (2012).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, Appl. Phys. Lett. 88, 161102 (2006).
[CrossRef]

Popov, E.

Popov, V. V.

T. V. Teperik, V. V. Popov, and F. J. G. de Abajo, Phys. Rev. B 71, 085408 (2005).
[CrossRef]

Pors, A.

A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, Sci. Rep. 3, 2155 (2013).
[CrossRef]

Radko, I. P.

A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, Sci. Rep. 3, 2155 (2013).
[CrossRef]

Smith, D. R.

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, Nature 492, 86 (2012).
[CrossRef]

Soref, R.

Sorger, V. J.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Sun, Z.

Z. Sun, X. Zuo, T. Guan, and W. Chen, Opt. Express 22, 4714 (2014).
[CrossRef]

Z. Sun and X. Zuo, Plasmonics 6, 83 (2011).
[CrossRef]

Y. S. Jung, Z. Sun, J. Wuenschell, and H. K. Kim, Appl. Phys. Lett. 88, 243105 (2006).
[CrossRef]

Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
[CrossRef]

Z. Sun, Y. S. Jung, and H. K. Kim, Appl. Phys. Lett. 83, 3021 (2003).
[CrossRef]

Tayeb, G.

Teperik, T. V.

T. V. Teperik, V. V. Popov, and F. J. G. de Abajo, Phys. Rev. B 71, 085408 (2005).
[CrossRef]

Tetienne, J.-P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Thio, T.

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

Trupke, T.

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, Appl. Phys. Lett. 88, 161102 (2006).
[CrossRef]

Wang, Q.

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, Nature 492, 86 (2012).
[CrossRef]

Weber, H. P.

Weiss, T.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[CrossRef]

Wiley, B. J.

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, Nature 492, 86 (2012).
[CrossRef]

Winn, J. N.

J. D. Joanopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Wolff, P. A.

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

Wuenschell, J.

Y. S. Jung, Z. Sun, J. Wuenschell, and H. K. Kim, Appl. Phys. Lett. 88, 243105 (2006).
[CrossRef]

Xiao, S.

S. Xiao, J. Zhang, L. Peng, C. Jeppesen, R. Malureanu, A. Kristensen, and N. A. Mortensen, Appl. Phys. Lett. 97, 071116 (2010).
[CrossRef]

Yu, N.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

Zentgraf, T.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Zhang, B.

Zhang, G.

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, Appl. Phys. Lett. 88, 161102 (2006).
[CrossRef]

Zhang, J.

S. Xiao, J. Zhang, L. Peng, C. Jeppesen, R. Malureanu, A. Kristensen, and N. A. Mortensen, Appl. Phys. Lett. 97, 071116 (2010).
[CrossRef]

Zhang, X.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Zhao, J.

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, Appl. Phys. Lett. 88, 161102 (2006).
[CrossRef]

Zhao, Y.

Zuo, X.

Appl. Opt. (1)

Appl. Phys. Lett. (5)

Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
[CrossRef]

S. Pillai, K. R. Catchpole, T. Trupke, G. Zhang, J. Zhao, and M. A. Green, Appl. Phys. Lett. 88, 161102 (2006).
[CrossRef]

Z. Sun, Y. S. Jung, and H. K. Kim, Appl. Phys. Lett. 83, 3021 (2003).
[CrossRef]

S. Xiao, J. Zhang, L. Peng, C. Jeppesen, R. Malureanu, A. Kristensen, and N. A. Mortensen, Appl. Phys. Lett. 97, 071116 (2010).
[CrossRef]

Y. S. Jung, Z. Sun, J. Wuenschell, and H. K. Kim, Appl. Phys. Lett. 88, 243105 (2006).
[CrossRef]

Langmuir (1)

A. G. Brolo, R. Gordon, B. Leathem, and K. L. Kavanagh, Langmuir 20, 4813 (2004).
[CrossRef]

Nano Lett. (1)

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[CrossRef]

Nat. Photonics (1)

M. A. Green and S. Pillai, Nat. Photonics 6, 130 (2012).
[CrossRef]

Nature (3)

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

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

A. Moreau, C. Ciracì, J. J. Mock, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti, and D. R. Smith, Nature 492, 86 (2012).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (1)

T. V. Teperik, V. V. Popov, and F. J. G. de Abajo, Phys. Rev. B 71, 085408 (2005).
[CrossRef]

Plasmonics (1)

Z. Sun and X. Zuo, Plasmonics 6, 83 (2011).
[CrossRef]

Sci. Rep. (1)

A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, Sci. Rep. 3, 2155 (2013).
[CrossRef]

Science (2)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011).
[CrossRef]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef]

Other (1)

J. D. Joanopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic illustration of the metal surface coated with arrayed dielectric stripes upon incidence of TE-polarized light. (b) Reflection spectrum of the structure (nd=4, td=20nm, p=400nm, w=340nm), in comparison with that of the metal surface with the dielectric layer being continuous.

Fig. 2.
Fig. 2.

(a) Illustration of the formation of the quasi-TE surface wave at a MDA surface. The bottom graph is plotted for nd=4, td=20nm at λ=500nm. (b) Real (solid line) and imaginary (dashed line) parts of the normalized propagation constants of the quasi-surface waves at MDA surfaces. (c)–(e) Dependences of the cut-off wavelength of the TE0 and TE1 modes in MDA waveguides (c), mode field width (d), and (absorption coefficient (e) on the dielectric thickness for nd=4 and 2 and at wavelengths of λ=500 and 600 nm.

Fig. 3.
Fig. 3.

(a)–(c) Distributions of the TE field (Ey) at the reflection minima in Fig. 1(b). The dielectric layer is too thin to show in the plots (but implied), and the HID stripes locate symmetrically in the middle on metal surfaces, whose width is labeled with w. (d) Schematic model describing resonant interactions of light at the metal surface.

Fig. 4.
Fig. 4.

Dependences of the reflection spectra on (a) structure parameters of period, (b) HID stripe width, and (d) thickness. (c) indicates stripe-width dependences of the second-order resonance position shown in (b), together with modeled optical path (Neff·w) and end phase shift of the Fabry–Perot resonance.

Fig. 5.
Fig. 5.

(a) Dependence of the reflection spectra on incidence angles (θ). (b)–(e) Field distributions (Ey) at resonance positions λ=526, 472.1, 392.1, and 361.3 nm (corresponding to m=1, 2, 3, 4) for θ=10° in (a). The grating ridges locate symmetrically in the middle on metal surfaces. The arrows indicate directions of the incidence plane wave and observed net power flow along the metal surface.

Equations (1)

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2ksw·w+φA+φB=2mπ(m=0,1,2,),

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