Abstract

We propose a modified effective-refractive-index model for the design of relief dielectric structures on a metal surface to realize phase modulation of surface-plasmon polaritons (SPPs). In this model, the length of the dielectric structure is optimized to reach phase shifting between the SPP waves transmitted through dielectric structure and those directly propagated with the consideration of SPP losses. Specifically, a one-dimensional dielectric Fresnel zone plate is designed by employing the proposed model to demonstrate phase modulation of SPPs for the highest focusing efficiency.

© 2010 Optical Society of America

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  1. H. Raether, Surface Plasmons (Springer, 1988).
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    [CrossRef] [PubMed]
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2010

2009

2008

2007

T. Holmgaard and S. I. Bozhevolnyi, Phys. Rev. B 75, 245405 (2007).
[CrossRef]

A. H. B. Steinberger, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenna, Appl. Phys. Lett. 91, 081111 (2007).
[CrossRef]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef] [PubMed]

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

2006

E. Ozbay, Science 311, 189 (2006).
[CrossRef] [PubMed]

2005

2003

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

2002

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Andersen, T. B.

Atwater, H. A.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, Nano Lett. 9, 897 (2009).
[CrossRef] [PubMed]

Aussenegg, F. R.

A. H. B. Steinberger, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenna, Appl. Phys. Lett. 91, 081111 (2007).
[CrossRef]

A. Hohenau, J. R. Krenn, A. L. Stepanov, A. Drezet, H. Ditlbacher, B. Steinberger, A. Leitner, and F. R. Aussenegg, Opt. Lett. 30, 893 (2005).
[CrossRef] [PubMed]

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Barnes, W. L.

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

Bozhevolnyi, S. I.

Choa, F.-S.

Davis, C. C.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef] [PubMed]

Dereux, A.

Diest, K.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, Nano Lett. 9, 897 (2009).
[CrossRef] [PubMed]

Dionne, J. A.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, Nano Lett. 9, 897 (2009).
[CrossRef] [PubMed]

Ditlbacher, H.

A. H. B. Steinberger, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenna, Appl. Phys. Lett. 91, 081111 (2007).
[CrossRef]

A. Hohenau, J. R. Krenn, A. L. Stepanov, A. Drezet, H. Ditlbacher, B. Steinberger, A. Leitner, and F. R. Aussenegg, Opt. Lett. 30, 893 (2005).
[CrossRef] [PubMed]

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Drezet, A.

Ebbesen, T. W.

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

Fainman, Y.

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

Feng, L.

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

Gmachl, C.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Gosciniak, J.

Hohenau, A.

Holmgaard, T.

T. Holmgaard and S. I. Bozhevolnyi, Phys. Rev. B 75, 245405 (2007).
[CrossRef]

Howard, S. S.

Hung, Y.-J.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef] [PubMed]

Kjelstrup-Hansen, J.

Krenn, J. R.

Krenna, J. R.

A. H. B. Steinberger, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenna, Appl. Phys. Lett. 91, 081111 (2007).
[CrossRef]

Leitner, A.

A. H. B. Steinberger, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenna, Appl. Phys. Lett. 91, 081111 (2007).
[CrossRef]

A. Hohenau, J. R. Krenn, A. L. Stepanov, A. Drezet, H. Ditlbacher, B. Steinberger, A. Leitner, and F. R. Aussenegg, Opt. Lett. 30, 893 (2005).
[CrossRef] [PubMed]

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Lomakin, V.

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

Markey, L.

Ozbay, E.

E. Ozbay, Science 311, 189 (2006).
[CrossRef] [PubMed]

Raether, H.

H. Raether, Surface Plasmons (Springer, 1988).

Ribaudo, T.

Schider, G.

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

Shaner, E. A.

Slutsky, B.

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

Smolyaninov, I. I.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef] [PubMed]

Steinberger, A. H. B.

A. H. B. Steinberger, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenna, Appl. Phys. Lett. 91, 081111 (2007).
[CrossRef]

Steinberger, B.

Stepanov, A. L.

Sweatlock, L. A.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, Nano Lett. 9, 897 (2009).
[CrossRef] [PubMed]

Tan, P. S.

Tetz, K. A.

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

Volkov, V. S.

Wang, Q.

Wang, X. J.

Wasserman, D.

Yuan, X.-C.

Zhang, D. G.

Appl. Phys. Lett.

H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, Appl. Phys. Lett. 81, 1762 (2002).
[CrossRef]

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

A. H. B. Steinberger, H. Ditlbacher, F. R. Aussenegg, A. Leitner, and J. R. Krenna, Appl. Phys. Lett. 91, 081111 (2007).
[CrossRef]

Nano Lett.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, Nano Lett. 9, 897 (2009).
[CrossRef] [PubMed]

Nature

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

Opt. Express

Opt. Lett.

Phys. Rev. B

T. Holmgaard and S. I. Bozhevolnyi, Phys. Rev. B 75, 245405 (2007).
[CrossRef]

Science

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef] [PubMed]

E. Ozbay, Science 311, 189 (2006).
[CrossRef] [PubMed]

Other

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

H. Raether, Surface Plasmons (Springer, 1988).

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Figures (3)

Fig. 1
Fig. 1

Theoretical results of PMMA structures of different t, w, and l in order to realize the π phase shift of the SPP waves.

Fig. 2
Fig. 2

FDTD simulation results of the SPP-based PMFZP intensity distribution on a plane located 20 nm above the Au surface. PMMA t is equal to 100 nm , 200 nm , and 300 nm , respectively. (a1)–(c1) l is designed according to the conventional waveguide effective-refractive-index method. (a2)–(c2) l is designed according to the modified effective- refractive-index model. The length scale is 1 μm .

Fig. 3
Fig. 3

(a) SEM image of the PMFZP profile, (b) NSOM scanning image of the PMFZP in the focal area, and (c) FDTD simulation result of the PMFZP in the focal area. The length scale is 1 μm .

Equations (2)

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Δ φ = 2 π λ SPP [ ( n eff ( t , w , l ) 1 ) ] × l .
n eff ( t , w , l ) = α × n eff ( t , w ) exp ( 2 Δ k SPP l ) × ( 1 R o R c exp ( 4 k SPP l ) ) ,

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