Abstract

We study light propagation in nanoscale periodic structures composed of dielectric and metal in the visible range. We demonstrate that diffraction can be tailored both in magnitude and in sign by varying the geometric features of the waveguides. Diffraction management on a subwavelength scale is demonstrated by numerical solution of Maxwell equations in the frequency domain.

© 2008 Optical Society of America

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References

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  1. S. A. Maier, Plasmonics: Fundamentals and Applications (Spinger, 2007).
  2. E. N. Economu, Phys. Rev. 182, 539 (1969).
    [CrossRef]
  3. E. Ozbay, Science 311, 189 (2006).
    [CrossRef] [PubMed]
  4. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  5. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  6. A. Hardy and W. Streifer, J. Lightwave Technol. LT-3, 1135 (1985).
    [CrossRef]
  7. D. Michaelis, U. Peschel, C. Wächter, and A. Bräuer, Phys. Rev. E 68, 065601(R) (2003).
    [CrossRef]
  8. X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
    [CrossRef] [PubMed]
  9. A. Zettl, Sturm-Liouville Theory (Mathematical Surveys and Monographs) (American Mathematical Society, 2005).
  10. C. M. de Sterke, L. C. Botten, A. A. Asatryan, T. P. White, and R. C. McPhedran, Opt. Lett. 29, 1384 (2004).
    [CrossRef]
  11. A. Locatelli, M. Conforti, D. Modotto, and C. De Angelis, Opt. Lett. 30, 2894 (2005).
    [CrossRef] [PubMed]
  12. M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, Opt. Lett. 23, 1331 (1998).
    [CrossRef]
  13. H. Chu, W. Ewe, E. Li, and R. Vahldieck, Opt. Express 15, 4216 (2007).
    [CrossRef] [PubMed]
  14. P. B. Catrysse, G. Veronis, H. Shin, J. Shen, and S. Fan, Appl. Phys. Lett. 88, 031101 (2006).
    [CrossRef]
  15. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
    [CrossRef] [PubMed]
  16. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
    [CrossRef] [PubMed]

2007 (1)

2006 (3)

P. B. Catrysse, G. Veronis, H. Shin, J. Shen, and S. Fan, Appl. Phys. Lett. 88, 031101 (2006).
[CrossRef]

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

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

2003 (1)

D. Michaelis, U. Peschel, C. Wächter, and A. Bräuer, Phys. Rev. E 68, 065601(R) (2003).
[CrossRef]

2002 (1)

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

2000 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

1998 (2)

M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, Opt. Lett. 23, 1331 (1998).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

1988 (1)

1985 (1)

A. Hardy and W. Streifer, J. Lightwave Technol. LT-3, 1135 (1985).
[CrossRef]

1969 (1)

E. N. Economu, Phys. Rev. 182, 539 (1969).
[CrossRef]

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Asatryan, A. A.

Aussenegg, F. R.

Botten, L. C.

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Bräuer, A.

D. Michaelis, U. Peschel, C. Wächter, and A. Bräuer, Phys. Rev. E 68, 065601(R) (2003).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Catrysse, P. B.

P. B. Catrysse, G. Veronis, H. Shin, J. Shen, and S. Fan, Appl. Phys. Lett. 88, 031101 (2006).
[CrossRef]

Chan, C. T.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

Christodoulides, D. N.

Chu, H.

Conforti, M.

De Angelis, C.

de Sterke, C. M.

Economu, E. N.

E. N. Economu, Phys. Rev. 182, 539 (1969).
[CrossRef]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Ewe, W.

Fan, S.

P. B. Catrysse, G. Veronis, H. Shin, J. Shen, and S. Fan, Appl. Phys. Lett. 88, 031101 (2006).
[CrossRef]

Fan, X.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

Hardy, A.

A. Hardy and W. Streifer, J. Lightwave Technol. LT-3, 1135 (1985).
[CrossRef]

Joseph, R. I.

Krenn, J. R.

Lederer, F.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Lee, J. C. W.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

Leitner, A.

Li, E.

Locatelli, A.

Maier, S. A.

S. A. Maier, Plasmonics: Fundamentals and Applications (Spinger, 2007).

McPhedran, R. C.

Michaelis, D.

D. Michaelis, U. Peschel, C. Wächter, and A. Bräuer, Phys. Rev. E 68, 065601(R) (2003).
[CrossRef]

Modotto, D.

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Ozbay, E.

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

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Peschel, U.

D. Michaelis, U. Peschel, C. Wächter, and A. Bräuer, Phys. Rev. E 68, 065601(R) (2003).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Quinten, M.

Shen, J.

P. B. Catrysse, G. Veronis, H. Shin, J. Shen, and S. Fan, Appl. Phys. Lett. 88, 031101 (2006).
[CrossRef]

Shin, H.

P. B. Catrysse, G. Veronis, H. Shin, J. Shen, and S. Fan, Appl. Phys. Lett. 88, 031101 (2006).
[CrossRef]

Silberberg, Y.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Streifer, W.

A. Hardy and W. Streifer, J. Lightwave Technol. LT-3, 1135 (1985).
[CrossRef]

Vahldieck, R.

Veronis, G.

P. B. Catrysse, G. Veronis, H. Shin, J. Shen, and S. Fan, Appl. Phys. Lett. 88, 031101 (2006).
[CrossRef]

Wächter, C.

D. Michaelis, U. Peschel, C. Wächter, and A. Bräuer, Phys. Rev. E 68, 065601(R) (2003).
[CrossRef]

Wang, G. P.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

White, T. P.

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Zettl, A.

A. Zettl, Sturm-Liouville Theory (Mathematical Surveys and Monographs) (American Mathematical Society, 2005).

Appl. Phys. Lett. (1)

P. B. Catrysse, G. Veronis, H. Shin, J. Shen, and S. Fan, Appl. Phys. Lett. 88, 031101 (2006).
[CrossRef]

J. Lightwave Technol. (1)

A. Hardy and W. Streifer, J. Lightwave Technol. LT-3, 1135 (1985).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. (1)

E. N. Economu, Phys. Rev. 182, 539 (1969).
[CrossRef]

Phys. Rev. E (1)

D. Michaelis, U. Peschel, C. Wächter, and A. Bräuer, Phys. Rev. E 68, 065601(R) (2003).
[CrossRef]

Phys. Rev. Lett. (4)

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Science (1)

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

Other (2)

A. Zettl, Sturm-Liouville Theory (Mathematical Surveys and Monographs) (American Mathematical Society, 2005).

S. A. Maier, Plasmonics: Fundamentals and Applications (Spinger, 2007).

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Figures (4)

Fig. 1
Fig. 1

(a) Dispersion relation of the fundamental (odd) and second-order (even) mode of the coupler DC1. (b) Fundamental (continuous curve) and second-order (dashed–dotted curve) mode at 600 nm .

Fig. 2
Fig. 2

(a) Dispersion relation of the coupler DC2. Thick curves, fundamental (even) and second-order (odd) mode. Dashed curves, high-order modes. The thin horizontal line denotes a wavelength of 600 nm . Dark shaded region, light cone; light shaded region, operating bandwidth 450 750 nm . (b) Fundamental and second-order mode at 600 nm .

Fig. 3
Fig. 3

Time-average power flow in the y direction (normalized to the maximum) in the diffraction-managed device at 600 nm .

Fig. 4
Fig. 4

Time-average power flow in the y direction (normalized to the maximum) in the diffraction-managed device at different wavelengths, (a) 450 and (b) 750 nm . (c) Diffraction coefficient times propagation length ( C × L ) for array A1 (lower curve), array A2 (upper curve), and for the entire device ( C 1 × L 1 + C 2 × L 2 ) (middle curve).

Equations (5)

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i d A 1 d y + β A 1 + C A 2 = 0 ,
i d A 2 d y + β A 2 + C A 1 = 0 ,
C = ω L y 2 L y 2 ( ε ε 1 ) ( e x 1 * e x 2 + ε 2 ε e y 1 * e y 2 ) d x d y 2 L y R e ( e x 1 h z 1 * d x ) ,
i d A n d y + β A n + C ( A n + 1 + A n 1 ) = 0 .
D = 2 C d 2 cos ( k x d ) ,

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