Abstract

Light propagation in uniform arrays of photonic crystal waveguides is studied. We demonstrate that, in stark contrast to the case of conventional waveguide arrays, diffraction can be tailored both in magnitude and sign by varying only the spacing between adjacent waveguides. Diffraction management in ultracompact arrays of straight photonic crystal waveguides is demonstrated by solving Maxwell’s equations through the time-domain finite-element method.

© 2005 Optical Society of America

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References

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  1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).
  2. S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 62, 8212 (2000).
    [CrossRef]
  3. S. Boscolo, M. Midrio, and C. G. Someda, IEEE J. Quantum Electron. 38, 47 (2002).
    [CrossRef]
  4. A. Locatelli, D. Modotto, D. Paloschi, and C. De Angelis, Opt. Commun. 237, 97 (2004).
    [CrossRef]
  5. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  6. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  7. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
    [CrossRef] [PubMed]
  8. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
    [CrossRef]
  9. C. M. de Sterke, L. C. Botten, A. A. Asatryan, T. P. White, and R. C. McPhedran, Opt. Lett. 29, 1384 (2004).
    [CrossRef]
  10. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).
  11. S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
    [CrossRef] [PubMed]
  12. P. Ciarlet and J. Zou, Numer. Math. 82, 193 (1999).
    [CrossRef]

2004 (2)

A. Locatelli, D. Modotto, D. Paloschi, and C. De Angelis, Opt. Commun. 237, 97 (2004).
[CrossRef]

C. M. de Sterke, L. C. Botten, A. A. Asatryan, T. P. White, and R. C. McPhedran, Opt. Lett. 29, 1384 (2004).
[CrossRef]

2002 (2)

S. Boscolo, M. Midrio, and C. G. Someda, IEEE J. Quantum Electron. 38, 47 (2002).
[CrossRef]

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

2001 (1)

2000 (2)

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

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 62, 8212 (2000).
[CrossRef]

1999 (1)

P. Ciarlet and J. Zou, Numer. Math. 82, 193 (1999).
[CrossRef]

1998 (1)

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

1988 (1)

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.

Boscolo, S.

S. Boscolo, M. Midrio, and C. G. Someda, IEEE J. Quantum Electron. 38, 47 (2002).
[CrossRef]

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.

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

Christodoulides, D. N.

Ciarlet, P.

P. Ciarlet and J. Zou, Numer. Math. 82, 193 (1999).
[CrossRef]

De Angelis, C.

A. Locatelli, D. Modotto, D. Paloschi, and C. De Angelis, Opt. Commun. 237, 97 (2004).
[CrossRef]

de Sterke, C. M.

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]

Fan, S.

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 62, 8212 (2000).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
[CrossRef] [PubMed]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 62, 8212 (2000).
[CrossRef]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Johnson, S. G.

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
[CrossRef] [PubMed]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 62, 8212 (2000).
[CrossRef]

Joseph, R. I.

Lederer, F.

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

Locatelli, A.

A. Locatelli, D. Modotto, D. Paloschi, and C. De Angelis, Opt. Commun. 237, 97 (2004).
[CrossRef]

McPhedran, R. C.

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Midrio, M.

S. Boscolo, M. Midrio, and C. G. Someda, IEEE J. Quantum Electron. 38, 47 (2002).
[CrossRef]

Modotto, D.

A. Locatelli, D. Modotto, D. Paloschi, and C. De Angelis, Opt. Commun. 237, 97 (2004).
[CrossRef]

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]

Paloschi, D.

A. Locatelli, D. Modotto, D. Paloschi, and C. De Angelis, Opt. Commun. 237, 97 (2004).
[CrossRef]

Pertsch, T.

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

Peschel, U.

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

Someda, C. G.

S. Boscolo, M. Midrio, and C. G. Someda, IEEE J. Quantum Electron. 38, 47 (2002).
[CrossRef]

Villeneuve, P. R.

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 62, 8212 (2000).
[CrossRef]

White, T. P.

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

Zentgraf, T.

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

Zou, J.

P. Ciarlet and J. Zou, Numer. Math. 82, 193 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. Boscolo, M. Midrio, and C. G. Someda, IEEE J. Quantum Electron. 38, 47 (2002).
[CrossRef]

Numer. Math. (1)

P. Ciarlet and J. Zou, Numer. Math. 82, 193 (1999).
[CrossRef]

Opt. Commun. (1)

A. Locatelli, D. Modotto, D. Paloschi, and C. De Angelis, Opt. Commun. 237, 97 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (1)

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, Phys. Rev. B 62, 8212 (2000).
[CrossRef]

Phys. Rev. Lett. (3)

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]

Other (2)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

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Figures (4)

Fig. 1
Fig. 1

Projected band structure for the four-rod coupler ( a 1 = 390 nm , r 1 = 117 nm ). Solid (dashed) curve, dispersion relation of the even (odd) mode. Thin horizontal line, operating frequency of the diffraction-managed device in Fig. 4 below.

Fig. 2
Fig. 2

Projected band structure for the three-rod coupler ( a 2 = 487 nm , r 2 = 80 nm ). Solid (dashed) curve, dispersion relation of the even (odd) mode. Thin horizontal line, operating frequency of the diffraction-managed device in Fig. 4 below.

Fig. 3
Fig. 3

Schematic view of the junction between two waveguides of the four-rod and the three-rod arrays. Note the change of the lattice constant that permits straight waveguides to be obtained with different spacings. The values of the geometric parameters are given in the text.

Fig. 4
Fig. 4

(Color online) Time-averaged intensity of the field in the diffraction-managed device. The gray scale was chosen such that high intensity corresponds to black. Central horizontal line, interface between the four-rod and the three-rod arrays. The units of the axes are micrometers.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

i d A n d z + β A n + C ( A n + 1 + A n 1 ) = 0 ,
C = 1 2 β ( 2 π λ 0 ) 2 W δ ϵ r ( x , z ) E 1 * ( x , z ) E 2 ( x , z ) d W W E 1 ( x , z ) 2 d W ,
D = 2 C d 2 cos ( k x d ) ,
C = β even β odd 2 .

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