Abstract

A waveguide array is presented that behaves as an oscillator, showing periodic image reconstruction, focusing, and transverse wave-packet oscillation. The oscillator has a finite width, which removes the need for premature truncation. The array waveguide oscillator shows properties analogous to those of a pedagogically important one-dimensional quantum harmonic oscillator, which are fundamentally different from previously demonstrated oscillations in Wannier–Stark waveguide arrays. Calculations of the entire array waveguide oscillator are presented that quantify higher-order corrections to the coupled-mode approach. These results can be extended to waveguide oscillators in other systems, such as electrons in superlattices.

© 2004 Optical Society of America

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References

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  1. A. A. Friesem, U. Levy, and Y. Silverberg, Proc. IEEE 71, 208 (1983), and references therein.
    [CrossRef]
  2. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silverberg, Phys. Rev. Lett. 83, 4756 (1999).
    [CrossRef]
  3. U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
    [CrossRef]
  4. T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
    [CrossRef]
  5. J. Bleuse, G. Bastard, and P. Voisin, Phys. Rev. Lett. 60, 220 (1988).
    [CrossRef] [PubMed]
  6. O. Taussky and J. Todd, Linear Algebr. Appl. 150, 341 (1991).
    [CrossRef]
  7. A. Yariv, Optical Electronics (Oxford University, New York, 1997).

1999 (2)

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silverberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

1998 (1)

1991 (1)

O. Taussky and J. Todd, Linear Algebr. Appl. 150, 341 (1991).
[CrossRef]

1988 (1)

J. Bleuse, G. Bastard, and P. Voisin, Phys. Rev. Lett. 60, 220 (1988).
[CrossRef] [PubMed]

1983 (1)

A. A. Friesem, U. Levy, and Y. Silverberg, Proc. IEEE 71, 208 (1983), and references therein.
[CrossRef]

Aitchison, J. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silverberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Bastard, G.

J. Bleuse, G. Bastard, and P. Voisin, Phys. Rev. Lett. 60, 220 (1988).
[CrossRef] [PubMed]

Bleuse, J.

J. Bleuse, G. Bastard, and P. Voisin, Phys. Rev. Lett. 60, 220 (1988).
[CrossRef] [PubMed]

Bräuer, A.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Dannberg, P.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Eisenberg, H. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silverberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Elflein, W.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Friesem, A. A.

A. A. Friesem, U. Levy, and Y. Silverberg, Proc. IEEE 71, 208 (1983), and references therein.
[CrossRef]

Lederer, F.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[CrossRef]

Levy, U.

A. A. Friesem, U. Levy, and Y. Silverberg, Proc. IEEE 71, 208 (1983), and references therein.
[CrossRef]

Morandotti, R.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silverberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Pertsch, T.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[CrossRef]

Peschel, U.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silverberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[CrossRef]

Silverberg, Y.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silverberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

A. A. Friesem, U. Levy, and Y. Silverberg, Proc. IEEE 71, 208 (1983), and references therein.
[CrossRef]

Taussky, O.

O. Taussky and J. Todd, Linear Algebr. Appl. 150, 341 (1991).
[CrossRef]

Todd, J.

O. Taussky and J. Todd, Linear Algebr. Appl. 150, 341 (1991).
[CrossRef]

Voisin, P.

J. Bleuse, G. Bastard, and P. Voisin, Phys. Rev. Lett. 60, 220 (1988).
[CrossRef] [PubMed]

Yariv, A.

A. Yariv, Optical Electronics (Oxford University, New York, 1997).

Linear Algebr. Appl. (1)

O. Taussky and J. Todd, Linear Algebr. Appl. 150, 341 (1991).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (3)

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silverberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

J. Bleuse, G. Bastard, and P. Voisin, Phys. Rev. Lett. 60, 220 (1988).
[CrossRef] [PubMed]

Proc. IEEE (1)

A. A. Friesem, U. Levy, and Y. Silverberg, Proc. IEEE 71, 208 (1983), and references therein.
[CrossRef]

Other (1)

A. Yariv, Optical Electronics (Oxford University, New York, 1997).

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Figures (3)

Fig. 1
Fig. 1

Spreading and refocusing of light injected into a single waveguide of the 25 waveguide FAWO (a) at the center and (b) offset by 5 waveguides. The image is inverted after a propagation distance of π/Δβ and reconstructed after twice that propagation distance. Darker gray corresponds to a larger electric field amplitude.

Fig. 2
Fig. 2

Transverse oscillations for injection of the fundamental mode of the FAWO when offset by (a) 2 waveguides and (b) 7 waveguides from the center of the 25 waveguides. Darker gray corresponds to a larger electric field amplitude.

Fig. 3
Fig. 3

Phase angle of the electric field for the transverse oscillations shown in Fig. 2. The scale from white to black corresponds to a 2π phase shift.

Equations (5)

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-idandz=βoan+κn,n-1an-1+κn,n+1an+1,
κn,n-1=κn-1,n=C22N+1n-n21/2,
Δβ=C.
βmax/βmin=N-1Δβ,
κmaxκminN2.

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