Abstract

A simple design of spatially finite one-dimensional and bidimensional waveguide arrays, showing self-imaging properties, is proposed. Image reconstruction insensitive to array truncation is achieved by the introduction of short waveguide interruptions (waveguide segmentation), which act as a focusing lens for discretized light.

© 2008 Optical Society of America

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References

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2007 (1)

2006 (1)

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

2005 (2)

2004 (2)

2003 (1)

G. Lenz, R. Parker, M. C. Wanke, and C. M. de Sterke, Opt. Commun. 218, 87 (2003).
[CrossRef]

2001 (1)

Yu. B. Ovchinnikov and T. Pfau, Phys. Rev. Lett. 87, 123901 (2001).
[CrossRef] [PubMed]

2000 (2)

C. Y. Wu, A. R. D. Somervell, T. G. Haskell, and T. H. Barnes, Opt. Commun. 175, 27 (2000).
[CrossRef]

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

1999 (2)

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

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

1995 (1)

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

1993 (3)

1992 (1)

J. M. Heaton, R. M. Jenkins, D. R. Wright, J. T. Parker, J. C. H. Birbeck, and K. P. Hilton, Appl. Phys. Lett. 61, 1754 (1992).
[CrossRef]

1990 (1)

D. Bierlein, D. B. Laubacher, J. B. Brown, and C. J. van der Poel, Appl. Phys. Lett. 56, 1725 (1990).
[CrossRef]

1989 (1)

K. Patorski, Prog. Opt. 27, 1 (1989).
[CrossRef]

1977 (1)

A. Simon and R. Ulrich, Appl. Phys. Lett. 31, 77 (1977).
[CrossRef]

1975 (2)

R. Ulrich, Opt. Commun. 13, 259 (1975).
[CrossRef]

R. Ulrich and G. Ankele, Appl. Phys. Lett. 27, 337 (1975).
[CrossRef]

1973 (1)

Appl. Phys. Lett. (4)

R. Ulrich and G. Ankele, Appl. Phys. Lett. 27, 337 (1975).
[CrossRef]

A. Simon and R. Ulrich, Appl. Phys. Lett. 31, 77 (1977).
[CrossRef]

J. M. Heaton, R. M. Jenkins, D. R. Wright, J. T. Parker, J. C. H. Birbeck, and K. P. Hilton, Appl. Phys. Lett. 61, 1754 (1992).
[CrossRef]

D. Bierlein, D. B. Laubacher, J. B. Brown, and C. J. van der Poel, Appl. Phys. Lett. 56, 1725 (1990).
[CrossRef]

J. Lightwave Technol. (2)

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

Z. Weissman and A. Hardy, J. Lightwave Technol. 11, 1831 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (3)

G. Lenz, R. Parker, M. C. Wanke, and C. M. de Sterke, Opt. Commun. 218, 87 (2003).
[CrossRef]

R. Ulrich, Opt. Commun. 13, 259 (1975).
[CrossRef]

C. Y. Wu, A. R. D. Somervell, T. G. Haskell, and T. H. Barnes, Opt. Commun. 175, 27 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. Lett. (5)

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

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

Yu. B. Ovchinnikov and T. Pfau, Phys. Rev. Lett. 87, 123901 (2001).
[CrossRef] [PubMed]

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

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

Prog. Opt. (1)

K. Patorski, Prog. Opt. 27, 1 (1989).
[CrossRef]

Other (1)

Lumped alternating π phase shifts can also be achieved by a sharp geometric tilt of waveguide axis with a bent angle α=λ/(4nea) (see ). However, the sharp turn point of waveguide axis at z=L/2 introduces high radiation losses.

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Figures (3)

Fig. 1
Fig. 1

Schematic of (a) a 1D waveguide array and (b) a rectangular-lattice 2D waveguide array with segmented waveguide sections [see the enlargement in (a)] for image reconstruction. In (b) the waveguides with segmentation at z = L 2 are those with solid circles.

Fig. 2
Fig. 2

(a) Self-imaging in a N = 9 waveguide array with ten segmented sections for input excitation of the n = 3 waveguide. Parameter values are a = 11 μ m , λ = 1.55 μ m , and Λ = 18 μ m . (b) Intensity field distribution at the output plane of the array with ten segmented sections for a few values of segmentation period Λ. Curve 1, Λ = 18 μ m ; curve 2: Λ = 22 μ m ; curve 3, Λ = 14 μ m . The inset shows the effective 1D refractive index profile of a single waveguide used in the numerical simulations. (c) Same as Fig. 1a but for a Wannier–Stark AWO with Bloch period equal to 3 cm . Note in this case disruption of SI due to array truncation.

Fig. 3
Fig. 3

Reconstruction of character F in a 2 cm long 7 × 7 square waveguide array with 12 interruptions of period Λ = 68 μ m . Images (a), (b), and (c) show the transverse field intensity distribution: (a) at object ( z = 0 ) , (b) at the middle ( z = 1 cm ) , and (c) at the image ( z = 2 cm ) planes

Equations (4)

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i d c n d z = Δ ( c n + 1 + c n 1 ) , n = 1 , 2 , 3 , , N ,
κ n ( l ) = 2 N + 1 sin ( Q l n )
κ n ( N + 1 l ) = ( 1 ) n + 1 κ n ( l ) , β N + 1 l = β l .
i d c n , m d z = Δ x ( c n + 1 , m + c n 1 , m ) Δ y ( c n , m + 1 + c n , m 1 ) ,

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