Abstract

An optical phase array with tunable phase step is demonstrated. The phase array consists of a two-dimensional hexagonal lattice of inverted ferroelectric domains fabricated on a Z-cut lithium niobate substrate. The electro-optically tunable phase step is obtained by the application of an external electric field along the z axis of the crystal via transparent electrodes. Theoretical analysis and experimental results are presented, showing that a tunable and flexible adaptive optical illuminator device can be realized by combining the electro-optic tunability with the Talbot effect. Generation of a multiplicity of light patterns is shown.

© 2006 Optical Society of America

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References

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2006 (2)

2002 (1)

2000 (1)

1995 (2)

1994 (1)

E. Bonet, P. Andres, J. C. Barreiro, and A. Pons, Opt. Commun. 106, 39 (1994).
[CrossRef]

1993 (1)

1990 (1)

1971 (1)

H. Dammann and K. Gortler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Andres, P.

E. Bonet, P. Andres, J. C. Barreiro, and A. Pons, Opt. Commun. 106, 39 (1994).
[CrossRef]

Arrizon, V.

Baker, K. L.

Barreiro, J. C.

E. Bonet, P. Andres, J. C. Barreiro, and A. Pons, Opt. Commun. 106, 39 (1994).
[CrossRef]

Bonet, E.

E. Bonet, P. Andres, J. C. Barreiro, and A. Pons, Opt. Commun. 106, 39 (1994).
[CrossRef]

Bosenberg, W. R.

Byer, R. L.

Dai, E.

Dammann, H.

H. Dammann and K. Gortler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Eckardt, R. C.

Fejer, M. M.

Gortler, K.

H. Dammann and K. Gortler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Liu, L.

Lohmann, A. W.

Madamopoulos, N.

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, 1991).

Millán, M. S.

Myers, L. E.

Ojeda-Castañeda, J.

Otón, J.

Patorski, K.

K. Patorski, Handbook of the Moirè Fringe Technique (Elsevier, 1993).

Pérez-Cabré, E.

Pierce, J. W.

Pons, A.

E. Bonet, P. Andres, J. C. Barreiro, and A. Pons, Opt. Commun. 106, 39 (1994).
[CrossRef]

Riza, N. A.

Stappaerts, E. A.

Thomas, J. A.

Xi, P.

Zhou, C.

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Figures (4)

Fig. 1
Fig. 1

Optical microscopy images of the (a) photolithography mask used in the fabrication process and (b) actual domain structure.

Fig. 2
Fig. 2

Scheme of the used optical setup.

Fig. 3
Fig. 3

Experimental patterns obtained for a phase step 2 Δ ϕ = π at (a) z = z t 2 , (b) z = z t 4 , and (c) z = z t 8 and (d)–(f) the respective numerical simulations. Patterns obtained for a phase step 2 Δ ϕ = 3 π 2 at (g) z = z t 2 , (h) z = z t 4 , and (i) z = z t 8 and (l)–(n) the respective numerical simulations.

Fig. 4
Fig. 4

Selection of interesting patterns obtained at different voltage and recording distances.

Equations (4)

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t ( x , y ) = u ( x , y ) 1 t x t y [ comb ( x t x ) comb ( y t y ) + comb ( x t x 1 2 ) comb ( y t y 1 2 ) ] ,
u z ( Δ ϕ ; x , y ) = n , m c n m ( Δ ϕ ) exp [ i 2 π ( n x t x + m y t y ) ] exp [ i π λ z ( n 2 t x 2 + m 2 t y 2 ) ] .
c 00 ( Δ ϕ ) = exp [ i ( Δ ϕ ) ] + α { exp [ i ( Δ ϕ ) ] exp [ i ( Δ ϕ ) ] } ,
c n m ( Δ ϕ ) = i { 1 + exp [ i π ( n + m ) ] } ( 1 ) n sin ( Δ ϕ ) n ( n 2 m 2 ) π 2 [ ( n + m ) cos ( 2 m 3 n 5 π ) 2 n cos ( n π 5 ) + ( n m ) cos ( 2 m + 3 n 5 π ) ] ,

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