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Electrically controlled Fresnel zone plates made from ring-shaped 180° domains

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Abstract

We present high efficiency, low noise electrically-controlled Fresnel phase zone plates that were made by creating ring-shaped 180° ferroelectric domains in a lithium niobate wafer. The primary focal lengths of these lenses ranged from 5 to 43 cm, and the light-gathering efficiency was over 37%, very close to the maximum theoretical value of 40.5%.

©2004 Optical Society of America

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Supplementary Material (1)

Media 1: GIF (244 KB)     

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Figures (5)

Fig. 1.
Fig. 1. Fresnel zone plate. (a) Photoresist pattern (dark yellow rings), (b) 180° domain structure observed through crossed polarizers (image obtained before the wafer was annealed).
Fig. 2.
Fig. 2. Arrays of zone plates recorded on a single LiNbO3 wafer. (a) No field is applied; (b) High voltage is applied (~2000 V).
Fig. 3.
Fig. 3. Efficiency of the primary lens vs. applied voltage. λ=632.8 nm
Fig. 4.
Fig. 4. Point spread function of one of the Fresnel lenses. (a) 3-dimensional plot; (b) intensity distribution along one direction. λ=632.8 nm, f 0=30 cm, lens diameter=5 mm.
Fig. 5.
Fig. 5. (0.2 MB) Movie of the performance of a 3×3 array of Fresnel zone plates.

Equations (7)

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Δ ϕ ( V ) = π n o 3 r 13 V λ ,
r m = f 0 λ 2 ( 2 m 1 ) ,
t ( r , Δ ϕ ) = cos Δ ϕ + i j = 0 a j { exp [ i π r 2 λ f 0 ( 2 j + 1 ) ] + exp [ i π r 2 λ f 0 ( 2 j + 1 ) ] } ,
a j = 2 π [ 2 j + 1 ] ( 1 ) j sin Δ ϕ .
η j = a j | 2 = ( 2 [ 2 j + 1 ] π sin Δ ϕ ) 2 .
η 0 exp = p ap p inc = A cos 2 ( V / V π / 2 ) + B sin 2 ( V / V π / 2 )
V π / 2 = λ 2 n 3 o r 13 .
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