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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References

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  1. M. DiDomenico, Jr. and S. H. Wemple, �??Oxygen-Octahedra Ferroelectrics. I. Theory of Electro-optical and Nonlinear optical Effects,�?? J. Appl. Phys. 40, 720-734 (1969).
    [CrossRef]
  2. Q. Chen, Y. Chiu, D. N Lambeth, T. E. Schlesinger, D. D. Stancil, �??Guided-wave electro-optic beam deflector using domain reversal in LiTaO3,�?? J. Lightwave Technol. 12, 1401-1404 (1994).
    [CrossRef]
  3. D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, J. L. Casson, R. Sander, J. M. Robinson, F. Muhammad, P. Chandramani, F. Kiamilev, �??Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics,�?? Appl. Phys. Lett. 81, 3140-3142 (2002).
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Appl. Opt. (2)

Appl. Phys. B (2)

M. Jazbinsek, M. Zgonik, �??Material tensor parameters of LiNbO3 relevant for electro-and elasto-optics,�?? Appl. Phys. B 74, 407-414 (2002).
[CrossRef]

M. Müller, E. Soergel, M.C. Wengler, K. Buse, �??Light deflection from ferroelectric domain boundaries,�?? Appl. Phys. B 78, 367-370 (2004).
[CrossRef]

Appl. Phys. Lett. (2)

H. Ren, Y. H. Fan, S. T. Wu, �??Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,�?? Appl. Phys. Lett. 83, 1515-1517 (2003).
[CrossRef]

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, J. L. Casson, R. Sander, J. M. Robinson, F. Muhammad, P. Chandramani, F. Kiamilev, �??Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics,�?? Appl. Phys. Lett. 81, 3140-3142 (2002).
[CrossRef]

J. Appl. Phys. (1)

M. DiDomenico, Jr. and S. H. Wemple, �??Oxygen-Octahedra Ferroelectrics. I. Theory of Electro-optical and Nonlinear optical Effects,�?? J. Appl. Phys. 40, 720-734 (1969).
[CrossRef]

J. Lightwave Technol. (2)

Q. Chen, Y. Chiu, D. N Lambeth, T. E. Schlesinger, D. D. Stancil, �??Guided-wave electro-optic beam deflector using domain reversal in LiTaO3,�?? J. Lightwave Technol. 12, 1401-1404 (1994).
[CrossRef]

Y. Chiu, V. Gopalan, M. J. Kawas, T. E. Schlesinger, D. D. Stancil, W. P. Risk, �??Integrated Optical Device with Second-Harmonic Generator, Electro-optic Lens and Electrooptic Scanner in LiTaO3,�?? J. Lightwave Technol. 17, 462-465 (1999).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

R. W. Eason, A. J. Boyland, S. Mailis, P. G. R. Smith, �??Electro-optically controlled beam deflection for grazing incidence geometry on a domain-engineered interface in LiNbO3,�?? Opt. Commun. 197, 201-207 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

G. J. Edwards, M. Lawrence, �??A temperature dependent dispersion for congruently grown lithium niobate,�?? Opt. Quantum Electron. 16, 373-374 (1984).
[CrossRef]

Phys. Solid State (1)

V. Ya. Shur, E. L. Rumyantsev, R. G. Batchko, G. D. Miller, M. M. Fejer, R. L. Byer, �??Domain kinetics in the formation of a periodic domain structure in lithium niobate,�?? Phys. Solid State 41, 1681-1687 (1999).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 2nd edition (McGraw-Hill, New York, 1996).

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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