A theoretical model of a new variable-focal-length lens design that uses an electro-optic wafer with two double-sided concentric ring electrodes is proposed on the basis of an original technique for calculating the induced refractive index. It is shown that the relationship between ring radii and wafer thickness produces the required distribution of the refractive index to create converging focusing elements.

© 1998 Optical Society of America

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1998 (1)

1997 (1)

1996 (1)

1995 (1)

1992 (1)

1990 (1)

Bussjager, R.

Castro, F.

Ito, H.

Kulishov, M.

Lee, S. H.

Masuda, S.

Nabet, B.

Nose, T.

Sato, H.

Sato, S.

Song, Q. W.

Takahashi, S.

Tatebayashi, T.

Title, M. A.

Wang, X.-M.

Yamamoto, T.

Yariv, A.

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart & Winston, New York, 1976).

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Figures (4)

Fig. 1
Fig. 1

Schematic representation of the problem to be studied.

Fig. 2
Fig. 2

Examples of the normalized electric potential distribution φr,h/V0 for 2h=100 µm, and (solid curve) a=50 µm and b=100 µm and (dashed curve) a=110 µm and b=120 µm.

Fig. 3
Fig. 3

Contour plots of refractive-index distribution for a=200 µm, b=400 µm, 2h=400 µm, and 2V0=240 V.

Fig. 4
Fig. 4

Simulated phase distributions (a) for different ring radius–wafer thickness ratios, (b) for several values of the ring electrode width, and (c) for three applied voltages. The insert is a three-dimensional view of the phase delay for -ar+a.

Equations (14)

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0A*ξtanhξhJ0ξrdξ=1,  arb,
εε0φr,hz=εε0V0h0ξhA*ξJ0ξrdξ=0,0r<a,  r>b,
ρr=n=0qncosnΨsinΨ,    arb,
cos Ψ=b2+a2-2r2b2-a2,sin Ψ=2b2-r2r2-a21/2b2-a2.
0ξhA*ξJ0ξrdξ=ρrarb00r<a,  r>b,
J0ξr=J0ξb2+a22-b2-a22cos Ψ1/2=J0b+a2ξJ0b-a2ξ+2m=1Jmb+a2ξ×Jmb-a2ξcosmΨ,
n=0Ωmnqn*=δm0,    m=0,1,,
Ωmn=tanh2hηa+bJmηJmαηJnηJnαηdη,η=b+aξ2,    α=b-ab+a,qn*=qnπb-a2h,    δm0=1m=00m=1,2,.
φr,z=V0n=0qn*0 sinh2ha+bηzcosh2ha+bηh×J02ra+bηJnαηJnηdη.