Abstract

A new dual focal point electro-optic lens that is switchable to focusing and unfocusing is proposed and successfully demonstrated. This electro-optic lens is constructed by coating transparent fine electrodes in the Fresnel-zone plate onto a PLZT ceramic plate. Its focal length changes from 1.25 m to binary at 515 nm with the external voltage of 210 V.

© 1992 Optical Society of America

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References

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  1. J. M. Hammer, “Digital electro-optic grating deflector and modulator,” Appl. Phys. Lett. 18, 147–149 (1971).
    [CrossRef]
  2. H. Sato, K. Toda, “A new electrically controllable diffraction grating using polarization reflection,” J. Appl. Phys. 47, 4031–4032 (1976).
    [CrossRef]
  3. H. Sato, K. Toda, “An application of Pb(Zr, Ti)O3 ceramic to opto-electronic devices,” Appl. Phys. 13, 25–28 (1977).
    [CrossRef]
  4. T. Utsunomiya, H. Sato, “Electrically deformable diffraction grating using a piezoelectric material,” Ferroelectrics 27, 27–30 (1980).
    [CrossRef]
  5. T. Tatebayashi, T. Yamamoto, H. Sato, “Electro-optic variable focal-length lens using PLZT ceramic,” Appl. Opt. 30, 5049–5055 (1991).
    [CrossRef] [PubMed]
  6. G. R. Fowles, Introduction to Modern Optics, (Holt, Rinehart & Winston, New York, 1968), p. 128.

1991 (1)

1980 (1)

T. Utsunomiya, H. Sato, “Electrically deformable diffraction grating using a piezoelectric material,” Ferroelectrics 27, 27–30 (1980).
[CrossRef]

1977 (1)

H. Sato, K. Toda, “An application of Pb(Zr, Ti)O3 ceramic to opto-electronic devices,” Appl. Phys. 13, 25–28 (1977).
[CrossRef]

1976 (1)

H. Sato, K. Toda, “A new electrically controllable diffraction grating using polarization reflection,” J. Appl. Phys. 47, 4031–4032 (1976).
[CrossRef]

1971 (1)

J. M. Hammer, “Digital electro-optic grating deflector and modulator,” Appl. Phys. Lett. 18, 147–149 (1971).
[CrossRef]

Fowles, G. R.

G. R. Fowles, Introduction to Modern Optics, (Holt, Rinehart & Winston, New York, 1968), p. 128.

Hammer, J. M.

J. M. Hammer, “Digital electro-optic grating deflector and modulator,” Appl. Phys. Lett. 18, 147–149 (1971).
[CrossRef]

Sato, H.

T. Tatebayashi, T. Yamamoto, H. Sato, “Electro-optic variable focal-length lens using PLZT ceramic,” Appl. Opt. 30, 5049–5055 (1991).
[CrossRef] [PubMed]

T. Utsunomiya, H. Sato, “Electrically deformable diffraction grating using a piezoelectric material,” Ferroelectrics 27, 27–30 (1980).
[CrossRef]

H. Sato, K. Toda, “An application of Pb(Zr, Ti)O3 ceramic to opto-electronic devices,” Appl. Phys. 13, 25–28 (1977).
[CrossRef]

H. Sato, K. Toda, “A new electrically controllable diffraction grating using polarization reflection,” J. Appl. Phys. 47, 4031–4032 (1976).
[CrossRef]

Tatebayashi, T.

Toda, K.

H. Sato, K. Toda, “An application of Pb(Zr, Ti)O3 ceramic to opto-electronic devices,” Appl. Phys. 13, 25–28 (1977).
[CrossRef]

H. Sato, K. Toda, “A new electrically controllable diffraction grating using polarization reflection,” J. Appl. Phys. 47, 4031–4032 (1976).
[CrossRef]

Utsunomiya, T.

T. Utsunomiya, H. Sato, “Electrically deformable diffraction grating using a piezoelectric material,” Ferroelectrics 27, 27–30 (1980).
[CrossRef]

Yamamoto, T.

Appl. Opt. (1)

Appl. Phys. (1)

H. Sato, K. Toda, “An application of Pb(Zr, Ti)O3 ceramic to opto-electronic devices,” Appl. Phys. 13, 25–28 (1977).
[CrossRef]

Appl. Phys. Lett. (1)

J. M. Hammer, “Digital electro-optic grating deflector and modulator,” Appl. Phys. Lett. 18, 147–149 (1971).
[CrossRef]

Ferroelectrics (1)

T. Utsunomiya, H. Sato, “Electrically deformable diffraction grating using a piezoelectric material,” Ferroelectrics 27, 27–30 (1980).
[CrossRef]

J. Appl. Phys. (1)

H. Sato, K. Toda, “A new electrically controllable diffraction grating using polarization reflection,” J. Appl. Phys. 47, 4031–4032 (1976).
[CrossRef]

Other (1)

G. R. Fowles, Introduction to Modern Optics, (Holt, Rinehart & Winston, New York, 1968), p. 128.

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Figures (7)

Fig. 1
Fig. 1

Transmissivity from the odd zones of FZP as a function of (a) actual scale ξ = (2/λf)x2 and (b) modified scale X = ξ. Transmissivity of even zones is exaggerated to zero.

Fig. 2
Fig. 2

Configuration of the DFP E-O lens used in the experiments.

Fig. 3
Fig. 3

Appearance of the fabricated DFP E-O lens, where four identical lenses are evaporated onto the same substrate; black spots are the contact of the lead cable.

Fig. 4
Fig. 4

Typical intensity distributions measured as a function of the applied voltage V at 515 nm, where asymmetry has been caused by a slight tilting of incident beam from normal incidence.

Fig. 5
Fig. 5

Normalized beam width as a function of distance from the E-O lens for various applied voltages, where all curves denote the theoretical calculations with the initial phase shift Δθ0 = 1.1 π.

Fig. 6
Fig. 6

Initial focusing effect without applied voltage for various wavelengths, where the theoretical curves are based on the use of Δθo = 1.3, 1.1, and 1.0π at 477, 515, and 633 nm, respectively; FWHM, full width, half maximum.

Fig. 7
Fig. 7

Typical binary beam widths observed at the focal plane, which correspond to (a) Δθ ≃ π and (b) Δθ = 2π; wavelength, 515 nm; distance, 1.25 m.

Tables (2)

Tables Icon

Table I Specification of the DFP E-O Lens

Tables Icon

Table II Obtained Focal Lengths with the DFP E-O Lens

Equations (28)

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r N = ( λ f 2 ) 1 / 2 ( 2 N - 1 ) 1 / 2 ,             N = 1 , 2 , 3 ,
f = 2 r 1 2 / λ .
c n = 1 4 - 2 2 t odd ( ξ ) exp ( i n π 2 ξ ) d ξ = 1 4 - 1 1 exp ( i n π 2 ξ ) d ξ ,
t odd ( x ) = 1 2 + 1 2 m = - sinc [ ( 2 m - 1 ) π 2 ] exp [ i k 2 ( 2 m - 1 ) f x 2 ] ,
t even ( x ) = 1 2 - 1 2 m = - sinc [ ( 2 m - 1 ) π 2 ] exp [ i k 2 ( 2 m - 1 ) f x 2 ] .
t total ( x ) = t odd ( x ) + t even ( x ) = 1.
x 2 n x 2 + y 2 n y 2 + z 2 n z 2 = 1 ,
n x = n y n 0 - n o 3 2 R 12 E z 2 = n 0 + Δ n ,
n z n 0 - n o 3 2 R 11 E z 2
Δ θ v ( V ) = Δ n k l = n 0 3 R 12 π V 2 λ l ,
Δ θ = Δ θ 0 + Δ θ v ( V ) ,
t total ( x ) = t odd ( x ) + t even ( x ) exp ( - i Δ θ ) .
u ( x , z ) = exp { - i [ k z - ( π / 4 ) ] } λ z × - u ( x 0 ) t ( x 0 ) exp [ - i k 2 ( x - x 0 ) 2 z ] d x 0 ,
u ( x , z ) = 1 + exp ( - i Δ θ ) 2 exp ( - i k z ) + 1 - exp ( - i Δ θ ) 2 exp ( - i k z ) × m = - sinc [ ( 2 m - 1 ) π 2 ] × ( f m f m - z ) 1 / 2 exp ( - i k 2 x 2 z - f m ) ,
u ( x 0 , y 0 ; 0 ) = ( 2 π ) 1 / 2 1 w 0 exp ( - i k 2 x 0 2 + y 0 2 q ˜ 0 ) ,
u ( x 0 , y 0 ; 0 ) = 1 + exp ( - i Δ θ ) 2 ( 2 π ) 1 / 2 1 w 0 exp ( - i k 2 x 0 2 + y 0 2 q ˜ 0 ) + 1 - exp ( - i Δ θ ) 2 ( 2 π ) 1 / 2 1 w 0 m = - sinc [ ( 2 m - 1 ) π 2 ] × exp { - i k 2 [ ( 1 q ˜ 0 - 1 f m ) x 0 2 + y 0 2 q ˜ 0 ] } .
u ( x , y ; z ) = 1 + exp ( - i Δ θ ) 2 ( 2 π ) 1 / 2 1 w ( z ) exp { - i [ k z - ϕ ( z ) ] } , × exp { - i k 2 [ x 2 + y 2 R ( z ) ] - [ x 2 + y 2 w 2 ( z ) ] } + 1 - exp ( - i Δ θ ) 2 ( 2 π ) 1 / 2 × m = - sinc [ ( 2 m - 1 ) π 2 ] ( 1 w ( z ) w m ( z ) ) 1 / 2 × exp { i [ k z - ϕ m ( z ) ] - i k 2 [ x 2 R m ( z ) + y 2 R ( z ) ] - [ x 2 w m 2 ( z ) + y 2 w 2 ( z ) ] } ,
w ( z ) = w 0 [ 1 + ( λ z / w 0 2 ) 2 ] 1 / 2 ,
w m ( z ) = w 0 [ ( 1 - z / f m ) 2 + ( λ z / w 0 2 ) 2 ] 1 / 2 ,
ϕ ( z ) = tan - 1 ( λ z π w 0 2 ) = 1 2 tan - 1 [ 2 λ z / π w 0 2 1 - ( λ z / π w 0 2 ) 2 ] ,
ϕ m ( z ) = 1 2 tan - 1 { ( 2 f m - z ) λ z / π w 0 2 f m [ 1 - ( λ z / π w 0 2 ) 2 ] - z } ,
R ( z ) = [ 1 + ( π w 0 2 λ z ) 2 ] z ,
R m ( z ) = [ f m 2 + ( f m - z ) 2 ( π w 0 2 / λ z ) 2 f m 2 - z ( f m - z ) ( π ω 0 2 / λ z ) 2 ] z .
I ( x , y ; z ) = A m 2 + B m 2 ,
A m = Re [ u ( x , y ; z ) ] = cos ( Δ θ 2 ) + sin ( Δ θ 2 ) × m = - sinc [ ( 2 m - 1 ) π 2 ] ( f m f m - z ) 1 / 2 sin ( k 2 x 2 z - f m ) ,
B m = Im [ u ( x , y ; z ) ] = sin ( Δ θ 2 ) m = - sinc [ ( 2 m - 1 ) π 2 ] ( f m f m - z ) 1 / 2 cos ( k 2 x 2 z - f m )
A m = Re [ u x , y ; z ) ] = ( 2 π ) 1 / 2 1 w ( z ) cos ( Δ θ 2 ) cos [ ϕ ( z ) - k 2 x 2 R ( z ) ] exp [ - x 2 + y 2 w 2 ( z ) ] - m = - sinc [ ( 2 m - 1 ) π 2 ] [ 2 π w ( z ) w m ( z ) ] 1 / 2 sin ( Δ θ 2 ) × sin [ ϕ m ( z ) - k 2 x 2 R m ( z ) ] exp [ - x 2 w m 2 ( z ) + y 2 w 2 ( z ) ] ,
B m = Im [ u ( x , y ; z ) ] = ( 2 π ) 1 / 2 1 w ( z ) cos ( Δ θ 2 ) sin [ ϕ ( z ) - k 2 x 2 R ( z ) ] exp [ - x 2 + y 2 w 2 ( z ) ] + m = - sinc [ ( 2 m - 1 ) π 2 ] [ 2 π w ( z ) w m ( z ) ] 1 / 2 sin ( Δ θ 2 ) × cos [ ϕ m ( z ) - k 2 x 2 R m ( z ) ] exp [ - x 2 w m 2 ( z ) + y 2 w 2 ( z ) ]

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