Abstract

A new type of beam scanner is discussed based on a 1-D Fresnel zone plate consisting of titanium-diffused channel waveguides on LiNbO3. By electrooptically controlling the guided-wave phase, both beam scanning and 1-D focusing are achieved without a condensing lens. It was experimentally confirmed using the scanner with twenty-one Fresnel zones that the beam spot with a diameter of ∼50 μm at half-power level of diffraction pattern is scanned over a distance of ±70 μm in the focal plane with an applied voltage of ±40 V at 633 nm.

© 1983 Optical Society of America

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References

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  1. P. R. Ashley, W. S. C. Chang, Appl. Phys. Lett. 33, 490 (1978).
    [CrossRef]
  2. G. Hatakoshi, S. Tanaka, Opt. Lett. 2, 142 (1978).
    [CrossRef] [PubMed]
  3. P. Mottier, S. Valette, Appl. Opt. 20, 1630 (1981).
    [CrossRef] [PubMed]
  4. T. Suhara, K. Kobayashi, H. Nishihara, J. Koyama, Appl. Opt. 21, 1966 (1982).
    [CrossRef] [PubMed]
  5. K. Takizawa, Opt. Commun. 37, 345 (1981).
    [CrossRef]
  6. I. P. Kaminow, L. W. Stultz, IEEE J. Quantum Electron. QE-11, 633 (1975).
    [CrossRef]
  7. C. S. Tsai, P. Saunier, Appl. Phys. Lett. 27, 248 (1975).
    [CrossRef]
  8. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 392.
  9. H. E. Green, IEEE Trans. Microwave Theory Tech. MTT-13, 676 (1965).
    [CrossRef]

1982

1981

1978

P. R. Ashley, W. S. C. Chang, Appl. Phys. Lett. 33, 490 (1978).
[CrossRef]

G. Hatakoshi, S. Tanaka, Opt. Lett. 2, 142 (1978).
[CrossRef] [PubMed]

1975

I. P. Kaminow, L. W. Stultz, IEEE J. Quantum Electron. QE-11, 633 (1975).
[CrossRef]

C. S. Tsai, P. Saunier, Appl. Phys. Lett. 27, 248 (1975).
[CrossRef]

1965

H. E. Green, IEEE Trans. Microwave Theory Tech. MTT-13, 676 (1965).
[CrossRef]

Ashley, P. R.

P. R. Ashley, W. S. C. Chang, Appl. Phys. Lett. 33, 490 (1978).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 392.

Chang, W. S. C.

P. R. Ashley, W. S. C. Chang, Appl. Phys. Lett. 33, 490 (1978).
[CrossRef]

Green, H. E.

H. E. Green, IEEE Trans. Microwave Theory Tech. MTT-13, 676 (1965).
[CrossRef]

Hatakoshi, G.

Kaminow, I. P.

I. P. Kaminow, L. W. Stultz, IEEE J. Quantum Electron. QE-11, 633 (1975).
[CrossRef]

Kobayashi, K.

Koyama, J.

Mottier, P.

Nishihara, H.

Saunier, P.

C. S. Tsai, P. Saunier, Appl. Phys. Lett. 27, 248 (1975).
[CrossRef]

Stultz, L. W.

I. P. Kaminow, L. W. Stultz, IEEE J. Quantum Electron. QE-11, 633 (1975).
[CrossRef]

Suhara, T.

Takizawa, K.

K. Takizawa, Opt. Commun. 37, 345 (1981).
[CrossRef]

Tanaka, S.

Tsai, C. S.

C. S. Tsai, P. Saunier, Appl. Phys. Lett. 27, 248 (1975).
[CrossRef]

Valette, S.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 392.

Appl. Opt.

Appl. Phys. Lett.

P. R. Ashley, W. S. C. Chang, Appl. Phys. Lett. 33, 490 (1978).
[CrossRef]

C. S. Tsai, P. Saunier, Appl. Phys. Lett. 27, 248 (1975).
[CrossRef]

IEEE J. Quantum Electron.

I. P. Kaminow, L. W. Stultz, IEEE J. Quantum Electron. QE-11, 633 (1975).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

H. E. Green, IEEE Trans. Microwave Theory Tech. MTT-13, 676 (1965).
[CrossRef]

Opt. Commun.

K. Takizawa, Opt. Commun. 37, 345 (1981).
[CrossRef]

Opt. Lett.

Other

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 392.

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Figures (10)

Fig. 1
Fig. 1

Basic configuration of the electrooptic Fresnel lens-scanner. Channel waveguides of the same length but different widths are fabricated in the odd-numbered Fresnel zones and interdigital electrodes are deposited in the even-numbered zones.

Fig. 2
Fig. 2

Calculated curves of relative intensity of diffraction pattern in the focal plane as a function of Δυ for the FLSs with M = 19 zones and M = 49 zones. θ1 is an electrooptically induced phase of guided wave in the first zone.

Fig. 3
Fig. 3

Calculated curves of SNR in the focal plane as a function of Δυs for the odd type of FLS with different numbers of M.

Fig. 4
Fig. 4

Calculated curves of NM as a function of M for the odd type of FLS. The solid line shows the maximum value of N limited by the deterioration of SNR with the applied voltage, which is estimated from Fig. 3. The dashed line shows the limit determined by the breakdown electric field of the crystal. The maximum value of N is restricted below both curves.

Fig. 5
Fig. 5

Calculated curves of SNR as a function of Δυs for the even type of FLS with several values of M.

Fig. 6
Fig. 6

Calculated curves of NM as a function of M for the even type of FLS.

Fig. 7
Fig. 7

Calculated curves of the distribution of the applied electric field across the channel waveguides in the first, seventh, and thirteenth zones.

Fig. 8
Fig. 8

Experimental arrangement for measuring the intensity distribution of light in the focal plane.

Fig. 9
Fig. 9

Diffraction patterns in the focal plane for several values of dc voltage. The focal spot is continuously scanned in the focal plane with the applied voltage.

Fig. 10
Fig. 10

Intensity distribution of light in the focal plane for several values of dc voltage.

Tables (2)

Tables Icon

Table I Ratio of the Calculated Electric Field to the Ideal Electric Field in Three Channel Waveguides of the FLSs with Different Electrode Widths

Tables Icon

Table II Experimental and Theoretical Parameters for the FLS with 21 zones at a Wavelength of 633 nm

Equations (13)

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Θ m = α π n 3 rlV λ ( Z m Z m 1 ) ,
Z m ( 2 m 1 ) f λ / 2 ,
2 π ( A Q ̅ B Q ̅ ) λ = 2 π λ [ ( A O + b ) 2 + f 2 ( B O b ) 2 + f 2 ] 4 π A O ̅ b f λ = 2 π b ( Z m + Z m 1 ) f λ = 2 θ m ,
V = b λ α n 3 r l .
I Q = 1 2 | m = 1 M δ m { υ m 1 Δ υ υ m Δ υ exp [ j ( π 2 υ 2 + θ m ) ] d υ + υ m 1 + Δ υ υ m + Δ υ exp [ j ( π 2 υ 2 θ m ) ] d υ + } | 2 ,
υ = z 2 f λ , υ m = z m 2 f λ = 2 m 1 , Δ υ = b 2 f λ ,
δ m = 1 for m = 1 , 3 , 5 , 7 , δ m = 0 for m = 2 , 4 , 6 , 8 . }
Δ V s = θ 1 / π V .
S S f λ 2 z 1 2 M 1 .
N = 2 b S S = 2 α n 3 r l | V | 2 m 1 z 1 λ .
V M = ( 2 M 1 2 M 3 ) Z 1 E B .
N M = 2 α n 3 r l | E B | 2 M 1 ( 2 M 1 2 M 3 ) / λ .
N M 2 α n 3 r l | E B | / λ .

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