Abstract

An integrated optical laser deflector employing the electrooptic effect is analyzed and shown to provide continuous angular deflection in one dimension. The angle of deflection is found to vary linearly with applied voltage. Because of the integrated optical configuration, significant deflection angles can be obtained for relatively low values of applied voltage. The presence of the deflector configuration within a thin-film cavity is shown to reduce the voltage required for a specific deflection. Waveguide mode coupling resulting from the induced refractive index variation is considered and found to be negligible for typical waveguide parameters.

© 1974 Optical Society of America

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References

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  1. E. I. Gordon, IEEE Proc. 54, 1391 (1966).
    [CrossRef]
  2. L. Kuhn, M. L. Dakss, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 17, 265 (1970).
    [CrossRef]
  3. P. K. Tien, R. Ulrich, J. Opt. Soc. Am. 60, 1325 (1970).
    [CrossRef]
  4. T. Takano, J. Hamasaki, IEEE J. Quantum Electron. QE-8, 206 (1972).
    [CrossRef]
  5. E. M. Garmire, H. Stoll, IEEE J. Quantum Electron. QE-8, 763 (1972).
    [CrossRef]
  6. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).
  7. A. Yariv, Quantum Electronics (Wiley, New York, 1967).
  8. J. T. Boyd, Appl. Opt. 11, 2635 (1972).
    [CrossRef] [PubMed]
  9. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  10. R. Ulrich, J. Opt. Soc. Am. 60, 1337 (1970).
    [CrossRef]
  11. I. P. Kaminow, E. H. Turner, Appl. Opt. 5, 1612 (1966).
    [CrossRef] [PubMed]
  12. D. Marcuse, Bell Syst. Tech. J. 48, 3187 (1969).
  13. J. T. Boyd, IEEE J Quantum Electron. QE-8, 788 (1972).
    [CrossRef]

1972 (4)

T. Takano, J. Hamasaki, IEEE J. Quantum Electron. QE-8, 206 (1972).
[CrossRef]

E. M. Garmire, H. Stoll, IEEE J. Quantum Electron. QE-8, 763 (1972).
[CrossRef]

J. T. Boyd, IEEE J Quantum Electron. QE-8, 788 (1972).
[CrossRef]

J. T. Boyd, Appl. Opt. 11, 2635 (1972).
[CrossRef] [PubMed]

1970 (3)

1969 (1)

D. Marcuse, Bell Syst. Tech. J. 48, 3187 (1969).

1966 (2)

Boyd, J. T.

J. T. Boyd, Appl. Opt. 11, 2635 (1972).
[CrossRef] [PubMed]

J. T. Boyd, IEEE J Quantum Electron. QE-8, 788 (1972).
[CrossRef]

Dakss, M. L.

L. Kuhn, M. L. Dakss, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 17, 265 (1970).
[CrossRef]

Garmire, E. M.

E. M. Garmire, H. Stoll, IEEE J. Quantum Electron. QE-8, 763 (1972).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Gordon, E. I.

E. I. Gordon, IEEE Proc. 54, 1391 (1966).
[CrossRef]

Hamasaki, J.

T. Takano, J. Hamasaki, IEEE J. Quantum Electron. QE-8, 206 (1972).
[CrossRef]

Heidrich, P. F.

L. Kuhn, M. L. Dakss, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 17, 265 (1970).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).

Kaminow, I. P.

Kuhn, L.

L. Kuhn, M. L. Dakss, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 17, 265 (1970).
[CrossRef]

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 48, 3187 (1969).

Scott, B. A.

L. Kuhn, M. L. Dakss, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 17, 265 (1970).
[CrossRef]

Stoll, H.

E. M. Garmire, H. Stoll, IEEE J. Quantum Electron. QE-8, 763 (1972).
[CrossRef]

Takano, T.

T. Takano, J. Hamasaki, IEEE J. Quantum Electron. QE-8, 206 (1972).
[CrossRef]

Tien, P. K.

Turner, E. H.

Ulrich, R.

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1967).

Appl. Opt. (2)

Appl. Phys. Lett. (1)

L. Kuhn, M. L. Dakss, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 17, 265 (1970).
[CrossRef]

Bell Syst. Tech. J. (1)

D. Marcuse, Bell Syst. Tech. J. 48, 3187 (1969).

IEEE J Quantum Electron. (1)

J. T. Boyd, IEEE J Quantum Electron. QE-8, 788 (1972).
[CrossRef]

IEEE J. Quantum Electron. (2)

T. Takano, J. Hamasaki, IEEE J. Quantum Electron. QE-8, 206 (1972).
[CrossRef]

E. M. Garmire, H. Stoll, IEEE J. Quantum Electron. QE-8, 763 (1972).
[CrossRef]

IEEE Proc. (1)

E. I. Gordon, IEEE Proc. 54, 1391 (1966).
[CrossRef]

J. Opt. Soc. Am. (2)

Other (3)

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).

A. Yariv, Quantum Electronics (Wiley, New York, 1967).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (2)

Fig. 1
Fig. 1

Integrated optical laser deflector configuration and refractive index profile.

Fig. 2
Fig. 2

Variation of the laser deflection angle as a function of applied voltage for two values of modulation length.

Equations (17)

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E ( r ) = C i = 1 4 q i ( r - r i ) r - r i 3 .
E ( x , y ) = - E 0 [ 2 y / d x + ( 2 x / d - 1 ) y ] ,
Δ n ( x ) = τ n 2 3 r e E y ( x ) = - τ n 2 3 r e E 0 ( 2 x / d - 1 ) ,
Δ Φ ( x ) = 2 π Δ n ( x ) l e / λ = - 2 π l e τ n 2 3 r e E 0 ( 2 x / d - 1 ) / λ ,
l e = l / ( α L - ln R ) ,
G ( u ) g ( ζ )             exp ( - j u ζ ) d ζ ,
u = k             sin θ ,
g ( ζ )             exp [ - j Δ Φ ( ζ ) ]
γ = 4 π l e τ n 2 3 r e E 0 / ( λ d ) .
θ d = sin - 1 ( γ / k ) .
θ d = sin - 1 [ ( 2 l e τ n 2 3 r e V 0 ) / ( t d ) ] .
θ d = ( 2 l e τ n 2 3 r e V 0 ) / ( t d ) .
l m = ( 1 / 4 f m ) [ ( 1 / v e ) - ( 1 / v 0 ) ] - 1 ,
d A m d z = k 2 exp ( j κ m z ) j κ m d m m A m ( z )             exp ( - j κ m z ) I m m ,
I m m = 2 n 2 0 d Δ n 2 ( x ) g 2 m ( x ) g 2 m ( x ) d x .
η m m 0 a s η m m 0 = [ ( k 4 I m m 0 2 l e 2 ) / ( κ m 2 d m 2 ) ] sinc 2 ( Δ l e / 2 ) ,
Δ = κ m - κ m 0 .

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