Abstract

A theoretical analysis of the problem of beam steering of semiconductor injection lasers is presented. The required modifications of the dielectric constant profile of the laser structure are derived, and a practical method for implementing the needed modification is outlined.

© 1983 Optical Society of America

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References

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  1. See, for example, A. Yariv, Quantum Electronics, (Wiley, New York, 1975).
  2. D. R. Scifres, W. Streifer, R. D. Burnham, Appl. Phys. Lett. 33, 702 (1978).
    [CrossRef]
  3. W. Streifer, R. D. Burnham, D. R. Scifres, IEEE J. Quantum Electron. QE-15, 136 (1979).
    [CrossRef]
  4. K. A. Shore, P. J. Hartnett, Opt. Quantum Electron. 14, 169 (1982).
    [CrossRef]
  5. G. A. Hockham, Electron. Lett. 9, 389 (1973).
    [CrossRef]
  6. L. Lewin, Electron. Lett. 10, 134 (1974).
    [CrossRef]
  7. J. K. Butler, J. Zoroofchi, IEEE J. Quantum Electron. QE-10, 809 (1974).
    [CrossRef]
  8. L. Lewin, J. Appl. Phys. 46, 2323 (1975).
    [CrossRef]
  9. L. Lewin, IEEE Trans. Microwave Theory Tech. MTT-23, 516 (1975).
  10. P. Dias, E. L. Portnoi, M. E. Raikh, B. S. Ryvkin, Sov. Tech. Phys. Lett. 2, 424 (1976).
  11. H. C. Casey, M. B. Panish, Heterostructure Lasers (Academic, New York, 1978), Chap. 2.7.
  12. T. Tsukada, J. Appl. Phys. 45, 4899 (1974).
    [CrossRef]
  13. K. Aiki, M. Nakamura, T. Kuroda, J. Umeda, R. Ito, N. Chinone, M. Maeda, IEEE J. Quantum Electron. QE-14, 89 (1978).
    [CrossRef]
  14. M. Ueno, H. Yonezu, IEEE J. Quantum Electron. QE-15, 1189 (1979).
    [CrossRef]
  15. H. Kressel, J. K. Butler, Semiconductor Lasers and Heterojunction LEDs (Academic, New York, 1977), Chap. 17.
  16. J. R. Manning, R. Olsharsky, Electron. Lett. 17, 506 (1981).
    [CrossRef]
  17. D. Wilt, A. Yariv, IEEE J. Quantum Electron. QE-17, 1941 (1981).
    [CrossRef]

1982

K. A. Shore, P. J. Hartnett, Opt. Quantum Electron. 14, 169 (1982).
[CrossRef]

1981

J. R. Manning, R. Olsharsky, Electron. Lett. 17, 506 (1981).
[CrossRef]

D. Wilt, A. Yariv, IEEE J. Quantum Electron. QE-17, 1941 (1981).
[CrossRef]

1979

M. Ueno, H. Yonezu, IEEE J. Quantum Electron. QE-15, 1189 (1979).
[CrossRef]

W. Streifer, R. D. Burnham, D. R. Scifres, IEEE J. Quantum Electron. QE-15, 136 (1979).
[CrossRef]

1978

D. R. Scifres, W. Streifer, R. D. Burnham, Appl. Phys. Lett. 33, 702 (1978).
[CrossRef]

K. Aiki, M. Nakamura, T. Kuroda, J. Umeda, R. Ito, N. Chinone, M. Maeda, IEEE J. Quantum Electron. QE-14, 89 (1978).
[CrossRef]

1976

P. Dias, E. L. Portnoi, M. E. Raikh, B. S. Ryvkin, Sov. Tech. Phys. Lett. 2, 424 (1976).

1975

L. Lewin, J. Appl. Phys. 46, 2323 (1975).
[CrossRef]

L. Lewin, IEEE Trans. Microwave Theory Tech. MTT-23, 516 (1975).

1974

L. Lewin, Electron. Lett. 10, 134 (1974).
[CrossRef]

J. K. Butler, J. Zoroofchi, IEEE J. Quantum Electron. QE-10, 809 (1974).
[CrossRef]

T. Tsukada, J. Appl. Phys. 45, 4899 (1974).
[CrossRef]

1973

G. A. Hockham, Electron. Lett. 9, 389 (1973).
[CrossRef]

Aiki, K.

K. Aiki, M. Nakamura, T. Kuroda, J. Umeda, R. Ito, N. Chinone, M. Maeda, IEEE J. Quantum Electron. QE-14, 89 (1978).
[CrossRef]

Burnham, R. D.

W. Streifer, R. D. Burnham, D. R. Scifres, IEEE J. Quantum Electron. QE-15, 136 (1979).
[CrossRef]

D. R. Scifres, W. Streifer, R. D. Burnham, Appl. Phys. Lett. 33, 702 (1978).
[CrossRef]

Butler, J. K.

J. K. Butler, J. Zoroofchi, IEEE J. Quantum Electron. QE-10, 809 (1974).
[CrossRef]

H. Kressel, J. K. Butler, Semiconductor Lasers and Heterojunction LEDs (Academic, New York, 1977), Chap. 17.

Casey, H. C.

H. C. Casey, M. B. Panish, Heterostructure Lasers (Academic, New York, 1978), Chap. 2.7.

Chinone, N.

K. Aiki, M. Nakamura, T. Kuroda, J. Umeda, R. Ito, N. Chinone, M. Maeda, IEEE J. Quantum Electron. QE-14, 89 (1978).
[CrossRef]

Dias, P.

P. Dias, E. L. Portnoi, M. E. Raikh, B. S. Ryvkin, Sov. Tech. Phys. Lett. 2, 424 (1976).

Hartnett, P. J.

K. A. Shore, P. J. Hartnett, Opt. Quantum Electron. 14, 169 (1982).
[CrossRef]

Hockham, G. A.

G. A. Hockham, Electron. Lett. 9, 389 (1973).
[CrossRef]

Ito, R.

K. Aiki, M. Nakamura, T. Kuroda, J. Umeda, R. Ito, N. Chinone, M. Maeda, IEEE J. Quantum Electron. QE-14, 89 (1978).
[CrossRef]

Kressel, H.

H. Kressel, J. K. Butler, Semiconductor Lasers and Heterojunction LEDs (Academic, New York, 1977), Chap. 17.

Kuroda, T.

K. Aiki, M. Nakamura, T. Kuroda, J. Umeda, R. Ito, N. Chinone, M. Maeda, IEEE J. Quantum Electron. QE-14, 89 (1978).
[CrossRef]

Lewin, L.

L. Lewin, J. Appl. Phys. 46, 2323 (1975).
[CrossRef]

L. Lewin, IEEE Trans. Microwave Theory Tech. MTT-23, 516 (1975).

L. Lewin, Electron. Lett. 10, 134 (1974).
[CrossRef]

Maeda, M.

K. Aiki, M. Nakamura, T. Kuroda, J. Umeda, R. Ito, N. Chinone, M. Maeda, IEEE J. Quantum Electron. QE-14, 89 (1978).
[CrossRef]

Manning, J. R.

J. R. Manning, R. Olsharsky, Electron. Lett. 17, 506 (1981).
[CrossRef]

Nakamura, M.

K. Aiki, M. Nakamura, T. Kuroda, J. Umeda, R. Ito, N. Chinone, M. Maeda, IEEE J. Quantum Electron. QE-14, 89 (1978).
[CrossRef]

Olsharsky, R.

J. R. Manning, R. Olsharsky, Electron. Lett. 17, 506 (1981).
[CrossRef]

Panish, M. B.

H. C. Casey, M. B. Panish, Heterostructure Lasers (Academic, New York, 1978), Chap. 2.7.

Portnoi, E. L.

P. Dias, E. L. Portnoi, M. E. Raikh, B. S. Ryvkin, Sov. Tech. Phys. Lett. 2, 424 (1976).

Raikh, M. E.

P. Dias, E. L. Portnoi, M. E. Raikh, B. S. Ryvkin, Sov. Tech. Phys. Lett. 2, 424 (1976).

Ryvkin, B. S.

P. Dias, E. L. Portnoi, M. E. Raikh, B. S. Ryvkin, Sov. Tech. Phys. Lett. 2, 424 (1976).

Scifres, D. R.

W. Streifer, R. D. Burnham, D. R. Scifres, IEEE J. Quantum Electron. QE-15, 136 (1979).
[CrossRef]

D. R. Scifres, W. Streifer, R. D. Burnham, Appl. Phys. Lett. 33, 702 (1978).
[CrossRef]

Shore, K. A.

K. A. Shore, P. J. Hartnett, Opt. Quantum Electron. 14, 169 (1982).
[CrossRef]

Streifer, W.

W. Streifer, R. D. Burnham, D. R. Scifres, IEEE J. Quantum Electron. QE-15, 136 (1979).
[CrossRef]

D. R. Scifres, W. Streifer, R. D. Burnham, Appl. Phys. Lett. 33, 702 (1978).
[CrossRef]

Tsukada, T.

T. Tsukada, J. Appl. Phys. 45, 4899 (1974).
[CrossRef]

Ueno, M.

M. Ueno, H. Yonezu, IEEE J. Quantum Electron. QE-15, 1189 (1979).
[CrossRef]

Umeda, J.

K. Aiki, M. Nakamura, T. Kuroda, J. Umeda, R. Ito, N. Chinone, M. Maeda, IEEE J. Quantum Electron. QE-14, 89 (1978).
[CrossRef]

Wilt, D.

D. Wilt, A. Yariv, IEEE J. Quantum Electron. QE-17, 1941 (1981).
[CrossRef]

Yariv, A.

D. Wilt, A. Yariv, IEEE J. Quantum Electron. QE-17, 1941 (1981).
[CrossRef]

See, for example, A. Yariv, Quantum Electronics, (Wiley, New York, 1975).

Yonezu, H.

M. Ueno, H. Yonezu, IEEE J. Quantum Electron. QE-15, 1189 (1979).
[CrossRef]

Zoroofchi, J.

J. K. Butler, J. Zoroofchi, IEEE J. Quantum Electron. QE-10, 809 (1974).
[CrossRef]

Appl. Phys. Lett.

D. R. Scifres, W. Streifer, R. D. Burnham, Appl. Phys. Lett. 33, 702 (1978).
[CrossRef]

Electron. Lett.

G. A. Hockham, Electron. Lett. 9, 389 (1973).
[CrossRef]

L. Lewin, Electron. Lett. 10, 134 (1974).
[CrossRef]

J. R. Manning, R. Olsharsky, Electron. Lett. 17, 506 (1981).
[CrossRef]

IEEE J. Quantum Electron.

D. Wilt, A. Yariv, IEEE J. Quantum Electron. QE-17, 1941 (1981).
[CrossRef]

K. Aiki, M. Nakamura, T. Kuroda, J. Umeda, R. Ito, N. Chinone, M. Maeda, IEEE J. Quantum Electron. QE-14, 89 (1978).
[CrossRef]

M. Ueno, H. Yonezu, IEEE J. Quantum Electron. QE-15, 1189 (1979).
[CrossRef]

J. K. Butler, J. Zoroofchi, IEEE J. Quantum Electron. QE-10, 809 (1974).
[CrossRef]

W. Streifer, R. D. Burnham, D. R. Scifres, IEEE J. Quantum Electron. QE-15, 136 (1979).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

L. Lewin, IEEE Trans. Microwave Theory Tech. MTT-23, 516 (1975).

J. Appl. Phys.

L. Lewin, J. Appl. Phys. 46, 2323 (1975).
[CrossRef]

T. Tsukada, J. Appl. Phys. 45, 4899 (1974).
[CrossRef]

Opt. Quantum Electron.

K. A. Shore, P. J. Hartnett, Opt. Quantum Electron. 14, 169 (1982).
[CrossRef]

Sov. Tech. Phys. Lett.

P. Dias, E. L. Portnoi, M. E. Raikh, B. S. Ryvkin, Sov. Tech. Phys. Lett. 2, 424 (1976).

Other

H. C. Casey, M. B. Panish, Heterostructure Lasers (Academic, New York, 1978), Chap. 2.7.

See, for example, A. Yariv, Quantum Electronics, (Wiley, New York, 1975).

H. Kressel, J. K. Butler, Semiconductor Lasers and Heterojunction LEDs (Academic, New York, 1977), Chap. 17.

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Figures (4)

Fig. 1
Fig. 1

Schematic configuration of semiconductor laser beam steering.

Fig. 2
Fig. 2

(a) A sech2 law dielectric constant distribution. (b) Modification of the dielectric constant needed for a beam deflection by an angle θ.

Fig. 3
Fig. 3

Dielectric constant distribution in a quadratic index pure gain guiding medium: (a) real part, (b) imaginary part.

Fig. 4
Fig. 4

Dielectric constant distribution in a 1-D three-layer slab waveguide: (a) real part, (b) imaginary part.

Tables (1)

Tables Icon

Table I Examples of Dielectric Constant Modification in Several Waveguide Structures

Equations (31)

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U ( ϕ ) α g ( ϕ ) E ( y ) exp [ i k ( ϕ ) y ] d y ,
k ( ϕ ) = 2 π λ sin ϕ .
d 2 E d y 2 + ( k 2 β 2 ) E = 0 ,
U [ k ( ϕ ) ] = U 0 [ k ( ϕ ) k ( θ ) ] ,
E ( y ) = E 0 ( y ) exp [ i k ( θ ) y ] .
d 2 E 0 d y 2 + [ 0 k 2 ( β 0 ) 2 ] E 0 = 0 ,
k 2 β 2 = [ 0 k ( β 0 ) 2 + k 2 ( θ ) ] E 0 ( y ) 2 i k ( θ ) d E 0 d y E 0 ( y ) .
Δ r + Δ r | E 0 | 2 d y | E 0 | 2 d y = 2 k ( θ ) k 2 d E r 0 d y E i 0 E r 0 d E i 0 d y ( E r 0 ) 2 + ( E i 0 ) 2 ,
Δ i = 2 k 2 ( β r 0 Δ β i + β i 0 Δ β r ) 2 k ( θ ) k 2 d E r 0 d y E r 0 + d E i 0 d y E i 0 ( E r 0 ) 2 + ( E i 0 ) 2 ,
Δ r = 2 k ( θ ) k 2 d E r 0 d y E i 0 E r 0 d E i 0 d y ( E r 0 ) 2 + ( E i 0 ) 2 ,
Δ i = 2 k ( θ ) k 2 d E r 0 d y E r 0 + d E i 0 d y E i 0 ( E r 0 ) 2 + ( E i 0 ) 2 .
a = ( 1 + i ) λ r 0 g m π S 2 a r + i a i ,
K = ( k a r 2 ) 2 ,
β 2 = 2 k 2 h 2 = 1 k 2 + q 2 .
d 2 E 0 d y 2 + [ 0 k 2 ( β 0 ) 2 ] E 0 = 0 ,
( β 0 ) 2 ( β r 0 + i β i 0 ) 2 ( β r 0 ) 2 + 2 i β r 0 β i 0 ,
( β r 0 ) 2 = k 2 r 0 | E 0 | 2 d y | d E 0 d y | 2 d y | E 0 | 2 d y ,
β i 0 = k 2 i 0 | E 0 | 2 d y 2 β r 0 | E 0 | 2 d y ,
E = E 0 exp [ i k ( θ ) y ] .
| E | 2 = | E 0 | 2
| d E d y | 2 = k 2 ( θ ) | E 0 | 2 + | d E 0 d y | 2 .
β r 2 = k 2 r | E | 2 d y | d E d y | 2 d y | E | 2 d y ,
β i = k 2 i | E | 2 d y 2 β r | E | 2 d y .
β r 2 = ( β r 0 ) 2 k 2 ( θ ) + k 2 Δ r | E 0 | 2 d y | E 0 | 2 d y ,
β i = ( 1 Δ β r β r 0 ) [ β i 0 + Δ i | E 0 | 2 d y | E 0 | 2 d y ] ,
Δ = 0 = ( r r 0 ) + i ( i i 0 ) Δ r + i Δ i
Δ β r β r β r 0 1 2 β r 0 [ Δ r | E 0 | 2 d y | E 0 | 2 d y k 2 ( θ ) ] .
Δ r ( y ) = Δ r ( y ) ,
Δ β r k 2 ( θ ) 2 β r 0 .
Δ i ( y ) = Δ i ( y ) ,
Δ β i = β i 0 · k 2 ( θ ) 2 ( β r 0 ) 2 .

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