Abstract

We apply coupled-wave theory to describe the lateral modes of semiconductor lasers with a periodic gain and refractive-index variation across their widths. The model is relevant to devices whose complex index of refraction is determined by current injection from closely spaced parallel electrodes. Good agreement is observed between the analytical modes and those computed numerically for comparison.

© 1988 Optical Society of America

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  1. E. Kapon, J. Katz, A. Yariv, Opt. Lett. 10, 125 (1984).
    [CrossRef]
  2. J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984).
    [CrossRef]
  3. E. Kapon, C. Lindsey, J. Katz, S. Margalit, A. Yariv, Appl. Phys. Lett. 44, 389 (1984).
    [CrossRef]
  4. J. P. Hohimer, G. R. Hadley, A. Owyoung, Appl. Phys. Lett. 48, 1504 (1986).
    [CrossRef]
  5. G. R. Hadley, J. P. Hohimer, A. Owyoung, Appl. Phys. Lett. 49, 684 (1986).
    [CrossRef]
  6. W. K. Marshall, J. Katz, IEEE J. Quantum Electron. QE-22, 827 (1986).
    [CrossRef]
  7. J. E. Epler, N. Holonyak, R. D. Burnham, T. L. Paoli, R. L. Thornton, M. M. Blourke, Appl. Phys. Lett. 47, 7 (1985).
    [CrossRef]
  8. H. Kogelnik, C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
    [CrossRef]
  9. J. R. Andrews, T. L. Paoli, R. D. Burnham, Appl. Phys. Lett. 51, 1676 (1987).
    [CrossRef]

1987 (1)

J. R. Andrews, T. L. Paoli, R. D. Burnham, Appl. Phys. Lett. 51, 1676 (1987).
[CrossRef]

1986 (3)

J. P. Hohimer, G. R. Hadley, A. Owyoung, Appl. Phys. Lett. 48, 1504 (1986).
[CrossRef]

G. R. Hadley, J. P. Hohimer, A. Owyoung, Appl. Phys. Lett. 49, 684 (1986).
[CrossRef]

W. K. Marshall, J. Katz, IEEE J. Quantum Electron. QE-22, 827 (1986).
[CrossRef]

1985 (1)

J. E. Epler, N. Holonyak, R. D. Burnham, T. L. Paoli, R. L. Thornton, M. M. Blourke, Appl. Phys. Lett. 47, 7 (1985).
[CrossRef]

1984 (3)

E. Kapon, J. Katz, A. Yariv, Opt. Lett. 10, 125 (1984).
[CrossRef]

J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[CrossRef]

E. Kapon, C. Lindsey, J. Katz, S. Margalit, A. Yariv, Appl. Phys. Lett. 44, 389 (1984).
[CrossRef]

1972 (1)

H. Kogelnik, C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
[CrossRef]

Ackley, D. E.

J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[CrossRef]

Andrews, J. R.

J. R. Andrews, T. L. Paoli, R. D. Burnham, Appl. Phys. Lett. 51, 1676 (1987).
[CrossRef]

Blourke, M. M.

J. E. Epler, N. Holonyak, R. D. Burnham, T. L. Paoli, R. L. Thornton, M. M. Blourke, Appl. Phys. Lett. 47, 7 (1985).
[CrossRef]

Botez, D.

J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[CrossRef]

Burnham, R. D.

J. R. Andrews, T. L. Paoli, R. D. Burnham, Appl. Phys. Lett. 51, 1676 (1987).
[CrossRef]

J. E. Epler, N. Holonyak, R. D. Burnham, T. L. Paoli, R. L. Thornton, M. M. Blourke, Appl. Phys. Lett. 47, 7 (1985).
[CrossRef]

Butler, J. K.

J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[CrossRef]

Epler, J. E.

J. E. Epler, N. Holonyak, R. D. Burnham, T. L. Paoli, R. L. Thornton, M. M. Blourke, Appl. Phys. Lett. 47, 7 (1985).
[CrossRef]

Hadley, G. R.

J. P. Hohimer, G. R. Hadley, A. Owyoung, Appl. Phys. Lett. 48, 1504 (1986).
[CrossRef]

G. R. Hadley, J. P. Hohimer, A. Owyoung, Appl. Phys. Lett. 49, 684 (1986).
[CrossRef]

Hohimer, J. P.

G. R. Hadley, J. P. Hohimer, A. Owyoung, Appl. Phys. Lett. 49, 684 (1986).
[CrossRef]

J. P. Hohimer, G. R. Hadley, A. Owyoung, Appl. Phys. Lett. 48, 1504 (1986).
[CrossRef]

Holonyak, N.

J. E. Epler, N. Holonyak, R. D. Burnham, T. L. Paoli, R. L. Thornton, M. M. Blourke, Appl. Phys. Lett. 47, 7 (1985).
[CrossRef]

Kapon, E.

E. Kapon, J. Katz, A. Yariv, Opt. Lett. 10, 125 (1984).
[CrossRef]

E. Kapon, C. Lindsey, J. Katz, S. Margalit, A. Yariv, Appl. Phys. Lett. 44, 389 (1984).
[CrossRef]

Katz, J.

W. K. Marshall, J. Katz, IEEE J. Quantum Electron. QE-22, 827 (1986).
[CrossRef]

E. Kapon, J. Katz, A. Yariv, Opt. Lett. 10, 125 (1984).
[CrossRef]

E. Kapon, C. Lindsey, J. Katz, S. Margalit, A. Yariv, Appl. Phys. Lett. 44, 389 (1984).
[CrossRef]

Kogelnik, H.

H. Kogelnik, C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
[CrossRef]

Lindsey, C.

E. Kapon, C. Lindsey, J. Katz, S. Margalit, A. Yariv, Appl. Phys. Lett. 44, 389 (1984).
[CrossRef]

Margalit, S.

E. Kapon, C. Lindsey, J. Katz, S. Margalit, A. Yariv, Appl. Phys. Lett. 44, 389 (1984).
[CrossRef]

Marshall, W. K.

W. K. Marshall, J. Katz, IEEE J. Quantum Electron. QE-22, 827 (1986).
[CrossRef]

Owyoung, A.

G. R. Hadley, J. P. Hohimer, A. Owyoung, Appl. Phys. Lett. 49, 684 (1986).
[CrossRef]

J. P. Hohimer, G. R. Hadley, A. Owyoung, Appl. Phys. Lett. 48, 1504 (1986).
[CrossRef]

Paoli, T. L.

J. R. Andrews, T. L. Paoli, R. D. Burnham, Appl. Phys. Lett. 51, 1676 (1987).
[CrossRef]

J. E. Epler, N. Holonyak, R. D. Burnham, T. L. Paoli, R. L. Thornton, M. M. Blourke, Appl. Phys. Lett. 47, 7 (1985).
[CrossRef]

Shank, C. V.

H. Kogelnik, C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
[CrossRef]

Thornton, R. L.

J. E. Epler, N. Holonyak, R. D. Burnham, T. L. Paoli, R. L. Thornton, M. M. Blourke, Appl. Phys. Lett. 47, 7 (1985).
[CrossRef]

Yariv, A.

E. Kapon, C. Lindsey, J. Katz, S. Margalit, A. Yariv, Appl. Phys. Lett. 44, 389 (1984).
[CrossRef]

E. Kapon, J. Katz, A. Yariv, Opt. Lett. 10, 125 (1984).
[CrossRef]

Appl. Phys. Lett. (6)

J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[CrossRef]

E. Kapon, C. Lindsey, J. Katz, S. Margalit, A. Yariv, Appl. Phys. Lett. 44, 389 (1984).
[CrossRef]

J. P. Hohimer, G. R. Hadley, A. Owyoung, Appl. Phys. Lett. 48, 1504 (1986).
[CrossRef]

G. R. Hadley, J. P. Hohimer, A. Owyoung, Appl. Phys. Lett. 49, 684 (1986).
[CrossRef]

J. E. Epler, N. Holonyak, R. D. Burnham, T. L. Paoli, R. L. Thornton, M. M. Blourke, Appl. Phys. Lett. 47, 7 (1985).
[CrossRef]

J. R. Andrews, T. L. Paoli, R. D. Burnham, Appl. Phys. Lett. 51, 1676 (1987).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. K. Marshall, J. Katz, IEEE J. Quantum Electron. QE-22, 827 (1986).
[CrossRef]

J. Appl. Phys. (1)

H. Kogelnik, C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
[CrossRef]

Opt. Lett. (1)

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Figures (3)

Fig. 1
Fig. 1

Plot of the lowest 14 eigenvalues (mode index and modal gain) found by numerical integration for the waveguide shown in the inset.

Fig. 2
Fig. 2

Near-field and far-field intensities for the ν = 1, 9, and 10 lateral modes found by numerical solution (solid lines) compared with the analytical solution (dashed lines).

Fig. 3
Fig. 3

Near-field and far-field intensities for the ν = 8 and ν = 11 lateral modes found by numerical solution (solid lines) compared with the analytical solution (dashed lines).

Equations (12)

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n 2 ( x ) = { n 0 2 + 2 n 1 2 cos ( 4 π x / Λ ) x < x 0 n ¯ 0 2 x x 0 ,
d 2 E d X 2 + [ Δ + κ ( e i 2 X + e - i 2 X ) ] E = 0 ,
Δ = Λ 2 λ 0 2 ( n 0 2 - η 2 ) ,             κ = Λ 2 λ 0 2 n 1 2 .
E ( X ) = a ( X ) e i X + b ( X ) e - i X .
2 i a = ( 1 - Δ ) a - κ b , - 2 i b = –κa + ( 1 - Δ ) b .
a ( X ) = A + e i Γ X + A - e - i Γ X , b ( X ) = B + e i Γ X + B - e - i Γ X ,
Γ ( Δ ) = 1 2 ( 1 - Δ ) 2 - κ 2 .
E ( X ) = [ r + e i ( 1 + Γ ) X + e - i ( 1 - Γ ) X ] + r - × B - B + [ e i ( 1 - Γ ) X + r + e - i ( 1 + Γ ) X ] ,
r ± A ± B ± = κ ( 1 - Δ ) ± 2 Γ ( Δ ) .
E E | X = ± X 0 = ± i Δ - Δ 0 ,
Δ 0 Λ 2 λ 0 2 ( n 0 2 - n ¯ 0 2 ) .
E even ( X ) = cos ( 1 - Γ ) X + r + cos ( 1 + Γ ) X , E odd ( X ) = sin ( 1 - Γ ) X - r + sin ( 1 + Γ ) X .

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