Abstract

An improved, more accurate analysis of phased-array diode lasers is presented, which yields results that differ both qualitatively and quantitatively from those previously employed. A numerical example indicating decreased splitting in array mode gains is included.

© 1985 Optical Society of America

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References

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  1. J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984).
    [Crossref]
  2. E. Kapon, J. Katz, A. Yariv, Opt. Lett. 10, 127 (1984).
  3. A. Hardy, W. Streifer, IEEE J. Lightwave Technol. (to be published).
  4. W. Streifer, A. Hardy, R. D. Burnham, D. R. Scifres, Electron. Lett. 21, 118 (1985).
    [Crossref]

1985 (1)

W. Streifer, A. Hardy, R. D. Burnham, D. R. Scifres, Electron. Lett. 21, 118 (1985).
[Crossref]

1984 (2)

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

E. Kapon, J. Katz, A. Yariv, Opt. Lett. 10, 127 (1984).

Ackley, D. E.

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

Botez, D.

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

Burnham, R. D.

W. Streifer, A. Hardy, R. D. Burnham, D. R. Scifres, Electron. Lett. 21, 118 (1985).
[Crossref]

Butler, J. K.

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

Hardy, A.

W. Streifer, A. Hardy, R. D. Burnham, D. R. Scifres, Electron. Lett. 21, 118 (1985).
[Crossref]

A. Hardy, W. Streifer, IEEE J. Lightwave Technol. (to be published).

Kapon, E.

E. Kapon, J. Katz, A. Yariv, Opt. Lett. 10, 127 (1984).

Katz, J.

E. Kapon, J. Katz, A. Yariv, Opt. Lett. 10, 127 (1984).

Scifres, D. R.

W. Streifer, A. Hardy, R. D. Burnham, D. R. Scifres, Electron. Lett. 21, 118 (1985).
[Crossref]

Streifer, W.

W. Streifer, A. Hardy, R. D. Burnham, D. R. Scifres, Electron. Lett. 21, 118 (1985).
[Crossref]

A. Hardy, W. Streifer, IEEE J. Lightwave Technol. (to be published).

Yariv, A.

E. Kapon, J. Katz, A. Yariv, Opt. Lett. 10, 127 (1984).

Appl. Phys. Lett. (1)

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

Electron. Lett. (1)

W. Streifer, A. Hardy, R. D. Burnham, D. R. Scifres, Electron. Lett. 21, 118 (1985).
[Crossref]

Opt. Lett. (1)

E. Kapon, J. Katz, A. Yariv, Opt. Lett. 10, 127 (1984).

Other (1)

A. Hardy, W. Streifer, IEEE J. Lightwave Technol. (to be published).

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Figures (4)

Fig. 1
Fig. 1

Illustrating the dielectric distribution for three coupled waveguides with additional perturbations between the guides. The functions Δ(p), p = 1, 2, 3 are also shown.

Fig. 2
Fig. 2

Comparison of Im(σνβ) at λ = 0.8 μm for three coupled waveguides as a function of τ. In Fig. 1, t = 0.15 μm, the guide indices are 3.6, the cladding indices are 3.4, and there is an additional perturbation of 30-cm−1 gain between the guides. The dotted curve for ν = 2 is zero, and for ν = 3 it is not shown since Im(σ3β) = −Im(σ1β).

Fig. 3
Fig. 3

Comparison of the array mode splitting as a function of τ as computed by the new and earlier theories.

Fig. 4
Fig. 4

Illustrating the array mode propagation constants as functions of τ.

Equations (11)

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E t ( ν ) = m = 1 N u m ( ν ) E t ( m ) ( x , y ) exp ( i σ ν z ) ,             ν = 1 , 2 , , N ,
( C - 1 B C + C - 1 K ) U ( ν ) = σ ν U ( ν ) ,             ν = 1 , 2 , , N ,
C p m = 2 z ^ - E t ( m ) × H t ( p ) d x d y ,             m , p = 1 , 2 , , N ,
C m m = 1 ,             m = 1 , 2 , , N .
κ ˜ p m = ω - Δ ( p ) [ E t ( p ) · E t ( m ) - ( m ) ( x , y ) ( x , y ) E z ( p ) E z ( m ) ] d x d y ,
Δ ( p ) = ( x , y ) - ( p ) ( x , y ) ,             p = 1 , 2 , , N .
det [ C - 1 B C + C - 1 K - σ ν I ] = 0 ,
det [ C - 1 K + ( β - σ ν ) I ] = 0.
σ 1 = β + ( ϕ + ψ ) / 2 ,             σ 2 = β + m 11 - m 13 ,             σ 3 = β + ( ϕ - ψ ) / 2 ,
ϕ = m 11 + m 13 + m 22
ψ = [ ( m 22 - m 11 - m 13 ) 2 + 8 m 12 m 21 ] 1 / 2 ,

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