Abstract

An approximate method is presented for the analysis of overcoupled distributed feedback lasers. A closed form expression is obtained for the power emitted by a laser normalized to the saturation power in terms of the loss coefficient αL, small signal gain coefficient α0, coupling parameter κ, and length of the laser L. The result is compared with published computer solutions, and good agreement is obtained in the range |κ|L > 4; qualitative agreement extends to |κ|L = 1. The closed form expression is adapted to predict the saturation behavior of leaky-wave lasers.

© 1975 Optical Society of America

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References

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  1. H. Kogelnik, C. V. Shank, J. Appl. Phys. 43, 2327 (1972).
    [Crossref]
  2. K. O. Hill, A. Watanabe, Appl. Opt. 14, 950 (1975).
    [Crossref] [PubMed]
  3. R. F. Harrington, Time Harmonic Electromagnetic Fields (McGraw-Hill, New York1961), p. 330.
  4. D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 26, 48 (1975).
    [Crossref]

1975 (2)

K. O. Hill, A. Watanabe, Appl. Opt. 14, 950 (1975).
[Crossref] [PubMed]

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 26, 48 (1975).
[Crossref]

1972 (1)

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

Burnham, R. D.

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 26, 48 (1975).
[Crossref]

Harrington, R. F.

R. F. Harrington, Time Harmonic Electromagnetic Fields (McGraw-Hill, New York1961), p. 330.

Hill, K. O.

Kogelnik, H.

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

Scifres, D. R.

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 26, 48 (1975).
[Crossref]

Shank, C. V.

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

Streifer, W.

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 26, 48 (1975).
[Crossref]

Watanabe, A.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

D. R. Scifres, R. D. Burnham, W. Streifer, Appl. Phys. Lett. 26, 48 (1975).
[Crossref]

J. Appl. Phys. (1)

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

Other (1)

R. F. Harrington, Time Harmonic Electromagnetic Fields (McGraw-Hill, New York1961), p. 330.

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Equations (20)

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R + ( α α L j δ ) R = j κ S ;
S + ( α α L j δ ) S = j κ * R .
δ = ( ω ω 0 ) / υ g ,
α = α 0 / ( 1 + | R | 2 + | S | 2 P s ) ,
d d z ( | R | 2 | S | 2 ) = 2 ( α α L ) ( | R | 2 + | S | 2 ) .
| R e | 2 + | S e | 2 = 2 L 2 L 2 ( α α L ) ( | R | 2 + | S | 2 ) d z .
R = A cos β z ,
( β L ) 2 = ( δ L ) 2 | κ L | 2 ,
δ L = ± | κ L | ( 1 + m 2 π 2 | κ L | 2 ) 1 / 2 .
S = δ κ A cos β z + β j κ A sin β z .
| β | | κ | ,
| δ | | κ |
| S | | A cos β z | = | R | .
S e = ( R / j κ ) .
| S e | 2 = | β κ | 2 | A | 2 = ( m π | κ | L ) 2 | A | 2 .
2 α L L + 2 m 2 π 2 ( | κ | L ) 2 = 2 α 0 d z 2 cos 2 β z 1 + 2 A 2 P s cos 2 β z
2 α 0 L = [ α L L + m 2 π 2 ( | κ | L ) 2 ] ( 1 + 2 | κ L m π | 2 P P s ) 1 / 2 × [ 1 + ( 1 + 2 | κ L m π | 2 P P s ) 1 / 2 ] ,
P = | A m π κ L | 2 .
P leaky = 2 α r L | A | 2 .
2 α 0 L = [ α r L + α l L + m 2 π 2 ( | κ | L ) 2 ] × ( 1 + 1 α r L P P s ) 1 / 2 [ 1 + ( 1 + 1 α r L P P s ) 1 / 2 ] .

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