Abstract

A classical approach for treating the noise properties of spatially inhomogeneous laser amplifiers is presented. Based on the Green’s function method, the amplifier output is related to the input and the amplified spontaneous emission noise. By using the correlation properties of spatially distributed spontaneous emission, the amplifier noise variance is obtained in a rigorous way. Compared with the density operator method, this approach can easily take into account the influence of spatially inhomogeneous amplifier structures, such as in the case of erbium-doped fiber amplifiers and distributed-feedback semiconductor amplifiers. The results show that the canonical expression of noise variance is valid for any type of amplifier if one defines an effective gain and noise power density, which can be accurately calculated by this approach.

© 1993 Optical Society of America

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  1. T. Mukai, Y. Yamamoto, IEEE J. Quantum Electron. QE-18, 564 (1982).
    [CrossRef]
  2. J. C. Simon, J. Opt. Commun. 4, 51 (1983).
    [CrossRef]
  3. T. Makino, J. Glinski, IEEE J. Quantum Electron. 24, 1507 (1988).
    [CrossRef]
  4. K. Kikushima, K. Nawata, M. Koga, IEEE J. Quantum Electron. 25, 163 (1989).
    [CrossRef]
  5. R. J. Mears, L. Reekie, I. M. Jauncey, D. N. Payne, Electron. Lett. 23, 1026 (1987).
    [CrossRef]
  6. E. Desurvire, J. R. Simpson, IEEE J. Lightwave Technol. 7, 835 (1989).
    [CrossRef]
  7. R. Olshansky, Electron. Lett. 24, 1363 (1988).
    [CrossRef]
  8. E. Desurvire, Appl. Opt. 29, 3118 (1990).
    [CrossRef] [PubMed]
  9. K. Kikuchi, Electron. Lett. 26, 1851 (1990).
    [CrossRef]
  10. C. H. Henry, IEEE J. Lightwave Technol. LT-4, 288 (1986).
    [CrossRef]
  11. G. H. Duan, P. Gallion, G. Debarge, IEEE J. Quantum Electron. 26, 32 (1990).
    [CrossRef]
  12. G. H. Duan, P. Gallion, G. P. Agrawal, “Dynamic and noise properties of tunable multi-electrode semiconductor lasers including spatial hole burning and nonlinear gain,”IEEE J. Quantum Electron. (to be published).
  13. K. Hinton, IEEE J. Quantum Electron. 26, 1176 (1990).
    [CrossRef]
  14. K. Kikuchi, IEEE J. Quantum Electron. 27, 416 (1991).
    [CrossRef]

1991 (1)

K. Kikuchi, IEEE J. Quantum Electron. 27, 416 (1991).
[CrossRef]

1990 (4)

G. H. Duan, P. Gallion, G. Debarge, IEEE J. Quantum Electron. 26, 32 (1990).
[CrossRef]

K. Hinton, IEEE J. Quantum Electron. 26, 1176 (1990).
[CrossRef]

E. Desurvire, Appl. Opt. 29, 3118 (1990).
[CrossRef] [PubMed]

K. Kikuchi, Electron. Lett. 26, 1851 (1990).
[CrossRef]

1989 (2)

E. Desurvire, J. R. Simpson, IEEE J. Lightwave Technol. 7, 835 (1989).
[CrossRef]

K. Kikushima, K. Nawata, M. Koga, IEEE J. Quantum Electron. 25, 163 (1989).
[CrossRef]

1988 (2)

R. Olshansky, Electron. Lett. 24, 1363 (1988).
[CrossRef]

T. Makino, J. Glinski, IEEE J. Quantum Electron. 24, 1507 (1988).
[CrossRef]

1987 (1)

R. J. Mears, L. Reekie, I. M. Jauncey, D. N. Payne, Electron. Lett. 23, 1026 (1987).
[CrossRef]

1986 (1)

C. H. Henry, IEEE J. Lightwave Technol. LT-4, 288 (1986).
[CrossRef]

1983 (1)

J. C. Simon, J. Opt. Commun. 4, 51 (1983).
[CrossRef]

1982 (1)

T. Mukai, Y. Yamamoto, IEEE J. Quantum Electron. QE-18, 564 (1982).
[CrossRef]

Agrawal, G. P.

G. H. Duan, P. Gallion, G. P. Agrawal, “Dynamic and noise properties of tunable multi-electrode semiconductor lasers including spatial hole burning and nonlinear gain,”IEEE J. Quantum Electron. (to be published).

Debarge, G.

G. H. Duan, P. Gallion, G. Debarge, IEEE J. Quantum Electron. 26, 32 (1990).
[CrossRef]

Desurvire, E.

E. Desurvire, Appl. Opt. 29, 3118 (1990).
[CrossRef] [PubMed]

E. Desurvire, J. R. Simpson, IEEE J. Lightwave Technol. 7, 835 (1989).
[CrossRef]

Duan, G. H.

G. H. Duan, P. Gallion, G. Debarge, IEEE J. Quantum Electron. 26, 32 (1990).
[CrossRef]

G. H. Duan, P. Gallion, G. P. Agrawal, “Dynamic and noise properties of tunable multi-electrode semiconductor lasers including spatial hole burning and nonlinear gain,”IEEE J. Quantum Electron. (to be published).

Gallion, P.

G. H. Duan, P. Gallion, G. Debarge, IEEE J. Quantum Electron. 26, 32 (1990).
[CrossRef]

G. H. Duan, P. Gallion, G. P. Agrawal, “Dynamic and noise properties of tunable multi-electrode semiconductor lasers including spatial hole burning and nonlinear gain,”IEEE J. Quantum Electron. (to be published).

Glinski, J.

T. Makino, J. Glinski, IEEE J. Quantum Electron. 24, 1507 (1988).
[CrossRef]

Henry, C. H.

C. H. Henry, IEEE J. Lightwave Technol. LT-4, 288 (1986).
[CrossRef]

Hinton, K.

K. Hinton, IEEE J. Quantum Electron. 26, 1176 (1990).
[CrossRef]

Jauncey, I. M.

R. J. Mears, L. Reekie, I. M. Jauncey, D. N. Payne, Electron. Lett. 23, 1026 (1987).
[CrossRef]

Kikuchi, K.

K. Kikuchi, IEEE J. Quantum Electron. 27, 416 (1991).
[CrossRef]

K. Kikuchi, Electron. Lett. 26, 1851 (1990).
[CrossRef]

Kikushima, K.

K. Kikushima, K. Nawata, M. Koga, IEEE J. Quantum Electron. 25, 163 (1989).
[CrossRef]

Koga, M.

K. Kikushima, K. Nawata, M. Koga, IEEE J. Quantum Electron. 25, 163 (1989).
[CrossRef]

Makino, T.

T. Makino, J. Glinski, IEEE J. Quantum Electron. 24, 1507 (1988).
[CrossRef]

Mears, R. J.

R. J. Mears, L. Reekie, I. M. Jauncey, D. N. Payne, Electron. Lett. 23, 1026 (1987).
[CrossRef]

Mukai, T.

T. Mukai, Y. Yamamoto, IEEE J. Quantum Electron. QE-18, 564 (1982).
[CrossRef]

Nawata, K.

K. Kikushima, K. Nawata, M. Koga, IEEE J. Quantum Electron. 25, 163 (1989).
[CrossRef]

Olshansky, R.

R. Olshansky, Electron. Lett. 24, 1363 (1988).
[CrossRef]

Payne, D. N.

R. J. Mears, L. Reekie, I. M. Jauncey, D. N. Payne, Electron. Lett. 23, 1026 (1987).
[CrossRef]

Reekie, L.

R. J. Mears, L. Reekie, I. M. Jauncey, D. N. Payne, Electron. Lett. 23, 1026 (1987).
[CrossRef]

Simon, J. C.

J. C. Simon, J. Opt. Commun. 4, 51 (1983).
[CrossRef]

Simpson, J. R.

E. Desurvire, J. R. Simpson, IEEE J. Lightwave Technol. 7, 835 (1989).
[CrossRef]

Yamamoto, Y.

T. Mukai, Y. Yamamoto, IEEE J. Quantum Electron. QE-18, 564 (1982).
[CrossRef]

Appl. Opt. (1)

Electron. Lett. (3)

K. Kikuchi, Electron. Lett. 26, 1851 (1990).
[CrossRef]

R. J. Mears, L. Reekie, I. M. Jauncey, D. N. Payne, Electron. Lett. 23, 1026 (1987).
[CrossRef]

R. Olshansky, Electron. Lett. 24, 1363 (1988).
[CrossRef]

IEEE J. Lightwave Technol. (2)

E. Desurvire, J. R. Simpson, IEEE J. Lightwave Technol. 7, 835 (1989).
[CrossRef]

C. H. Henry, IEEE J. Lightwave Technol. LT-4, 288 (1986).
[CrossRef]

IEEE J. Quantum Electron. (6)

G. H. Duan, P. Gallion, G. Debarge, IEEE J. Quantum Electron. 26, 32 (1990).
[CrossRef]

T. Mukai, Y. Yamamoto, IEEE J. Quantum Electron. QE-18, 564 (1982).
[CrossRef]

T. Makino, J. Glinski, IEEE J. Quantum Electron. 24, 1507 (1988).
[CrossRef]

K. Kikushima, K. Nawata, M. Koga, IEEE J. Quantum Electron. 25, 163 (1989).
[CrossRef]

K. Hinton, IEEE J. Quantum Electron. 26, 1176 (1990).
[CrossRef]

K. Kikuchi, IEEE J. Quantum Electron. 27, 416 (1991).
[CrossRef]

J. Opt. Commun. (1)

J. C. Simon, J. Opt. Commun. 4, 51 (1983).
[CrossRef]

Other (1)

G. H. Duan, P. Gallion, G. P. Agrawal, “Dynamic and noise properties of tunable multi-electrode semiconductor lasers including spatial hole burning and nonlinear gain,”IEEE J. Quantum Electron. (to be published).

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Equations (25)

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z 2 E ω ( z ) + k 0 2 ω ( z ) E ω ( z ) = F ω ( z ) + μ E in δ ( z ) ,
ω ( z ) = [ n j ( g α L ) / ( 2 k 0 ) ] 2 ,
F ω ( z 1 ) F ω * ( z 2 ) = 2 D F F * δ ( z 1 z 2 ) , 2 D F F * = 2 ω 3 h π c 3 n ( z ) g ( z ) n sp ( z ) ,
F ω m ( z ) = 0 , F ω * m ( z ) = 0 , m = 1 , 2 , 3 ,
F ω * m ( z 1 ) F ω n ( z 2 ) = 0 , m n , m , n = 1 , 2 , 3 ,
F ω ( z 1 ) F ω ( z 2 ) F ω * ( z 3 ) F ω * ( z 4 ) = F ω ( z 1 ) F ω * ( z 3 ) F ω ( z 2 ) F ω * ( z 4 ) + F ω ( z 1 ) F ω * ( z 4 ) F ω ( z 2 ) F ω * ( z 3 ) = 4 D F F * ( z 1 , z 3 ) D F F * ( z 2 , z 4 ) δ ( z 1 z 3 ) δ ( z 2 z 4 ) + 4 D F F * ( z 1 , z 4 ) D F F * ( z 2 , z 3 ) δ ( z 1 z 4 ) δ ( z 2 z 3 ) .
E ω ( z ) = ( L ) G ω ( z , z ) [ F ω ( z ) + μ E in δ ( z ) ] d z ,
G ω ( z , z ) = Z + ( z ) Z ( z ) W ,
E ω ( L ) = Z + ( L ) W [ ( L ) Z ( z ) F ω ( z ) d z + Z ( 0 ) μ E in ] .
Z ± ( z ) = R ± ( z ) exp ( j β 0 z ) + S ± ( z ) exp ( j β 0 z ) ,
E out ( ω ) = R + ( L ) W [ ( L ) Z ( z ) F ω ( z ) d z + Z ( 0 ) μ E in ] .
P out ( ω ) = η | E out ( ω ) | 2 ,
P out ( ω ) = | R + ( L ) W | 2 [ | μ Z ( 0 ) | 2 P in ( ω ) + η Z * ( 0 ) μ * E in * ( L ) Z ( z ) F ω ( z ) d z + c . c . + η ( L ) ( L ) Z ( z ) F ω ( z ) Z * ( z ) F ω * ( z ) d z d z ] ,
P out = 1 2 π Δ ω P out ( ω ) d ω = | R + ( L ) W | 2 × [ | μ Z ( 0 ) | 2 P in + η ( L ) | Z ( z ) | 2 2 D F F * ( z ) d z Δ f ] .
P out = G P in + N ( ω 0 ) Δ f ,
G ( L ) = | μ R + ( L ) Z ( 0 ) W | 2 ,
N ( ω 0 ) = η | R + ( L ) W | 2 ( L ) | Z ( z ) | 2 2 D F F * ( z ) d z = η G ( L ) | Z ( z ) μ Z ( 0 ) | 2 2 D F F * ( z ) d z .
σ 2 = P out P out 2 = 2 G P in N + N 2 Δ f .
σ 2 = 2 G P in N + N 2 Δ f + G P in + N Δ f + G 2 ( P in 2 P in 2 P in ) .
Z + ( z ) = A exp [ j k 0 n z + 0 Z g ( z ) d z / 2 ] ,
Z ( z ) = B exp [ j k 0 n z 0 Z g ( z ) d z / 2 ] ,
W = j 2 k 0 n A B .
G ( z ) = exp [ 0 Z g ( z ) d z ] ,
N ( ω 0 ) = G ( L ) h ν 0 L g ( z ) n sp ( z ) G ( z ) d z .
G = exp ( g L ) , N = ( G 1 ) n sp h ν .

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