Abstract

Modal noise caused by the nonuniform quantum efficiency of a detector is analyzed. Laser partition noise is taken into account in the analysis. The signal-to-noise ratio degrades to about 30 dB in the presence of only a 2% nonuniform detector quantum efficiency. The signal-to-noise ratio dependence on laser-partition noise is clarified.

© 1985 Optical Society of America

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References

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  1. R. E. Epworth, “The phenomenon of modal noise in analog and digital optical fiber systems,” in Proceedings of Fourth Conference on Optical Communication (Institute for Applied Physics, Swiss Federal Institute of Technology, Zurich, 1978), pp. 492–501.
  2. H. Olsen, “Dependence on modal noise on source coherence and fiber length,” Electron. Lett. 16, 217–218 (1980).
    [CrossRef]
  3. G. E. Rawson, J. W. Goodman, R. E. Norton, “Frequency dependence of modal noise in multimode optical fibers,” J. Opt. Soc. Am. 70, 968–976 (1980).
    [CrossRef]
  4. K. O. Hill, Y. Tremblay, S. Kawasaki, “Modal noise in multimode fiber links: theory and experiment,” Opt. Lett. 5, 270–272 (1980).
    [CrossRef] [PubMed]
  5. Y. Tremblay, B. S. Kawasaki, K. O. Hill, “Modal noise in optical fibers: open and closed speckle pattern regims,” Appl. Opt. 20, 1652–1655 (1981).
    [CrossRef] [PubMed]
  6. T. Tanifuji, M. Tokuda, “Amplitude fluctuation of laser signal transmitted through a long multimode fiber,” IEEE J. Quantum Electron. QE-17, 2228–2233 (1981).
    [CrossRef]
  7. T. Torikai, Y. Sugimoto, K. Taguchi, H. Ishihara, K. Minemura, T. Iwakami, K. Kobayashi, “Low noise and high temperature InP/InGaAsP/InGaAs avalanche photo diodes with a planar structure grown by vapor phase epitaxy,” in Proceedings of Tenth European Conference on Optical Communication (SEL Research Center, Stuttgart, 1984), pp. 220–221.
  8. R. Olshansky, “Pulse broadening caused by deviation from optimal index profiles,” Appl. Opt. 15, 782–788 (1976).
    [CrossRef] [PubMed]
  9. K. Ogawa, “Analysis of mode partition noise in laser transmission system,” IEEE J. Quantum Electron. QE-18, 849–855 (1982).
    [CrossRef]

1982

K. Ogawa, “Analysis of mode partition noise in laser transmission system,” IEEE J. Quantum Electron. QE-18, 849–855 (1982).
[CrossRef]

1981

T. Tanifuji, M. Tokuda, “Amplitude fluctuation of laser signal transmitted through a long multimode fiber,” IEEE J. Quantum Electron. QE-17, 2228–2233 (1981).
[CrossRef]

Y. Tremblay, B. S. Kawasaki, K. O. Hill, “Modal noise in optical fibers: open and closed speckle pattern regims,” Appl. Opt. 20, 1652–1655 (1981).
[CrossRef] [PubMed]

1980

1976

Epworth, R. E.

R. E. Epworth, “The phenomenon of modal noise in analog and digital optical fiber systems,” in Proceedings of Fourth Conference on Optical Communication (Institute for Applied Physics, Swiss Federal Institute of Technology, Zurich, 1978), pp. 492–501.

Goodman, J. W.

Hill, K. O.

Ishihara, H.

T. Torikai, Y. Sugimoto, K. Taguchi, H. Ishihara, K. Minemura, T. Iwakami, K. Kobayashi, “Low noise and high temperature InP/InGaAsP/InGaAs avalanche photo diodes with a planar structure grown by vapor phase epitaxy,” in Proceedings of Tenth European Conference on Optical Communication (SEL Research Center, Stuttgart, 1984), pp. 220–221.

Iwakami, T.

T. Torikai, Y. Sugimoto, K. Taguchi, H. Ishihara, K. Minemura, T. Iwakami, K. Kobayashi, “Low noise and high temperature InP/InGaAsP/InGaAs avalanche photo diodes with a planar structure grown by vapor phase epitaxy,” in Proceedings of Tenth European Conference on Optical Communication (SEL Research Center, Stuttgart, 1984), pp. 220–221.

Kawasaki, B. S.

Kawasaki, S.

Kobayashi, K.

T. Torikai, Y. Sugimoto, K. Taguchi, H. Ishihara, K. Minemura, T. Iwakami, K. Kobayashi, “Low noise and high temperature InP/InGaAsP/InGaAs avalanche photo diodes with a planar structure grown by vapor phase epitaxy,” in Proceedings of Tenth European Conference on Optical Communication (SEL Research Center, Stuttgart, 1984), pp. 220–221.

Minemura, K.

T. Torikai, Y. Sugimoto, K. Taguchi, H. Ishihara, K. Minemura, T. Iwakami, K. Kobayashi, “Low noise and high temperature InP/InGaAsP/InGaAs avalanche photo diodes with a planar structure grown by vapor phase epitaxy,” in Proceedings of Tenth European Conference on Optical Communication (SEL Research Center, Stuttgart, 1984), pp. 220–221.

Norton, R. E.

Ogawa, K.

K. Ogawa, “Analysis of mode partition noise in laser transmission system,” IEEE J. Quantum Electron. QE-18, 849–855 (1982).
[CrossRef]

Olsen, H.

H. Olsen, “Dependence on modal noise on source coherence and fiber length,” Electron. Lett. 16, 217–218 (1980).
[CrossRef]

Olshansky, R.

Rawson, G. E.

Sugimoto, Y.

T. Torikai, Y. Sugimoto, K. Taguchi, H. Ishihara, K. Minemura, T. Iwakami, K. Kobayashi, “Low noise and high temperature InP/InGaAsP/InGaAs avalanche photo diodes with a planar structure grown by vapor phase epitaxy,” in Proceedings of Tenth European Conference on Optical Communication (SEL Research Center, Stuttgart, 1984), pp. 220–221.

Taguchi, K.

T. Torikai, Y. Sugimoto, K. Taguchi, H. Ishihara, K. Minemura, T. Iwakami, K. Kobayashi, “Low noise and high temperature InP/InGaAsP/InGaAs avalanche photo diodes with a planar structure grown by vapor phase epitaxy,” in Proceedings of Tenth European Conference on Optical Communication (SEL Research Center, Stuttgart, 1984), pp. 220–221.

Tanifuji, T.

T. Tanifuji, M. Tokuda, “Amplitude fluctuation of laser signal transmitted through a long multimode fiber,” IEEE J. Quantum Electron. QE-17, 2228–2233 (1981).
[CrossRef]

Tokuda, M.

T. Tanifuji, M. Tokuda, “Amplitude fluctuation of laser signal transmitted through a long multimode fiber,” IEEE J. Quantum Electron. QE-17, 2228–2233 (1981).
[CrossRef]

Torikai, T.

T. Torikai, Y. Sugimoto, K. Taguchi, H. Ishihara, K. Minemura, T. Iwakami, K. Kobayashi, “Low noise and high temperature InP/InGaAsP/InGaAs avalanche photo diodes with a planar structure grown by vapor phase epitaxy,” in Proceedings of Tenth European Conference on Optical Communication (SEL Research Center, Stuttgart, 1984), pp. 220–221.

Tremblay, Y.

Appl. Opt.

Electron. Lett.

H. Olsen, “Dependence on modal noise on source coherence and fiber length,” Electron. Lett. 16, 217–218 (1980).
[CrossRef]

IEEE J. Quantum Electron.

T. Tanifuji, M. Tokuda, “Amplitude fluctuation of laser signal transmitted through a long multimode fiber,” IEEE J. Quantum Electron. QE-17, 2228–2233 (1981).
[CrossRef]

K. Ogawa, “Analysis of mode partition noise in laser transmission system,” IEEE J. Quantum Electron. QE-18, 849–855 (1982).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

Other

T. Torikai, Y. Sugimoto, K. Taguchi, H. Ishihara, K. Minemura, T. Iwakami, K. Kobayashi, “Low noise and high temperature InP/InGaAsP/InGaAs avalanche photo diodes with a planar structure grown by vapor phase epitaxy,” in Proceedings of Tenth European Conference on Optical Communication (SEL Research Center, Stuttgart, 1984), pp. 220–221.

R. E. Epworth, “The phenomenon of modal noise in analog and digital optical fiber systems,” in Proceedings of Fourth Conference on Optical Communication (Institute for Applied Physics, Swiss Federal Institute of Technology, Zurich, 1978), pp. 492–501.

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Figures (6)

Fig. 1
Fig. 1

Statistical model of laser-partition noise; time-average amplitude of each logitudinal mode is assumed to be 1/n.

Fig. 2
Fig. 2

ρ as a function of radial quantum-efficiency fluctuation period M calculated by Eq. (7).

Fig. 3
Fig. 3

ρ between different modes calculated by Eq. (8).

Fig. 4
Fig. 4

Signal-to-noise ratio as a function of azimuthal quantum-efficiency variation period M.

Fig. 5
Fig. 5

Spatial form of the detector-surface quantum efficiency for (a) M = 1, (b) M = 2, and (c) M = 3 for Δη = 0.1.

Fig. 6
Fig. 6

Signal-to-noise ratio dependence on the number of longitudinal modes of a laser diodes.

Equations (18)

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I s E out E out * η ( r , θ ) d S ,
E out = μ ν E μ ν ( r , θ ) i = 1 n a i 1 / 2 exp [ j ( ω i t β μ ν ( i ) z ) ] ,
I μ 1 ν 1 s | E μ 1 ν 1 ( r , θ ) | 2 η ( r , θ ) d S ( i = 1 n a i ) + μ 1 ν 1 μ 2 ν 2 s E μ 1 ν 1 ( r , θ ) E μ 2 ν 2 ( r , θ ) η ( r , θ ) d S × ( i = 1 n a i cos Δ β μ 1 ν 1 μ 2 ν 2 ( i ) z ) .
E μ ν ( r , θ ) = F μ ν ( r ) cos ν θ , F μ ν ( r ) = ( ν ! ( μ + ν ) ! ) 1 / 2 1 W 2 ( 2 r 2 W 2 ) L μ ν ( 2 r 2 W 2 ) exp ( r 2 / W 2 ) , W = ( a k n 1 2 Δ ) 1 / 2 ,
β μ ν 2 = ( k n 1 ) 2 [ 1 2 ( 2 μ + ν + 1 ) 2 Δ k n 1 a ] .
η ( r , θ ) = η 0 + Δ η cos ( 2 π N r 2 W 2 ) cos ( M θ ) ( η 0 Δ η ) .
ρ ( μ 1 , ν 1 , μ 2 , ν 2 ) = s E μ 1 ν 1 ( r , θ ) E μ 2 ν 2 ( r , θ ) η ( r , θ ) d S = Δ η s X μ 1 + ν 2 / 2 L μ 1 ν 1 ( X ) L μ 2 ν 2 ( X ) × exp ( X ) cos ν 1 θ cos ν 2 θ × cos 2 π N X cos M θ d S .
ρ ( μ 1 , ν 1 , μ 2 , ν 2 ) = π 4 Δ η ( μ 1 + ν 1 μ 1 ) ( μ 2 + ν 2 μ 2 ) r = 0 μ 1 r = 0 μ 2 ( μ 1 r ) ( μ 2 r ) × ( ν + r + r ) ( ν + 1 ) ( ν + r ) ( ν + 1 ) ( ν + r ) [ 1 + ( 2 π N ) 2 ] ( ν + r + r + 1 ) / 2 cos [ ( ν + r + r + 1 ) tan 1 ( 2 π N ) ] .
ν 1 + ν 2 = M , ν 1 ν 2 = M , ν 1 ν 2 = M ,
ρ ( μ 1 , ν 1 , μ 2 , ν 2 ) = π 8 ( μ 1 + ν 1 μ 1 ) ( μ 2 + ν 2 μ 2 ) r = 0 μ 1 r = 0 μ 2 ( μ 1 r ) ( μ 2 r ) × 1 ( ν 1 + 1 ) ( ν 1 + r ) ( ν 2 + 1 ) ( ν 2 + r ) × Γ ( ν 1 + ν 2 2 + r + r + 1 ) .
Δ I = I a 1 Δ a 1 + I a 2 Δ a 2 + + I a n Δ a n .
Δ I = I a 1 Δ a 1 + I a 2 Δ a 2 ) + + I a n Δ a n .
σ 2 = Δ I 2 = i = 1 n ( I a i ) 2 Δ a i 2 + i = 1 n j i n ( I a i ) ( I a j ) Δ a i Δ a j ,
I a i ~ μ 1 ν 1 μ 2 ν 2 ρ ( μ 1 , ν 1 , μ 2 , ν 2 ) cos Δ β u 1 ν 1 μ 2 ν 2 ( i ) z ( i = 1 , n ) .
σ 2 = i = 1 n j i n [ ( I a i ) ( I a j ) ( I a i ) 2 ] Δ a i Δ a j .
Δ a i 2 = 1 n 2 ( n 1 n ) ( i = 1 , 2 , n )
Δ a i Δ a j = 1 n Δ a i 2 ( i = 1 , 2 , n ) .
SNR = I / σ .

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