Abstract

For the first time, an integral equation approach for the numerical assessment of Semiconductor Optical Amplifiers (SOAs) is proposed. Performance comparisons between the suggested formulation and the traditional transfer matrix method are carried out in terms of the computation costs in solving the multi-wave mixing process in bidirectional, high-power SOAs. Computation efficiency improvement by more than an order of magnitude was observed with the proposed formulation, achieving better accuracy at equivalent spatial resolution.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Y. J Chu, H. Ghafouri-Shiraz, "Analysis of gain and saturation characteristics of a semiconductor laser optical amplifier using transfer matrices," J. Lightwave Technol. 12, 1378-1386 (1994).
    [CrossRef]
  2. S. L. Zhang and J. J. O’Reilly, "Modelling of four-wave-mixing wavelength conversion in a semiconductor laser amplifier," Physical Modelling of Semiconductor Devices, IEE Colloquium on, 5/1-5/6 (1995).
  3. H. Lee, H. Yoon, Y. Kim, J. Jeong, "Theoretical study of frequency chirping and extinction ratio of wavelength-converted optical signals by XGM and XPM using SOA’s," IEEE J. Quantum Electron. 35, 1213-1219 (1999).
    [CrossRef]
  4. M. J. Connelly, "Wideband semiconductor optical amplifier steady-state numerical model," IEEE J. Quantum Electron. 37, 439-447 (2001).
    [CrossRef]
  5. B. Min, W. J. Lee, and N. Park, "Efficient formulation of Raman amplifier propagation equations with average power analysis," IEEE Photonics Technol. Lett. 12, 1486-1488 (2000).
    [CrossRef]
  6. N. Park, P. Kim, J. Park, L. K. Choi, "Integral form expansion of fiber Raman amplifier problem," Opt. Fiber Technol.,  11, 111-130 (2005).
    [CrossRef]
  7. J. Park, P. Kim, J. Park, H. Lee, and N. Park, "Closed integral form expansion of Raman equation for efficient gain optimization process," IEEE Photonics Technol. Lett. 16, 1649-1651 (2004).
    [CrossRef]
  8. M. A. Summerfield, and R. S. Tucker, "Frequency domain model of multiwave mixing in bulk semiconductor optical amplifiers," IEEE J. Sel. Top. Quantum Electron. 5, 839-850 (1999).
    [CrossRef]

2005

N. Park, P. Kim, J. Park, L. K. Choi, "Integral form expansion of fiber Raman amplifier problem," Opt. Fiber Technol.,  11, 111-130 (2005).
[CrossRef]

2004

J. Park, P. Kim, J. Park, H. Lee, and N. Park, "Closed integral form expansion of Raman equation for efficient gain optimization process," IEEE Photonics Technol. Lett. 16, 1649-1651 (2004).
[CrossRef]

2001

M. J. Connelly, "Wideband semiconductor optical amplifier steady-state numerical model," IEEE J. Quantum Electron. 37, 439-447 (2001).
[CrossRef]

2000

B. Min, W. J. Lee, and N. Park, "Efficient formulation of Raman amplifier propagation equations with average power analysis," IEEE Photonics Technol. Lett. 12, 1486-1488 (2000).
[CrossRef]

1999

H. Lee, H. Yoon, Y. Kim, J. Jeong, "Theoretical study of frequency chirping and extinction ratio of wavelength-converted optical signals by XGM and XPM using SOA’s," IEEE J. Quantum Electron. 35, 1213-1219 (1999).
[CrossRef]

M. A. Summerfield, and R. S. Tucker, "Frequency domain model of multiwave mixing in bulk semiconductor optical amplifiers," IEEE J. Sel. Top. Quantum Electron. 5, 839-850 (1999).
[CrossRef]

1994

C. Y. J Chu, H. Ghafouri-Shiraz, "Analysis of gain and saturation characteristics of a semiconductor laser optical amplifier using transfer matrices," J. Lightwave Technol. 12, 1378-1386 (1994).
[CrossRef]

Choi, L. K.

N. Park, P. Kim, J. Park, L. K. Choi, "Integral form expansion of fiber Raman amplifier problem," Opt. Fiber Technol.,  11, 111-130 (2005).
[CrossRef]

Chu, C. Y. J

C. Y. J Chu, H. Ghafouri-Shiraz, "Analysis of gain and saturation characteristics of a semiconductor laser optical amplifier using transfer matrices," J. Lightwave Technol. 12, 1378-1386 (1994).
[CrossRef]

Connelly, M. J.

M. J. Connelly, "Wideband semiconductor optical amplifier steady-state numerical model," IEEE J. Quantum Electron. 37, 439-447 (2001).
[CrossRef]

Ghafouri-Shiraz, H.

C. Y. J Chu, H. Ghafouri-Shiraz, "Analysis of gain and saturation characteristics of a semiconductor laser optical amplifier using transfer matrices," J. Lightwave Technol. 12, 1378-1386 (1994).
[CrossRef]

Jeong, J.

H. Lee, H. Yoon, Y. Kim, J. Jeong, "Theoretical study of frequency chirping and extinction ratio of wavelength-converted optical signals by XGM and XPM using SOA’s," IEEE J. Quantum Electron. 35, 1213-1219 (1999).
[CrossRef]

Kim, P.

N. Park, P. Kim, J. Park, L. K. Choi, "Integral form expansion of fiber Raman amplifier problem," Opt. Fiber Technol.,  11, 111-130 (2005).
[CrossRef]

J. Park, P. Kim, J. Park, H. Lee, and N. Park, "Closed integral form expansion of Raman equation for efficient gain optimization process," IEEE Photonics Technol. Lett. 16, 1649-1651 (2004).
[CrossRef]

Kim, Y.

H. Lee, H. Yoon, Y. Kim, J. Jeong, "Theoretical study of frequency chirping and extinction ratio of wavelength-converted optical signals by XGM and XPM using SOA’s," IEEE J. Quantum Electron. 35, 1213-1219 (1999).
[CrossRef]

Lee, H.

J. Park, P. Kim, J. Park, H. Lee, and N. Park, "Closed integral form expansion of Raman equation for efficient gain optimization process," IEEE Photonics Technol. Lett. 16, 1649-1651 (2004).
[CrossRef]

H. Lee, H. Yoon, Y. Kim, J. Jeong, "Theoretical study of frequency chirping and extinction ratio of wavelength-converted optical signals by XGM and XPM using SOA’s," IEEE J. Quantum Electron. 35, 1213-1219 (1999).
[CrossRef]

Lee, W. J.

B. Min, W. J. Lee, and N. Park, "Efficient formulation of Raman amplifier propagation equations with average power analysis," IEEE Photonics Technol. Lett. 12, 1486-1488 (2000).
[CrossRef]

Min, B.

B. Min, W. J. Lee, and N. Park, "Efficient formulation of Raman amplifier propagation equations with average power analysis," IEEE Photonics Technol. Lett. 12, 1486-1488 (2000).
[CrossRef]

Park, J.

N. Park, P. Kim, J. Park, L. K. Choi, "Integral form expansion of fiber Raman amplifier problem," Opt. Fiber Technol.,  11, 111-130 (2005).
[CrossRef]

J. Park, P. Kim, J. Park, H. Lee, and N. Park, "Closed integral form expansion of Raman equation for efficient gain optimization process," IEEE Photonics Technol. Lett. 16, 1649-1651 (2004).
[CrossRef]

J. Park, P. Kim, J. Park, H. Lee, and N. Park, "Closed integral form expansion of Raman equation for efficient gain optimization process," IEEE Photonics Technol. Lett. 16, 1649-1651 (2004).
[CrossRef]

Park, N.

N. Park, P. Kim, J. Park, L. K. Choi, "Integral form expansion of fiber Raman amplifier problem," Opt. Fiber Technol.,  11, 111-130 (2005).
[CrossRef]

J. Park, P. Kim, J. Park, H. Lee, and N. Park, "Closed integral form expansion of Raman equation for efficient gain optimization process," IEEE Photonics Technol. Lett. 16, 1649-1651 (2004).
[CrossRef]

B. Min, W. J. Lee, and N. Park, "Efficient formulation of Raman amplifier propagation equations with average power analysis," IEEE Photonics Technol. Lett. 12, 1486-1488 (2000).
[CrossRef]

Summerfield, M. A.

M. A. Summerfield, and R. S. Tucker, "Frequency domain model of multiwave mixing in bulk semiconductor optical amplifiers," IEEE J. Sel. Top. Quantum Electron. 5, 839-850 (1999).
[CrossRef]

Tucker, R. S.

M. A. Summerfield, and R. S. Tucker, "Frequency domain model of multiwave mixing in bulk semiconductor optical amplifiers," IEEE J. Sel. Top. Quantum Electron. 5, 839-850 (1999).
[CrossRef]

Yoon, H.

H. Lee, H. Yoon, Y. Kim, J. Jeong, "Theoretical study of frequency chirping and extinction ratio of wavelength-converted optical signals by XGM and XPM using SOA’s," IEEE J. Quantum Electron. 35, 1213-1219 (1999).
[CrossRef]

IEEE J. Quantum Electron.

H. Lee, H. Yoon, Y. Kim, J. Jeong, "Theoretical study of frequency chirping and extinction ratio of wavelength-converted optical signals by XGM and XPM using SOA’s," IEEE J. Quantum Electron. 35, 1213-1219 (1999).
[CrossRef]

M. J. Connelly, "Wideband semiconductor optical amplifier steady-state numerical model," IEEE J. Quantum Electron. 37, 439-447 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. A. Summerfield, and R. S. Tucker, "Frequency domain model of multiwave mixing in bulk semiconductor optical amplifiers," IEEE J. Sel. Top. Quantum Electron. 5, 839-850 (1999).
[CrossRef]

IEEE Photonics Technol. Lett.

J. Park, P. Kim, J. Park, H. Lee, and N. Park, "Closed integral form expansion of Raman equation for efficient gain optimization process," IEEE Photonics Technol. Lett. 16, 1649-1651 (2004).
[CrossRef]

B. Min, W. J. Lee, and N. Park, "Efficient formulation of Raman amplifier propagation equations with average power analysis," IEEE Photonics Technol. Lett. 12, 1486-1488 (2000).
[CrossRef]

J. Lightwave Technol.

C. Y. J Chu, H. Ghafouri-Shiraz, "Analysis of gain and saturation characteristics of a semiconductor laser optical amplifier using transfer matrices," J. Lightwave Technol. 12, 1378-1386 (1994).
[CrossRef]

Opt. Fiber Technol.

N. Park, P. Kim, J. Park, L. K. Choi, "Integral form expansion of fiber Raman amplifier problem," Opt. Fiber Technol.,  11, 111-130 (2005).
[CrossRef]

Other

S. L. Zhang and J. J. O’Reilly, "Modelling of four-wave-mixing wavelength conversion in a semiconductor laser amplifier," Physical Modelling of Semiconductor Devices, IEE Colloquium on, 5/1-5/6 (1995).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Schematic diagrams comparing the multi-wave SOA analysis method based on (a) coupled differential equation, and (b) suggested integral equation method

Fig. 2.
Fig. 2.

Comparison of the result with previous publication (Ref. [8])

Fig. 3.
Fig. 3.

L-I curves (forward output power) obtained with differential / integral equation method

Fig. 4.
Fig. 4.

field distribution (left) and carrier density (right) in the SOA (Dark square + dotted line: finite difference method with 10 segments, Hollow circle + dotted line: proposed integral equation method with 10 segments, Solid line: finite difference method, 2000 SOA segments)

Fig. 5.
Fig. 5.

Forward / backward signal power distributions in the SOA cavity Upper graphs Forward (left) / Backward (right) waves solved with differential equation Lower graphs : Forward (left) / Backward (right) waves solved with integral equation

Fig. 6.
Fig. 6.

Convergence error (forward output power) and required computation time plotted as a function of number of SOA segments (driving current = 500mA. Dash: finite difference method [4], Dash dot: Runge-Kutta, Solid line: proposed integral equation method)

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

d a l dz = 1 2 g l ( N ) [ ( 1 ) a l m = cpp , shb , ch ( Δ ω ij ( 1 j β m ) ε m 1 + j Δ ω ij τ m a i * a j a k ) ] γ sc a l 2
a l ( z ) = a l ( 0 ) + 0 z 1 2 g l ( N ) [ ( 1 ) a l m ( Δ ω ij ( 1 j β m ) ε m 1 + j Δ ω ij τ m a i * a j a k ) γ sc a l 2 dz ]
a l n ( z ) = a l ( n 1 ) ( 0 ) + 0 z 1 2 g l ( N ( n 1 ) ) ( 1 ) a l ( n 1 ) m ( Δ ω ij ( 1 j β m ) ε m 1 + j Δ ω ij τ m a i ( n 1 ) * a j ( n 1 ) a k ( n 1 ) ) γ sc a l ( n 1 ) 2 dz
A n = F ( n 1 ) T
A n = A n A n , F n = F n F n , T = T T
A n = a 1 n ( 0 ) a 1 n ( x Δ z ) a y n ( 0 ) a y n ( x Δ z ) , A n = a 1 n ( 0 ) a 1 n ( x Δ z ) a y n ( 0 ) a y n ( x Δ z )
F n = a 1 n ( 0 ) f ( 0 ) f ( x Δ z ) a 1 n ( 0 ) f ( 0 ) f ( x Δ z ) , F n = f ( 0 ) f ( ( x 1 ) · Δ z ) a 1 n ( x Δ z ) f ( 0 ) f ( ( x 1 ) · Δ z ) a y n ( x Δ z )
f ( z ) = ( 1 2 g l ( N ( z ) ) [ ( 1 ) a l ( z ) m ( Δ ω ij ( 1 j β m ) ε m 1 + j Δ ω ij τ m a i * ( z ) a j ( z ) a k ( z ) ) ] γ sc a l ( z ) 2 ) × Δz
f ( z ) = ( 1 2 g l ( N ( z ) ) [ ( 1 ) a l ( z ) m ( Δ ω ij ( 1 j β m ) ε m 1 + j Δ ω ij τ m a i * ( z ) a j ( z ) a k ( z ) ) ] γ sc a l ( z ) 2 ) × Δz
T = 1 1 1 1 1 0 1 2 1 2 1 2 1 2 0 1 2 1 1 1 0 0 1 2 1 1 0 0 0 1 2 1 1 0 0 0 0 0 1 2 , T = 1 1 1 1 1 1 2 1 2 1 2 1 2 0 1 1 1 1 2 0 1 1 1 2 0 1 1 2 0 0 0 1 2 0 0 0 0 0

Metrics