Abstract

A two-electrode semiconductor optical amplifier that has two sections and two separated electrodes is proposed for an all-optical wavelength converter. Pattern effect reduction based on dynamic gain compensation is theoretically investigated using a time-domain model that takes into account the carrier diffusion process between the two sections, and the Q factor of the converted light is calculated to evaluate pattern effects. Simulation results show that the Q factor is greatly improved when the section lengths and the currents are appropriately selected.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2009 (2)

2008 (4)

P. Tian, L. Huang, L. Yan, and D. Huang, “Chirp characteristics of wavelength converter in multi-electrode semiconductor optical amplifiers,” Proc. SPIE 7279, 727919 (2008).
[CrossRef]

E. B. Zhou, F. Oehman, C. Cheng, X. L. Zhang, W. Hong, J. Mork, and D. X. Huang, “Reduction of patterning effects in SOA-based wavelength converters by combining cross-gain and cross-absorption modulation,” Opt. Express 16, 21522–21528 (2008).
[CrossRef] [PubMed]

L. Huang, S. Yu, and D. Huang, “Gain spectrum and saturation characteristics of two-segment semiconductor optical amplifier,” Proc. SPIE 7135, 71352C (2008).
[CrossRef]

K. E. Zoiros, T. Siarkos, and C. S. Koukourlis, “Theoretical analysis of pattern effect suppression in semiconductor optical amplifier utilizing optical delay interferometer,” Opt. Commun. 281, 3648–3657 (2008).
[CrossRef]

2007 (2)

J. Wang, A. Marculescu, J. S. Li, P. Vorreau, S. Tzadok, S. Ben Ezra, S. Tsadka, W. Freude, and J. Leuthold, “Pattern effect removal technique for semiconductor-optical-amplifier-based wavelength conversion,” IEEE Photonics Technol. Lett. 19, 1955–1957 (2007).
[CrossRef]

J. J. Dong, X. L. Zhang, J. Xu, and D. X. Huang, “All-optical ultrawideband monocycle generation utilizing gain saturation of a dark return-to-zero signal in a semiconductor optical amplifier,” Opt. Lett. 32, 2158–2160 (2007).
[CrossRef] [PubMed]

2006 (3)

2005 (1)

2002 (4)

M. Tsurusawa, K. Nishimura, and M. Usami, “First demonstration of pattern effect reduction in 40Gb/s semiconductor optical amplifier based all-optical switch utilizing transparent cw assist light,” Jpn. J. Appl. Phys. 41, 1199–1202 (2002).
[CrossRef]

M. T. Hill, E. Tangdiongga, H. de Waardt, G. D. Khoe, and H. J. S. Dorren, “Carrier recovery time in semiconductor optical amplifiers that employ holding beams,” Opt. Lett. 27, 1625–1627 (2002).
[CrossRef]

M. J. Connelly, “Wideband dynamic numerical model of a tapered buried ridge strip semiconductor optical amplifier gate,” IEE Proc. -Circuits Devices Syst. 149, 173–178 (2002).
[CrossRef]

K. Djordjev, S. J. Choi, W. J. Choi, S. J. Choi, I. Kim, and P. D. Dapkus, “Two-segment spectrally inhomogeneous traveling wave semiconductor optical amplifiers applied to spectral equalization,” IEEE Photonics Technol. Lett. 14, 603–605(2002).
[CrossRef]

2001 (2)

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

M. J. Connelly, “Corrections to “Wideband semiconductor optical amplifier steady-state numerical model”,” IEEE J. Quantum Electron. 37, 1103–1103 (2001).
[CrossRef]

2000 (1)

1998 (1)

K. Inoue, “Technique to compensate waveform distortion in a gain-saturated semiconductor optical amplifier using a semiconductor saturable absorber,” Electron. Lett. 34, 376–378(1998).
[CrossRef]

1997 (1)

D. X. Zhu, S. Dubovitsky, W. H. Steier, J. Burger, D. Tishinin, K. Uppal, and P. D. Dapkus, “Ambipolar diffusion coefficient and carrier lifetime in a compressively strained InGaAsP multiple quantum well device,” Appl. Phys. Lett. 71, 647–649(1997).
[CrossRef]

1996 (1)

S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. 14, 955–966(1996).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, 2002).
[CrossRef]

Burger, J.

D. X. Zhu, S. Dubovitsky, W. H. Steier, J. Burger, D. Tishinin, K. Uppal, and P. D. Dapkus, “Ambipolar diffusion coefficient and carrier lifetime in a compressively strained InGaAsP multiple quantum well device,” Appl. Phys. Lett. 71, 647–649(1997).
[CrossRef]

Chen, Z.

Cheng, C.

Cheng, T. H.

Z. H. Li, Y. Dong, C. Lu, Y. J. Wen, Y. X. Wang, W. S. Hu, and T. H. Cheng, “Comparison of cross-gain modulation effect of Manchester-duobinary, RZ-DPSK, NRZ-DPSK, RZ, and NRZ modulation formats in SOAs,” IEEE Photonics Technol. Lett. 18, 2680–2682 (2006).
[CrossRef]

Choi, B. S.

Choi, S. J.

K. Djordjev, S. J. Choi, W. J. Choi, S. J. Choi, I. Kim, and P. D. Dapkus, “Two-segment spectrally inhomogeneous traveling wave semiconductor optical amplifiers applied to spectral equalization,” IEEE Photonics Technol. Lett. 14, 603–605(2002).
[CrossRef]

K. Djordjev, S. J. Choi, W. J. Choi, S. J. Choi, I. Kim, and P. D. Dapkus, “Two-segment spectrally inhomogeneous traveling wave semiconductor optical amplifiers applied to spectral equalization,” IEEE Photonics Technol. Lett. 14, 603–605(2002).
[CrossRef]

Choi, W. J.

K. Djordjev, S. J. Choi, W. J. Choi, S. J. Choi, I. Kim, and P. D. Dapkus, “Two-segment spectrally inhomogeneous traveling wave semiconductor optical amplifiers applied to spectral equalization,” IEEE Photonics Technol. Lett. 14, 603–605(2002).
[CrossRef]

Chung, H. S.

Connelly, M. J.

M. J. Connelly, “Wideband dynamic numerical model of a tapered buried ridge strip semiconductor optical amplifier gate,” IEE Proc. -Circuits Devices Syst. 149, 173–178 (2002).
[CrossRef]

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

M. J. Connelly, “Corrections to “Wideband semiconductor optical amplifier steady-state numerical model”,” IEEE J. Quantum Electron. 37, 1103–1103 (2001).
[CrossRef]

Dapkus, P. D.

K. Djordjev, S. J. Choi, W. J. Choi, S. J. Choi, I. Kim, and P. D. Dapkus, “Two-segment spectrally inhomogeneous traveling wave semiconductor optical amplifiers applied to spectral equalization,” IEEE Photonics Technol. Lett. 14, 603–605(2002).
[CrossRef]

D. X. Zhu, S. Dubovitsky, W. H. Steier, J. Burger, D. Tishinin, K. Uppal, and P. D. Dapkus, “Ambipolar diffusion coefficient and carrier lifetime in a compressively strained InGaAsP multiple quantum well device,” Appl. Phys. Lett. 71, 647–649(1997).
[CrossRef]

de Waardt, H.

Djordjev, K.

K. Djordjev, S. J. Choi, W. J. Choi, S. J. Choi, I. Kim, and P. D. Dapkus, “Two-segment spectrally inhomogeneous traveling wave semiconductor optical amplifiers applied to spectral equalization,” IEEE Photonics Technol. Lett. 14, 603–605(2002).
[CrossRef]

Dong, J. J.

Dong, Y.

Z. H. Li, Y. Dong, C. Lu, Y. J. Wen, Y. X. Wang, W. S. Hu, and T. H. Cheng, “Comparison of cross-gain modulation effect of Manchester-duobinary, RZ-DPSK, NRZ-DPSK, RZ, and NRZ modulation formats in SOAs,” IEEE Photonics Technol. Lett. 18, 2680–2682 (2006).
[CrossRef]

Dorren, H. J. S.

Dubovitsky, S.

D. X. Zhu, S. Dubovitsky, W. H. Steier, J. Burger, D. Tishinin, K. Uppal, and P. D. Dapkus, “Ambipolar diffusion coefficient and carrier lifetime in a compressively strained InGaAsP multiple quantum well device,” Appl. Phys. Lett. 71, 647–649(1997).
[CrossRef]

Dutta, N. K.

Ellis, A. D.

R. J. Manning, X. Yang, R. P. Webb, R. Giller, F. C. Garcia Gunning, and A. D. Ellis, “The ‘turbo-switch’—a novel technique to increase the high-speed response of SOAs for wavelength conversion,” in Optical Fiber Communication Conference (OSA, 2006).
[CrossRef]

Ezra, S. Ben

J. Wang, A. Marculescu, J. S. Li, P. Vorreau, S. Tzadok, S. Ben Ezra, S. Tsadka, W. Freude, and J. Leuthold, “Pattern effect removal technique for semiconductor-optical-amplifier-based wavelength conversion,” IEEE Photonics Technol. Lett. 19, 1955–1957 (2007).
[CrossRef]

Filios, A.

Freude, W.

J. Wang, A. Marculescu, J. S. Li, P. Vorreau, S. Tzadok, S. Ben Ezra, S. Tsadka, W. Freude, and J. Leuthold, “Pattern effect removal technique for semiconductor-optical-amplifier-based wavelength conversion,” IEEE Photonics Technol. Lett. 19, 1955–1957 (2007).
[CrossRef]

Giller, R.

R. J. Manning, X. Yang, R. P. Webb, R. Giller, F. C. Garcia Gunning, and A. D. Ellis, “The ‘turbo-switch’—a novel technique to increase the high-speed response of SOAs for wavelength conversion,” in Optical Fiber Communication Conference (OSA, 2006).
[CrossRef]

Guegan, M.

Gunning, F. C. Garcia

R. J. Manning, X. Yang, R. P. Webb, R. Giller, F. C. Garcia Gunning, and A. D. Ellis, “The ‘turbo-switch’—a novel technique to increase the high-speed response of SOAs for wavelength conversion,” in Optical Fiber Communication Conference (OSA, 2006).
[CrossRef]

Gutierrez-Castrejon, R.

Harrison, P.

P. Harrison, Quantum Wells, Wires and Dots: Theoretical and Computational Physics of Semiconductor Nanostructures (Wiley, 2005), Chap. 4.
[CrossRef] [PubMed]

Hill, M. T.

Hong, W.

Hu, W. S.

Z. H. Li, Y. Dong, C. Lu, Y. J. Wen, Y. X. Wang, W. S. Hu, and T. H. Cheng, “Comparison of cross-gain modulation effect of Manchester-duobinary, RZ-DPSK, NRZ-DPSK, RZ, and NRZ modulation formats in SOAs,” IEEE Photonics Technol. Lett. 18, 2680–2682 (2006).
[CrossRef]

Huang, D.

P. Tian, L. Huang, L. Yan, and D. Huang, “Chirp characteristics of wavelength converter in multi-electrode semiconductor optical amplifiers,” Proc. SPIE 7279, 727919 (2008).
[CrossRef]

L. Huang, S. Yu, and D. Huang, “Gain spectrum and saturation characteristics of two-segment semiconductor optical amplifier,” Proc. SPIE 7135, 71352C (2008).
[CrossRef]

Huang, D. X.

Huang, L.

L. Huang, S. Yu, and D. Huang, “Gain spectrum and saturation characteristics of two-segment semiconductor optical amplifier,” Proc. SPIE 7135, 71352C (2008).
[CrossRef]

P. Tian, L. Huang, L. Yan, and D. Huang, “Chirp characteristics of wavelength converter in multi-electrode semiconductor optical amplifiers,” Proc. SPIE 7279, 727919 (2008).
[CrossRef]

Inohara, R.

Inoue, K.

K. Inoue, “Technique to compensate waveform distortion in a gain-saturated semiconductor optical amplifier using a semiconductor saturable absorber,” Electron. Lett. 34, 376–378(1998).
[CrossRef]

Khoe, G. D.

Kim, D. C.

Kim, H. S.

Kim, I.

K. Djordjev, S. J. Choi, W. J. Choi, S. J. Choi, I. Kim, and P. D. Dapkus, “Two-segment spectrally inhomogeneous traveling wave semiconductor optical amplifiers applied to spectral equalization,” IEEE Photonics Technol. Lett. 14, 603–605(2002).
[CrossRef]

Kim, K. S.

Koukourlis, C. S.

K. E. Zoiros, T. Siarkos, and C. S. Koukourlis, “Theoretical analysis of pattern effect suppression in semiconductor optical amplifier utilizing optical delay interferometer,” Opt. Commun. 281, 3648–3657 (2008).
[CrossRef]

Kwon, O. K.

Leuthold, J.

J. Wang, A. Marculescu, J. S. Li, P. Vorreau, S. Tzadok, S. Ben Ezra, S. Tsadka, W. Freude, and J. Leuthold, “Pattern effect removal technique for semiconductor-optical-amplifier-based wavelength conversion,” IEEE Photonics Technol. Lett. 19, 1955–1957 (2007).
[CrossRef]

Li, J. S.

J. Wang, A. Marculescu, J. S. Li, P. Vorreau, S. Tzadok, S. Ben Ezra, S. Tsadka, W. Freude, and J. Leuthold, “Pattern effect removal technique for semiconductor-optical-amplifier-based wavelength conversion,” IEEE Photonics Technol. Lett. 19, 1955–1957 (2007).
[CrossRef]

Li, Z. H.

Z. H. Li, Y. Dong, C. Lu, Y. J. Wen, Y. X. Wang, W. S. Hu, and T. H. Cheng, “Comparison of cross-gain modulation effect of Manchester-duobinary, RZ-DPSK, NRZ-DPSK, RZ, and NRZ modulation formats in SOAs,” IEEE Photonics Technol. Lett. 18, 2680–2682 (2006).
[CrossRef]

Lu, C.

Z. H. Li, Y. Dong, C. Lu, Y. J. Wen, Y. X. Wang, W. S. Hu, and T. H. Cheng, “Comparison of cross-gain modulation effect of Manchester-duobinary, RZ-DPSK, NRZ-DPSK, RZ, and NRZ modulation formats in SOAs,” IEEE Photonics Technol. Lett. 18, 2680–2682 (2006).
[CrossRef]

Ma, S.

Manning, R. J.

R. J. Manning, X. Yang, R. P. Webb, R. Giller, F. C. Garcia Gunning, and A. D. Ellis, “The ‘turbo-switch’—a novel technique to increase the high-speed response of SOAs for wavelength conversion,” in Optical Fiber Communication Conference (OSA, 2006).
[CrossRef]

Marculescu, A.

J. Wang, A. Marculescu, J. S. Li, P. Vorreau, S. Tzadok, S. Ben Ezra, S. Tsadka, W. Freude, and J. Leuthold, “Pattern effect removal technique for semiconductor-optical-amplifier-based wavelength conversion,” IEEE Photonics Technol. Lett. 19, 1955–1957 (2007).
[CrossRef]

Mork, J.

Nielsen, M. L.

Nishimura, K.

H. S. Chung, R. Inohara, K. Nishimura, and M. Usami, “Effect of copropagating and counterpropagating directions on a semiconductor optical amplifier—Mach-Zehnder interferometer based wavelength converter using a continuous-wave assist light,” Opt. Lett. 30, 1716–1718 (2005).
[CrossRef] [PubMed]

M. Tsurusawa, K. Nishimura, and M. Usami, “First demonstration of pattern effect reduction in 40Gb/s semiconductor optical amplifier based all-optical switch utilizing transparent cw assist light,” Jpn. J. Appl. Phys. 41, 1199–1202 (2002).
[CrossRef]

Oehman, F.

Oh, D. K.

Sakaguchi, J.

Sharaiha, A.

Siarkos, T.

K. E. Zoiros, T. Siarkos, and C. S. Koukourlis, “Theoretical analysis of pattern effect suppression in semiconductor optical amplifier utilizing optical delay interferometer,” Opt. Commun. 281, 3648–3657 (2008).
[CrossRef]

Steier, W. H.

D. X. Zhu, S. Dubovitsky, W. H. Steier, J. Burger, D. Tishinin, K. Uppal, and P. D. Dapkus, “Ambipolar diffusion coefficient and carrier lifetime in a compressively strained InGaAsP multiple quantum well device,” Appl. Phys. Lett. 71, 647–649(1997).
[CrossRef]

Sun, H.

Suzuki, R.

Tangdiongga, E.

Tian, P.

P. Tian, L. Huang, L. Yan, and D. Huang, “Chirp characteristics of wavelength converter in multi-electrode semiconductor optical amplifiers,” Proc. SPIE 7279, 727919 (2008).
[CrossRef]

Tishinin, D.

D. X. Zhu, S. Dubovitsky, W. H. Steier, J. Burger, D. Tishinin, K. Uppal, and P. D. Dapkus, “Ambipolar diffusion coefficient and carrier lifetime in a compressively strained InGaAsP multiple quantum well device,” Appl. Phys. Lett. 71, 647–649(1997).
[CrossRef]

Tsadka, S.

J. Wang, A. Marculescu, J. S. Li, P. Vorreau, S. Tzadok, S. Ben Ezra, S. Tsadka, W. Freude, and J. Leuthold, “Pattern effect removal technique for semiconductor-optical-amplifier-based wavelength conversion,” IEEE Photonics Technol. Lett. 19, 1955–1957 (2007).
[CrossRef]

Tsurusawa, M.

M. Tsurusawa, K. Nishimura, and M. Usami, “First demonstration of pattern effect reduction in 40Gb/s semiconductor optical amplifier based all-optical switch utilizing transparent cw assist light,” Jpn. J. Appl. Phys. 41, 1199–1202 (2002).
[CrossRef]

Tzadok, S.

J. Wang, A. Marculescu, J. S. Li, P. Vorreau, S. Tzadok, S. Ben Ezra, S. Tsadka, W. Freude, and J. Leuthold, “Pattern effect removal technique for semiconductor-optical-amplifier-based wavelength conversion,” IEEE Photonics Technol. Lett. 19, 1955–1957 (2007).
[CrossRef]

Ueno, Y.

Uppal, K.

D. X. Zhu, S. Dubovitsky, W. H. Steier, J. Burger, D. Tishinin, K. Uppal, and P. D. Dapkus, “Ambipolar diffusion coefficient and carrier lifetime in a compressively strained InGaAsP multiple quantum well device,” Appl. Phys. Lett. 71, 647–649(1997).
[CrossRef]

Usami, M.

H. S. Chung, R. Inohara, K. Nishimura, and M. Usami, “Effect of copropagating and counterpropagating directions on a semiconductor optical amplifier—Mach-Zehnder interferometer based wavelength converter using a continuous-wave assist light,” Opt. Lett. 30, 1716–1718 (2005).
[CrossRef] [PubMed]

M. Tsurusawa, K. Nishimura, and M. Usami, “First demonstration of pattern effect reduction in 40Gb/s semiconductor optical amplifier based all-optical switch utilizing transparent cw assist light,” Jpn. J. Appl. Phys. 41, 1199–1202 (2002).
[CrossRef]

Vorreau, P.

J. Wang, A. Marculescu, J. S. Li, P. Vorreau, S. Tzadok, S. Ben Ezra, S. Tsadka, W. Freude, and J. Leuthold, “Pattern effect removal technique for semiconductor-optical-amplifier-based wavelength conversion,” IEEE Photonics Technol. Lett. 19, 1955–1957 (2007).
[CrossRef]

Wang, J.

J. Wang, A. Marculescu, J. S. Li, P. Vorreau, S. Tzadok, S. Ben Ezra, S. Tsadka, W. Freude, and J. Leuthold, “Pattern effect removal technique for semiconductor-optical-amplifier-based wavelength conversion,” IEEE Photonics Technol. Lett. 19, 1955–1957 (2007).
[CrossRef]

Wang, Y. X.

Z. H. Li, Y. Dong, C. Lu, Y. J. Wen, Y. X. Wang, W. S. Hu, and T. H. Cheng, “Comparison of cross-gain modulation effect of Manchester-duobinary, RZ-DPSK, NRZ-DPSK, RZ, and NRZ modulation formats in SOAs,” IEEE Photonics Technol. Lett. 18, 2680–2682 (2006).
[CrossRef]

Webb, R. P.

R. J. Manning, X. Yang, R. P. Webb, R. Giller, F. C. Garcia Gunning, and A. D. Ellis, “The ‘turbo-switch’—a novel technique to increase the high-speed response of SOAs for wavelength conversion,” in Optical Fiber Communication Conference (OSA, 2006).
[CrossRef]

Wen, Y. J.

Z. H. Li, Y. Dong, C. Lu, Y. J. Wen, Y. X. Wang, W. S. Hu, and T. H. Cheng, “Comparison of cross-gain modulation effect of Manchester-duobinary, RZ-DPSK, NRZ-DPSK, RZ, and NRZ modulation formats in SOAs,” IEEE Photonics Technol. Lett. 18, 2680–2682 (2006).
[CrossRef]

Xu, J.

Yan, L.

P. Tian, L. Huang, L. Yan, and D. Huang, “Chirp characteristics of wavelength converter in multi-electrode semiconductor optical amplifiers,” Proc. SPIE 7279, 727919 (2008).
[CrossRef]

Yang, X.

R. J. Manning, X. Yang, R. P. Webb, R. Giller, F. C. Garcia Gunning, and A. D. Ellis, “The ‘turbo-switch’—a novel technique to increase the high-speed response of SOAs for wavelength conversion,” in Optical Fiber Communication Conference (OSA, 2006).
[CrossRef]

Yoo, S. J. B.

S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. 14, 955–966(1996).
[CrossRef]

Yu, S.

L. Huang, S. Yu, and D. Huang, “Gain spectrum and saturation characteristics of two-segment semiconductor optical amplifier,” Proc. SPIE 7135, 71352C (2008).
[CrossRef]

Zhang, X. L.

Zhou, E. B.

Zhu, D. X.

D. X. Zhu, S. Dubovitsky, W. H. Steier, J. Burger, D. Tishinin, K. Uppal, and P. D. Dapkus, “Ambipolar diffusion coefficient and carrier lifetime in a compressively strained InGaAsP multiple quantum well device,” Appl. Phys. Lett. 71, 647–649(1997).
[CrossRef]

Zoiros, K. E.

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Figures (8)

Fig. 1
Fig. 1

Schematic views of wavelength converters by using (a) a common SOA, (b) a two-electrode SOA.

Fig. 2
Fig. 2

Schematic view of dynamic model for the two-electrode SOA.

Fig. 3
Fig. 3

Carrier density distributions for common SOA and two-electrode SOA with different diffusion lengths.

Fig. 4
Fig. 4

Normalized output power of converted light for (a) a single amplified SOA, (b) a single absorbed SOA, (c) a two-electrode SOA with a SOA–absorber configuration, and (d) a common SOA.

Fig. 5
Fig. 5

Normalized power for 10 Gb / s NRZ signal: (a) input pump light; (b) converted light by using a common SOA; (c) converted light by using a two-electrode SOA with absorber–SOA configuration; (d) converted light by using two-electrode SOA with SOA–absorber configuration.

Fig. 6
Fig. 6

The Q factor and gains of two-electrode SOA versus I 1 .

Fig. 7
Fig. 7

Normalized eye diagrams for converted light at (a) I 1 = 10 mA , (b) I 1 = 60 mA , and (c) I 1 = 160 mA .

Fig. 8
Fig. 8

Q factor contour as a function of I 1 and L 1 .

Tables (1)

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Table 1 Parameters Used in This Paper

Equations (12)

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N t = J e d R ( N ) v g j = p , s g m ( ν j , N ) ( S j + + S j ) v g k = 1 N m g m ( ν k , N ) K ( S k ASE + + S k ASE ) + D 2 N z 2 ,
R ( N ) = ( A rad + A nrad ) N + B rad N 2 + C aug N 3 ,
g m ( ν , N ) = g m c ( ν , N ) 1 + ε S ,
g m c ( ν , N i ) = c 2 4 2 π 3 / 2 n eq 2 τ ν 2 [ 2 m e m h h ( m e + m h h ) ] 3 / 2 ν E g ( N i ) h × [ f c ( ν , N i ) f v ( ν , N i ) ] ,
g m ( ν , N i ) = c 2 4 2 π 3 / 2 n eq 2 τ ν 2 [ 2 m e m h h ( m e + m h h ) ] 3 / 2 ν E g ( N i ) h × f c ( ν , N i ) ( 1 f v ( ν , N i ) ) ,
d S i , j ± d z = ± [ Γ g m ( ν j , N i ) α ( N i ) ] S i , j ± ,
d S i , k ASE ± d z = ± [ Γ g m ( ν k , N i ) α ( N i ) ] S i , k ASE ± + R s p i ( ν k , N i ) ,
R s p i ( ν k , N i ) = Γ w d V g g m ( ν k , N i ) K Δ ν m ,
N t = A 1 + A 2 ,
N 0 t = A 1 .
N = 0.5 N d erfc ( z 2 L diff ) ,
Q = μ 1 μ 0 σ 1 + σ 0 ,

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