Abstract

By spectrally slicing a single longitudinal-mode from a master weak-resonant-cavity Fabry-Perot laser diode with transient wavelength scanning and tracking functions, the broadened self-injection-locking of a slave weak-resonant-cavity Fabry-Perot laser diode is demonstrated to achieve bi-directional transmission in a 200-GHz array-waveguide-grating channelized dense-wavelength-division-multiplexing passive optical network system. Both the down- and up-stream slave weak-resonant-cavity Fabry-Perot laser diodes are non-return-to-zero modulated below threshold and coherently injection-locked to deliver the pulsed carrier for 25-km bi-directional 2.5 Gbits/s return-to-zero transmission. The master weak-resonant-cavity Fabry-Perot laser diode is gain-switched at near threshold condition and delivers an optical coherent pulse-train with its mode linewidth broadened from 0.2 to 0.8 nm by transient wavelength scanning, which facilitates the broadband injection-locking of the slave weak-resonant-cavity Fabry-Perot laser diodes with a threshold current reducing by 10 mA. Such a transient wavelength scanning induced spectral broadening greatly releases the limitation on wavelength injection-locking range required for the slave weak-resonant-cavity Fabry-Perot laser diode. The theoretical modeling and numerical simulation on the wavelength scanning and tracking effects of the master and slave weak-resonant-cavity Fabry-Perot laser diodes are performed. The receiving power sensitivity for back-to-back transmission at bit-error-rate <10−10 is −25.6 dBm, and the power penalty added after 25-km transmission is less than 2 dB for all 16 channels.

© 2012 OSA

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References

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  1. S. J. Park, C. H. Lee, K. T. Jeong, H. J. Park, J. G. Ahn, and K. H. Song, “Fiber to the home services based on wavelength division multiplexing passive optical network,” J. Lightwave Technol. 22(11), 2582–2591 (2004).
    [CrossRef]
  2. K. Lee, J. H. Song, H. K. Lee, and W. V. Sorin, “Multistage access network for bidirectional DWDM transmission using ASE-injected FP-LD,” IEEE Photon. Technol. Lett. 18(6), 761–763 (2006).
    [CrossRef]
  3. W. Lee, M.-Y. Park, S.-H. Cho, J. Lee, C. Kim, G. Jeong, and B.-W. Kim, “Bidirectional WDM-PON based on gain-saturated reflective semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 17(11), 2460–2462 (2005).
    [CrossRef]
  4. S. C. Lin, S. L. Lee, and C. K. Liu, “Simple approach for bidirectional performance enhancement on WDM-PONs with directmodulation lasers and RSOAs,” Opt. Express 16(6), 3636–3643 (2008).
    [CrossRef] [PubMed]
  5. J. Prat, C. Arellano, V. Polo, and C. Bock, “Optical network unit based on a bidirectional reflective semiconductor optical amplifier for fiber-to-the-home networks,” IEEE Photon. Technol. Lett. 17(1), 250–252 (2005).
    [CrossRef]
  6. G.-R. Lin, T.-K. Cheng, Y.-C. Chi, G.-C. Lin, H.-L. Wang, and Y.-H. Lin, “200-GHz and 50-GHz AWG channelized linewidth dependent transmission of weak-resonant-cavity FPLD injection-locked by spectrally sliced ASE,” Opt. Express 17(20), 17739–17746 (2009).
    [CrossRef] [PubMed]
  7. K.-M. Choi, J.-S. Baik, and C.-H. Lee, “Broad-band light source using mutually injected Fabry-Pérot laser diodes for WDM-PON,” IEEE Photon. Technol. Lett. 17(12), 2529–2531 (2005).
    [CrossRef]
  8. Q. T. Nguyen, P. Besnard, L. Bramerie, A. Shen, C. Kazmierski, P. Chanlou, G.-H. Duan, and J.-C. Simon, “Bidirectional 2.5-Gb/s WDM-PON using FP-LDs wavelength-locked by a multiple-wavelength seeding source based on a mode-locked laser,” IEEE Photon. Technol. Lett. 22(11), 733–735 (2010).
    [CrossRef]
  9. Z. Xu, Y.-J. Wen, W.-D. Zhong, C.-J. Chae, X.-F. Cheng, Y. Wang, C. Lu, and J. Shankar, “High-speed WDM-PON using CW injection-locked Fabry-Pérot laser diodes,” Opt. Express 15(6), 2953–2962 (2007).
    [CrossRef] [PubMed]
  10. S. Sivaprakasam and R. Singh, “Gain change and threshold reduction of diode laser by injection-locking,” Opt. Commun. 151(4-6), 253–256 (1998).
    [CrossRef]
  11. Y.-C. Chang, Y.-H. Lin, J. H. Chen, and G.-R. Lin, “All-optical NRZ-to-PRZ format transformer with an injection-locked Fabry-Pérot laser diode at unlasing condition,” Opt. Express 12(19), 4449–4456 (2004).
    [CrossRef] [PubMed]
  12. L. Li, “Static and dynamic properties of injection-locked semiconductor lasers,” IEEE J. Quantum Electron. 30(8), 1701–1708 (1994).
    [CrossRef]
  13. C. C. Lin, Y. C. Chi, H. C. Kuo, P. C. Peng, C. J. Chang-Hasnain, and G.-R. Lin, “Beyond-bandwidth electrical-pulse modulation of a TO-can packaged VCSEL for 10 Gbit/s injection-locked NRZ-to-RZ transmission,” J. Lightwave Technol. 29(6), 830–841 (2011).
    [CrossRef]
  14. Y.-C. Chang, Y. H. Lin, J. H. Chen, and G.-R. Lin, “All-optical NRZ-to-PRZ format transformer with an injection-locked Fabry-Pérot laser diode at unlasing condition,” Opt. Express 12(19), 4449–4456 (2004).
    [CrossRef] [PubMed]
  15. E.-K. Lau, L.-J. Wong, and M.-C. Wu, “Enhanced Modulation Characteristics of Optical Injection-Locked Lasers: A Tutorial,” IEEE J. Sel. Top. Quantum Electron. 15(3), 618–633 (2009).
    [CrossRef]
  16. P. P. Vasil’ev, Ultrafast Diode Lasers: Fundamentals and Applications (Artech House, 1995), Chap. 3.

2011 (1)

2010 (1)

Q. T. Nguyen, P. Besnard, L. Bramerie, A. Shen, C. Kazmierski, P. Chanlou, G.-H. Duan, and J.-C. Simon, “Bidirectional 2.5-Gb/s WDM-PON using FP-LDs wavelength-locked by a multiple-wavelength seeding source based on a mode-locked laser,” IEEE Photon. Technol. Lett. 22(11), 733–735 (2010).
[CrossRef]

2009 (2)

2008 (1)

2007 (1)

2006 (1)

K. Lee, J. H. Song, H. K. Lee, and W. V. Sorin, “Multistage access network for bidirectional DWDM transmission using ASE-injected FP-LD,” IEEE Photon. Technol. Lett. 18(6), 761–763 (2006).
[CrossRef]

2005 (3)

W. Lee, M.-Y. Park, S.-H. Cho, J. Lee, C. Kim, G. Jeong, and B.-W. Kim, “Bidirectional WDM-PON based on gain-saturated reflective semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 17(11), 2460–2462 (2005).
[CrossRef]

J. Prat, C. Arellano, V. Polo, and C. Bock, “Optical network unit based on a bidirectional reflective semiconductor optical amplifier for fiber-to-the-home networks,” IEEE Photon. Technol. Lett. 17(1), 250–252 (2005).
[CrossRef]

K.-M. Choi, J.-S. Baik, and C.-H. Lee, “Broad-band light source using mutually injected Fabry-Pérot laser diodes for WDM-PON,” IEEE Photon. Technol. Lett. 17(12), 2529–2531 (2005).
[CrossRef]

2004 (3)

1998 (1)

S. Sivaprakasam and R. Singh, “Gain change and threshold reduction of diode laser by injection-locking,” Opt. Commun. 151(4-6), 253–256 (1998).
[CrossRef]

1994 (1)

L. Li, “Static and dynamic properties of injection-locked semiconductor lasers,” IEEE J. Quantum Electron. 30(8), 1701–1708 (1994).
[CrossRef]

Ahn, J. G.

Arellano, C.

J. Prat, C. Arellano, V. Polo, and C. Bock, “Optical network unit based on a bidirectional reflective semiconductor optical amplifier for fiber-to-the-home networks,” IEEE Photon. Technol. Lett. 17(1), 250–252 (2005).
[CrossRef]

Baik, J.-S.

K.-M. Choi, J.-S. Baik, and C.-H. Lee, “Broad-band light source using mutually injected Fabry-Pérot laser diodes for WDM-PON,” IEEE Photon. Technol. Lett. 17(12), 2529–2531 (2005).
[CrossRef]

Besnard, P.

Q. T. Nguyen, P. Besnard, L. Bramerie, A. Shen, C. Kazmierski, P. Chanlou, G.-H. Duan, and J.-C. Simon, “Bidirectional 2.5-Gb/s WDM-PON using FP-LDs wavelength-locked by a multiple-wavelength seeding source based on a mode-locked laser,” IEEE Photon. Technol. Lett. 22(11), 733–735 (2010).
[CrossRef]

Bock, C.

J. Prat, C. Arellano, V. Polo, and C. Bock, “Optical network unit based on a bidirectional reflective semiconductor optical amplifier for fiber-to-the-home networks,” IEEE Photon. Technol. Lett. 17(1), 250–252 (2005).
[CrossRef]

Bramerie, L.

Q. T. Nguyen, P. Besnard, L. Bramerie, A. Shen, C. Kazmierski, P. Chanlou, G.-H. Duan, and J.-C. Simon, “Bidirectional 2.5-Gb/s WDM-PON using FP-LDs wavelength-locked by a multiple-wavelength seeding source based on a mode-locked laser,” IEEE Photon. Technol. Lett. 22(11), 733–735 (2010).
[CrossRef]

Chae, C.-J.

Chang, Y.-C.

Chang-Hasnain, C. J.

Chanlou, P.

Q. T. Nguyen, P. Besnard, L. Bramerie, A. Shen, C. Kazmierski, P. Chanlou, G.-H. Duan, and J.-C. Simon, “Bidirectional 2.5-Gb/s WDM-PON using FP-LDs wavelength-locked by a multiple-wavelength seeding source based on a mode-locked laser,” IEEE Photon. Technol. Lett. 22(11), 733–735 (2010).
[CrossRef]

Chen, J. H.

Cheng, T.-K.

Cheng, X.-F.

Chi, Y. C.

Chi, Y.-C.

Cho, S.-H.

W. Lee, M.-Y. Park, S.-H. Cho, J. Lee, C. Kim, G. Jeong, and B.-W. Kim, “Bidirectional WDM-PON based on gain-saturated reflective semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 17(11), 2460–2462 (2005).
[CrossRef]

Choi, K.-M.

K.-M. Choi, J.-S. Baik, and C.-H. Lee, “Broad-band light source using mutually injected Fabry-Pérot laser diodes for WDM-PON,” IEEE Photon. Technol. Lett. 17(12), 2529–2531 (2005).
[CrossRef]

Duan, G.-H.

Q. T. Nguyen, P. Besnard, L. Bramerie, A. Shen, C. Kazmierski, P. Chanlou, G.-H. Duan, and J.-C. Simon, “Bidirectional 2.5-Gb/s WDM-PON using FP-LDs wavelength-locked by a multiple-wavelength seeding source based on a mode-locked laser,” IEEE Photon. Technol. Lett. 22(11), 733–735 (2010).
[CrossRef]

Jeong, G.

W. Lee, M.-Y. Park, S.-H. Cho, J. Lee, C. Kim, G. Jeong, and B.-W. Kim, “Bidirectional WDM-PON based on gain-saturated reflective semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 17(11), 2460–2462 (2005).
[CrossRef]

Jeong, K. T.

Kazmierski, C.

Q. T. Nguyen, P. Besnard, L. Bramerie, A. Shen, C. Kazmierski, P. Chanlou, G.-H. Duan, and J.-C. Simon, “Bidirectional 2.5-Gb/s WDM-PON using FP-LDs wavelength-locked by a multiple-wavelength seeding source based on a mode-locked laser,” IEEE Photon. Technol. Lett. 22(11), 733–735 (2010).
[CrossRef]

Kim, B.-W.

W. Lee, M.-Y. Park, S.-H. Cho, J. Lee, C. Kim, G. Jeong, and B.-W. Kim, “Bidirectional WDM-PON based on gain-saturated reflective semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 17(11), 2460–2462 (2005).
[CrossRef]

Kim, C.

W. Lee, M.-Y. Park, S.-H. Cho, J. Lee, C. Kim, G. Jeong, and B.-W. Kim, “Bidirectional WDM-PON based on gain-saturated reflective semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 17(11), 2460–2462 (2005).
[CrossRef]

Kuo, H. C.

Lau, E.-K.

E.-K. Lau, L.-J. Wong, and M.-C. Wu, “Enhanced Modulation Characteristics of Optical Injection-Locked Lasers: A Tutorial,” IEEE J. Sel. Top. Quantum Electron. 15(3), 618–633 (2009).
[CrossRef]

Lee, C. H.

Lee, C.-H.

K.-M. Choi, J.-S. Baik, and C.-H. Lee, “Broad-band light source using mutually injected Fabry-Pérot laser diodes for WDM-PON,” IEEE Photon. Technol. Lett. 17(12), 2529–2531 (2005).
[CrossRef]

Lee, H. K.

K. Lee, J. H. Song, H. K. Lee, and W. V. Sorin, “Multistage access network for bidirectional DWDM transmission using ASE-injected FP-LD,” IEEE Photon. Technol. Lett. 18(6), 761–763 (2006).
[CrossRef]

Lee, J.

W. Lee, M.-Y. Park, S.-H. Cho, J. Lee, C. Kim, G. Jeong, and B.-W. Kim, “Bidirectional WDM-PON based on gain-saturated reflective semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 17(11), 2460–2462 (2005).
[CrossRef]

Lee, K.

K. Lee, J. H. Song, H. K. Lee, and W. V. Sorin, “Multistage access network for bidirectional DWDM transmission using ASE-injected FP-LD,” IEEE Photon. Technol. Lett. 18(6), 761–763 (2006).
[CrossRef]

Lee, S. L.

Lee, W.

W. Lee, M.-Y. Park, S.-H. Cho, J. Lee, C. Kim, G. Jeong, and B.-W. Kim, “Bidirectional WDM-PON based on gain-saturated reflective semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 17(11), 2460–2462 (2005).
[CrossRef]

Li, L.

L. Li, “Static and dynamic properties of injection-locked semiconductor lasers,” IEEE J. Quantum Electron. 30(8), 1701–1708 (1994).
[CrossRef]

Lin, C. C.

Lin, G.-C.

Lin, G.-R.

Lin, S. C.

Lin, Y. H.

Lin, Y.-H.

Liu, C. K.

Lu, C.

Nguyen, Q. T.

Q. T. Nguyen, P. Besnard, L. Bramerie, A. Shen, C. Kazmierski, P. Chanlou, G.-H. Duan, and J.-C. Simon, “Bidirectional 2.5-Gb/s WDM-PON using FP-LDs wavelength-locked by a multiple-wavelength seeding source based on a mode-locked laser,” IEEE Photon. Technol. Lett. 22(11), 733–735 (2010).
[CrossRef]

Park, H. J.

Park, M.-Y.

W. Lee, M.-Y. Park, S.-H. Cho, J. Lee, C. Kim, G. Jeong, and B.-W. Kim, “Bidirectional WDM-PON based on gain-saturated reflective semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 17(11), 2460–2462 (2005).
[CrossRef]

Park, S. J.

Peng, P. C.

Polo, V.

J. Prat, C. Arellano, V. Polo, and C. Bock, “Optical network unit based on a bidirectional reflective semiconductor optical amplifier for fiber-to-the-home networks,” IEEE Photon. Technol. Lett. 17(1), 250–252 (2005).
[CrossRef]

Prat, J.

J. Prat, C. Arellano, V. Polo, and C. Bock, “Optical network unit based on a bidirectional reflective semiconductor optical amplifier for fiber-to-the-home networks,” IEEE Photon. Technol. Lett. 17(1), 250–252 (2005).
[CrossRef]

Shankar, J.

Shen, A.

Q. T. Nguyen, P. Besnard, L. Bramerie, A. Shen, C. Kazmierski, P. Chanlou, G.-H. Duan, and J.-C. Simon, “Bidirectional 2.5-Gb/s WDM-PON using FP-LDs wavelength-locked by a multiple-wavelength seeding source based on a mode-locked laser,” IEEE Photon. Technol. Lett. 22(11), 733–735 (2010).
[CrossRef]

Simon, J.-C.

Q. T. Nguyen, P. Besnard, L. Bramerie, A. Shen, C. Kazmierski, P. Chanlou, G.-H. Duan, and J.-C. Simon, “Bidirectional 2.5-Gb/s WDM-PON using FP-LDs wavelength-locked by a multiple-wavelength seeding source based on a mode-locked laser,” IEEE Photon. Technol. Lett. 22(11), 733–735 (2010).
[CrossRef]

Singh, R.

S. Sivaprakasam and R. Singh, “Gain change and threshold reduction of diode laser by injection-locking,” Opt. Commun. 151(4-6), 253–256 (1998).
[CrossRef]

Sivaprakasam, S.

S. Sivaprakasam and R. Singh, “Gain change and threshold reduction of diode laser by injection-locking,” Opt. Commun. 151(4-6), 253–256 (1998).
[CrossRef]

Song, J. H.

K. Lee, J. H. Song, H. K. Lee, and W. V. Sorin, “Multistage access network for bidirectional DWDM transmission using ASE-injected FP-LD,” IEEE Photon. Technol. Lett. 18(6), 761–763 (2006).
[CrossRef]

Song, K. H.

Sorin, W. V.

K. Lee, J. H. Song, H. K. Lee, and W. V. Sorin, “Multistage access network for bidirectional DWDM transmission using ASE-injected FP-LD,” IEEE Photon. Technol. Lett. 18(6), 761–763 (2006).
[CrossRef]

Wang, H.-L.

Wang, Y.

Wen, Y.-J.

Wong, L.-J.

E.-K. Lau, L.-J. Wong, and M.-C. Wu, “Enhanced Modulation Characteristics of Optical Injection-Locked Lasers: A Tutorial,” IEEE J. Sel. Top. Quantum Electron. 15(3), 618–633 (2009).
[CrossRef]

Wu, M.-C.

E.-K. Lau, L.-J. Wong, and M.-C. Wu, “Enhanced Modulation Characteristics of Optical Injection-Locked Lasers: A Tutorial,” IEEE J. Sel. Top. Quantum Electron. 15(3), 618–633 (2009).
[CrossRef]

Xu, Z.

Zhong, W.-D.

IEEE J. Quantum Electron. (1)

L. Li, “Static and dynamic properties of injection-locked semiconductor lasers,” IEEE J. Quantum Electron. 30(8), 1701–1708 (1994).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

E.-K. Lau, L.-J. Wong, and M.-C. Wu, “Enhanced Modulation Characteristics of Optical Injection-Locked Lasers: A Tutorial,” IEEE J. Sel. Top. Quantum Electron. 15(3), 618–633 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (5)

K. Lee, J. H. Song, H. K. Lee, and W. V. Sorin, “Multistage access network for bidirectional DWDM transmission using ASE-injected FP-LD,” IEEE Photon. Technol. Lett. 18(6), 761–763 (2006).
[CrossRef]

W. Lee, M.-Y. Park, S.-H. Cho, J. Lee, C. Kim, G. Jeong, and B.-W. Kim, “Bidirectional WDM-PON based on gain-saturated reflective semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 17(11), 2460–2462 (2005).
[CrossRef]

J. Prat, C. Arellano, V. Polo, and C. Bock, “Optical network unit based on a bidirectional reflective semiconductor optical amplifier for fiber-to-the-home networks,” IEEE Photon. Technol. Lett. 17(1), 250–252 (2005).
[CrossRef]

K.-M. Choi, J.-S. Baik, and C.-H. Lee, “Broad-band light source using mutually injected Fabry-Pérot laser diodes for WDM-PON,” IEEE Photon. Technol. Lett. 17(12), 2529–2531 (2005).
[CrossRef]

Q. T. Nguyen, P. Besnard, L. Bramerie, A. Shen, C. Kazmierski, P. Chanlou, G.-H. Duan, and J.-C. Simon, “Bidirectional 2.5-Gb/s WDM-PON using FP-LDs wavelength-locked by a multiple-wavelength seeding source based on a mode-locked laser,” IEEE Photon. Technol. Lett. 22(11), 733–735 (2010).
[CrossRef]

J. Lightwave Technol. (2)

Opt. Commun. (1)

S. Sivaprakasam and R. Singh, “Gain change and threshold reduction of diode laser by injection-locking,” Opt. Commun. 151(4-6), 253–256 (1998).
[CrossRef]

Opt. Express (5)

Other (1)

P. P. Vasil’ev, Ultrafast Diode Lasers: Fundamentals and Applications (Artech House, 1995), Chap. 3.

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Figures (9)

Fig. 1
Fig. 1

Bi-directional quasi-color-free WRC-FPLD-based 2.5-Gbit/s RZ DWDM-PON with a pulsed coherent injection locker. Lower right inset: the bird’s-eye view magnified image of the WRC-FPLD packed in a TO-can mount with bonding wires linked to the cathode and anode pins of the mount.

Fig. 2
Fig. 2

(a) The power-current curve of the slave WRC-FPLD injection-locked by the master WRC-FPLD at different power levels. (b) The principle of the PRBS directly encoded slave WRC-FPLD RZ transmitter triggered by externally pulsated master WRC-FPLD injection.

Fig. 3
Fig. 3

Left: the optical spectra of the master WRC-FPLD operated at free-running (gray) and gain-switching (red) condition. Upper right: the normalized mode spectra at free-running (gray) and gain-switching (red) conditions. Lower right: the linewidth and pulsewidth of the master WRC-FPLD with different RF modulation powers.

Fig. 4
Fig. 4

The injection-locking power dependent wavelength lock-in range and the corresponding (a) SMSR and (b) BER of the slave WRC-FPLD transmitter.

Fig. 5
Fig. 5

(a) Free-running AWG sliced WRC-FPLD. (b) Gain-switched AWG sliced WRC-FPLD. (c) Free-running slave WRC-FPLD injected by gain-switched WRC-FPLD. (d) NRZ modulated slave WRC-FPLD injected by gain-switched WRC-FPLD.

Fig. 6
Fig. 6

Left: the simulated change of the linewidth and wavelength shift for the slave WRC-FPLD as a function of the delay time and the injection power of the master WRC-FPLD injection with Gaussian profile. Right: the net wavelength shift and linewidth of one injection-locked longitudinal mode in the slave WRC-FPLD under the injection of the pulsed master WRC-FPLD injection at different powers.

Fig. 7
Fig. 7

The schematic diagram of single-wavelength injection and gain-switched injection.

Fig. 8
Fig. 8

(a) The optical spectrum and (b) the BER of injected WRC-FPLD at temperature from 21°C to 29°C.

Fig. 9
Fig. 9

BER analysis of wavelength injection locked WRC-FPLD at different channels for up- (left) and down-stream (right) transmission, and the measured pulsed RZ eye diagrams (inset).

Tables (1)

Tables Icon

Table 1 Injection-locked WRC-FPLD parameters

Equations (10)

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Δ I th = qV τ c ( 2κ g 1 1+ α 2 S inj S 0 ),
dS(t) dt = 1 2 [ g(N(t) N tr ) γ p ]S(t)+κ S inj (t)S(t) cos(ϕ(t)),
dϕ(t) dt = α 2 [ g(N(t) N tr ) γ p ]κ S inj (t) S(t) sinϕ(t)Δ ω inj ,
dN(t) dt =I(t) γ n N(t)g[N(t) N tr ]S(t),
Δ ω inj =κ 1+ α 2 S inj S 0 sin( tan 1 α+ϕ ),
Δ λ shift ( t )= λ freerun λ gainswitching ( t )= λ 0 n 0 dn dN [ N( t ) N th ]= λ 0 n 0 dn dN τ c qV [ I( t ) I th,inj ' ] = λ 0 n 0 dn dN τ c qV [ I( t ) I th + qV τ c ( 2κ g 1 1+ α 2 S i S o e t τ 0 ) ],
Δ λ linewidth (t)= λ 0 2 C Δ ν linewidth (t)= λ 0 2 C v g α m hv R sp 4π P slave,out ( t ) ( α 2 +1) = λ 0 2 C v g α m hv R sp ( α 2 +1) 4π { η i hν α eff τ c [ N( t ) N th +( 2κ g 1 1+ α 2 S i S o e t 2 τ o 2 ) ] } 1 = λ 0 2 C v g α m R sp ( α 2 +1) τ c 4π η i α eff [ N( t ) N th +( 2κ g 1 1+ α 2 S i S o e t 2 τ o 2 ) ] 1 = λ 0 2 C v g α m R sp ( α 2 +1) τ c 4π η i α eff [ τ c q [ I( t ) I th ]+( 2κ g 1 1+ α 2 S i S o e t 2 τ o 2 ) ] 1 ,
Δ λ total ( t )= λ 0 n 0 dn dN τ c 2 q 2 V [ I( t ) I th + qV τ c ( 2κ g 1 1+ α 2 S i S o e t 2 τ 0 2 ) ] 2 + λ 0 2 C v g α m R sp ( α 2 +1) τ c 4π η i α eff τ c q [ I( t ) I th + qV τ c ( 2κ g 1 1+ α 2 S i S o e t 2 τ 0 2 ) ] ,
P out (t)= η i α eff [I(t) I th ]= η i α eff ΔIsin(2π f m t),
Δ λ total ( t ) λ 0 n 0 dn dN τ c 2 q 2 V [ ΔIsin( 2π f m t )+ qV τ c ( 2κ g 1 1+ α 2 S i S o e t 2 τ 0 2 ) ] 2 + λ 0 2 C v g α m R sp ( α 2 +1) τ c 4π η i α eff τ c q [ ΔIsin( 2π f m t )+ qV τ c ( 2κ g 1 1+ α 2 S i S o e t 2 τ 0 2 ) ] ,

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