Abstract

The sensitivity of quantum-dot semiconductor lasers to optical feedback is analyzed with a Lang–Kobayashi approach applied to a standard quantum-dot laser model. The carriers are injected into a quantum well and are captured by, or escape from, the quantum dots through either carrier–carrier or phonon–carrier interaction. Because of Pauli blocking, the capture rate into the dots depends on the carrier occupancy level in the dots. Here we show that different carrier capture dynamics lead to a strong modification of the damping of the relaxation oscillations. Regions of increased damping display reduced sensitivity to optical feedback even for a relatively large α factor.

© 2004 Optical Society of America

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H. Su, L. Zhang, A. L. Gray, R. Wang, T. C. Newell, K. Malloy, and L. F. Lester, IEEE Photon. Technol. Lett. 15, 1504 (2003).
[CrossRef]

D. O’Brien, S. Hegarty, G. Huyet, J. McInerney, D. Bimberg, C. Ribbat, V. Ustinov, A. Zhukov, S. Mikbrin, A. R. Kovsh, J. White, K. Hinzer, and A. SpringThorpe, Electron. Lett. 39, 1819 (2003).
[CrossRef]

C. Ribbat, R. Sellin, I. Kaiander, F. Hopfer, N. N. Ledenstov, D. Bimberg, A. R. Kovsch, V. Ustinov, A. E. Zhukov, and M. Maximov, Appl. Phys. Lett. 82, 952 (2003).
[CrossRef]

2002

P. M. Smowton and E. J. Pearce, Appl. Phys. Lett. 81, 3251 (2002).
[CrossRef]

M. Kuntz, N. Ledentsov, D. Bimberg, A. Kovsch, V. Ustinov, A. Zhukov, and Y. M. Shernyakov, Appl. Phys. Lett. 81, 3846 (2002).
[CrossRef]

2001

A. Uskov, I. Magnusdottir, B. Tromberg, J. Mork, and R. Land, Appl. Phys. Lett. 79, 1679 (2001).
[CrossRef]

2000

H. Saito, K. Nishi, A. Kamei, and S. Sugou, IEEE Photon. Technol. Lett. 12, 1298 (2000).
[CrossRef]

G. Huyet, P. Porta, S. P. Hegarty, J. McInerney, and F. Holland, Opt. Commun. 180, 339 (2000).
[CrossRef]

1999

T. Newell, D. Bossert, A. Stintz, B. Fuchs, K. Malloy, and L. Lester, IEEE Photon. Technol. Lett. 11, 1527 (1999).
[CrossRef]

1998

A. Uskov, Y. Boucher, J. L. Bihan, and J. McInerney, Appl. Phys. Lett. 11, 1499 (1998).
[CrossRef]

1997

M. Sugawara, K. Mukai, and H. Shoji, Appl. Phys. Lett. 71, 2791 (1997).
[CrossRef]

1995

G. van Tartwijk, A. Levine, and D. Lenstra, IEEE J. Sel. Top. Quantum Electron. 1, 466 (1995).
[CrossRef]

A. M. Levine, G. H. M. van Tartwijk, D. Lestra, and T. Erneux, Phys. Rev. A 52, R3436 (1995).
[CrossRef]

1994

T. Sano, Phys. Rev. A 50, 2719 (1994).
[CrossRef] [PubMed]

1993

1990

J. Helms and K. Petermann, IEEE J. Quantum Electron. 26, 833 (1990).
[CrossRef]

1980

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Bihan, J. L.

A. Uskov, Y. Boucher, J. L. Bihan, and J. McInerney, Appl. Phys. Lett. 11, 1499 (1998).
[CrossRef]

Bimberg, D.

D. O’Brien, S. Hegarty, G. Huyet, J. McInerney, D. Bimberg, C. Ribbat, V. Ustinov, A. Zhukov, S. Mikbrin, A. R. Kovsh, J. White, K. Hinzer, and A. SpringThorpe, Electron. Lett. 39, 1819 (2003).
[CrossRef]

C. Ribbat, R. Sellin, I. Kaiander, F. Hopfer, N. N. Ledenstov, D. Bimberg, A. R. Kovsch, V. Ustinov, A. E. Zhukov, and M. Maximov, Appl. Phys. Lett. 82, 952 (2003).
[CrossRef]

M. Kuntz, N. Ledentsov, D. Bimberg, A. Kovsch, V. Ustinov, A. Zhukov, and Y. M. Shernyakov, Appl. Phys. Lett. 81, 3846 (2002).
[CrossRef]

Bossert, D.

T. Newell, D. Bossert, A. Stintz, B. Fuchs, K. Malloy, and L. Lester, IEEE Photon. Technol. Lett. 11, 1527 (1999).
[CrossRef]

Boucher, Y.

A. Uskov, Y. Boucher, J. L. Bihan, and J. McInerney, Appl. Phys. Lett. 11, 1499 (1998).
[CrossRef]

Erneux, T.

A. M. Levine, G. H. M. van Tartwijk, D. Lestra, and T. Erneux, Phys. Rev. A 52, R3436 (1995).
[CrossRef]

Fuchs, B.

T. Newell, D. Bossert, A. Stintz, B. Fuchs, K. Malloy, and L. Lester, IEEE Photon. Technol. Lett. 11, 1527 (1999).
[CrossRef]

Gray, A. L.

H. Su, L. Zhang, A. L. Gray, R. Wang, T. C. Newell, K. Malloy, and L. F. Lester, IEEE Photon. Technol. Lett. 15, 1504 (2003).
[CrossRef]

Haug, H.

Hegarty, S.

D. O’Brien, S. Hegarty, G. Huyet, J. McInerney, D. Bimberg, C. Ribbat, V. Ustinov, A. Zhukov, S. Mikbrin, A. R. Kovsh, J. White, K. Hinzer, and A. SpringThorpe, Electron. Lett. 39, 1819 (2003).
[CrossRef]

Hegarty, S. P.

G. Huyet, P. Porta, S. P. Hegarty, J. McInerney, and F. Holland, Opt. Commun. 180, 339 (2000).
[CrossRef]

Helms, J.

J. Helms and K. Petermann, IEEE J. Quantum Electron. 26, 833 (1990).
[CrossRef]

Hinzer, K.

D. O’Brien, S. Hegarty, G. Huyet, J. McInerney, D. Bimberg, C. Ribbat, V. Ustinov, A. Zhukov, S. Mikbrin, A. R. Kovsh, J. White, K. Hinzer, and A. SpringThorpe, Electron. Lett. 39, 1819 (2003).
[CrossRef]

Holland, F.

G. Huyet, P. Porta, S. P. Hegarty, J. McInerney, and F. Holland, Opt. Commun. 180, 339 (2000).
[CrossRef]

Hopfer, F.

C. Ribbat, R. Sellin, I. Kaiander, F. Hopfer, N. N. Ledenstov, D. Bimberg, A. R. Kovsch, V. Ustinov, A. E. Zhukov, and M. Maximov, Appl. Phys. Lett. 82, 952 (2003).
[CrossRef]

Huyet, G.

D. O’Brien, S. Hegarty, G. Huyet, J. McInerney, D. Bimberg, C. Ribbat, V. Ustinov, A. Zhukov, S. Mikbrin, A. R. Kovsh, J. White, K. Hinzer, and A. SpringThorpe, Electron. Lett. 39, 1819 (2003).
[CrossRef]

G. Huyet, P. Porta, S. P. Hegarty, J. McInerney, and F. Holland, Opt. Commun. 180, 339 (2000).
[CrossRef]

Kaiander, I.

C. Ribbat, R. Sellin, I. Kaiander, F. Hopfer, N. N. Ledenstov, D. Bimberg, A. R. Kovsch, V. Ustinov, A. E. Zhukov, and M. Maximov, Appl. Phys. Lett. 82, 952 (2003).
[CrossRef]

Kamei, A.

H. Saito, K. Nishi, A. Kamei, and S. Sugou, IEEE Photon. Technol. Lett. 12, 1298 (2000).
[CrossRef]

Kobayashi, K.

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Kovsch, A.

M. Kuntz, N. Ledentsov, D. Bimberg, A. Kovsch, V. Ustinov, A. Zhukov, and Y. M. Shernyakov, Appl. Phys. Lett. 81, 3846 (2002).
[CrossRef]

Kovsch, A. R.

C. Ribbat, R. Sellin, I. Kaiander, F. Hopfer, N. N. Ledenstov, D. Bimberg, A. R. Kovsch, V. Ustinov, A. E. Zhukov, and M. Maximov, Appl. Phys. Lett. 82, 952 (2003).
[CrossRef]

Kovsh, A. R.

D. O’Brien, S. Hegarty, G. Huyet, J. McInerney, D. Bimberg, C. Ribbat, V. Ustinov, A. Zhukov, S. Mikbrin, A. R. Kovsh, J. White, K. Hinzer, and A. SpringThorpe, Electron. Lett. 39, 1819 (2003).
[CrossRef]

Krauskopf, B.

B. Krauskopf and D. Lenstra, Fundamental Issues of Nonlinear Laser Dynamics (AIP, Melville, N.Y., 2000).

Kuntz, M.

M. Kuntz, N. Ledentsov, D. Bimberg, A. Kovsch, V. Ustinov, A. Zhukov, and Y. M. Shernyakov, Appl. Phys. Lett. 81, 3846 (2002).
[CrossRef]

Land, R.

A. Uskov, I. Magnusdottir, B. Tromberg, J. Mork, and R. Land, Appl. Phys. Lett. 79, 1679 (2001).
[CrossRef]

Lang, R.

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Ledenstov, N. N.

C. Ribbat, R. Sellin, I. Kaiander, F. Hopfer, N. N. Ledenstov, D. Bimberg, A. R. Kovsch, V. Ustinov, A. E. Zhukov, and M. Maximov, Appl. Phys. Lett. 82, 952 (2003).
[CrossRef]

Ledentsov, N.

M. Kuntz, N. Ledentsov, D. Bimberg, A. Kovsch, V. Ustinov, A. Zhukov, and Y. M. Shernyakov, Appl. Phys. Lett. 81, 3846 (2002).
[CrossRef]

Lenstra, D.

G. van Tartwijk, A. Levine, and D. Lenstra, IEEE J. Sel. Top. Quantum Electron. 1, 466 (1995).
[CrossRef]

B. Krauskopf and D. Lenstra, Fundamental Issues of Nonlinear Laser Dynamics (AIP, Melville, N.Y., 2000).

Lester, L.

T. Newell, D. Bossert, A. Stintz, B. Fuchs, K. Malloy, and L. Lester, IEEE Photon. Technol. Lett. 11, 1527 (1999).
[CrossRef]

Lester, L. F.

H. Su, L. Zhang, A. L. Gray, R. Wang, T. C. Newell, K. Malloy, and L. F. Lester, IEEE Photon. Technol. Lett. 15, 1504 (2003).
[CrossRef]

Lestra, D.

A. M. Levine, G. H. M. van Tartwijk, D. Lestra, and T. Erneux, Phys. Rev. A 52, R3436 (1995).
[CrossRef]

Levine, A.

G. van Tartwijk, A. Levine, and D. Lenstra, IEEE J. Sel. Top. Quantum Electron. 1, 466 (1995).
[CrossRef]

Levine, A. M.

A. M. Levine, G. H. M. van Tartwijk, D. Lestra, and T. Erneux, Phys. Rev. A 52, R3436 (1995).
[CrossRef]

Magnusdottir, I.

A. Uskov, I. Magnusdottir, B. Tromberg, J. Mork, and R. Land, Appl. Phys. Lett. 79, 1679 (2001).
[CrossRef]

Malloy, K.

H. Su, L. Zhang, A. L. Gray, R. Wang, T. C. Newell, K. Malloy, and L. F. Lester, IEEE Photon. Technol. Lett. 15, 1504 (2003).
[CrossRef]

T. Newell, D. Bossert, A. Stintz, B. Fuchs, K. Malloy, and L. Lester, IEEE Photon. Technol. Lett. 11, 1527 (1999).
[CrossRef]

Maximov, M.

C. Ribbat, R. Sellin, I. Kaiander, F. Hopfer, N. N. Ledenstov, D. Bimberg, A. R. Kovsch, V. Ustinov, A. E. Zhukov, and M. Maximov, Appl. Phys. Lett. 82, 952 (2003).
[CrossRef]

McInerney, J.

D. O’Brien, S. Hegarty, G. Huyet, J. McInerney, D. Bimberg, C. Ribbat, V. Ustinov, A. Zhukov, S. Mikbrin, A. R. Kovsh, J. White, K. Hinzer, and A. SpringThorpe, Electron. Lett. 39, 1819 (2003).
[CrossRef]

G. Huyet, P. Porta, S. P. Hegarty, J. McInerney, and F. Holland, Opt. Commun. 180, 339 (2000).
[CrossRef]

A. Uskov, Y. Boucher, J. L. Bihan, and J. McInerney, Appl. Phys. Lett. 11, 1499 (1998).
[CrossRef]

Mikbrin, S.

D. O’Brien, S. Hegarty, G. Huyet, J. McInerney, D. Bimberg, C. Ribbat, V. Ustinov, A. Zhukov, S. Mikbrin, A. R. Kovsh, J. White, K. Hinzer, and A. SpringThorpe, Electron. Lett. 39, 1819 (2003).
[CrossRef]

Mork, J.

A. Uskov, I. Magnusdottir, B. Tromberg, J. Mork, and R. Land, Appl. Phys. Lett. 79, 1679 (2001).
[CrossRef]

Mukai, K.

M. Sugawara, K. Mukai, and H. Shoji, Appl. Phys. Lett. 71, 2791 (1997).
[CrossRef]

Newell, T.

T. Newell, D. Bossert, A. Stintz, B. Fuchs, K. Malloy, and L. Lester, IEEE Photon. Technol. Lett. 11, 1527 (1999).
[CrossRef]

Newell, T. C.

H. Su, L. Zhang, A. L. Gray, R. Wang, T. C. Newell, K. Malloy, and L. F. Lester, IEEE Photon. Technol. Lett. 15, 1504 (2003).
[CrossRef]

Nishi, K.

H. Saito, K. Nishi, A. Kamei, and S. Sugou, IEEE Photon. Technol. Lett. 12, 1298 (2000).
[CrossRef]

O’Brien, D.

D. O’Brien, S. Hegarty, G. Huyet, J. McInerney, D. Bimberg, C. Ribbat, V. Ustinov, A. Zhukov, S. Mikbrin, A. R. Kovsh, J. White, K. Hinzer, and A. SpringThorpe, Electron. Lett. 39, 1819 (2003).
[CrossRef]

Pearce, E. J.

P. M. Smowton and E. J. Pearce, Appl. Phys. Lett. 81, 3251 (2002).
[CrossRef]

Petermann, K.

J. Helms and K. Petermann, IEEE J. Quantum Electron. 26, 833 (1990).
[CrossRef]

Porta, P.

G. Huyet, P. Porta, S. P. Hegarty, J. McInerney, and F. Holland, Opt. Commun. 180, 339 (2000).
[CrossRef]

Ribbat, C.

C. Ribbat, R. Sellin, I. Kaiander, F. Hopfer, N. N. Ledenstov, D. Bimberg, A. R. Kovsch, V. Ustinov, A. E. Zhukov, and M. Maximov, Appl. Phys. Lett. 82, 952 (2003).
[CrossRef]

D. O’Brien, S. Hegarty, G. Huyet, J. McInerney, D. Bimberg, C. Ribbat, V. Ustinov, A. Zhukov, S. Mikbrin, A. R. Kovsh, J. White, K. Hinzer, and A. SpringThorpe, Electron. Lett. 39, 1819 (2003).
[CrossRef]

Ritter, A.

Saito, H.

H. Saito, K. Nishi, A. Kamei, and S. Sugou, IEEE Photon. Technol. Lett. 12, 1298 (2000).
[CrossRef]

Sano, T.

T. Sano, Phys. Rev. A 50, 2719 (1994).
[CrossRef] [PubMed]

Sellin, R.

C. Ribbat, R. Sellin, I. Kaiander, F. Hopfer, N. N. Ledenstov, D. Bimberg, A. R. Kovsch, V. Ustinov, A. E. Zhukov, and M. Maximov, Appl. Phys. Lett. 82, 952 (2003).
[CrossRef]

Shernyakov, Y. M.

M. Kuntz, N. Ledentsov, D. Bimberg, A. Kovsch, V. Ustinov, A. Zhukov, and Y. M. Shernyakov, Appl. Phys. Lett. 81, 3846 (2002).
[CrossRef]

Shoji, H.

M. Sugawara, K. Mukai, and H. Shoji, Appl. Phys. Lett. 71, 2791 (1997).
[CrossRef]

Smowton, P. M.

P. M. Smowton and E. J. Pearce, Appl. Phys. Lett. 81, 3251 (2002).
[CrossRef]

SpringThorpe, A.

D. O’Brien, S. Hegarty, G. Huyet, J. McInerney, D. Bimberg, C. Ribbat, V. Ustinov, A. Zhukov, S. Mikbrin, A. R. Kovsh, J. White, K. Hinzer, and A. SpringThorpe, Electron. Lett. 39, 1819 (2003).
[CrossRef]

Stintz, A.

T. Newell, D. Bossert, A. Stintz, B. Fuchs, K. Malloy, and L. Lester, IEEE Photon. Technol. Lett. 11, 1527 (1999).
[CrossRef]

Su, H.

H. Su, L. Zhang, A. L. Gray, R. Wang, T. C. Newell, K. Malloy, and L. F. Lester, IEEE Photon. Technol. Lett. 15, 1504 (2003).
[CrossRef]

Sugawara, M.

M. Sugawara, K. Mukai, and H. Shoji, Appl. Phys. Lett. 71, 2791 (1997).
[CrossRef]

Sugou, S.

H. Saito, K. Nishi, A. Kamei, and S. Sugou, IEEE Photon. Technol. Lett. 12, 1298 (2000).
[CrossRef]

Tromberg, B.

A. Uskov, I. Magnusdottir, B. Tromberg, J. Mork, and R. Land, Appl. Phys. Lett. 79, 1679 (2001).
[CrossRef]

Uskov, A.

A. Uskov, I. Magnusdottir, B. Tromberg, J. Mork, and R. Land, Appl. Phys. Lett. 79, 1679 (2001).
[CrossRef]

A. Uskov, Y. Boucher, J. L. Bihan, and J. McInerney, Appl. Phys. Lett. 11, 1499 (1998).
[CrossRef]

Ustinov, V.

C. Ribbat, R. Sellin, I. Kaiander, F. Hopfer, N. N. Ledenstov, D. Bimberg, A. R. Kovsch, V. Ustinov, A. E. Zhukov, and M. Maximov, Appl. Phys. Lett. 82, 952 (2003).
[CrossRef]

D. O’Brien, S. Hegarty, G. Huyet, J. McInerney, D. Bimberg, C. Ribbat, V. Ustinov, A. Zhukov, S. Mikbrin, A. R. Kovsh, J. White, K. Hinzer, and A. SpringThorpe, Electron. Lett. 39, 1819 (2003).
[CrossRef]

M. Kuntz, N. Ledentsov, D. Bimberg, A. Kovsch, V. Ustinov, A. Zhukov, and Y. M. Shernyakov, Appl. Phys. Lett. 81, 3846 (2002).
[CrossRef]

van Tartwijk, G.

G. van Tartwijk, A. Levine, and D. Lenstra, IEEE J. Sel. Top. Quantum Electron. 1, 466 (1995).
[CrossRef]

van Tartwijk, G. H. M.

A. M. Levine, G. H. M. van Tartwijk, D. Lestra, and T. Erneux, Phys. Rev. A 52, R3436 (1995).
[CrossRef]

Wang, R.

H. Su, L. Zhang, A. L. Gray, R. Wang, T. C. Newell, K. Malloy, and L. F. Lester, IEEE Photon. Technol. Lett. 15, 1504 (2003).
[CrossRef]

White, J.

D. O’Brien, S. Hegarty, G. Huyet, J. McInerney, D. Bimberg, C. Ribbat, V. Ustinov, A. Zhukov, S. Mikbrin, A. R. Kovsh, J. White, K. Hinzer, and A. SpringThorpe, Electron. Lett. 39, 1819 (2003).
[CrossRef]

Zhang, L.

H. Su, L. Zhang, A. L. Gray, R. Wang, T. C. Newell, K. Malloy, and L. F. Lester, IEEE Photon. Technol. Lett. 15, 1504 (2003).
[CrossRef]

Zhukov, A.

D. O’Brien, S. Hegarty, G. Huyet, J. McInerney, D. Bimberg, C. Ribbat, V. Ustinov, A. Zhukov, S. Mikbrin, A. R. Kovsh, J. White, K. Hinzer, and A. SpringThorpe, Electron. Lett. 39, 1819 (2003).
[CrossRef]

M. Kuntz, N. Ledentsov, D. Bimberg, A. Kovsch, V. Ustinov, A. Zhukov, and Y. M. Shernyakov, Appl. Phys. Lett. 81, 3846 (2002).
[CrossRef]

Zhukov, A. E.

C. Ribbat, R. Sellin, I. Kaiander, F. Hopfer, N. N. Ledenstov, D. Bimberg, A. R. Kovsch, V. Ustinov, A. E. Zhukov, and M. Maximov, Appl. Phys. Lett. 82, 952 (2003).
[CrossRef]

Appl. Phys. Lett.

P. M. Smowton and E. J. Pearce, Appl. Phys. Lett. 81, 3251 (2002).
[CrossRef]

C. Ribbat, R. Sellin, I. Kaiander, F. Hopfer, N. N. Ledenstov, D. Bimberg, A. R. Kovsch, V. Ustinov, A. E. Zhukov, and M. Maximov, Appl. Phys. Lett. 82, 952 (2003).
[CrossRef]

M. Kuntz, N. Ledentsov, D. Bimberg, A. Kovsch, V. Ustinov, A. Zhukov, and Y. M. Shernyakov, Appl. Phys. Lett. 81, 3846 (2002).
[CrossRef]

A. Uskov, Y. Boucher, J. L. Bihan, and J. McInerney, Appl. Phys. Lett. 11, 1499 (1998).
[CrossRef]

M. Sugawara, K. Mukai, and H. Shoji, Appl. Phys. Lett. 71, 2791 (1997).
[CrossRef]

A. Uskov, I. Magnusdottir, B. Tromberg, J. Mork, and R. Land, Appl. Phys. Lett. 79, 1679 (2001).
[CrossRef]

Electron. Lett.

D. O’Brien, S. Hegarty, G. Huyet, J. McInerney, D. Bimberg, C. Ribbat, V. Ustinov, A. Zhukov, S. Mikbrin, A. R. Kovsh, J. White, K. Hinzer, and A. SpringThorpe, Electron. Lett. 39, 1819 (2003).
[CrossRef]

IEEE J. Quantum Electron.

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Figures (3)

Fig. 1
Fig. 1

Quantum-dot occupation probability ρ versus drive current J. How the operating point of the laser varies as g0 changes is shown in the inset. The two different operating points investigated are shown (A and B). C=10-20 m4/s, Resc=0, B=0,Nd=2×1015 m-2, ϑ=2.4×1022 m-3, τn=τd=1 ns, and τs=3 ps.

Fig. 2
Fig. 2

Damping of relaxation oscillation as a function of ρth for different values of the Auger carrier capture rate C×10-20 m4/s and for the reduced equations in S and N and S and ρ. The values of C were chosen to yield capture times from 0.5 to 50 ps at transparency. For values of goϑ<1/τs the laser can never meet the lasing condition. (Other values are the same as in Fig. 1).

Fig. 3
Fig. 3

Temporal behavior of lasers A and B at different operating points subjected to different amounts of optical feedback: photon density S×1018 m-3 versus time. Free-running turn-on transient top, with the feedback level increasing going down γ=0,0.01,0.02,0.025 ps-1. External-cavity round-trip time τ=100 ps. Operating point taken as 1.5 threshold. β1=0 and β2=2, yielding a value of the α factor of 2. (Other values are the same as in Fig. 1).

Equations (3)

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E·=-E2τs+g0ϑ22ρ-1E+iδω2E+γ2Et-τ,ρ·=-ρτd-g02ρ-1E2+FN,ρ,N·=J-Nτn-2NdFN,ρ,
S·=-Sτs+g0ϑ2ρ-1S,ρ·=-ρτd-g02ρ-1S+FN,ρ,N·=J-Nτn-2NdFN,ρ,
E·=-E2τs+g0ϑ22ρ-1E+iδω2E+γ2Et-τ,ρ·=-ρτd-g02ρ-1E2+JNd.

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