Abstract

Mode locking of solid-state lasers using metal nanocomposites as slow saturable absorbers (SAs) is studied theoretically. The derived equation for the transient nonlinear response of metal nanocomposites is based on the semiclassical two-temperature model. The model is confirmed experimentally by pump-probe measurements on Au nanoparticles (NPs). The theory was applied to study passive mode locking of a solid-state laser containing Au NPs as SA in the green spectral range. Pulse durations as short as 100 fs are predicted, and design criteria of metal NP SAs are derived.

© 2012 Optical Society of America

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References

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  1. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd ed. (Elsevier, 2006).
  2. U. Keller, Appl. Phys. B 100, 15 (2010).
    [CrossRef]
  3. W. B. Cho, J. H. Yim, S. Y. Choi, S. Lee, A. Schmidt, G. Steinmeyer, U. Griebner, V. Petrov, D.-I. Yeom, K. Kim, and F. Rotermund, Adv. Funct. Mater. 20, 1937 (2010).
    [CrossRef]
  4. H. Zhang, Q. Bao, D. Tang, L. Zhao, and K. Loh, Appl. Phys. Lett. 95, 141103 (2009).
    [CrossRef]
  5. J. Herrmann and B. Wilhelmi, Lasers for Ultrashort Light Pulses (Akademie-Verlag, 1987).
  6. R. A. Ganeev, A. I. Ryasnyanskii, A. L. Stepanov, and T. Usmanov, Quantum Electron. 33, 1081 (2003).
    [CrossRef]
  7. K.-H. Kim, A. Husakou, and J. Herrmann, Opt. Express 18, 21918 (2010).
    [CrossRef]
  8. J.-Y. Bigot, V. Halte, J.-C. Merle, and A. Daunois, Chem. Phys. 251, 181 (2000).
    [CrossRef]
  9. R. A. Ganeev, R. I. Tugushev, and T. Usmanov, Appl. Phys. B 94, 647 (2009).
    [CrossRef]
  10. D. Paboeuf, O. Mhibik, F. Bretenaker, P. Goldner, D. Parisi, and M. Tonelli, Opt. Lett. 36, 280 (2011).
    [CrossRef]
  11. C.-K. Sun, F. Valle, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, Phys. Rev. B 50, 15337 (1994).
    [CrossRef]
  12. S. Lysenko, J. Jimenez, G. Zhang, and H. Liu, J. Electron. Mater. 35, 1715 (2006).
    [CrossRef]
  13. C. Voisin, N. D. Fatti, D. Christofilos, and F. Valle, J. Phys. Chem. B 105, 2264 (2001).
    [CrossRef]
  14. D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, J. Appl. Phys. 86, 6200 (1999).
    [CrossRef]
  15. F. X. Kaertner, I. D. Jung, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 2, 540 (1996).
    [CrossRef]
  16. B. M. Walsh, N. P. Barnes, and B. D. Bartolo, J. Appl. Phys. 83, 2772 (1998).
    [CrossRef]
  17. P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, J. Phys. Chem. B 110, 7238 (2006).
    [CrossRef]
  18. B. M. Walsh, N. P. Barnes, J. Yu, and U. N. Singh, J. Appl. Phys. 95, 3255 (2004).
    [CrossRef]
  19. R. Paschotta and U. Keller, Appl. Phys. B 73, 653(2001).
    [CrossRef]

2011 (1)

2010 (3)

K.-H. Kim, A. Husakou, and J. Herrmann, Opt. Express 18, 21918 (2010).
[CrossRef]

U. Keller, Appl. Phys. B 100, 15 (2010).
[CrossRef]

W. B. Cho, J. H. Yim, S. Y. Choi, S. Lee, A. Schmidt, G. Steinmeyer, U. Griebner, V. Petrov, D.-I. Yeom, K. Kim, and F. Rotermund, Adv. Funct. Mater. 20, 1937 (2010).
[CrossRef]

2009 (2)

H. Zhang, Q. Bao, D. Tang, L. Zhao, and K. Loh, Appl. Phys. Lett. 95, 141103 (2009).
[CrossRef]

R. A. Ganeev, R. I. Tugushev, and T. Usmanov, Appl. Phys. B 94, 647 (2009).
[CrossRef]

2006 (2)

S. Lysenko, J. Jimenez, G. Zhang, and H. Liu, J. Electron. Mater. 35, 1715 (2006).
[CrossRef]

P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, J. Phys. Chem. B 110, 7238 (2006).
[CrossRef]

2004 (1)

B. M. Walsh, N. P. Barnes, J. Yu, and U. N. Singh, J. Appl. Phys. 95, 3255 (2004).
[CrossRef]

2003 (1)

R. A. Ganeev, A. I. Ryasnyanskii, A. L. Stepanov, and T. Usmanov, Quantum Electron. 33, 1081 (2003).
[CrossRef]

2001 (2)

R. Paschotta and U. Keller, Appl. Phys. B 73, 653(2001).
[CrossRef]

C. Voisin, N. D. Fatti, D. Christofilos, and F. Valle, J. Phys. Chem. B 105, 2264 (2001).
[CrossRef]

2000 (1)

J.-Y. Bigot, V. Halte, J.-C. Merle, and A. Daunois, Chem. Phys. 251, 181 (2000).
[CrossRef]

1999 (1)

D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, J. Appl. Phys. 86, 6200 (1999).
[CrossRef]

1998 (1)

B. M. Walsh, N. P. Barnes, and B. D. Bartolo, J. Appl. Phys. 83, 2772 (1998).
[CrossRef]

1996 (1)

F. X. Kaertner, I. D. Jung, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 2, 540 (1996).
[CrossRef]

1994 (1)

C.-K. Sun, F. Valle, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, Phys. Rev. B 50, 15337 (1994).
[CrossRef]

Acioli, L. H.

C.-K. Sun, F. Valle, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, Phys. Rev. B 50, 15337 (1994).
[CrossRef]

Baker, L. A.

D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, J. Appl. Phys. 86, 6200 (1999).
[CrossRef]

Bao, Q.

H. Zhang, Q. Bao, D. Tang, L. Zhao, and K. Loh, Appl. Phys. Lett. 95, 141103 (2009).
[CrossRef]

Barnes, N. P.

B. M. Walsh, N. P. Barnes, J. Yu, and U. N. Singh, J. Appl. Phys. 95, 3255 (2004).
[CrossRef]

B. M. Walsh, N. P. Barnes, and B. D. Bartolo, J. Appl. Phys. 83, 2772 (1998).
[CrossRef]

Bartolo, B. D.

B. M. Walsh, N. P. Barnes, and B. D. Bartolo, J. Appl. Phys. 83, 2772 (1998).
[CrossRef]

Bigot, J.-Y.

J.-Y. Bigot, V. Halte, J.-C. Merle, and A. Daunois, Chem. Phys. 251, 181 (2000).
[CrossRef]

Boyd, R. W.

D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, J. Appl. Phys. 86, 6200 (1999).
[CrossRef]

Bretenaker, F.

Campbell, J. K.

D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, J. Appl. Phys. 86, 6200 (1999).
[CrossRef]

Cho, W. B.

W. B. Cho, J. H. Yim, S. Y. Choi, S. Lee, A. Schmidt, G. Steinmeyer, U. Griebner, V. Petrov, D.-I. Yeom, K. Kim, and F. Rotermund, Adv. Funct. Mater. 20, 1937 (2010).
[CrossRef]

Choi, S. Y.

W. B. Cho, J. H. Yim, S. Y. Choi, S. Lee, A. Schmidt, G. Steinmeyer, U. Griebner, V. Petrov, D.-I. Yeom, K. Kim, and F. Rotermund, Adv. Funct. Mater. 20, 1937 (2010).
[CrossRef]

Christofilos, D.

C. Voisin, N. D. Fatti, D. Christofilos, and F. Valle, J. Phys. Chem. B 105, 2264 (2001).
[CrossRef]

Crooks, R. M.

D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, J. Appl. Phys. 86, 6200 (1999).
[CrossRef]

Daunois, A.

J.-Y. Bigot, V. Halte, J.-C. Merle, and A. Daunois, Chem. Phys. 251, 181 (2000).
[CrossRef]

Diels, J.-C.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd ed. (Elsevier, 2006).

El-Sayed, I. H.

P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, J. Phys. Chem. B 110, 7238 (2006).
[CrossRef]

El-Sayed, M. A.

P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, J. Phys. Chem. B 110, 7238 (2006).
[CrossRef]

Fatti, N. D.

C. Voisin, N. D. Fatti, D. Christofilos, and F. Valle, J. Phys. Chem. B 105, 2264 (2001).
[CrossRef]

Fujimoto, J. G.

C.-K. Sun, F. Valle, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, Phys. Rev. B 50, 15337 (1994).
[CrossRef]

Ganeev, R. A.

R. A. Ganeev, R. I. Tugushev, and T. Usmanov, Appl. Phys. B 94, 647 (2009).
[CrossRef]

R. A. Ganeev, A. I. Ryasnyanskii, A. L. Stepanov, and T. Usmanov, Quantum Electron. 33, 1081 (2003).
[CrossRef]

George, M.

D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, J. Appl. Phys. 86, 6200 (1999).
[CrossRef]

Goldner, P.

Griebner, U.

W. B. Cho, J. H. Yim, S. Y. Choi, S. Lee, A. Schmidt, G. Steinmeyer, U. Griebner, V. Petrov, D.-I. Yeom, K. Kim, and F. Rotermund, Adv. Funct. Mater. 20, 1937 (2010).
[CrossRef]

Halte, V.

J.-Y. Bigot, V. Halte, J.-C. Merle, and A. Daunois, Chem. Phys. 251, 181 (2000).
[CrossRef]

Herrmann, J.

K.-H. Kim, A. Husakou, and J. Herrmann, Opt. Express 18, 21918 (2010).
[CrossRef]

J. Herrmann and B. Wilhelmi, Lasers for Ultrashort Light Pulses (Akademie-Verlag, 1987).

Husakou, A.

Ippen, E. P.

C.-K. Sun, F. Valle, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, Phys. Rev. B 50, 15337 (1994).
[CrossRef]

Jain, P. K.

P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, J. Phys. Chem. B 110, 7238 (2006).
[CrossRef]

Jimenez, J.

S. Lysenko, J. Jimenez, G. Zhang, and H. Liu, J. Electron. Mater. 35, 1715 (2006).
[CrossRef]

Jung, I. D.

F. X. Kaertner, I. D. Jung, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 2, 540 (1996).
[CrossRef]

Kaertner, F. X.

F. X. Kaertner, I. D. Jung, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 2, 540 (1996).
[CrossRef]

Keller, U.

U. Keller, Appl. Phys. B 100, 15 (2010).
[CrossRef]

R. Paschotta and U. Keller, Appl. Phys. B 73, 653(2001).
[CrossRef]

F. X. Kaertner, I. D. Jung, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 2, 540 (1996).
[CrossRef]

Kim, K.

W. B. Cho, J. H. Yim, S. Y. Choi, S. Lee, A. Schmidt, G. Steinmeyer, U. Griebner, V. Petrov, D.-I. Yeom, K. Kim, and F. Rotermund, Adv. Funct. Mater. 20, 1937 (2010).
[CrossRef]

Kim, K.-H.

Lee, K. S.

P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, J. Phys. Chem. B 110, 7238 (2006).
[CrossRef]

Lee, S.

W. B. Cho, J. H. Yim, S. Y. Choi, S. Lee, A. Schmidt, G. Steinmeyer, U. Griebner, V. Petrov, D.-I. Yeom, K. Kim, and F. Rotermund, Adv. Funct. Mater. 20, 1937 (2010).
[CrossRef]

Liu, H.

S. Lysenko, J. Jimenez, G. Zhang, and H. Liu, J. Electron. Mater. 35, 1715 (2006).
[CrossRef]

Loh, K.

H. Zhang, Q. Bao, D. Tang, L. Zhao, and K. Loh, Appl. Phys. Lett. 95, 141103 (2009).
[CrossRef]

Lysenko, S.

S. Lysenko, J. Jimenez, G. Zhang, and H. Liu, J. Electron. Mater. 35, 1715 (2006).
[CrossRef]

Merle, J.-C.

J.-Y. Bigot, V. Halte, J.-C. Merle, and A. Daunois, Chem. Phys. 251, 181 (2000).
[CrossRef]

Mhibik, O.

Paboeuf, D.

Parisi, D.

Paschotta, R.

R. Paschotta and U. Keller, Appl. Phys. B 73, 653(2001).
[CrossRef]

Petrov, V.

W. B. Cho, J. H. Yim, S. Y. Choi, S. Lee, A. Schmidt, G. Steinmeyer, U. Griebner, V. Petrov, D.-I. Yeom, K. Kim, and F. Rotermund, Adv. Funct. Mater. 20, 1937 (2010).
[CrossRef]

Rotermund, F.

W. B. Cho, J. H. Yim, S. Y. Choi, S. Lee, A. Schmidt, G. Steinmeyer, U. Griebner, V. Petrov, D.-I. Yeom, K. Kim, and F. Rotermund, Adv. Funct. Mater. 20, 1937 (2010).
[CrossRef]

Rudolph, W.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd ed. (Elsevier, 2006).

Ryasnyanskii, A. I.

R. A. Ganeev, A. I. Ryasnyanskii, A. L. Stepanov, and T. Usmanov, Quantum Electron. 33, 1081 (2003).
[CrossRef]

Schmidt, A.

W. B. Cho, J. H. Yim, S. Y. Choi, S. Lee, A. Schmidt, G. Steinmeyer, U. Griebner, V. Petrov, D.-I. Yeom, K. Kim, and F. Rotermund, Adv. Funct. Mater. 20, 1937 (2010).
[CrossRef]

Singh, U. N.

B. M. Walsh, N. P. Barnes, J. Yu, and U. N. Singh, J. Appl. Phys. 95, 3255 (2004).
[CrossRef]

Smith, D. D.

D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, J. Appl. Phys. 86, 6200 (1999).
[CrossRef]

Steinmeyer, G.

W. B. Cho, J. H. Yim, S. Y. Choi, S. Lee, A. Schmidt, G. Steinmeyer, U. Griebner, V. Petrov, D.-I. Yeom, K. Kim, and F. Rotermund, Adv. Funct. Mater. 20, 1937 (2010).
[CrossRef]

Stepanov, A. L.

R. A. Ganeev, A. I. Ryasnyanskii, A. L. Stepanov, and T. Usmanov, Quantum Electron. 33, 1081 (2003).
[CrossRef]

Sun, C.-K.

C.-K. Sun, F. Valle, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, Phys. Rev. B 50, 15337 (1994).
[CrossRef]

Tang, D.

H. Zhang, Q. Bao, D. Tang, L. Zhao, and K. Loh, Appl. Phys. Lett. 95, 141103 (2009).
[CrossRef]

Tonelli, M.

Tugushev, R. I.

R. A. Ganeev, R. I. Tugushev, and T. Usmanov, Appl. Phys. B 94, 647 (2009).
[CrossRef]

Usmanov, T.

R. A. Ganeev, R. I. Tugushev, and T. Usmanov, Appl. Phys. B 94, 647 (2009).
[CrossRef]

R. A. Ganeev, A. I. Ryasnyanskii, A. L. Stepanov, and T. Usmanov, Quantum Electron. 33, 1081 (2003).
[CrossRef]

Valle, F.

C. Voisin, N. D. Fatti, D. Christofilos, and F. Valle, J. Phys. Chem. B 105, 2264 (2001).
[CrossRef]

C.-K. Sun, F. Valle, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, Phys. Rev. B 50, 15337 (1994).
[CrossRef]

Voisin, C.

C. Voisin, N. D. Fatti, D. Christofilos, and F. Valle, J. Phys. Chem. B 105, 2264 (2001).
[CrossRef]

Walsh, B. M.

B. M. Walsh, N. P. Barnes, J. Yu, and U. N. Singh, J. Appl. Phys. 95, 3255 (2004).
[CrossRef]

B. M. Walsh, N. P. Barnes, and B. D. Bartolo, J. Appl. Phys. 83, 2772 (1998).
[CrossRef]

Wilhelmi, B.

J. Herrmann and B. Wilhelmi, Lasers for Ultrashort Light Pulses (Akademie-Verlag, 1987).

Yeom, D.-I.

W. B. Cho, J. H. Yim, S. Y. Choi, S. Lee, A. Schmidt, G. Steinmeyer, U. Griebner, V. Petrov, D.-I. Yeom, K. Kim, and F. Rotermund, Adv. Funct. Mater. 20, 1937 (2010).
[CrossRef]

Yim, J. H.

W. B. Cho, J. H. Yim, S. Y. Choi, S. Lee, A. Schmidt, G. Steinmeyer, U. Griebner, V. Petrov, D.-I. Yeom, K. Kim, and F. Rotermund, Adv. Funct. Mater. 20, 1937 (2010).
[CrossRef]

Yoon, Y.

D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, J. Appl. Phys. 86, 6200 (1999).
[CrossRef]

Yu, J.

B. M. Walsh, N. P. Barnes, J. Yu, and U. N. Singh, J. Appl. Phys. 95, 3255 (2004).
[CrossRef]

Zhang, G.

S. Lysenko, J. Jimenez, G. Zhang, and H. Liu, J. Electron. Mater. 35, 1715 (2006).
[CrossRef]

Zhang, H.

H. Zhang, Q. Bao, D. Tang, L. Zhao, and K. Loh, Appl. Phys. Lett. 95, 141103 (2009).
[CrossRef]

Zhao, L.

H. Zhang, Q. Bao, D. Tang, L. Zhao, and K. Loh, Appl. Phys. Lett. 95, 141103 (2009).
[CrossRef]

Adv. Funct. Mater. (1)

W. B. Cho, J. H. Yim, S. Y. Choi, S. Lee, A. Schmidt, G. Steinmeyer, U. Griebner, V. Petrov, D.-I. Yeom, K. Kim, and F. Rotermund, Adv. Funct. Mater. 20, 1937 (2010).
[CrossRef]

Appl. Phys. B (3)

U. Keller, Appl. Phys. B 100, 15 (2010).
[CrossRef]

R. A. Ganeev, R. I. Tugushev, and T. Usmanov, Appl. Phys. B 94, 647 (2009).
[CrossRef]

R. Paschotta and U. Keller, Appl. Phys. B 73, 653(2001).
[CrossRef]

Appl. Phys. Lett. (1)

H. Zhang, Q. Bao, D. Tang, L. Zhao, and K. Loh, Appl. Phys. Lett. 95, 141103 (2009).
[CrossRef]

Chem. Phys. (1)

J.-Y. Bigot, V. Halte, J.-C. Merle, and A. Daunois, Chem. Phys. 251, 181 (2000).
[CrossRef]

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

F. X. Kaertner, I. D. Jung, and U. Keller, IEEE J. Sel. Top. Quantum Electron. 2, 540 (1996).
[CrossRef]

J. Appl. Phys. (3)

B. M. Walsh, N. P. Barnes, and B. D. Bartolo, J. Appl. Phys. 83, 2772 (1998).
[CrossRef]

D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, J. Appl. Phys. 86, 6200 (1999).
[CrossRef]

B. M. Walsh, N. P. Barnes, J. Yu, and U. N. Singh, J. Appl. Phys. 95, 3255 (2004).
[CrossRef]

J. Electron. Mater. (1)

S. Lysenko, J. Jimenez, G. Zhang, and H. Liu, J. Electron. Mater. 35, 1715 (2006).
[CrossRef]

J. Phys. Chem. B (2)

C. Voisin, N. D. Fatti, D. Christofilos, and F. Valle, J. Phys. Chem. B 105, 2264 (2001).
[CrossRef]

P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, J. Phys. Chem. B 110, 7238 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

C.-K. Sun, F. Valle, L. H. Acioli, E. P. Ippen, and J. G. Fujimoto, Phys. Rev. B 50, 15337 (1994).
[CrossRef]

Quantum Electron. (1)

R. A. Ganeev, A. I. Ryasnyanskii, A. L. Stepanov, and T. Usmanov, Quantum Electron. 33, 1081 (2003).
[CrossRef]

Other (2)

J. Herrmann and B. Wilhelmi, Lasers for Ultrashort Light Pulses (Akademie-Verlag, 1987).

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd ed. (Elsevier, 2006).

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Figures (4)

Fig. 1.
Fig. 1.

Transient response of aqueous Au nanocolloid (NP diameter is 40 nm). Dots represent the experimental data, and the red solid curve shows the theoretical model. The excitation wavelength is 530 nm, and the pulse duration 100 fs.

Fig. 2.
Fig. 2.

Dependence of pulse duration on the group delay dispersion of a Ho:YLF laser mode locked by Au NPs-doped glass as SA.

Fig. 3.
Fig. 3.

Shortest pulse of the Au-NP mode-locked Ho:YLF laser corresponding to D=20fs2. The blue solid line represents the pulse intensity, the green dashed–dotted line the phase, and the red dashed line the net gain.

Fig. 4.
Fig. 4.

Dependencies of pulse duration (blue solid line) and energy (green dashed line) on the Au-NP filling factor of the Ho:YLF laser.

Equations (5)

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

N.=N/τeeN/τep+δP(t)CeT.e=G(TeTL)+N/τee,CLT.L=G(TeTL)+N/τep,
ΔTe.=ΔTeτep+δtP(t)ettτeedt,
Δεm(t)=ηΔTe,
ε.m=εmεm0τep+χm(3)τeeτept|x(t)E(t)|2ettτeedt,
TRA(T,t)T=iD2At2+iγ|A|2A+[gl+Dg,f2At2q(T,t)]A(T,t),

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