Abstract

We theoretically demonstrate that in a laser cavity mode-locked by a set of waveplates and passive polarizer, the energy performance can be increased by incorporating a second set of waveplates and polarizer in the cavity. The two nonlinear transmission functions acting in combination can be engineered so as to suppress the multi-pulsing instability responsible for limiting the single pulse per round trip energy in a myriad of mode-locked cavities. In a single parameter sweep, the energy is demonstrated to double. It is anticipated that further engineering and optimization of the transmission functions by tuning the eight waveplates, fiber birefringence, two polarizers and two lengths of transmission fiber can lead to further significant increases. Moreover, the analysis suggests a general design and engineering principle that can potentially realize the goal of making fiber based lasers directly competitive with solid state devices. The technique is feasible and easy to implement without requiring a new cavity design paradigm.

© 2011 OSA

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References

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  1. D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27, B63–B92 (2010).
    [CrossRef]
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    [CrossRef]
  3. K. Tamura, E.P. Ippen, H.A. Haus, and L.E. Nelson, “77-fs Pulse Generation From a Stretched-Pulse Mode-Locked All-Fiber Ring Laser,” Opt. Lett. 18, 1080–1082 (1993).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  6. F. Ö. Ilday, J. Buckley, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser cavity,” Phys. Rev. Lett. 92, 213902 (2004).
    [CrossRef] [PubMed]
  7. W. H. Renninger, A. Chong, and F. W. Wise“Self-similar pulse evolution in an all-normal-dispersion laser.” Phys. Rev. A 82, 021805 (2010).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Laser Mode Locking Using a Saturable Absorber Incorporating Carbon Nanotubes,” J. Lightwave Technol. 22, 51–56 (2004).
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    [CrossRef] [PubMed]
  18. H. Zhang, “Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95, 141103 (2009).
    [CrossRef]
  19. H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17, 17630–17635 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  24. C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron. 23, 174–176 (1987).
    [CrossRef]
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2011 (1)

E. Ding, E. Shlizerman, and J. N. Kutz, “Generalized Master Equation for High-Energy Passive Mode-Locking: The Sinusoidal Ginzburg-Landau Equation,” IEEE J. Quantum Electron. 47, 705–714 (2011).
[CrossRef]

2010 (5)

2009 (3)

2008 (2)

2006 (1)

R. Herda, O. G. Okhotnikov, E. U. Rafailov, W. Sibbett, P. Crittenden, and A. Starodumov, “Semiconductor quantum-dot saturable absorber mode-locked fiber laser,” IEEE Photon. Technol. Lett. 18, 157–159 (2006).
[CrossRef]

2005 (1)

A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A 71, 053809 (2005).
[CrossRef]

2004 (3)

2000 (1)

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quant. Elec. 6, 1173–1185 (2000).
[CrossRef]

1997 (1)

1995 (2)

G. Lenz, K. Tamura, H. A. Haus, and E. P. Ippen, “All-solid-state femtosecond source at 1.55 μm,” Opt. Lett. 20, 1289–1291 (1995).
[CrossRef] [PubMed]

K. Tamura and M. Nakazawa, “Optimizing power extraction in stretched pulse fiber ring lasers,” Appl. Phys. Lett. 67, 3691–3693 (1995).
[CrossRef]

1993 (1)

1989 (1)

C. R. Menyuk, “Pulse propagation in an elliptically birefringent Kerr media,” IEEE J. Quantum Electron. 25, 2674–2682 (1989).
[CrossRef]

1987 (1)

C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron. 23, 174–176 (1987).
[CrossRef]

Bale, B.

Bale, B. G.

Bao, Q. L.

Basko, D. M.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano 4, 803–810 (2010).
[CrossRef] [PubMed]

Bonaccorso, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano 4, 803–810 (2010).
[CrossRef] [PubMed]

Buckley, J.

F. Ö. Ilday, J. Buckley, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser cavity,” Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Chong, A.

W. H. Renninger, A. Chong, and F. W. Wise“Self-similar pulse evolution in an all-normal-dispersion laser.” Phys. Rev. A 82, 021805 (2010).
[CrossRef]

A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B 25, 140–148 (2008).
[CrossRef]

Clarkson, W. A.

Crittenden, P.

R. Herda, O. G. Okhotnikov, E. U. Rafailov, W. Sibbett, P. Crittenden, and A. Starodumov, “Semiconductor quantum-dot saturable absorber mode-locked fiber laser,” IEEE Photon. Technol. Lett. 18, 157–159 (2006).
[CrossRef]

Devaney, R.

R. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd ed. (Addison-Wesley, Redwood City, 1989).

Ding, E.

E. Ding, E. Shlizerman, and J. N. Kutz, “Generalized Master Equation for High-Energy Passive Mode-Locking: The Sinusoidal Ginzburg-Landau Equation,” IEEE J. Quantum Electron. 47, 705–714 (2011).
[CrossRef]

Drazin, P. G.

P. G. Drazin, Nonlinear systems, (Cambridge, 1992)

Ferrari, A. C.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano 4, 803–810 (2010).
[CrossRef] [PubMed]

Hasan, T.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano 4, 803–810 (2010).
[CrossRef] [PubMed]

Haus, H. A.

Haus, H.A.

Herda, R.

R. Herda, O. G. Okhotnikov, E. U. Rafailov, W. Sibbett, P. Crittenden, and A. Starodumov, “Semiconductor quantum-dot saturable absorber mode-locked fiber laser,” IEEE Photon. Technol. Lett. 18, 157–159 (2006).
[CrossRef]

Ilday, F. Ö.

F. Ö. Ilday, J. Buckley, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser cavity,” Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Inoue, Y.

Ippen, E. P.

Ippen, E.P.

Jablonski, M.

Kieu, K.

Komarov, A.

A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A 71, 053809 (2005).
[CrossRef]

Kutz, J. N.

Leblond, H.

A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A 71, 053809 (2005).
[CrossRef]

Lenz, G.

Li, F.

Loh, K. P.

Maruyama, S.

Menyuk, C. R.

C. R. Menyuk, “Pulse propagation in an elliptically birefringent Kerr media,” IEEE J. Quantum Electron. 25, 2674–2682 (1989).
[CrossRef]

C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron. 23, 174–176 (1987).
[CrossRef]

Murakami, Y.

Nakazawa, M.

K. Tamura and M. Nakazawa, “Optimizing power extraction in stretched pulse fiber ring lasers,” Appl. Phys. Lett. 67, 3691–3693 (1995).
[CrossRef]

Namiki, S.

Nelson, L.E.

Nilsson, J.

Okhotnikov, O. G.

R. Herda, O. G. Okhotnikov, E. U. Rafailov, W. Sibbett, P. Crittenden, and A. Starodumov, “Semiconductor quantum-dot saturable absorber mode-locked fiber laser,” IEEE Photon. Technol. Lett. 18, 157–159 (2006).
[CrossRef]

Popa, D.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano 4, 803–810 (2010).
[CrossRef] [PubMed]

Privitera, G.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano 4, 803–810 (2010).
[CrossRef] [PubMed]

Rafailov, E. U.

R. Herda, O. G. Okhotnikov, E. U. Rafailov, W. Sibbett, P. Crittenden, and A. Starodumov, “Semiconductor quantum-dot saturable absorber mode-locked fiber laser,” IEEE Photon. Technol. Lett. 18, 157–159 (2006).
[CrossRef]

Renninger, W. H.

W. H. Renninger, A. Chong, and F. W. Wise“Self-similar pulse evolution in an all-normal-dispersion laser.” Phys. Rev. A 82, 021805 (2010).
[CrossRef]

A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B 25, 140–148 (2008).
[CrossRef]

Richardson, D. J.

Sanchez, F.

A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A 71, 053809 (2005).
[CrossRef]

Sandstede, B.

Set, S. Y.

Shlizerman, E.

E. Ding, E. Shlizerman, and J. N. Kutz, “Generalized Master Equation for High-Energy Passive Mode-Locking: The Sinusoidal Ginzburg-Landau Equation,” IEEE J. Quantum Electron. 47, 705–714 (2011).
[CrossRef]

Sibbett, W.

R. Herda, O. G. Okhotnikov, E. U. Rafailov, W. Sibbett, P. Crittenden, and A. Starodumov, “Semiconductor quantum-dot saturable absorber mode-locked fiber laser,” IEEE Photon. Technol. Lett. 18, 157–159 (2006).
[CrossRef]

Starodumov, A.

R. Herda, O. G. Okhotnikov, E. U. Rafailov, W. Sibbett, P. Crittenden, and A. Starodumov, “Semiconductor quantum-dot saturable absorber mode-locked fiber laser,” IEEE Photon. Technol. Lett. 18, 157–159 (2006).
[CrossRef]

Sun, Z.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano 4, 803–810 (2010).
[CrossRef] [PubMed]

Tamura, K.

Tanaka, Y.

Tang, D. Y.

Torrisi, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano 4, 803–810 (2010).
[CrossRef] [PubMed]

Wabnitz, S.

Wai, P. K. A.

Wang, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano 4, 803–810 (2010).
[CrossRef] [PubMed]

Wise, F.

Wise, F. W.

W. H. Renninger, A. Chong, and F. W. Wise“Self-similar pulse evolution in an all-normal-dispersion laser.” Phys. Rev. A 82, 021805 (2010).
[CrossRef]

A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B 25, 140–148 (2008).
[CrossRef]

F. Ö. Ilday, J. Buckley, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser cavity,” Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Yaguchi, H.

Yamashita, S.

Yu, C. X.

Zhang, H.

H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17, 17630–17635 (2009).
[CrossRef] [PubMed]

H. Zhang, “Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95, 141103 (2009).
[CrossRef]

Zhao, L. M.

ACS Nano (1)

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene Mode-Locked Ultrafast Laser,” ACS Nano 4, 803–810 (2010).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

H. Zhang, “Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95, 141103 (2009).
[CrossRef]

K. Tamura and M. Nakazawa, “Optimizing power extraction in stretched pulse fiber ring lasers,” Appl. Phys. Lett. 67, 3691–3693 (1995).
[CrossRef]

IEEE J. Quantum Electron. (3)

E. Ding, E. Shlizerman, and J. N. Kutz, “Generalized Master Equation for High-Energy Passive Mode-Locking: The Sinusoidal Ginzburg-Landau Equation,” IEEE J. Quantum Electron. 47, 705–714 (2011).
[CrossRef]

C. R. Menyuk, “Pulse propagation in an elliptically birefringent Kerr media,” IEEE J. Quantum Electron. 25, 2674–2682 (1989).
[CrossRef]

C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron. 23, 174–176 (1987).
[CrossRef]

IEEE J. Sel. Top. Quant. Elec. (1)

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quant. Elec. 6, 1173–1185 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

R. Herda, O. G. Okhotnikov, E. U. Rafailov, W. Sibbett, P. Crittenden, and A. Starodumov, “Semiconductor quantum-dot saturable absorber mode-locked fiber laser,” IEEE Photon. Technol. Lett. 18, 157–159 (2006).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (4)

Opt. Express (3)

Opt. Lett. (4)

Phys. Rev. A (2)

A. Komarov, H. Leblond, and F. Sanchez, “Multistability and hysteresis phenomena in passively mode-locked fiber lasers,” Phys. Rev. A 71, 053809 (2005).
[CrossRef]

W. H. Renninger, A. Chong, and F. W. Wise“Self-similar pulse evolution in an all-normal-dispersion laser.” Phys. Rev. A 82, 021805 (2010).
[CrossRef]

Phys. Rev. Lett. (1)

F. Ö. Ilday, J. Buckley, and F. W. Wise, “Self-similar evolution of parabolic pulses in a laser cavity,” Phys. Rev. Lett. 92, 213902 (2004).
[CrossRef] [PubMed]

Other (2)

R. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd ed. (Addison-Wesley, Redwood City, 1989).

P. G. Drazin, Nonlinear systems, (Cambridge, 1992)

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Figures (6)

Fig. 1
Fig. 1

(a) Experimental configuration of a generic ring cavity laser that includes four quarter-waveplates (α1, α2, β1, β2), two half-waveplates (α3, β3), two passive polarizers (αp, αp), and one or two ytterbium-doped amplifiers. The Yb-doped and standard single-mode fiber sections are fused together and the gain will be treated distributed. The birefringence of each fiber section can be adjusted by the coiled polarization controllers. The waveplate and polarizer angles (αj, αj) can all be measured accurately in experiment. (b) Idealization of the physical cavity with T1 and T2 representing the nonlinear, periodic transmission functions generated from the waveplate and polarizers. Transmission T1 is generated from the α parameters while T2 is generated from the β parameters. In both configurations, the second gain element are optional. It can be inserted to adjust the effective T2 curve if needed.

Fig. 2
Fig. 2

The individual performance of the first, (a) T1, and second, (b) T2, nonlinear transmission functions generated by the waveplates and polarizer acting in combination. The parameter T is the combined transmission function, (c)T2(T1(E)E)T1(E). The dotted line in the bottom of each figure is the multipulse transition threshold, which is the small signal transmission of the illustrated transmission function. By enlarging the region that the transmission function stays above this curve, the single pulse energy can be significantly enhanced [13] since the multipulsing threshold (red dots) can be pushed out from (a) 4.4 and (b) 6.3 to (c) 16.9.

Fig. 3
Fig. 3

The saturating gain and nonlinear loss (effective transmission) curves of the laser cavity with single NPR (a) and dual NPRs(b). The blue solid lines are the outputĩnput of T1(E) defined in Eq. (4) and T(E) in Eq. (1). The black dotted lines are the multipulse transition thresholds defined same as Fig. 2. The red curves are saturable gain curves for the cases of 1-pulse, 2-pulse or 3-pulses per round trip. The red dot at the cross point of the loss curves and threshold line are the threshold points of multi-pulsing. The laser output will be determined by the cross points of gain and loss curves. Note that before the cross point of the 1-pulse gain curve and loss curve reaches the threshold points, there will be only one pulse in the cavity. With the increase of Esat, the 1-pulse solution point will pass the threshold which will trigger the multi-pulsing which will lead to the 2-pulse solutions in the cavity. The 1-pulse gain curve in (b) also shows the transition point from stable solutions to chaotic solutions. Note that the laser cavity in (b) has much larger threshold than in (a) which can afford much larger single pulse energy before the multi-pulse transition. The parameters used here are identical to those of Fig. 2 with the saturable gain g0 = log(1000) which correspond to small signal gain 30 dB. The fiber length of the gain is 1 meter. Here (a) Esat = 0.5 and (b) Esat = 1.8.

Fig. 4
Fig. 4

The pulse energy per pulse with the increase of Esat. The upper panel (a) is for the cavity with a single transmission function for generating nonlinear polarization rotation (NPR), and the bottom panel is for dual NPRs. The cavity parameters are the same as those used in Fig. 3. With a single NPR, the pulse energy will trigger the multi-pulse transition (red dot) at energy of approximately 4. The dual NPR cavity remains stable (red dot) up to an energy of approximately 13 before generating chaotic solutions. Thus the dual transmission can enhance the pulse energy by a factor of three. The blue vertical dash lines indicate the multi-pulse transition points.

Fig. 5
Fig. 5

The stable mode-locked pulse shape is shown as a function of increasing saturation energy e0,j in (a) for a single NPR laser cavity and (b) for a dual NPRs laser cavity. Panel (c) shows the pulse peak power and energy variation with e0,j for both lasers. The vertical blue lines indicate the multi-pulsing transition threshold. In the top panel of (c), the line with square marks shows the peak power and the line with circle marks shows the pulse energy. The zoomed solid square and hollow circle at e0,1 = 6.2 indicate the maximum peak power and pulse energy that can be obtained in this laser. There are two pair of zoomed marks in the bottom panel of (c). The left pair marks at e0,1 = 30 show the pulse with maximum pulse energy and the right pair marks at e0,1 = 64 show the pulse with maximum peak power. The three pulses indicated by the three pair zoomed marks are shown in (d). The black dot line shows the pulse with maximum energy and peak power obtained in single NPR system shown in (a) and the top panel of (c). The blue dash line/red solid line shows the pulse with maximum energy/peak power in dual NPR system shown in (b) and the bottom panel of (c). The parameters of the single NPR system are α1 = 0, α = 0.49π, α = 0.2π, αp = 0.45π, K1 = 0.1, D1 = −0.4, τ1 = 0.1, Γ1 = 0.1, g0,1 = 1.73 and e0,1 is varied. The parameters in the dual NPR system are same as the single NPR system only except that the variables g0,2 = 0 and e0,2 = 0, which means the second NPR set is passive. Other parameters of the second set NPR are same to the first set.

Fig. 6
Fig. 6

The peak power (blue line with square marks) and pulse energy (red line with circle marks) with the maximum e0,1 without triggering the multipulsing at different β3 in dual NPRs cavity. The red dot line and blue dash line are the maximum pulse energy and peak power can be obtained in single NPR cavity. The zoomed blue square and red circle marks correspond to the results with dual NPRs in Fig. 5.

Equations (13)

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

T ( E ) = T 2 ( T 1 ( E ) E ) T 1 ( E )
d E j d Z = g 0 1 + j = 1 N E j / E sat E j
E out = T ( E in ) E in
T 1 ( E ) = 0.5 0.2 cos ( 1.0 E + 0.3 π )
T 2 ( E ) = 0.7 0.2 cos ( 0.9 E + 0.1 π ) .
i u z + D j 2 2 u t 2 K j u + ( | u | 2 + A | v | 2 ) u + B v 2 u * = i R j u ,
i v z + D j 2 2 v t 2 + K j v + ( | v | 2 + A | u | 2 ) v + B u 2 v * = i R j v ,
R j = 2 g 0 , j 1 + ( u 2 + v 2 ) / e 0 , j ( 1 + τ j 2 t 2 ) Γ j .
W λ 4 = ( e i π / 4 0 0 e i π / 4 ) ,
W λ 2 = ( i 0 0 i ) ,
W p = ( 1 0 0 0 ) .
J j = R ( α j ) W R ( α j ) ,
R ( α j ) = ( cos α j sin α j sin α j cos α j ) .

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