Abstract

We theoretically demonstrate that in a laser cavity mode-locked by nonlinear polarization rotation (NPR) using sets of waveplates and passive polarizer, the energy performance can be significantly increased by incorporating multiple NPR filters. The NPR filters are engineered so as to mitigate the multi-pulsing instability in the laser cavity which is responsible for limiting the single pulse per round trip energy in a myriad of mode-locked cavities. Engineering of the NPR filters for performance is accomplished by implementing a genetic algorithm that is capable of systematically identifying viable and optimal NPR settings in a vast parameter space. Our study shows that five NPR filters can increase the cavity energy by approximately a factor of five, with additional NPRs contributing little or no enhancements beyond this. With the advent and demonstration of electronic controls for waveplates and polarizers, the analysis suggests a general design and engineering principle that can potentially close the order of magnitude energy gap between fiber based mode-locked lasers and their solid state counterparts.

© 2013 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. B27, B63–B92 (2010).
    [CrossRef]
  2. H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quant. Elec.6, 1173–1185 (2000).
    [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]
  4. K. Tamura and M. Nakazawa, “Optimizing power extraction in stretched pulse fiber ring lasers,” App. Phys. Lett.67, 3691–3693 (1995).
    [CrossRef]
  5. 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]
  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. A82, 021805 (2010).
    [CrossRef]
  8. B. Bale and S. Wabnitz, “Strong spectral filtering for a mode-locked similariton fiber laser,” Opt. Lett.35, 2466–2468 (2010).
    [CrossRef] [PubMed]
  9. A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B25, 140–148 (2008).
    [CrossRef]
  10. S. Namiki, E. P. Ippen, H. A. Haus, and C. X. Yu, “Energy rate equations for mode-locked lasers,” J. Opt. Soc. Am. B14, 2099–2111 (1997).
    [CrossRef]
  11. B. G. Bale, K. Kieu, J. N. Kutz, and F. Wise, “Transition dynamics for multi-pulsing in mode-locked lasers,” Opt. Express17, 23137–23146 (2009).
    [CrossRef]
  12. E. Ding, E. Shlizerman, and J. N. Kutz, “Generalized master equation for high-energy passive mode-locking: the sinusoidal Ginzburg-Landau equation,” IEEE J. Quant. Electron.47, 705–714 (2011).
    [CrossRef]
  13. F. Li, P. K. A. Wai, and J. N. Kutz, “Geometrical description of the onset of multi-pulsing in mode-locked laser cavities,” J. Opt. Soc. Am. B27, 2068–2077 (2010).
    [CrossRef]
  14. 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]
  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).
    [CrossRef]
  16. S. Yamashita, Y. Inoue, S. Maruyama, Y. Murakami, H. Yaguchi, M. Jablonski, and S. Y. Set, “Saturable absorbers incorporating carbon nanotubes directly synthesized onto substrates and fibersand their application to mode-locked fiber lasers,” Opt. Lett.29, 1581–1583 (2004).
    [CrossRef] [PubMed]
  17. 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 Nano4, 803–810 (2010).
    [CrossRef] [PubMed]
  18. H. Zhang, “Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker,” App. 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. Express17, 17630–17635 (2009).
    [CrossRef] [PubMed]
  20. F. Li, E. Ding, J. N. Kutz, and P. K. A. Wai, “Dual transmission filters for enhanced energy in mode-locked fiber lasers,” Opt. Express19, 23408–23419 (2011).
    [CrossRef]
  21. P. Grelu, W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonance as a guideline for high-energy pulse laser oscillators,” J. Opt. Soc. Am. B27, 2336–2341 (2010).
    [CrossRef]
  22. E. Ding, P. Grelu, and J. N. Kutz, “Dissipative soliton resonance in a passively mode-locked fiber laser,” Opt. Lett.36, 1146–1148 (2011).
    [CrossRef] [PubMed]
  23. X. Shen, W. Li, M. Yan, and H. Zeng, “Electronic control of nonlinear-polarization-rotation mode locking in Yb-doped fiber lasers,” Opt. Lett.37, 3426–3428 (2012).
    [CrossRef]
  24. E. Ding and J. N. Kutz, “Operating regimes and performance optimization in mode-locked fiber lasers,” Optics and Spectroscopy111, 166–177 (2011).
    [CrossRef]
  25. C. R. Menyuk, “Pulse propagation in an elliptically birefringent Kerr media,” IEEE J. Quant. Electron.25, 2674–2682 (1989).
    [CrossRef]
  26. C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quant. Electron.23, 174–176 (1987).
    [CrossRef]

2012 (1)

2011 (4)

E. Ding and J. N. Kutz, “Operating regimes and performance optimization in mode-locked fiber lasers,” Optics and Spectroscopy111, 166–177 (2011).
[CrossRef]

F. Li, E. Ding, J. N. Kutz, and P. K. A. Wai, “Dual transmission filters for enhanced energy in mode-locked fiber lasers,” Opt. Express19, 23408–23419 (2011).
[CrossRef]

E. Ding, P. Grelu, and J. N. Kutz, “Dissipative soliton resonance in a passively mode-locked fiber laser,” Opt. Lett.36, 1146–1148 (2011).
[CrossRef] [PubMed]

E. Ding, E. Shlizerman, and J. N. Kutz, “Generalized master equation for high-energy passive mode-locking: the sinusoidal Ginzburg-Landau equation,” IEEE J. Quant. Electron.47, 705–714 (2011).
[CrossRef]

2010 (6)

2009 (3)

2008 (1)

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]

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)

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

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]

1993 (1)

1989 (1)

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

1987 (1)

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

Akhmediev, N.

Ankiewicz, A.

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 Nano4, 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 Nano4, 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]

Chang, W.

Chong, A.

W. H. Renninger, A. Chong, and F. W. Wise, “Self-similar pulse evolution in an all-normal-dispersion laser.” Phys. Rev. A82, 021805 (2010).
[CrossRef]

A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B25, 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]

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. Quant. Electron.47, 705–714 (2011).
[CrossRef]

F. Li, E. Ding, J. N. Kutz, and P. K. A. Wai, “Dual transmission filters for enhanced energy in mode-locked fiber lasers,” Opt. Express19, 23408–23419 (2011).
[CrossRef]

E. Ding, P. Grelu, and J. N. Kutz, “Dissipative soliton resonance in a passively mode-locked fiber laser,” Opt. Lett.36, 1146–1148 (2011).
[CrossRef] [PubMed]

E. Ding and J. N. Kutz, “Operating regimes and performance optimization in mode-locked fiber lasers,” Optics and Spectroscopy111, 166–177 (2011).
[CrossRef]

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 Nano4, 803–810 (2010).
[CrossRef] [PubMed]

Grelu, P.

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 Nano4, 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.

Kutz, J. N.

Lenz, G.

Li, F.

Li, W.

Loh, K. P.

Maruyama, S.

Menyuk, C. R.

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

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

Murakami, Y.

Nakazawa, M.

K. Tamura and M. Nakazawa, “Optimizing power extraction in stretched pulse fiber ring lasers,” App. 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 Nano4, 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 Nano4, 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. A82, 021805 (2010).
[CrossRef]

A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B25, 140–148 (2008).
[CrossRef]

Richardson, D. J.

Set, S. Y.

Shen, X.

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. Quant. 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]

Soto-Crespo, J. M.

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 Nano4, 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 Nano4, 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 Nano4, 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. A82, 021805 (2010).
[CrossRef]

A. Chong, W. H. Renninger, and F. W. Wise, “Properties of normal-dispersion femtosecond fiber lasers,” J. Opt. Soc. Am. B25, 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.

Yan, M.

Yu, C. X.

Zeng, H.

Zhang, H.

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

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. Express17, 17630–17635 (2009).
[CrossRef] [PubMed]

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 Nano4, 803–810 (2010).
[CrossRef] [PubMed]

App. Phys. Lett. (2)

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

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

IEEE J. Quant. 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. Quant. Electron.47, 705–714 (2011).
[CrossRef]

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

C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quant. 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 (5)

Opt. Express (3)

Opt. Lett. (6)

Optics and Spectroscopy (1)

E. Ding and J. N. Kutz, “Operating regimes and performance optimization in mode-locked fiber lasers,” Optics and Spectroscopy111, 166–177 (2011).
[CrossRef]

Phys. Rev. A (1)

W. H. Renninger, A. Chong, and F. W. Wise, “Self-similar pulse evolution in an all-normal-dispersion laser.” Phys. Rev. A82, 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]

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Figures (4)

Fig. 1
Fig. 1

(a) Experimental configuration of the multiple transmission filters ring cavity laser system that includes N NPR sections. The output of the lasers is taken between the 1st and 2nd NPR section. (b) Each NPR section contains two quarter-wave plates (αj,1 and αj,2), one half-wave plate (αj,3), one passive polarizer (αj,p), one amplifier and one gain source. Thus a minimum of 6 parameters must be tuned in each NPR section.

Fig. 2
Fig. 2

(a) Prototypical example of the periodic transmission function Tn(E) of a single NPR. As shown in Ref. [13,20], the onset of MPI occurs when the transmission curve intersects the small signal gain threshold (dotted line). Thus noise fluctuations below the dotted line would produce a new mode-locked pulse and induce MPI. (b) Prototypical example of the transmission function T(E) given two periodic transmission filters used together as in (1). In this case, the onset of MPI is greatly suppressed and higher energy mode-locked states can be achieved [20]. Our goal is to engineer T(E) using multiple transmission curves in order to achieve optimal mode-locking performance.

Fig. 3
Fig. 3

Optimal mode-locking dynamics achieved for a laser cavity with 1-, 2-, 3-, 4-, 5- and 6-NPR filters (top left to bottom right). A factor of 5 improvement can be made with the inclusion of additional filters.

Fig. 4
Fig. 4

Optimal mode-locking dynamics achieved for a laser cavity with 1-, 2-, 3-, 4-, 5- and 6-NPR filters (top left to bottom right). A factor of 5 improvement can be made with the inclusion of additional filters.

Tables (2)

Tables Icon

Table 2 Waveplate and polarizer settings for optimizing 5-NPRs

Equations (14)

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

T ( E ) = T 2 ( T 1 ( E ) E ) T 1 ( E )
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 ) u + B u 2 v * = i R j v
R j = 2 g 0 , j 1 + 1 e 0 , j ( | u | 2 + | v | 2 ) d t ( 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 k = R ( α j , k ) W R ( α j , k )
R ( α k ) = ( cos ( α j , k ) sin ( α j , k ) sin ( α j , k ) cos ( α j , k ) )
minimize [ E ( x ) N ( x ) ]
E ( x ) = | u | 2 + | v | 2 d t
N ( x ) = { 1 For stationary single pulse solution 0 Else
x i , i = 1 , 2 , , p
x i , i = p + 1 , p + 2 , , m

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