Abstract

In this paper, we use a genetic algorithm and pulse-propagation analysis to design and optimize optical parametric oscillators based on soft-glass microstructured optical fibers. The maximum parametric gain, phase-match, walk-off between pump (1560 nm) and signal (880 nm) pulses, signal feedback ratio and signal-pump synchronization of the cavity are optimized. Pulse propagation analysis suggests that one can implement a fiber optical parametric oscillator capable of generating approximately 200-fs pulses at 880 nm with 43% peak-power conversion, high output pulse quality (time-bandwidth product ≈ 0.43) and a wavelength tuning range that is limited only by the glass transmission windows.

© 2010 Optical Society of America

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  1. J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. Knight, W. J. Wadsworth, and P. S. Russell, "Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber," Opt. Lett. 28, 2225-2227 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. T. Torounidis and P. Andrekson, "Broadband Single-Pumped Fiber-Optic parametric amplifiers," IEEE Photon. Technol. Lett. 19, 650-652 (2007).
    [CrossRef]
  4. K. Garay-Palmett, A. B. U’Ren, R. Rangel-Rojo, R. Evans, and S. Camacho-Lopez, "Ultrabroadband photon pair preparation by spontaneous four-wave mixing in a dispersion-engineered optical fiber," Phys. Rev. A 78, 043827 (2008).
    [CrossRef]
  5. J. Sharping, "Microstructure fiber based optical parametric oscillators," J. Lightwave Technol. 26, 2184-2191 (2008).
    [CrossRef]
  6. H. Chen, H. Wang, M. N. Slipchenko, Y. Jung, Y. Shi, J. Zhu, K. K. Buhman, and J. Cheng, "A multimodal platform for nonlinear optical microscopy and microspectroscopy," Opt. Express 17, 1282-1290 (2009).
    [CrossRef] [PubMed]
  7. K. Kieu, B. G. Saar, G. R. Holtom, X. S. Xie, and F. W. Wise, "High-power picosecond fiber source for coherent raman microscopy," Opt. Lett. 34, 2051-2053 (2009).
    [CrossRef] [PubMed]
  8. A. F. Pegoraro, A. Ridsdale, D. J. Moffatt, J. P. Pezacki, B. K. Thomas, L. Fu, L. Dong, M. E. Fermann, and A. Stolow, "All-fiber CARS microscopy of live cells," Opt. Express 17, 20700-20706 (2009).
    [CrossRef] [PubMed]
  9. C. Xia, M. Kumar, O. R. Kulkarni, M. N. Islam, F. L. Terry, and M. J. Freeman, "Mid-infrared supercontinuum generation to 4.5μm in ZBLAN fluoride fibers by nanosecond diode pumping," Opt. Lett. 31, 2553-2555 (2006).
    [CrossRef] [PubMed]
  10. K. K. Chow, K. Kikuchi, T. Nagashima, T. Hasegawa, S. Ohara, and N. Sugimoto, "Four-wave mixing based widely tunablewavelength conversion using 1-m dispersion-shifted bismuth-oxide photonic crystal fiber," Opt. Express 15, 15418-15423 (2007).
    [CrossRef] [PubMed]
  11. P. Domachuk, N. A. Wolchover, M. Cronin-Golomb, A. Wang, A. K. George, C. M. B. Cordeiro, J. C. Knight, and F. G. Omenetto, "Over 4000 nm bandwidth of mid-IR supercontinuum generation in sub-centimeter segments of highly nonlinear tellurite PCFs," Opt. Express 16, 7161-7168 (2008).
    [CrossRef] [PubMed]
  12. H. Hundertmark, S. Rammler, T. Wilken, R. Holzwarth, T. W. Hansch, and P. S. Russell, "Octave-spanning supercontinuum generated in SF6-glass PCF by a 1060 nm mode-locked fibre laser delivering 20 pJ per pulse," Opt. Express 17, 1919-1924 (2009).
    [CrossRef] [PubMed]
  13. W. Q. Zhang, S. Afshar V., and T. M. Monro, "A genetic algorithm based approach to fiber design for high coherence and large bandwidth supercontinuum generation," Opt. Express 17, 19311-19327 (2009).
    [CrossRef]
  14. X. Feng, W. H. Loh, J. C. Flanagan, A. Camerlingo, S. Dasgupta, P. Petropoulos, P. Horak, K. E. Frampton, N. M. White, J. H. Price, H. N. Rutt, and D. J. Richardson, "Single-mode tellurite glass holey fiber with extremely large mode area for infrared nonlinear applications," Opt. Express 16, 13651-13656 (2008)
    [CrossRef] [PubMed]
  15. T. M. Monro and H. Ebendorff-Heidepriem, "Progress in microstructured optical fibers," Annu. Rev. Mater. Res. 36, 467-495 (2006).
    [CrossRef]
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  17. M. Dantus and V. V. Lozovoy, "Experimental coherent laser control of physicochemical processes," Chem. Rev. 104, 1813-1860 (2004).
    [CrossRef] [PubMed]
  18. G. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001), 3rd ed.
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    [CrossRef]
  20. L. Davis, Handbook Of Genetic Algorithms (Thomson Publishing Group, 1991), 1st ed.
  21. F. Poletti, V. Finazzi, and T. M. Monro, N.G.R. Broderick, V. Tse, and D.J. Richardson, "Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers," Opt. Express 13, 3728-3736 (2005).
    [CrossRef] [PubMed]
  22. M. Gao, C. Jiang, W. Hu, and J. Wang, "Optimized design of two-pump fiber optical parametric amplifier with twosection nonlinear fibers using genetic algorithm", Opt. Express 12, 5603-5613 (2004).
    [CrossRef] [PubMed]
  23. M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
    [CrossRef]
  24. K. S. Kim, R. H. Stolen, W. A. Reed, and K. W. Quoi, "Measurement of the nonlinear index of silica-core and dispersion-shifted fibers," Opt. Lett. 19, 257-259 (1994).
    [CrossRef] [PubMed]
  25. J. Tukey, "An introduction to the calculations of numerical spectrum analysis," Spectral Analysis of Time Series, pp. 25-46 (1967).

2009 (5)

2008 (4)

2007 (3)

T. Torounidis and P. Andrekson, "Broadband Single-Pumped Fiber-Optic parametric amplifiers," IEEE Photon. Technol. Lett. 19, 650-652 (2007).
[CrossRef]

M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
[CrossRef]

K. K. Chow, K. Kikuchi, T. Nagashima, T. Hasegawa, S. Ohara, and N. Sugimoto, "Four-wave mixing based widely tunablewavelength conversion using 1-m dispersion-shifted bismuth-oxide photonic crystal fiber," Opt. Express 15, 15418-15423 (2007).
[CrossRef] [PubMed]

2006 (3)

C. Xia, M. Kumar, O. R. Kulkarni, M. N. Islam, F. L. Terry, and M. J. Freeman, "Mid-infrared supercontinuum generation to 4.5μm in ZBLAN fluoride fibers by nanosecond diode pumping," Opt. Lett. 31, 2553-2555 (2006).
[CrossRef] [PubMed]

J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

T. M. Monro and H. Ebendorff-Heidepriem, "Progress in microstructured optical fibers," Annu. Rev. Mater. Res. 36, 467-495 (2006).
[CrossRef]

2005 (2)

2004 (2)

2003 (1)

1994 (1)

Agrawal, G. P.

Andrekson, P.

T. Torounidis and P. Andrekson, "Broadband Single-Pumped Fiber-Optic parametric amplifiers," IEEE Photon. Technol. Lett. 19, 650-652 (2007).
[CrossRef]

Broderick, N.G.R.

Buhman, K. K.

Camerlingo, A.

Cardinal, T.

M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
[CrossRef]

Chen, H.

Cheng, J.

Chow, K. K.

Coen, S.

Cordeiro, C. M. B.

Couzi, M.

M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
[CrossRef]

Cronin-Golomb, M.

Dantus, M.

M. Dantus and V. V. Lozovoy, "Experimental coherent laser control of physicochemical processes," Chem. Rev. 104, 1813-1860 (2004).
[CrossRef] [PubMed]

Dasgupta, S.

Deng, Y.

Domachuk, P.

Dong, L.

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

Ebendorff-Heidepriem, H.

T. M. Monro and H. Ebendorff-Heidepriem, "Progress in microstructured optical fibers," Annu. Rev. Mater. Res. 36, 467-495 (2006).
[CrossRef]

Feng, X.

Fermann, M. E.

Finazzi, V.

Flanagan, J. C.

Frampton, K. E.

Freeman, M. J.

Fu, L.

Furniss, D.

M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
[CrossRef]

Gao, M.

Garay-Palmett, K.

K. Garay-Palmett, A. B. U’Ren, R. Rangel-Rojo, R. Evans, and S. Camacho-Lopez, "Ultrabroadband photon pair preparation by spontaneous four-wave mixing in a dispersion-engineered optical fiber," Phys. Rev. A 78, 043827 (2008).
[CrossRef]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

George, A. K.

Hansch, T. W.

Harvey, J. D.

Hasegawa, T.

Holtom, G. R.

Holzwarth, R.

Horak, P.

Hu, W.

Hundertmark, H.

Islam, M. N.

Jiang, C.

Jung, Y.

Kieu, K.

Kikuchi, K.

Kim, K. S.

Knight, J.

Knight, J. C.

Knox, W. H.

Kulkarni, O. R.

Kumar, M.

Leonhardt, R.

Lin, Q.

Loh, W. H.

Lozovoy, V. V.

M. Dantus and V. V. Lozovoy, "Experimental coherent laser control of physicochemical processes," Chem. Rev. 104, 1813-1860 (2004).
[CrossRef] [PubMed]

Lu, F.

Moffatt, D. J.

Monro, T. M.

Nagashima, T.

O’Donnell, M. D.

M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
[CrossRef]

Ohara, S.

Omenetto, F. G.

Pegoraro, A. F.

Petropoulos, P.

Pezacki, J. P.

Poletti, F.

Price, J. H.

Quoi, K. W.

Ramme, M.

M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
[CrossRef]

Rammler, S.

Reed, W. A.

Richardson, D. J.

Richardson, D.J.

Richardson, K.

M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
[CrossRef]

Ridsdale, A.

Rivero, C.

M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
[CrossRef]

Russell, P. S.

Rutt, H. N.

Saar, B. G.

Seddon, A. B.

M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
[CrossRef]

Sharping, J.

Shi, Y.

Slipchenko, M. N.

Stegeman, G.

M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
[CrossRef]

Stegeman, R.

M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
[CrossRef]

Stolen, R.

M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
[CrossRef]

Stolen, R. H.

Stolow, A.

Sugimoto, N.

Terry, F. L.

Thomas, B. K.

Tikhomirov, V. K.

M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
[CrossRef]

Torounidis, T.

T. Torounidis and P. Andrekson, "Broadband Single-Pumped Fiber-Optic parametric amplifiers," IEEE Photon. Technol. Lett. 19, 650-652 (2007).
[CrossRef]

Tse, V.

Wadsworth, W. J.

Wang, A.

Wang, H.

Wang, J.

White, N. M.

Wilken, T.

Wise, F. W.

Wolchover, N. A.

Wong, G. K. L.

Xia, C.

Xie, X. S.

Zhang, W. Q.

Zhu, J.

Annu. Rev. Mater. Res. (1)

T. M. Monro and H. Ebendorff-Heidepriem, "Progress in microstructured optical fibers," Annu. Rev. Mater. Res. 36, 467-495 (2006).
[CrossRef]

Chem. Rev. (1)

M. Dantus and V. V. Lozovoy, "Experimental coherent laser control of physicochemical processes," Chem. Rev. 104, 1813-1860 (2004).
[CrossRef] [PubMed]

IEEE Photon. Technol. Lett. (1)

T. Torounidis and P. Andrekson, "Broadband Single-Pumped Fiber-Optic parametric amplifiers," IEEE Photon. Technol. Lett. 19, 650-652 (2007).
[CrossRef]

J. Am. Ceram. Soc. (1)

M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, "Tellurite and fluorotellurite glasses for fiberoptic raman amplifiers: Glass characterization, optical properties, raman gain, preliminary fiberization, and fiber characterization," J. Am. Ceram. Soc. 90, 1448-1457 (2007).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Express (9)

H. Chen, H. Wang, M. N. Slipchenko, Y. Jung, Y. Shi, J. Zhu, K. K. Buhman, and J. Cheng, "A multimodal platform for nonlinear optical microscopy and microspectroscopy," Opt. Express 17, 1282-1290 (2009).
[CrossRef] [PubMed]

A. F. Pegoraro, A. Ridsdale, D. J. Moffatt, J. P. Pezacki, B. K. Thomas, L. Fu, L. Dong, M. E. Fermann, and A. Stolow, "All-fiber CARS microscopy of live cells," Opt. Express 17, 20700-20706 (2009).
[CrossRef] [PubMed]

K. K. Chow, K. Kikuchi, T. Nagashima, T. Hasegawa, S. Ohara, and N. Sugimoto, "Four-wave mixing based widely tunablewavelength conversion using 1-m dispersion-shifted bismuth-oxide photonic crystal fiber," Opt. Express 15, 15418-15423 (2007).
[CrossRef] [PubMed]

P. Domachuk, N. A. Wolchover, M. Cronin-Golomb, A. Wang, A. K. George, C. M. B. Cordeiro, J. C. Knight, and F. G. Omenetto, "Over 4000 nm bandwidth of mid-IR supercontinuum generation in sub-centimeter segments of highly nonlinear tellurite PCFs," Opt. Express 16, 7161-7168 (2008).
[CrossRef] [PubMed]

H. Hundertmark, S. Rammler, T. Wilken, R. Holzwarth, T. W. Hansch, and P. S. Russell, "Octave-spanning supercontinuum generated in SF6-glass PCF by a 1060 nm mode-locked fibre laser delivering 20 pJ per pulse," Opt. Express 17, 1919-1924 (2009).
[CrossRef] [PubMed]

W. Q. Zhang, S. Afshar V., and T. M. Monro, "A genetic algorithm based approach to fiber design for high coherence and large bandwidth supercontinuum generation," Opt. Express 17, 19311-19327 (2009).
[CrossRef]

X. Feng, W. H. Loh, J. C. Flanagan, A. Camerlingo, S. Dasgupta, P. Petropoulos, P. Horak, K. E. Frampton, N. M. White, J. H. Price, H. N. Rutt, and D. J. Richardson, "Single-mode tellurite glass holey fiber with extremely large mode area for infrared nonlinear applications," Opt. Express 16, 13651-13656 (2008)
[CrossRef] [PubMed]

F. Poletti, V. Finazzi, and T. M. Monro, N.G.R. Broderick, V. Tse, and D.J. Richardson, "Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers," Opt. Express 13, 3728-3736 (2005).
[CrossRef] [PubMed]

M. Gao, C. Jiang, W. Hu, and J. Wang, "Optimized design of two-pump fiber optical parametric amplifier with twosection nonlinear fibers using genetic algorithm", Opt. Express 12, 5603-5613 (2004).
[CrossRef] [PubMed]

Opt. Lett. (5)

Phys. Rev. A (1)

K. Garay-Palmett, A. B. U’Ren, R. Rangel-Rojo, R. Evans, and S. Camacho-Lopez, "Ultrabroadband photon pair preparation by spontaneous four-wave mixing in a dispersion-engineered optical fiber," Phys. Rev. A 78, 043827 (2008).
[CrossRef]

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

Other (4)

L. Davis, Handbook Of Genetic Algorithms (Thomson Publishing Group, 1991), 1st ed.

J. Tukey, "An introduction to the calculations of numerical spectrum analysis," Spectral Analysis of Time Series, pp. 25-46 (1967).

G. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001), 3rd ed.

J. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena: Fundamentals, Techniques, and Applications on a Femtosecond Time Scale, Optics and photonics (Academic Press, San Diego, 1996).

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Figures (9)

Fig. 1.
Fig. 1.

Initial design of the fiber structure.

Fig. 2.
Fig. 2.

(a) Convergence of the fitness values as a function of generation number. Circles are the average fitness of the whole population and diamonds are the maximum fitness of an individual within the population. The red dashed line is the target. (b) The optimized fiber geometry.

Fig. 3.
Fig. 3.

(a) Propagation constants β, β 1, nonlinear coefficient γ and group velocity dispersion GVD as functions of wavelength. (b) FWM gain map when pumped with a 5-kW source at 1560 nm.

Fig. 4.
Fig. 4.

FOPO configuration. SPF: short-pass filter (to remove pump light). BPF: band-pass filter. BS: beam splitter. L1 & L2: lens. M1-3: mirrors.

Fig. 5.
Fig. 5.

Peak power (a) and time-bandwidth product (TBP) (b) of output pulses averaged over the last 20 passes as a function of offset time with a fixed feed-back ratio of 0.5

Fig. 6.
Fig. 6.

Peak power (a) and TBP (b) of output pulses averaged over the last 20 passes as a function of feedback ratio and 0.55 ps offset.

Fig. 7.
Fig. 7.

The evolution of the temporal (left column) and spectral (right column) intensity profiles of signal pulses as a function of pass number at different feedback ratio. Each figure is normalized to its maximum intensity.

Fig. 8.
Fig. 8.

Pulse shape (a) and spectrum (b) of a globally optimized FOPO at the fiber output.

Fig. 9.
Fig. 9.

Output pulse shape (a) and spectrum (b) of a globally optimized FOPO

Equations (11)

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g = ( γ P 0 ) 2 ( κ 2 ) 2 ,
F = γ κ · Δ β 1 .
( γ P 0 ) 2 ( κ 2 ) 2 0.97 γ P 0 ,
κ 0.48 γ P 0 0.5 γ P 0 .
κ = { κ , κ > 0.5 γ P 0 0.5 γ P 0 , κ 0.5 γ P 0
L walk off = T 0 Δ β 1 4 × 3 × 10 3 m
Δ β 1 T 0 12 × 10 3 ( 80 m 1 ) T 0 .
Δ β 1 = { Δ β 1 , Δ β 1 > ( 80 m 1 ) T 0 80 T 0 , Δ β 1 ( 80 m 1 ) T 0 .
F target = γ 0.5 γ P 0 · ( 80 m 1 ) T 0 .
A ( z , t ) z + α 2 A ( z , t ) β A ( z , t ) =
i γ ( 1 + i τ shock T ) ( A ( z , t ) R ( T ) × A ( z , T T ) 2 d T ) ,

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