Abstract

We present a method to maximize the soliton self-frequency shift (SSFS) in microwires with diameter profiles varying nonuniformly along the soliton propagation path. The method is divided into two steps. The first step consists in selecting the input microwire diameter that leads to the highest rate of frequency shift per unit of propagation length. The second step consists in increasing gradually the microwire diameter along the soliton path to suppress dispersive wave emission and maintain a large rate of frequency shift per unit of propagation length. We first propose and apply a rule to select the initial diameter using the adiabatic theory. The optimal diameter profile is then achieved by maintaining the redshifting soliton at a fixed spectral separation from the zero-dispersion wavelengths. The optimized profile supports solitons with different input energies that allow a wavelength shift up to 650 nm from the 2100 nm pump wavelength in a 20 cm microwire length. We compare our results with the SSFS generated in microwires with uniform diameter profile to illustrate the enhancement of wavelength shift in the designed nonuniform microwire.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Kivisto, T. Hakulinen, M. Guina, and O. Okhotnikov, “Tunable Raman soliton source using mode-locked Tm–Ho fiber laser,” IEEE Photon. Technol. Lett. 19, 934–936 (2007).
    [CrossRef]
  2. F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986).
    [CrossRef]
  3. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662–664 (1986).
    [CrossRef]
  4. P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
    [CrossRef]
  5. D. A. Chestnut and J. R. Taylor, “Soliton self-frequency shift in highly nonlinear fiber with extension by external Raman pumping,” Opt. Lett. 28, 2512–2514 (2003).
    [CrossRef]
  6. X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler, “Soliton self-frequency shift in a short tapered air–silica microstructure fiber,” Opt. Lett. 26, 358–360 (2001).
    [CrossRef]
  7. B. Washburn, S. Ralph, P. Lacourt, J. Dudley, W. Rhodes, R. Windeler, and S. Coen, “Tunable near-infrared femtosecond soliton generation in photonic crystal fibres,” Electron. Lett. 37, 1510–1512 (2001).
    [CrossRef]
  8. I. Cormack, D. Reid, W. Wadsworth, J. Knight, and P. Russell, “Observation of soliton self-frequency shift in photonic crystal fibre,” Electron. Lett. 38, 167–169 (2002).
    [CrossRef]
  9. D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
    [CrossRef]
  10. S. M. Kobtsev, S. V. Kukarin, N. V. Fateevand, and S. V. Smirnov, “Generation of self-frequency-shifted solitons in tapered fibers in the presence of femtosecond pumping,” Laser Phys. 14, 748–751 (2004).
  11. J. C. Knight, T. A. Birks, P. S. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
    [CrossRef]
  12. A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
    [CrossRef]
  13. J. Knight, J. Arriaga, T. Birks, A. Ortigosa-Blanch, W. Wadsworth, and P. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Technol. Lett. 12, 807–809(2000).
    [CrossRef]
  14. N. Nishizawa and T. Goto, “Compact system of wavelength-tunable femtosecond soliton pulse generation using optical fibers,” IEEE Photon. Technol. Lett. 11, 325–327 (1999).
    [CrossRef]
  15. M.-C. Chan, S.-H. Chia, T.-M. Liu, T.-H. Tsai, M.-C. Ho, A. A. Ivanov, A. M. Zheltikov, J.-Y. Liu, H.-L. Liu, and C.-K. Sun, “1.2- to 2.2-μm tunable Raman soliton source based on a Cr:forsterite laser and a photonic-crystal fiber,” IEEE Photon. Technol. Lett. 20, 900–902 (2008).
    [CrossRef]
  16. H. Lim, J. Buckley, A. Chong, and F. Wise, “Fibre-based source of femtosecond pulses tunable from 1.0 to 1.3 μm,” Electron. Lett. 40, 1523–1525 (2004).
    [CrossRef]
  17. I. Gris-Sánchez, B. Mangan, and J. Knight, “Reducing spectral attenuation in small-core photonic crystal fibers,” Opt. Mater. Express 1, 179–184 (2011).
    [CrossRef]
  18. C. Baker and M. Rochette, “A generalized heat-brush approach for precise control of the waist profile in fiber tapers,” Opt. Mater. Express 1, 1065–1076 (2011).
    [CrossRef]
  19. J. S. Sanghera, L. B. Shaw, P. Pureza, V. Q. Nguyen, D. Gibson, L. Busse, I. D. Aggarwal, C. M. Florea, and F. H. Kung, “Nonlinear properties of chalcogenide glass fibers,” Int. J. Appl. Glass Sci. 1, 296–308 (2010).
    [CrossRef]
  20. D.-I. Yeom, E. C. Mägi, M. R. E. Lamont, M. A. F. Roelens, L. Fu, and B. J. Eggleton, “Low-threshold supercontinuum generation in highly nonlinear chalcogenide nanowires,” Opt. Lett. 33, 660–662 (2008).
    [CrossRef]
  21. C. Baker and M. Rochette, “Highly nonlinear hybrid AsSe–PMMA microtapers,” Opt. Express 18, 12391–12398 (2010).
    [CrossRef]
  22. Z. Chen, A. J. Taylor, and A. Efimov, “Coherent mid-infrared broadband continuum generation in non-uniform ZBLAN fiber taper,” Opt. Express 17, 5852–5860 (2009).
    [CrossRef]
  23. N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607(1995).
    [CrossRef]
  24. W. J. Tomlinson, R. H. Stolen, and A. M. Johnson, “Optical wave breaking of pulses in nonlinear optical fibers,” Opt. Lett. 10, 457–459 (1985).
    [CrossRef]
  25. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098.
    [CrossRef]
  26. A. C. Judge, O. Bang, B. J. Eggleton, B. T. Kuhlmey, E. C. Mägi, R. Pant, and C. M. de Sterke, “Optimization of the soliton self-frequency shift in a tapered photonic crystal fiber,” J. Opt. Soc. Am. B 26, 2064–2071 (2009).
    [CrossRef]
  27. K. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
    [CrossRef]
  28. J. G. Kuzyk, Polymer Fiber Optics: Materials, Physics, and Applications (CRC Press, 2009).
  29. H. Lin, W. Dechent, D. Day, and J. Stoffer, “Preparation and properties of mid-infrared glass fibres and poly (chlorotrifluoroethylene) composites,” J. Mater. Sci. 32, 6573–6578 (1997).
    [CrossRef]
  30. R. E. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers,” J. Opt. Soc. Am. B 21, 1146–1155 (2004).
    [CrossRef]
  31. G. Snopatin, V. Shiryaev, V. Plotnichenko, E. Dianov, and M. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater. 45, 1439–1460 (2009).
    [CrossRef]
  32. J. Hult, “A fourth-order Runge–Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers,” J. Lightwave Technol. 25, 3770–3775(2007).
    [CrossRef]
  33. J. Herrmann and A. Nazarkin, “Soliton self-frequency shift for pulses with a duration less than the period of molecular oscillations,” Opt. Lett. 19, 2065–2067 (1994).
    [CrossRef]
  34. R. Pant, A. C. Judge, E. C. Magi, B. T. Kuhlmey, M. de Sterke, and B. J. Eggleton, “Characterization and optimization of photonic crystal fibers for enhanced soliton self-frequency shift,” J. Opt. Soc. Am. B 27, 1894–1901 (2010).
    [CrossRef]
  35. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159–1166 (1989).
    [CrossRef]
  36. J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Maximizing the bandwidth of supercontinuum generation in As2Se3 chalcogenide fibers,” Opt. Express 18, 6722–6739 (2010).
    [CrossRef]
  37. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

2011

2010

2009

2008

D.-I. Yeom, E. C. Mägi, M. R. E. Lamont, M. A. F. Roelens, L. Fu, and B. J. Eggleton, “Low-threshold supercontinuum generation in highly nonlinear chalcogenide nanowires,” Opt. Lett. 33, 660–662 (2008).
[CrossRef]

M.-C. Chan, S.-H. Chia, T.-M. Liu, T.-H. Tsai, M.-C. Ho, A. A. Ivanov, A. M. Zheltikov, J.-Y. Liu, H.-L. Liu, and C.-K. Sun, “1.2- to 2.2-μm tunable Raman soliton source based on a Cr:forsterite laser and a photonic-crystal fiber,” IEEE Photon. Technol. Lett. 20, 900–902 (2008).
[CrossRef]

2007

S. Kivisto, T. Hakulinen, M. Guina, and O. Okhotnikov, “Tunable Raman soliton source using mode-locked Tm–Ho fiber laser,” IEEE Photon. Technol. Lett. 19, 934–936 (2007).
[CrossRef]

J. Hult, “A fourth-order Runge–Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers,” J. Lightwave Technol. 25, 3770–3775(2007).
[CrossRef]

2004

R. E. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Large Raman gain and nonlinear phase shifts in high-purity As2Se3 chalcogenide fibers,” J. Opt. Soc. Am. B 21, 1146–1155 (2004).
[CrossRef]

S. M. Kobtsev, S. V. Kukarin, N. V. Fateevand, and S. V. Smirnov, “Generation of self-frequency-shifted solitons in tapered fibers in the presence of femtosecond pumping,” Laser Phys. 14, 748–751 (2004).

H. Lim, J. Buckley, A. Chong, and F. Wise, “Fibre-based source of femtosecond pulses tunable from 1.0 to 1.3 μm,” Electron. Lett. 40, 1523–1525 (2004).
[CrossRef]

2003

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[CrossRef]

D. A. Chestnut and J. R. Taylor, “Soliton self-frequency shift in highly nonlinear fiber with extension by external Raman pumping,” Opt. Lett. 28, 2512–2514 (2003).
[CrossRef]

2002

I. Cormack, D. Reid, W. Wadsworth, J. Knight, and P. Russell, “Observation of soliton self-frequency shift in photonic crystal fibre,” Electron. Lett. 38, 167–169 (2002).
[CrossRef]

2001

B. Washburn, S. Ralph, P. Lacourt, J. Dudley, W. Rhodes, R. Windeler, and S. Coen, “Tunable near-infrared femtosecond soliton generation in photonic crystal fibres,” Electron. Lett. 37, 1510–1512 (2001).
[CrossRef]

X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler, “Soliton self-frequency shift in a short tapered air–silica microstructure fiber,” Opt. Lett. 26, 358–360 (2001).
[CrossRef]

2000

J. Knight, J. Arriaga, T. Birks, A. Ortigosa-Blanch, W. Wadsworth, and P. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Technol. Lett. 12, 807–809(2000).
[CrossRef]

1999

N. Nishizawa and T. Goto, “Compact system of wavelength-tunable femtosecond soliton pulse generation using optical fibers,” IEEE Photon. Technol. Lett. 11, 325–327 (1999).
[CrossRef]

1997

H. Lin, W. Dechent, D. Day, and J. Stoffer, “Preparation and properties of mid-infrared glass fibres and poly (chlorotrifluoroethylene) composites,” J. Mater. Sci. 32, 6573–6578 (1997).
[CrossRef]

1996

1995

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607(1995).
[CrossRef]

1994

1989

K. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159–1166 (1989).
[CrossRef]

1987

P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
[CrossRef]

1986

1985

1973

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Aggarwal, I. D.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

Ahmad, F. R.

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[CrossRef]

Akhmediev, N.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607(1995).
[CrossRef]

Arriaga, J.

J. Knight, J. Arriaga, T. Birks, A. Ortigosa-Blanch, W. Wadsworth, and P. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Technol. Lett. 12, 807–809(2000).
[CrossRef]

Atkin, D. M.

Baker, C.

Bang, O.

Beaud, P.

P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
[CrossRef]

Birks, T.

J. Knight, J. Arriaga, T. Birks, A. Ortigosa-Blanch, W. Wadsworth, and P. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Technol. Lett. 12, 807–809(2000).
[CrossRef]

Birks, T. A.

Blow, K.

K. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

Buckley, J.

H. Lim, J. Buckley, A. Chong, and F. Wise, “Fibre-based source of femtosecond pulses tunable from 1.0 to 1.3 μm,” Electron. Lett. 40, 1523–1525 (2004).
[CrossRef]

Busse, L.

J. S. Sanghera, L. B. Shaw, P. Pureza, V. Q. Nguyen, D. Gibson, L. Busse, I. D. Aggarwal, C. M. Florea, and F. H. Kung, “Nonlinear properties of chalcogenide glass fibers,” Int. J. Appl. Glass Sci. 1, 296–308 (2010).
[CrossRef]

Chan, M.-C.

M.-C. Chan, S.-H. Chia, T.-M. Liu, T.-H. Tsai, M.-C. Ho, A. A. Ivanov, A. M. Zheltikov, J.-Y. Liu, H.-L. Liu, and C.-K. Sun, “1.2- to 2.2-μm tunable Raman soliton source based on a Cr:forsterite laser and a photonic-crystal fiber,” IEEE Photon. Technol. Lett. 20, 900–902 (2008).
[CrossRef]

Chandalia, J. K.

Chen, Z.

Chestnut, D. A.

Chia, S.-H.

M.-C. Chan, S.-H. Chia, T.-M. Liu, T.-H. Tsai, M.-C. Ho, A. A. Ivanov, A. M. Zheltikov, J.-Y. Liu, H.-L. Liu, and C.-K. Sun, “1.2- to 2.2-μm tunable Raman soliton source based on a Cr:forsterite laser and a photonic-crystal fiber,” IEEE Photon. Technol. Lett. 20, 900–902 (2008).
[CrossRef]

Chong, A.

H. Lim, J. Buckley, A. Chong, and F. Wise, “Fibre-based source of femtosecond pulses tunable from 1.0 to 1.3 μm,” Electron. Lett. 40, 1523–1525 (2004).
[CrossRef]

Churbanov, M.

G. Snopatin, V. Shiryaev, V. Plotnichenko, E. Dianov, and M. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater. 45, 1439–1460 (2009).
[CrossRef]

Coen, S.

B. Washburn, S. Ralph, P. Lacourt, J. Dudley, W. Rhodes, R. Windeler, and S. Coen, “Tunable near-infrared femtosecond soliton generation in photonic crystal fibres,” Electron. Lett. 37, 1510–1512 (2001).
[CrossRef]

Cormack, I.

I. Cormack, D. Reid, W. Wadsworth, J. Knight, and P. Russell, “Observation of soliton self-frequency shift in photonic crystal fibre,” Electron. Lett. 38, 167–169 (2002).
[CrossRef]

Day, D.

H. Lin, W. Dechent, D. Day, and J. Stoffer, “Preparation and properties of mid-infrared glass fibres and poly (chlorotrifluoroethylene) composites,” J. Mater. Sci. 32, 6573–6578 (1997).
[CrossRef]

de Sterke, C. M.

de Sterke, M.

Dechent, W.

H. Lin, W. Dechent, D. Day, and J. Stoffer, “Preparation and properties of mid-infrared glass fibres and poly (chlorotrifluoroethylene) composites,” J. Mater. Sci. 32, 6573–6578 (1997).
[CrossRef]

Dianov, E.

G. Snopatin, V. Shiryaev, V. Plotnichenko, E. Dianov, and M. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater. 45, 1439–1460 (2009).
[CrossRef]

Dudley, J.

B. Washburn, S. Ralph, P. Lacourt, J. Dudley, W. Rhodes, R. Windeler, and S. Coen, “Tunable near-infrared femtosecond soliton generation in photonic crystal fibres,” Electron. Lett. 37, 1510–1512 (2001).
[CrossRef]

Efimov, A.

Eggleton, B. J.

Fateevand, N. V.

S. M. Kobtsev, S. V. Kukarin, N. V. Fateevand, and S. V. Smirnov, “Generation of self-frequency-shifted solitons in tapered fibers in the presence of femtosecond pumping,” Laser Phys. 14, 748–751 (2004).

Florea, C. M.

J. S. Sanghera, L. B. Shaw, P. Pureza, V. Q. Nguyen, D. Gibson, L. Busse, I. D. Aggarwal, C. M. Florea, and F. H. Kung, “Nonlinear properties of chalcogenide glass fibers,” Int. J. Appl. Glass Sci. 1, 296–308 (2010).
[CrossRef]

Fu, L.

Gaeta, A. L.

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[CrossRef]

Gallagher, M. T.

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[CrossRef]

Gibson, D.

J. S. Sanghera, L. B. Shaw, P. Pureza, V. Q. Nguyen, D. Gibson, L. Busse, I. D. Aggarwal, C. M. Florea, and F. H. Kung, “Nonlinear properties of chalcogenide glass fibers,” Int. J. Appl. Glass Sci. 1, 296–308 (2010).
[CrossRef]

Gordon, J. P.

Goto, T.

N. Nishizawa and T. Goto, “Compact system of wavelength-tunable femtosecond soliton pulse generation using optical fibers,” IEEE Photon. Technol. Lett. 11, 325–327 (1999).
[CrossRef]

Gris-Sánchez, I.

Guina, M.

S. Kivisto, T. Hakulinen, M. Guina, and O. Okhotnikov, “Tunable Raman soliton source using mode-locked Tm–Ho fiber laser,” IEEE Photon. Technol. Lett. 19, 934–936 (2007).
[CrossRef]

Hakulinen, T.

S. Kivisto, T. Hakulinen, M. Guina, and O. Okhotnikov, “Tunable Raman soliton source using mode-locked Tm–Ho fiber laser,” IEEE Photon. Technol. Lett. 19, 934–936 (2007).
[CrossRef]

Hasegawa, A.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Haus, H. A.

Herrmann, J.

Ho, M.-C.

M.-C. Chan, S.-H. Chia, T.-M. Liu, T.-H. Tsai, M.-C. Ho, A. A. Ivanov, A. M. Zheltikov, J.-Y. Liu, H.-L. Liu, and C.-K. Sun, “1.2- to 2.2-μm tunable Raman soliton source based on a Cr:forsterite laser and a photonic-crystal fiber,” IEEE Photon. Technol. Lett. 20, 900–902 (2008).
[CrossRef]

Hodel, W.

P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
[CrossRef]

Hodelin, J.

Hu, J.

Hult, J.

Ivanov, A. A.

M.-C. Chan, S.-H. Chia, T.-M. Liu, T.-H. Tsai, M.-C. Ho, A. A. Ivanov, A. M. Zheltikov, J.-Y. Liu, H.-L. Liu, and C.-K. Sun, “1.2- to 2.2-μm tunable Raman soliton source based on a Cr:forsterite laser and a photonic-crystal fiber,” IEEE Photon. Technol. Lett. 20, 900–902 (2008).
[CrossRef]

Johnson, A. M.

Judge, A. C.

Karlsson, M.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607(1995).
[CrossRef]

Kivisto, S.

S. Kivisto, T. Hakulinen, M. Guina, and O. Okhotnikov, “Tunable Raman soliton source using mode-locked Tm–Ho fiber laser,” IEEE Photon. Technol. Lett. 19, 934–936 (2007).
[CrossRef]

Knight, J.

I. Gris-Sánchez, B. Mangan, and J. Knight, “Reducing spectral attenuation in small-core photonic crystal fibers,” Opt. Mater. Express 1, 179–184 (2011).
[CrossRef]

I. Cormack, D. Reid, W. Wadsworth, J. Knight, and P. Russell, “Observation of soliton self-frequency shift in photonic crystal fibre,” Electron. Lett. 38, 167–169 (2002).
[CrossRef]

J. Knight, J. Arriaga, T. Birks, A. Ortigosa-Blanch, W. Wadsworth, and P. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Technol. Lett. 12, 807–809(2000).
[CrossRef]

Knight, J. C.

Knox, W. H.

Kobtsev, S. M.

S. M. Kobtsev, S. V. Kukarin, N. V. Fateevand, and S. V. Smirnov, “Generation of self-frequency-shifted solitons in tapered fibers in the presence of femtosecond pumping,” Laser Phys. 14, 748–751 (2004).

Koch, K. W.

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[CrossRef]

Kosinski, S. G.

Kuhlmey, B. T.

Kukarin, S. V.

S. M. Kobtsev, S. V. Kukarin, N. V. Fateevand, and S. V. Smirnov, “Generation of self-frequency-shifted solitons in tapered fibers in the presence of femtosecond pumping,” Laser Phys. 14, 748–751 (2004).

Kung, F. H.

J. S. Sanghera, L. B. Shaw, P. Pureza, V. Q. Nguyen, D. Gibson, L. Busse, I. D. Aggarwal, C. M. Florea, and F. H. Kung, “Nonlinear properties of chalcogenide glass fibers,” Int. J. Appl. Glass Sci. 1, 296–308 (2010).
[CrossRef]

Kuzyk, J. G.

J. G. Kuzyk, Polymer Fiber Optics: Materials, Physics, and Applications (CRC Press, 2009).

Lacourt, P.

B. Washburn, S. Ralph, P. Lacourt, J. Dudley, W. Rhodes, R. Windeler, and S. Coen, “Tunable near-infrared femtosecond soliton generation in photonic crystal fibres,” Electron. Lett. 37, 1510–1512 (2001).
[CrossRef]

Lamont, M. R. E.

Lenz, G.

Lim, H.

H. Lim, J. Buckley, A. Chong, and F. Wise, “Fibre-based source of femtosecond pulses tunable from 1.0 to 1.3 μm,” Electron. Lett. 40, 1523–1525 (2004).
[CrossRef]

Lin, H.

H. Lin, W. Dechent, D. Day, and J. Stoffer, “Preparation and properties of mid-infrared glass fibres and poly (chlorotrifluoroethylene) composites,” J. Mater. Sci. 32, 6573–6578 (1997).
[CrossRef]

Liu, H.-L.

M.-C. Chan, S.-H. Chia, T.-M. Liu, T.-H. Tsai, M.-C. Ho, A. A. Ivanov, A. M. Zheltikov, J.-Y. Liu, H.-L. Liu, and C.-K. Sun, “1.2- to 2.2-μm tunable Raman soliton source based on a Cr:forsterite laser and a photonic-crystal fiber,” IEEE Photon. Technol. Lett. 20, 900–902 (2008).
[CrossRef]

Liu, J.-Y.

M.-C. Chan, S.-H. Chia, T.-M. Liu, T.-H. Tsai, M.-C. Ho, A. A. Ivanov, A. M. Zheltikov, J.-Y. Liu, H.-L. Liu, and C.-K. Sun, “1.2- to 2.2-μm tunable Raman soliton source based on a Cr:forsterite laser and a photonic-crystal fiber,” IEEE Photon. Technol. Lett. 20, 900–902 (2008).
[CrossRef]

Liu, T.-M.

M.-C. Chan, S.-H. Chia, T.-M. Liu, T.-H. Tsai, M.-C. Ho, A. A. Ivanov, A. M. Zheltikov, J.-Y. Liu, H.-L. Liu, and C.-K. Sun, “1.2- to 2.2-μm tunable Raman soliton source based on a Cr:forsterite laser and a photonic-crystal fiber,” IEEE Photon. Technol. Lett. 20, 900–902 (2008).
[CrossRef]

Liu, X.

Magi, E. C.

Mägi, E. C.

Mangan, B.

Menyuk, C. R.

Mitschke, F. M.

Mollenauer, L. F.

F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986).
[CrossRef]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098.
[CrossRef]

Muller, D.

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[CrossRef]

Nazarkin, A.

Nguyen, V. Q.

J. S. Sanghera, L. B. Shaw, P. Pureza, V. Q. Nguyen, D. Gibson, L. Busse, I. D. Aggarwal, C. M. Florea, and F. H. Kung, “Nonlinear properties of chalcogenide glass fibers,” Int. J. Appl. Glass Sci. 1, 296–308 (2010).
[CrossRef]

Nishizawa, N.

N. Nishizawa and T. Goto, “Compact system of wavelength-tunable femtosecond soliton pulse generation using optical fibers,” IEEE Photon. Technol. Lett. 11, 325–327 (1999).
[CrossRef]

Okhotnikov, O.

S. Kivisto, T. Hakulinen, M. Guina, and O. Okhotnikov, “Tunable Raman soliton source using mode-locked Tm–Ho fiber laser,” IEEE Photon. Technol. Lett. 19, 934–936 (2007).
[CrossRef]

Ortigosa-Blanch, A.

J. Knight, J. Arriaga, T. Birks, A. Ortigosa-Blanch, W. Wadsworth, and P. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Technol. Lett. 12, 807–809(2000).
[CrossRef]

Ouzounov, D. G.

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[CrossRef]

Pant, R.

Plotnichenko, V.

G. Snopatin, V. Shiryaev, V. Plotnichenko, E. Dianov, and M. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater. 45, 1439–1460 (2009).
[CrossRef]

Pureza, P.

J. S. Sanghera, L. B. Shaw, P. Pureza, V. Q. Nguyen, D. Gibson, L. Busse, I. D. Aggarwal, C. M. Florea, and F. H. Kung, “Nonlinear properties of chalcogenide glass fibers,” Int. J. Appl. Glass Sci. 1, 296–308 (2010).
[CrossRef]

Ralph, S.

B. Washburn, S. Ralph, P. Lacourt, J. Dudley, W. Rhodes, R. Windeler, and S. Coen, “Tunable near-infrared femtosecond soliton generation in photonic crystal fibres,” Electron. Lett. 37, 1510–1512 (2001).
[CrossRef]

Reid, D.

I. Cormack, D. Reid, W. Wadsworth, J. Knight, and P. Russell, “Observation of soliton self-frequency shift in photonic crystal fibre,” Electron. Lett. 38, 167–169 (2002).
[CrossRef]

Rhodes, W.

B. Washburn, S. Ralph, P. Lacourt, J. Dudley, W. Rhodes, R. Windeler, and S. Coen, “Tunable near-infrared femtosecond soliton generation in photonic crystal fibres,” Electron. Lett. 37, 1510–1512 (2001).
[CrossRef]

Rochette, M.

Roelens, M. A. F.

Russell, P.

I. Cormack, D. Reid, W. Wadsworth, J. Knight, and P. Russell, “Observation of soliton self-frequency shift in photonic crystal fibre,” Electron. Lett. 38, 167–169 (2002).
[CrossRef]

J. Knight, J. Arriaga, T. Birks, A. Ortigosa-Blanch, W. Wadsworth, and P. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Technol. Lett. 12, 807–809(2000).
[CrossRef]

Russell, P. S. J.

Sanghera, J.

Sanghera, J. S.

J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Maximizing the bandwidth of supercontinuum generation in As2Se3 chalcogenide fibers,” Opt. Express 18, 6722–6739 (2010).
[CrossRef]

J. S. Sanghera, L. B. Shaw, P. Pureza, V. Q. Nguyen, D. Gibson, L. Busse, I. D. Aggarwal, C. M. Florea, and F. H. Kung, “Nonlinear properties of chalcogenide glass fibers,” Int. J. Appl. Glass Sci. 1, 296–308 (2010).
[CrossRef]

Shaw, L. B.

Shiryaev, V.

G. Snopatin, V. Shiryaev, V. Plotnichenko, E. Dianov, and M. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater. 45, 1439–1460 (2009).
[CrossRef]

Silcox, J.

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[CrossRef]

Slusher, R. E.

Smirnov, S. V.

S. M. Kobtsev, S. V. Kukarin, N. V. Fateevand, and S. V. Smirnov, “Generation of self-frequency-shifted solitons in tapered fibers in the presence of femtosecond pumping,” Laser Phys. 14, 748–751 (2004).

Snopatin, G.

G. Snopatin, V. Shiryaev, V. Plotnichenko, E. Dianov, and M. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater. 45, 1439–1460 (2009).
[CrossRef]

Stoffer, J.

H. Lin, W. Dechent, D. Day, and J. Stoffer, “Preparation and properties of mid-infrared glass fibres and poly (chlorotrifluoroethylene) composites,” J. Mater. Sci. 32, 6573–6578 (1997).
[CrossRef]

Stolen, R. H.

Sun, C.-K.

M.-C. Chan, S.-H. Chia, T.-M. Liu, T.-H. Tsai, M.-C. Ho, A. A. Ivanov, A. M. Zheltikov, J.-Y. Liu, H.-L. Liu, and C.-K. Sun, “1.2- to 2.2-μm tunable Raman soliton source based on a Cr:forsterite laser and a photonic-crystal fiber,” IEEE Photon. Technol. Lett. 20, 900–902 (2008).
[CrossRef]

Tappert, F.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Taylor, A. J.

Taylor, J. R.

Thomas, M. G.

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[CrossRef]

Tomlinson, W. J.

Tsai, T.-H.

M.-C. Chan, S.-H. Chia, T.-M. Liu, T.-H. Tsai, M.-C. Ho, A. A. Ivanov, A. M. Zheltikov, J.-Y. Liu, H.-L. Liu, and C.-K. Sun, “1.2- to 2.2-μm tunable Raman soliton source based on a Cr:forsterite laser and a photonic-crystal fiber,” IEEE Photon. Technol. Lett. 20, 900–902 (2008).
[CrossRef]

Venkataraman, N.

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[CrossRef]

Wadsworth, W.

I. Cormack, D. Reid, W. Wadsworth, J. Knight, and P. Russell, “Observation of soliton self-frequency shift in photonic crystal fibre,” Electron. Lett. 38, 167–169 (2002).
[CrossRef]

J. Knight, J. Arriaga, T. Birks, A. Ortigosa-Blanch, W. Wadsworth, and P. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Technol. Lett. 12, 807–809(2000).
[CrossRef]

Washburn, B.

B. Washburn, S. Ralph, P. Lacourt, J. Dudley, W. Rhodes, R. Windeler, and S. Coen, “Tunable near-infrared femtosecond soliton generation in photonic crystal fibres,” Electron. Lett. 37, 1510–1512 (2001).
[CrossRef]

Weber, H.

P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
[CrossRef]

Windeler, R.

B. Washburn, S. Ralph, P. Lacourt, J. Dudley, W. Rhodes, R. Windeler, and S. Coen, “Tunable near-infrared femtosecond soliton generation in photonic crystal fibres,” Electron. Lett. 37, 1510–1512 (2001).
[CrossRef]

Windeler, R. S.

Wise, F.

H. Lim, J. Buckley, A. Chong, and F. Wise, “Fibre-based source of femtosecond pulses tunable from 1.0 to 1.3 μm,” Electron. Lett. 40, 1523–1525 (2004).
[CrossRef]

Wood, D.

K. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

Xu, C.

Yeom, D.-I.

Zheltikov, A. M.

M.-C. Chan, S.-H. Chia, T.-M. Liu, T.-H. Tsai, M.-C. Ho, A. A. Ivanov, A. M. Zheltikov, J.-Y. Liu, H.-L. Liu, and C.-K. Sun, “1.2- to 2.2-μm tunable Raman soliton source based on a Cr:forsterite laser and a photonic-crystal fiber,” IEEE Photon. Technol. Lett. 20, 900–902 (2008).
[CrossRef]

Zysset, B.

P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
[CrossRef]

Appl. Phys. Lett.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Electron. Lett.

B. Washburn, S. Ralph, P. Lacourt, J. Dudley, W. Rhodes, R. Windeler, and S. Coen, “Tunable near-infrared femtosecond soliton generation in photonic crystal fibres,” Electron. Lett. 37, 1510–1512 (2001).
[CrossRef]

I. Cormack, D. Reid, W. Wadsworth, J. Knight, and P. Russell, “Observation of soliton self-frequency shift in photonic crystal fibre,” Electron. Lett. 38, 167–169 (2002).
[CrossRef]

H. Lim, J. Buckley, A. Chong, and F. Wise, “Fibre-based source of femtosecond pulses tunable from 1.0 to 1.3 μm,” Electron. Lett. 40, 1523–1525 (2004).
[CrossRef]

IEEE J. Quantum Electron.

K. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

P. Beaud, W. Hodel, B. Zysset, and H. Weber, “Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1938–1946 (1987).
[CrossRef]

IEEE Photon. Technol. Lett.

S. Kivisto, T. Hakulinen, M. Guina, and O. Okhotnikov, “Tunable Raman soliton source using mode-locked Tm–Ho fiber laser,” IEEE Photon. Technol. Lett. 19, 934–936 (2007).
[CrossRef]

J. Knight, J. Arriaga, T. Birks, A. Ortigosa-Blanch, W. Wadsworth, and P. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Technol. Lett. 12, 807–809(2000).
[CrossRef]

N. Nishizawa and T. Goto, “Compact system of wavelength-tunable femtosecond soliton pulse generation using optical fibers,” IEEE Photon. Technol. Lett. 11, 325–327 (1999).
[CrossRef]

M.-C. Chan, S.-H. Chia, T.-M. Liu, T.-H. Tsai, M.-C. Ho, A. A. Ivanov, A. M. Zheltikov, J.-Y. Liu, H.-L. Liu, and C.-K. Sun, “1.2- to 2.2-μm tunable Raman soliton source based on a Cr:forsterite laser and a photonic-crystal fiber,” IEEE Photon. Technol. Lett. 20, 900–902 (2008).
[CrossRef]

Inorg. Mater.

G. Snopatin, V. Shiryaev, V. Plotnichenko, E. Dianov, and M. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater. 45, 1439–1460 (2009).
[CrossRef]

Int. J. Appl. Glass Sci.

J. S. Sanghera, L. B. Shaw, P. Pureza, V. Q. Nguyen, D. Gibson, L. Busse, I. D. Aggarwal, C. M. Florea, and F. H. Kung, “Nonlinear properties of chalcogenide glass fibers,” Int. J. Appl. Glass Sci. 1, 296–308 (2010).
[CrossRef]

J. Lightwave Technol.

J. Mater. Sci.

H. Lin, W. Dechent, D. Day, and J. Stoffer, “Preparation and properties of mid-infrared glass fibres and poly (chlorotrifluoroethylene) composites,” J. Mater. Sci. 32, 6573–6578 (1997).
[CrossRef]

J. Opt. Soc. Am. B

Laser Phys.

S. M. Kobtsev, S. V. Kukarin, N. V. Fateevand, and S. V. Smirnov, “Generation of self-frequency-shifted solitons in tapered fibers in the presence of femtosecond pumping,” Laser Phys. 14, 748–751 (2004).

Opt. Express

Opt. Lett.

Opt. Mater. Express

Phys. Rev. A

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607(1995).
[CrossRef]

Phys. Rev. Lett.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098.
[CrossRef]

Science

D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003).
[CrossRef]

Other

J. G. Kuzyk, Polymer Fiber Optics: Materials, Physics, and Applications (CRC Press, 2009).

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1.

(a) Schematic of the nonuniform As2Se3-layer microwire. The microwire consists of a uniform and a nonuniform segments. (b) Typical GVD profile for a single-mode microwire.

Fig. 2.
Fig. 2.

Spectral response function of As2Se3-layer microwire calculated for a 0.88 μm core diameter. The function is calculated from Eq. 3, and peaks at a pulse width of 29 fs.

Fig. 3.
Fig. 3.

(a) Coefficient (κ) calculated as a function of the uniform segment diameter of As2Se3-layer microwire. The value is normalized to the maximum among coefficient values. (b) Rate of SSFS per unit of propagation length given in Eq. 6 calculated for two uniform segments with diameters of 0.88 and 0.89 μm.

Fig. 4.
Fig. 4.

(a) Dispersion profile along the propagation path of nonuniform As2Se3-layer microwires designed using the threshold conditions: GVD [|β2(δ¯)|min in Eq. 9; blue solid curve] and CSB (|Δδ¯|min in Eq. 10; green dotted curve). (b) Schematic diagram of the spectral separation and magnitude of GVD threshold required to avoid DW emission for redshifted solitons generated from soliton of N=1,1.25, and 1.4.

Fig. 5.
Fig. 5.

(a) Schematic diagram of a uniform microwire with 0.97 μm diameter. (b) Dispersion profile of uniform microwire with diameters of 0.97 μm (black solid curve) and 1.01 μm (red dotted curve).

Fig. 6.
Fig. 6.

SSFS after propagation through a uniform microwire for soliton orders N=1, N=1.25, and N=1.4. The length of the As2Se3-layer microwire used is 20 cm with 0.97 μm diameter.

Fig. 7.
Fig. 7.

Contour plot of the (a) output wavelength shift and (b) remaining energy obtained using GVD-threshold conditions appropriate to input soliton orders varying between N=1 and 1.4.

Fig. 8.
Fig. 8.

Contour plot of the (a) output wavelength shift and (b) remaining energy obtained using GVD-threshold conditions appropriate to input soliton orders varying between N=1 and 1.4.

Fig. 9.
Fig. 9.

(a) Maximum wavelength shift obtained for a soliton with N=1.4 in nonuniform microwires designed with a GVD condition appropriate for N=1.4 (green dotted–dashed curve) and CSB condition appropriate for N=1.25 (red solid curve). (b) Optimum nonuniform microwire profiles designed based on GVD- (green dotted–dashed curve) and CSB-threshold (red solid curve) conditions with a uniform segment based on the approach proposed above, and optimum profiles designed based on [26] (blue dashed curve).

Fig. 10.
Fig. 10.

Wavelength shift versus input soliton order generated from microwires with uniform (red data, bottom curve) and nonuniform (black data, top curve) diameter profiles. The input soliton order varies between N=1 and 1.4. The nonuniform microwire profiles are designed based on CSB-threshold conditions.

Equations (10)

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

Azin2inβn(z,δ)τnn!A(z,τ)=iγ(1+iδot)(A(z,τ)R(τ)|A(z,ττ)|2dτ),
dδ¯dz=|β2(δ¯)|τs3(δ¯)fR1fRR(τs(δ¯)),
R(τs(δ¯))=π2τs4(δ¯)60dδ2πgR(δ)δ3sinh2(πτsδ/2).
hR(τ)=τ12+τ22τ2τ22exp(ττ2)sin(ττ1).
τs(δ¯)=2|β2(δ¯)|γ(δ)E(δ).
dδ¯dz=γ3(δ¯)E3(δ¯)8|β2(δ¯)|2fR1fRR(τs(δ¯)).
dδ¯dz=γ3(δo)E3(δo)8|β2(δo)|2fR1fRR(τs(δo)),
ΔΩ=δ¯δDW=3β2(δ¯)β3(δ¯)=Δδ¯+δZDW2δDW,
|ΔΩ|min=3(|β2(δ¯)|minGVD)|β3(δ¯)|.
|ΔΩ|min=(|Δδ¯|minCSB)+|δZDW2δDW|.

Metrics