Abstract

We numerically investigate polarization instability of soliton fission and the polarization dynamics of Raman solitons ejected during supercontinuum generation in a photonics crystal fiber using the coupled vector generalized nonlinear Schrödinger equations for both linear and circular birefringent fibers. The evolution of the state of polarizations of the ejected Raman soliton as representated on the Poincaré sphere is affected by both nonlinear and linear polarization rotations on the Poincaré sphere. The polarization dynamics reveal the presence of a polarization separatrix and the emergence of stable slow and unstable fast eigen-polarizations for the Raman solitons ejected in the supercontinuum generation process. Circularly birefringent fiber is investigated and found to simplify the nonlinear polarization dynamics.

© 2015 Optical Society of America

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References

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  1. H. G. Winful, “Self-induced polarization changes in birefringent optical fibers,” Appl. Phys. Lett. 47, 213–215 (1985).
    [Crossref]
  2. H. G. Winful, “Polarization instabilities in birefringent nonlinear media: application to fiber-optic devices,” Opt. Lett. 11, 33–35 (1986).
    [Crossref] [PubMed]
  3. G. Gregori and S. Wabnitz, “New exact solutions and bifurcations in the spatial distribution of polarization in third-order nonlinear optical interactions,” Phys. Rev. Lett. 56, 600 (1986).
    [Crossref] [PubMed]
  4. B. Daino, G. Gregori, and S. Wabnitz, “New all-optical devices based on third-order nonlinearity of birefringent fibers,” Opt. Lett. 11, 42–44 (1986).
    [Crossref] [PubMed]
  5. J. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Soliton propagation in optical devices with two-component fields: a comparative study,” J. Opt. Soc. Am. B 12, 1100–1109 (1995).
    [Crossref]
  6. Y. Barad and Y. Silberberg, “Polarization evolution and polarization instability of solitons in a birefringent optical fiber,” Phys. Rev. Lett. 78, 3290 (1997).
    [Crossref]
  7. S.G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
  8. M. N. Islam, U. C. Paek, C. E. Soccolich, and J. P. Gordon, “Soliton intensity-dependent polarization rotation,” Opt. Lett. 15, 21–23 (1990).
    [Crossref] [PubMed]
  9. K. J. Blow, N. J. Doran, and D. Wood, “Polarization instabilities for solitons in birefringent fibers,” Opt. Lett. 12, 202–204 (1987).
    [Crossref] [PubMed]
  10. C. R. Menyuk, “Stability of solitons in birefringent optical fibers. ll Arbitrary amplitudes,” J. Opt. Soc. Am. B 5, 392–402 (1988).
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    [Crossref] [PubMed]
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    [Crossref]
  13. Z. M. Zhu and T. G. Brown, “Experimental studies of polarization properties of supercontinua generated in a birefringent photonic crystal fiber,” Opt. Express 12, 791–796 (2004).
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    [Crossref]
  15. V. L. Kalashnikov, P. Dombi, T. Fuji, W. J. Wadsworth, J. C. Knight, P. S. J. Russell, R. S. Windeler, and A. Apolonski, “Maximization of supercontinua in photonic crystal fibers by using double pulses and polarization effects,” Appl. Phys. B 77, 319–324 (2003).
    [Crossref]
  16. M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003).
    [Crossref]
  17. S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, J. W. Wadsworth, and P. S. J. Russell, “Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 753–764 (2002).
    [Crossref]
  18. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135 (2006).
    [Crossref]
  19. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).
  20. F. Luan, A. Yulin, J. C. Knight, and D. V. Skryabin, “Polarization instability of solitons in photonic crystal fibers,” Opt. Express 14, 6550–6556 (2006).
    [Crossref] [PubMed]
  21. F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
    [Crossref] [PubMed]
  22. H. H. Tu, Y. Liu, X. M. Liu, D. Turchinovich, J. Lægsgaard, and S. A. Boppart, “Nonlinear polarization dynamics in a weakly birefringent all-normal dispersion photonic crystal fiber: toward a practical coherent fiber supercontinuum laser,” Opt. Express 20, 1113–1128 (2012).
    [Crossref] [PubMed]
  23. Q. Lin and G. P. Agrawal, “Raman response function for silica fibers,” Opt. Lett. 31, 3086–3088 (2006).
    [Crossref] [PubMed]
  24. K. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
    [Crossref]
  25. Y. Kodama and A. Hasegawa, “Nonlinear pulse propagation in a monomode dielectric guide,” IEEE J. Quantum Electron. 23, 510–524 (1987).
    [Crossref]
  26. A. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
    [Crossref] [PubMed]
  27. R. Driben, B. A. Malomed, A. Yulin, and D. Skryabin, “Newton’s cradles in optics: From N-soliton fission to soliton chains,” Phys. Rev. A 87, 063808 (2013).
    [Crossref]
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    [Crossref] [PubMed]

2013 (1)

R. Driben, B. A. Malomed, A. Yulin, and D. Skryabin, “Newton’s cradles in optics: From N-soliton fission to soliton chains,” Phys. Rev. A 87, 063808 (2013).
[Crossref]

2012 (1)

2006 (3)

2004 (3)

2003 (2)

V. L. Kalashnikov, P. Dombi, T. Fuji, W. J. Wadsworth, J. C. Knight, P. S. J. Russell, R. S. Windeler, and A. Apolonski, “Maximization of supercontinua in photonic crystal fibers by using double pulses and polarization effects,” Appl. Phys. B 77, 319–324 (2003).
[Crossref]

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003).
[Crossref]

2002 (2)

2001 (1)

A. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[Crossref] [PubMed]

1997 (1)

Y. Barad and Y. Silberberg, “Polarization evolution and polarization instability of solitons in a birefringent optical fiber,” Phys. Rev. Lett. 78, 3290 (1997).
[Crossref]

1995 (1)

1992 (1)

S.G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).

1990 (1)

1989 (1)

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

1988 (2)

1987 (2)

K. J. Blow, N. J. Doran, and D. Wood, “Polarization instabilities for solitons in birefringent fibers,” Opt. Lett. 12, 202–204 (1987).
[Crossref] [PubMed]

Y. Kodama and A. Hasegawa, “Nonlinear pulse propagation in a monomode dielectric guide,” IEEE J. Quantum Electron. 23, 510–524 (1987).
[Crossref]

1986 (3)

1985 (1)

H. G. Winful, “Self-induced polarization changes in birefringent optical fibers,” Appl. Phys. Lett. 47, 213–215 (1985).
[Crossref]

1979 (1)

Agrawal, G. P.

Q. Lin and G. P. Agrawal, “Raman response function for silica fibers,” Opt. Lett. 31, 3086–3088 (2006).
[Crossref] [PubMed]

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
[Crossref] [PubMed]

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

Akhmediev, N.

Ankiewicz, A.

Aplolonski, A.

Apolonski, A.

V. L. Kalashnikov, P. Dombi, T. Fuji, W. J. Wadsworth, J. C. Knight, P. S. J. Russell, R. S. Windeler, and A. Apolonski, “Maximization of supercontinua in photonic crystal fibers by using double pulses and polarization effects,” Appl. Phys. B 77, 319–324 (2003).
[Crossref]

Barad, Y.

Y. Barad and Y. Silberberg, “Polarization evolution and polarization instability of solitons in a birefringent optical fiber,” Phys. Rev. Lett. 78, 3290 (1997).
[Crossref]

Bergano, N. S.

S.G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).

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]

Blow, K. J.

Boppart, S. A.

Brown, T. G.

Chau, A. H. L.

Christodoulides, D. N.

Coen, S.

Daino, B.

Dombi, P.

V. L. Kalashnikov, P. Dombi, T. Fuji, W. J. Wadsworth, J. C. Knight, P. S. J. Russell, R. S. Windeler, and A. Apolonski, “Maximization of supercontinua in photonic crystal fibers by using double pulses and polarization effects,” Appl. Phys. B 77, 319–324 (2003).
[Crossref]

Doran, N. J.

Drexler, W.

Driben, R.

R. Driben, B. A. Malomed, A. Yulin, and D. Skryabin, “Newton’s cradles in optics: From N-soliton fission to soliton chains,” Phys. Rev. A 87, 063808 (2013).
[Crossref]

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135 (2006).
[Crossref]

Evangelides, S.G.

S.G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).

Fuji, T.

V. L. Kalashnikov, P. Dombi, T. Fuji, W. J. Wadsworth, J. C. Knight, P. S. J. Russell, R. S. Windeler, and A. Apolonski, “Maximization of supercontinua in photonic crystal fibers by using double pulses and polarization effects,” Appl. Phys. B 77, 319–324 (2003).
[Crossref]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135 (2006).
[Crossref]

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003).
[Crossref]

Gordon, J. P.

S.G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).

M. N. Islam, U. C. Paek, C. E. Soccolich, and J. P. Gordon, “Soliton intensity-dependent polarization rotation,” Opt. Lett. 15, 21–23 (1990).
[Crossref] [PubMed]

Gregori, G.

B. Daino, G. Gregori, and S. Wabnitz, “New all-optical devices based on third-order nonlinearity of birefringent fibers,” Opt. Lett. 11, 42–44 (1986).
[Crossref] [PubMed]

G. Gregori and S. Wabnitz, “New exact solutions and bifurcations in the spatial distribution of polarization in third-order nonlinear optical interactions,” Phys. Rev. Lett. 56, 600 (1986).
[Crossref] [PubMed]

Harvey, J. D.

Hasegawa, A.

Y. Kodama and A. Hasegawa, “Nonlinear pulse propagation in a monomode dielectric guide,” IEEE J. Quantum Electron. 23, 510–524 (1987).
[Crossref]

Herrmann, J.

A. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[Crossref] [PubMed]

Husakou, A.

A. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[Crossref] [PubMed]

Islam, M. N.

Joseph, R. I.

Kaivola, M.

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003).
[Crossref]

Kalashnikov, V. L.

V. L. Kalashnikov, P. Dombi, T. Fuji, W. J. Wadsworth, J. C. Knight, P. S. J. Russell, R. S. Windeler, and A. Apolonski, “Maximization of supercontinua in photonic crystal fibers by using double pulses and polarization effects,” Appl. Phys. B 77, 319–324 (2003).
[Crossref]

Knight, J. C.

Knox, W. H.

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
[Crossref] [PubMed]

Kodama, Y.

Y. Kodama and A. Hasegawa, “Nonlinear pulse propagation in a monomode dielectric guide,” IEEE J. Quantum Electron. 23, 510–524 (1987).
[Crossref]

Lægsgaard, J.

Lehtonen, M.

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003).
[Crossref]

Leonhardt, R.

Lin, Q.

Q. Lin and G. P. Agrawal, “Raman response function for silica fibers,” Opt. Lett. 31, 3086–3088 (2006).
[Crossref] [PubMed]

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
[Crossref] [PubMed]

Liu, X. M.

Liu, Y.

Lu, F.

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
[Crossref] [PubMed]

Luan, F.

Ludvigsen, H.

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003).
[Crossref]

Malomed, B. A.

R. Driben, B. A. Malomed, A. Yulin, and D. Skryabin, “Newton’s cradles in optics: From N-soliton fission to soliton chains,” Phys. Rev. A 87, 063808 (2013).
[Crossref]

Menyuk, C. R.

Mollenauer, L. F.

S.G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).

Paek, U. C.

Povazay, B.

Russell, P. S. J.

Silberberg, Y.

Y. Barad and Y. Silberberg, “Polarization evolution and polarization instability of solitons in a birefringent optical fiber,” Phys. Rev. Lett. 78, 3290 (1997).
[Crossref]

Simon, A.

Skryabin, D.

R. Driben, B. A. Malomed, A. Yulin, and D. Skryabin, “Newton’s cradles in optics: From N-soliton fission to soliton chains,” Phys. Rev. A 87, 063808 (2013).
[Crossref]

Skryabin, D. V.

Soccolich, C. E.

Soto-Crespo, J.

Tu, H. H.

Turchinovich, D.

Ulrich, R.

Unterhuber, A.

Wabnitz, S.

B. Daino, G. Gregori, and S. Wabnitz, “New all-optical devices based on third-order nonlinearity of birefringent fibers,” Opt. Lett. 11, 42–44 (1986).
[Crossref] [PubMed]

G. Gregori and S. Wabnitz, “New exact solutions and bifurcations in the spatial distribution of polarization in third-order nonlinear optical interactions,” Phys. Rev. Lett. 56, 600 (1986).
[Crossref] [PubMed]

Wadsworth, J. W.

Wadsworth, W. J.

V. L. Kalashnikov, P. Dombi, T. Fuji, W. J. Wadsworth, J. C. Knight, P. S. J. Russell, R. S. Windeler, and A. Apolonski, “Maximization of supercontinua in photonic crystal fibers by using double pulses and polarization effects,” Appl. Phys. B 77, 319–324 (2003).
[Crossref]

A. Aplolonski, B. Povazay, A. Unterhuber, W. Drexler, W. J. Wadsworth, J. C. Knight, and P. S. J. Russell, “Spectral shaping of supercontinuum in a cobweb photonic-crystal fiber with sub-20-fs pulses,” J. Opt. Soc. Am. B 19, 2165–2170 (2002).
[Crossref]

Windeler, R. S.

V. L. Kalashnikov, P. Dombi, T. Fuji, W. J. Wadsworth, J. C. Knight, P. S. J. Russell, R. S. Windeler, and A. Apolonski, “Maximization of supercontinua in photonic crystal fibers by using double pulses and polarization effects,” Appl. Phys. B 77, 319–324 (2003).
[Crossref]

Winful, H. G.

H. G. Winful, “Polarization instabilities in birefringent nonlinear media: application to fiber-optic devices,” Opt. Lett. 11, 33–35 (1986).
[Crossref] [PubMed]

H. G. Winful, “Self-induced polarization changes in birefringent optical fibers,” Appl. Phys. Lett. 47, 213–215 (1985).
[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]

K. J. Blow, N. J. Doran, and D. Wood, “Polarization instabilities for solitons in birefringent fibers,” Opt. Lett. 12, 202–204 (1987).
[Crossref] [PubMed]

Yulin, A.

R. Driben, B. A. Malomed, A. Yulin, and D. Skryabin, “Newton’s cradles in optics: From N-soliton fission to soliton chains,” Phys. Rev. A 87, 063808 (2013).
[Crossref]

F. Luan, A. Yulin, J. C. Knight, and D. V. Skryabin, “Polarization instability of solitons in photonic crystal fibers,” Opt. Express 14, 6550–6556 (2006).
[Crossref] [PubMed]

Zhu, Z. M.

Appl. Opt. (1)

Appl. Phys. B (1)

V. L. Kalashnikov, P. Dombi, T. Fuji, W. J. Wadsworth, J. C. Knight, P. S. J. Russell, R. S. Windeler, and A. Apolonski, “Maximization of supercontinua in photonic crystal fibers by using double pulses and polarization effects,” Appl. Phys. B 77, 319–324 (2003).
[Crossref]

Appl. Phys. Lett. (2)

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003).
[Crossref]

H. G. Winful, “Self-induced polarization changes in birefringent optical fibers,” Appl. Phys. Lett. 47, 213–215 (1985).
[Crossref]

IEEE J. Quantum Electron. (2)

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

Y. Kodama and A. Hasegawa, “Nonlinear pulse propagation in a monomode dielectric guide,” IEEE J. Quantum Electron. 23, 510–524 (1987).
[Crossref]

J. Lightwave Technol. (1)

S.G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).

J. Opt. Soc. Am. B (5)

Opt. Express (3)

Opt. Lett. (6)

Phys. Rev. A (1)

R. Driben, B. A. Malomed, A. Yulin, and D. Skryabin, “Newton’s cradles in optics: From N-soliton fission to soliton chains,” Phys. Rev. A 87, 063808 (2013).
[Crossref]

Phys. Rev. Lett. (4)

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
[Crossref] [PubMed]

A. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[Crossref] [PubMed]

G. Gregori and S. Wabnitz, “New exact solutions and bifurcations in the spatial distribution of polarization in third-order nonlinear optical interactions,” Phys. Rev. Lett. 56, 600 (1986).
[Crossref] [PubMed]

Y. Barad and Y. Silberberg, “Polarization evolution and polarization instability of solitons in a birefringent optical fiber,” Phys. Rev. Lett. 78, 3290 (1997).
[Crossref]

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135 (2006).
[Crossref]

Other (1)

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

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Figures (7)

Fig. 1
Fig. 1 (a) to (f) Temporal and spectral evolutions of supercontinuum generation in PCF for B = 1 × 105 for linear input polarization with θ = 45°: (a) to (c) are log-scale and color coded x, y and total temporal intensities, respectively; (d) to (f) are log-scale x, y and total power spectrums, respectively, color bars are in dB scale; (g) is zoomed-in temporal evolution of the total power showing the details of soliton fission from (c). The dotted black line indicates the beginning of our analysis of the polarization dynamics of the ejected Raman soliton.
Fig. 2
Fig. 2 Simulated spectra of supercontinuum generation at the output of 8 cm long PCF with birefringence B = 1 × 105, for varying linear input polarization with θ = 5°, 25°, 45°, 65° and 85°. The blue horizontal bracket represent short wavelength region of dispersive waves, the arrows point towards the first Raman solitons (black arrows) and second Raman solitons (green arrows).
Fig. 3
Fig. 3 Poincaré sphere representations of the ejected Raman soliton SOP after soliton fission at a distance of z = 2.4 cm as a function of fiber birefringence and input polarizations. Input SOPs: (a) Linear and (f) Elliptical. Ejected Raman soliton pulse polarizations: (b) to (e) and (g) to (j) are for the linear and elliptical input SOP, respectively. B = 1 × 108 for (b) and (g), 1 × 105 for (c) and (h), 2.5 × 105 for (d) and (i), and 5×104 for (e) and (j). The 3D Poincaré sphere is supplemented with front and back views along the s1-axis (slow = x and fast = y), and top and bottom views along the s3-axis (RHC and LHC).
Fig. 4
Fig. 4 Poincaré sphere representations of the polarization evolution of the first ejected Raman soliton. (a) to (d) and (e) to (h) are polarization evolutions for linear and elliptical polarizations inputs to the PCF for SC generation, respectively. Birefringence B = 1×108 for (a) and (e), 1×105 for (b) and (f), 2.5×105 for (c) and (g) and 5×104 for (d) and (h). For these plots in addition to the 3D Poincaré sphere view, additional front and back views along +s1-axis (slow = x) and −s1-axis (fast = y) are shown, as well as top and side views along along +s3-axis and +s2-axis.
Fig. 5
Fig. 5 Temporal evolution of supercontinuum generation in circularly birefringent PCF for Bc = 105 in log-scale showing the fast and slow components, for the case of a linear input polarization with θ = 45°. Note that the slow component gains power as it propagates.
Fig. 6
Fig. 6 Spectral evolution of supercontinuum generation in circularly birefringent PCF for Bc = 105 in log-scale for fast and slow components, for the case of linear input polarization with θ = 45°.
Fig. 7
Fig. 7 Poincaré sphere representations of Raman soliton polarization evolution for a circularly birefringent PCF. (a) to (c) and (d) to (f) are the polarization evolutions for the Raman soliton ejected during SC for linear and elliptical input polarizations, respectively. The fast circular component is at the north pole and the slow circular component is at the south pole. From (a) to (c) and (d) to (f), birefringence Bc = 108, 106 and 105, respectively.

Equations (4)

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A ± z + 1 2 α A ± + n 2 N i n 1 β n n ! n A ± T n i ( Δ β 0 2 Δ β 1 2 T ) A = i γ ( ω 0 ) ( 1 + i ω 0 T ) ( A ± ( z , T ) [ f R 0 R ( T ) [ | A ± ( z , T T ) | 2 + | A ( z , T T ) | 2 ] d T + ( 1 f R ) [ 2 3 | A ± ( z , T ) | 2 + 4 3 | A ( z , T ) | 2 ] ] )
A + = A x + i A y 2 , A = A x i A y 2
R ( t ) = ( 1 f R ) σ ( t ) + f R ( f a h a ( t ) + f b h b ( t ) + f c h c ( t ) )
h a ( t ) = t 1 ( t 1 2 + t 2 2 ) e t t 2 sin ( t t 1 ) , h b ( t ) = e t t b 2 t b t t b 2

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