Abstract

A full-vectorial nonlinear propagation equation for short pulses in tapered optical fibers is developed. Specific emphasis is placed on the importance of the field normalization convention for the structure of the equations, and the interpretation of the resulting field amplitudes. Different numerical schemes for interpolation of fiber parameters along the taper are discussed and tested in numerical simulations on soliton propagation and generation of continuum radiation in short photonic-crystal fiber tapers.

© 2012 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25, 1415–1417 (2000).
    [CrossRef]
  2. L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
    [CrossRef]
  3. G. Brambilla, V. Finazzi, and D. Richardson, “Ultra-low-loss optical fiber nanotapers,” Opt. Express 12, 2258–2263 (2004).
    [CrossRef]
  4. S. Leon-Saval, T. Birks, W. Wadsworth, P. S. J. Russell, and M. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express 12, 2864–2869 (2004).
    [CrossRef]
  5. M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
    [CrossRef]
  6. R. R. Gattass, G. T. Svacha, L. Tong, and E. Mazur, “Supercontinuum generation in submicrometer diameter silica fibers,” Opt. Express 14, 9408–9414(2006).
    [CrossRef]
  7. A. Kudlinski, A. George, J. Knight, J. Travers, A. Rulkov, S. Popov, and J. Taylor, “Zero-dispersion wavelength decreasing photonic crystal fibers for ultraviolet-extended supercontinuum generation,” Opt. Express 14, 5715–5722 (2006).
    [CrossRef]
  8. J. C. Travers and J. R. Taylor, “Soliton trapping of dispersive waves in tapered optical fibers,” Opt. Lett. 34, 115–117(2009).
    [CrossRef]
  9. A. Kudlinski, M. Lelek, B. Barviau, L. Audry, and A. Mussot, “Efficient blue conversion from a 1064 nm microchip laser in long photonic crystal fiber tapers for fluorescence microscopy,” Opt. Express 18, 16640–16645 (2010).
    [CrossRef]
  10. S. T. Sørensen, A. Judge, C. L. Thomsen, and O. Bang, “Optimum fiber tapers for increasing the power in the blue edge of a supercontinuum—group-acceleration matching,” Opt. Lett. 36, 816–818 (2011).
    [CrossRef]
  11. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
    [CrossRef]
  12. F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photon. Rev. 2, 58–73 (2008).
    [CrossRef]
  13. X. Liu, J. Lægsgaard, and D. Turchinovich, “Self-stabilization of a mode-locked femtosecond fiber laser using a photonic bandgap fiber,” Opt. Lett. 35, 913–915 (2010).
    [CrossRef]
  14. X. Liu, J. Lægsgaard, and D. Turchinovich, “Highly-stable monolithic femtosecond yb-fiber laser system based on photonic crystal fibers,” Opt. Express 18, 15475–15483 (2010).
    [CrossRef]
  15. X. Liu, J. Lægsgaard, U. Møller, H. Tu, S. A. Boppart, and D. Turchinovich, “All-fiber femtosecond Cherenkov radiation source,” Opt. Lett. 37, 2769–2771 (2012).
    [CrossRef]
  16. O. Vanvincq, J. C. Travers, and A. Kudlinski, “Conservation of the photon number in the generalized nonlinear Schrödinger equation in axially varying optical fibers,” Phys. Rev. A 84, 063820 (2011).
    [CrossRef]
  17. M. Kolesik, E. M. Wright, and J. V. Moloney, “Simulation of femtosecond pulse propagation in sub-micron diameter tapered fibers,” Appl. Phys. B 79, 293–300 (2004).
    [CrossRef]
  18. S. A. Vahid and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express 17, 2298–2318 (2009).
    [CrossRef]
  19. M. D. Turner, T. M. Monro, and S. A. Vahid, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part II: stimulated Raman scattering,” Opt. Express 17, 11565–11581 (2009).
    [CrossRef]
  20. R. W. Hellwarth, “3rd-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1–68 (1977).
    [CrossRef]
  21. J. Lægsgaard, “Mode profile dispersion in the generalised nonlinear Schrödinger equation,” Opt. Express 15, 16110–16123 (2007).
    [CrossRef]
  22. J. Lægsgaard and P. J. Roberts, “Dispersive pulse compression in hollow-core photonic bandgap fibers,” Opt. Express 16, 9628–9644 (2008).
    [CrossRef]
  23. K. J. Blow and D. Wood, “Theoretical description of transient stimulated “Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
    [CrossRef]
  24. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).
  25. J. Lægsgaard, A. Bjarklev, and S. E. B. Libori, “Chromatic dispersion in photonic crystal fibers: fast and accurate scheme for calculation,” J. Opt. Soc. Am. B 20, 443–448 (2003).
    [CrossRef]
  26. A. V. Gorbach and D. V. Skryabin, “Theory of radiation trapping by the accelerating solitons in optical fibers,” Phys. Rev. A 76, 053803 (2007).
    [CrossRef]

2012 (1)

2011 (2)

S. T. Sørensen, A. Judge, C. L. Thomsen, and O. Bang, “Optimum fiber tapers for increasing the power in the blue edge of a supercontinuum—group-acceleration matching,” Opt. Lett. 36, 816–818 (2011).
[CrossRef]

O. Vanvincq, J. C. Travers, and A. Kudlinski, “Conservation of the photon number in the generalized nonlinear Schrödinger equation in axially varying optical fibers,” Phys. Rev. A 84, 063820 (2011).
[CrossRef]

2010 (3)

2009 (3)

2008 (2)

F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photon. Rev. 2, 58–73 (2008).
[CrossRef]

J. Lægsgaard and P. J. Roberts, “Dispersive pulse compression in hollow-core photonic bandgap fibers,” Opt. Express 16, 9628–9644 (2008).
[CrossRef]

2007 (2)

J. Lægsgaard, “Mode profile dispersion in the generalised nonlinear Schrödinger equation,” Opt. Express 15, 16110–16123 (2007).
[CrossRef]

A. V. Gorbach and D. V. Skryabin, “Theory of radiation trapping by the accelerating solitons in optical fibers,” Phys. Rev. A 76, 053803 (2007).
[CrossRef]

2006 (3)

2005 (1)

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

2004 (3)

2003 (2)

J. Lægsgaard, A. Bjarklev, and S. E. B. Libori, “Chromatic dispersion in photonic crystal fibers: fast and accurate scheme for calculation,” J. Opt. Soc. Am. B 20, 443–448 (2003).
[CrossRef]

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

2000 (1)

1989 (1)

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

1977 (1)

R. W. Hellwarth, “3rd-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1–68 (1977).
[CrossRef]

Agrawal, G. P.

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

Ashcom, J. B.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Audry, L.

Bang, O.

Barviau, B.

Birks, T.

Birks, T. A.

Bjarklev, A.

Blow, K. J.

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

Boppart, S. A.

Brambilla, G.

Cao, Q.

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

Chong, A.

F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photon. Rev. 2, 58–73 (2008).
[CrossRef]

Coen, S.

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

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]

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

Finazzi, V.

Foster, M. A.

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

Gaeta, A. L.

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

Gattass, R. R.

R. R. Gattass, G. T. Svacha, L. Tong, and E. Mazur, “Supercontinuum generation in submicrometer diameter silica fibers,” Opt. Express 14, 9408–9414(2006).
[CrossRef]

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[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.

Gorbach, A. V.

A. V. Gorbach and D. V. Skryabin, “Theory of radiation trapping by the accelerating solitons in optical fibers,” Phys. Rev. A 76, 053803 (2007).
[CrossRef]

He, S.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Hellwarth, R. W.

R. W. Hellwarth, “3rd-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1–68 (1977).
[CrossRef]

Judge, A.

Kibler, B.

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

Knight, J.

Kolesik, M.

M. Kolesik, E. M. Wright, and J. V. Moloney, “Simulation of femtosecond pulse propagation in sub-micron diameter tapered fibers,” Appl. Phys. B 79, 293–300 (2004).
[CrossRef]

Kudlinski, A.

Lægsgaard, J.

Lee, D.

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

Lelek, M.

Leon-Saval, S.

Libori, S. E. B.

Liu, X.

Lou, J.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Mason, M.

Maxwell, I.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Mazur, E.

R. R. Gattass, G. T. Svacha, L. Tong, and E. Mazur, “Supercontinuum generation in submicrometer diameter silica fibers,” Opt. Express 14, 9408–9414(2006).
[CrossRef]

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Møller, U.

Moloney, J. V.

M. Kolesik, E. M. Wright, and J. V. Moloney, “Simulation of femtosecond pulse propagation in sub-micron diameter tapered fibers,” Appl. Phys. B 79, 293–300 (2004).
[CrossRef]

Monro, T. M.

Mussot, A.

Popov, S.

Renninger, W. H.

F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photon. Rev. 2, 58–73 (2008).
[CrossRef]

Richardson, D.

Roberts, P. J.

Rulkov, A.

Russell, P. S. J.

Shen, M.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Skryabin, D. V.

A. V. Gorbach and D. V. Skryabin, “Theory of radiation trapping by the accelerating solitons in optical fibers,” Phys. Rev. A 76, 053803 (2007).
[CrossRef]

Sørensen, S. T.

Svacha, G. T.

Taylor, J.

Taylor, J. R.

Thomsen, C. L.

Tong, L.

R. R. Gattass, G. T. Svacha, L. Tong, and E. Mazur, “Supercontinuum generation in submicrometer diameter silica fibers,” Opt. Express 14, 9408–9414(2006).
[CrossRef]

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Travers, J.

Travers, J. C.

O. Vanvincq, J. C. Travers, and A. Kudlinski, “Conservation of the photon number in the generalized nonlinear Schrödinger equation in axially varying optical fibers,” Phys. Rev. A 84, 063820 (2011).
[CrossRef]

J. C. Travers and J. R. Taylor, “Soliton trapping of dispersive waves in tapered optical fibers,” Opt. Lett. 34, 115–117(2009).
[CrossRef]

Trebino, R.

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

Tu, H.

Turchinovich, D.

Turner, M. D.

Vahid, S. A.

Vanvincq, O.

O. Vanvincq, J. C. Travers, and A. Kudlinski, “Conservation of the photon number in the generalized nonlinear Schrödinger equation in axially varying optical fibers,” Phys. Rev. A 84, 063820 (2011).
[CrossRef]

Wadsworth, W.

Wadsworth, W. J.

Wise, F. W.

F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photon. Rev. 2, 58–73 (2008).
[CrossRef]

Wood, D.

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

Wright, E. M.

M. Kolesik, E. M. Wright, and J. V. Moloney, “Simulation of femtosecond pulse propagation in sub-micron diameter tapered fibers,” Appl. Phys. B 79, 293–300 (2004).
[CrossRef]

Appl. Phys. B (2)

M. A. Foster, J. M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B 81, 363–367 (2005).
[CrossRef]

M. Kolesik, E. M. Wright, and J. V. Moloney, “Simulation of femtosecond pulse propagation in sub-micron diameter tapered fibers,” Appl. Phys. B 79, 293–300 (2004).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

J. Opt. Soc. Am. B (1)

Laser Photon. Rev. (1)

F. W. Wise, A. Chong, and W. H. Renninger, “High-energy femtosecond fiber lasers based on pulse propagation at normal dispersion,” Laser Photon. Rev. 2, 58–73 (2008).
[CrossRef]

Nature (1)

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[CrossRef]

Opt. Express (10)

G. Brambilla, V. Finazzi, and D. Richardson, “Ultra-low-loss optical fiber nanotapers,” Opt. Express 12, 2258–2263 (2004).
[CrossRef]

S. Leon-Saval, T. Birks, W. Wadsworth, P. S. J. Russell, and M. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express 12, 2864–2869 (2004).
[CrossRef]

A. Kudlinski, M. Lelek, B. Barviau, L. Audry, and A. Mussot, “Efficient blue conversion from a 1064 nm microchip laser in long photonic crystal fiber tapers for fluorescence microscopy,” Opt. Express 18, 16640–16645 (2010).
[CrossRef]

R. R. Gattass, G. T. Svacha, L. Tong, and E. Mazur, “Supercontinuum generation in submicrometer diameter silica fibers,” Opt. Express 14, 9408–9414(2006).
[CrossRef]

A. Kudlinski, A. George, J. Knight, J. Travers, A. Rulkov, S. Popov, and J. Taylor, “Zero-dispersion wavelength decreasing photonic crystal fibers for ultraviolet-extended supercontinuum generation,” Opt. Express 14, 5715–5722 (2006).
[CrossRef]

X. Liu, J. Lægsgaard, and D. Turchinovich, “Highly-stable monolithic femtosecond yb-fiber laser system based on photonic crystal fibers,” Opt. Express 18, 15475–15483 (2010).
[CrossRef]

S. A. Vahid and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express 17, 2298–2318 (2009).
[CrossRef]

M. D. Turner, T. M. Monro, and S. A. Vahid, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part II: stimulated Raman scattering,” Opt. Express 17, 11565–11581 (2009).
[CrossRef]

J. Lægsgaard, “Mode profile dispersion in the generalised nonlinear Schrödinger equation,” Opt. Express 15, 16110–16123 (2007).
[CrossRef]

J. Lægsgaard and P. J. Roberts, “Dispersive pulse compression in hollow-core photonic bandgap fibers,” Opt. Express 16, 9628–9644 (2008).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (2)

O. Vanvincq, J. C. Travers, and A. Kudlinski, “Conservation of the photon number in the generalized nonlinear Schrödinger equation in axially varying optical fibers,” Phys. Rev. A 84, 063820 (2011).
[CrossRef]

A. V. Gorbach and D. V. Skryabin, “Theory of radiation trapping by the accelerating solitons in optical fibers,” Phys. Rev. A 76, 053803 (2007).
[CrossRef]

Prog. Quantum Electron. (1)

R. W. Hellwarth, “3rd-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5, 1–68 (1977).
[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 (1)

G. P. Agrawal, Nonlinear Fiber Optics (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.


Metrics