Abstract

We numerically demonstrate that bright solitons in tapered optical fibers can emit polychromatic Cherenkov radiation providing they remain spectrally close to the zero dispersion wavelength during propagation along the fiber. The prime role in this phenomenon is played by the soliton self-frequency shift driving efficiency of the radiation and tuning of its frequency. Depending on tapering and input pulse power, the radiation is emitted either as a train of pulses at different frequencies or as a single temporally broad and strongly chirped pulse.

© 2012 Optical Society of America

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  1. J. C. Travers, J. M. Stone, A. B. Rulkov, B. A. Cumberland, A. K. George, S. V. Popov, J. C. Knight, and J. R. Taylor, “Optical pulse compression in dispersion decreasing photonic crystal fiber,” Opt. Express 15, 13203–13211 (2007).
    [CrossRef]
  2. F. Gérôme, K. Cook, A. K. George, W. J. Wadsworth, and J. C. Knight, “Delivery of sub-100 fs pulses through 8 m of hollow-core fiber using soliton compression,” Opt. Express 15, 7126–7131 (2007).
    [CrossRef]
  3. A. Kudlinski, A. K. George, J. C. Knight, J. C. Travers, A. B. Rulkov, S. V. Popov, and J. R. Taylor, “Zero-dispersion wavelength decreasing photonic crystal fibers for ultraviolet-extended supercontinuum generation,” Opt. Express 14, 5715–5722 (2006).
    [CrossRef]
  4. P. Falk, M. Frosz, and O. Bang, “Supercontinuum generation in a photonic crystal fiber with two zero-dispersion wavelengths tapered to normal dispersion at all wavelengths,” Opt. Express 13, 7535–7540 (2005).
    [CrossRef]
  5. N. Vukovic and N. G. R. Broderick, “Method for improving the spectral flatness of the supercontinuum at 1.55 μm in tapered microstructured optical fibers,” Phys. Rev. A 82, 043840 (2010).
    [CrossRef]
  6. J. C. Travers and J. R. Taylor, “Soliton trapping of dispersive waves in tapered optical fibers,” Opt. Lett. 34, 115–117 (2009).
    [CrossRef]
  7. A. C. Judge, O. Bang, and C. M. de Sterke, “Theory of dispersive wave frequency shift via trapping by a soliton in an axially nonuniform optical fiber,” J. Opt. Soc. Am. B 27, 2195–2202 (2010).
    [CrossRef]
  8. 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]
  9. 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]
  10. 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]
  11. 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]
  12. S. P. Stark, A. Podlipensky, and St. P.J. Russell, “Soliton blueshift in tapered photonic crystal fibers,” Phys. Rev. Lett. 106, 083903 (2011).
    [CrossRef]
  13. A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105, 116804 (2010).
    [CrossRef]
  14. A. I. Latkin, S. K. Turitsyn, and A. A. Sysoliatin, “Theory of parabolic pulse generation in tapered fiber,” Opt. Lett. 32, 331–333 (2007).
    [CrossRef]
  15. C. Finot, B. Barviau, G. Millot, A. Guryanov, A. Sysoliatin, and S. Wabnitz, “Parabolic pulse generation with active or passive dispersion decreasing optical fibers,” Opt. Express 15, 15824–15835 (2007).
    [CrossRef]
  16. D. V. Skryabin and A. V. Gorbach, “Colloquium: looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
    [CrossRef]
  17. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).
  18. V. S. Afshar 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. 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]
  20. N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
    [CrossRef]
  21. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662–664 (1986).
    [CrossRef]
  22. R. P. Kenny, T. A. Birks, and K. P. Oakley, “Control of optical fibre taper shape,” Electron. Lett. 27, 1654–1656 (1991).
    [CrossRef]

2011

2010

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef]

D. V. Skryabin and A. V. Gorbach, “Colloquium: looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[CrossRef]

N. Vukovic and N. G. R. Broderick, “Method for improving the spectral flatness of the supercontinuum at 1.55 μm in tapered microstructured optical fibers,” Phys. Rev. A 82, 043840 (2010).
[CrossRef]

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]

A. C. Judge, O. Bang, and C. M. de Sterke, “Theory of dispersive wave frequency shift via trapping by a soliton in an axially nonuniform optical fiber,” J. Opt. Soc. Am. B 27, 2195–2202 (2010).
[CrossRef]

2009

2007

2006

2005

1995

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

1991

R. P. Kenny, T. A. Birks, and K. P. Oakley, “Control of optical fibre taper shape,” Electron. Lett. 27, 1654–1656 (1991).
[CrossRef]

1989

1986

Afshar, V. S.

Agrawal, G. P.

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

Akhmediev, N.

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

Bang, O.

Barviau, B.

Birks, T. A.

R. P. Kenny, T. A. Birks, and K. P. Oakley, “Control of optical fibre taper shape,” Electron. Lett. 27, 1654–1656 (1991).
[CrossRef]

Broderick, N. G. R.

N. Vukovic and N. G. R. Broderick, “Method for improving the spectral flatness of the supercontinuum at 1.55 μm in tapered microstructured optical fibers,” Phys. Rev. A 82, 043840 (2010).
[CrossRef]

Chen, Z.

Cook, K.

Cumberland, B. A.

Davoyan, A. R.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef]

de Sterke, C. M.

de Sterke, M.

Efimov, A.

Eggleton, B. J.

Falk, P.

Finot, C.

Frosz, M.

George, A. K.

Gérôme, F.

Gorbach, A. V.

D. V. Skryabin and A. V. Gorbach, “Colloquium: looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[CrossRef]

Gordon, J. P.

Gramotnev, D. K.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef]

Guryanov, A.

Haus, H. A.

Judge, A.

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]

Kenny, R. P.

R. P. Kenny, T. A. Birks, and K. P. Oakley, “Control of optical fibre taper shape,” Electron. Lett. 27, 1654–1656 (1991).
[CrossRef]

Kivshar, Y. S.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef]

Knight, J. C.

Kudlinski, A.

Kuhlmey, B. T.

Latkin, A. I.

Magi, E. C.

Mägi, E. C.

Millot, G.

Monro, T. M.

Oakley, K. P.

R. P. Kenny, T. A. Birks, and K. P. Oakley, “Control of optical fibre taper shape,” Electron. Lett. 27, 1654–1656 (1991).
[CrossRef]

Pant, R.

Podlipensky, A.

S. P. Stark, A. Podlipensky, and St. P.J. Russell, “Soliton blueshift in tapered photonic crystal fibers,” Phys. Rev. Lett. 106, 083903 (2011).
[CrossRef]

Popov, S. V.

Rulkov, A. B.

Russell, St. P.J.

S. P. Stark, A. Podlipensky, and St. P.J. Russell, “Soliton blueshift in tapered photonic crystal fibers,” Phys. Rev. Lett. 106, 083903 (2011).
[CrossRef]

Shadrivov, I. V.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef]

Skryabin, D. V.

D. V. Skryabin and A. V. Gorbach, “Colloquium: looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[CrossRef]

Sørensen, S. T.

Stark, S. P.

S. P. Stark, A. Podlipensky, and St. P.J. Russell, “Soliton blueshift in tapered photonic crystal fibers,” Phys. Rev. Lett. 106, 083903 (2011).
[CrossRef]

Stolen, R. H.

Stone, J. M.

Sysoliatin, A.

Sysoliatin, A. A.

Taylor, A. J.

Taylor, J. R.

Thomsen, C. L.

Tomlinson, W. J.

Travers, J. C.

Turitsyn, S. K.

Vukovic, N.

N. Vukovic and N. G. R. Broderick, “Method for improving the spectral flatness of the supercontinuum at 1.55 μm in tapered microstructured optical fibers,” Phys. Rev. A 82, 043840 (2010).
[CrossRef]

Wabnitz, S.

Wadsworth, W. J.

Zharov, A. A.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef]

Electron. Lett.

R. P. Kenny, T. A. Birks, and K. P. Oakley, “Control of optical fibre taper shape,” Electron. Lett. 27, 1654–1656 (1991).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

F. Gérôme, K. Cook, A. K. George, W. J. Wadsworth, and J. C. Knight, “Delivery of sub-100 fs pulses through 8 m of hollow-core fiber using soliton compression,” Opt. Express 15, 7126–7131 (2007).
[CrossRef]

J. C. Travers, J. M. Stone, A. B. Rulkov, B. A. Cumberland, A. K. George, S. V. Popov, J. C. Knight, and J. R. Taylor, “Optical pulse compression in dispersion decreasing photonic crystal fiber,” Opt. Express 15, 13203–13211 (2007).
[CrossRef]

C. Finot, B. Barviau, G. Millot, A. Guryanov, A. Sysoliatin, and S. Wabnitz, “Parabolic pulse generation with active or passive dispersion decreasing optical fibers,” Opt. Express 15, 15824–15835 (2007).
[CrossRef]

P. Falk, M. Frosz, and O. Bang, “Supercontinuum generation in a photonic crystal fiber with two zero-dispersion wavelengths tapered to normal dispersion at all wavelengths,” Opt. Express 13, 7535–7540 (2005).
[CrossRef]

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

V. S. Afshar 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]

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]

Opt. Lett.

Phys. Rev. A

N. Vukovic and N. G. R. Broderick, “Method for improving the spectral flatness of the supercontinuum at 1.55 μm in tapered microstructured optical fibers,” Phys. Rev. A 82, 043840 (2010).
[CrossRef]

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

Phys. Rev. Lett.

S. P. Stark, A. Podlipensky, and St. P.J. Russell, “Soliton blueshift in tapered photonic crystal fibers,” Phys. Rev. Lett. 106, 083903 (2011).
[CrossRef]

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, “Nonlinear nanofocusing in tapered plasmonic waveguides,” Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef]

Rev. Mod. Phys.

D. V. Skryabin and A. V. Gorbach, “Colloquium: looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[CrossRef]

Other

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

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Figures (7)

Fig. 1.
Fig. 1.

Matching between a fundamental soliton (straight lines) and the linear waves (curves) in (a) uniform and (b) tapered fibers. The thick dots mark the resonant radiation wavelength, and the dashed lines mark the soliton carrier. The distances, z, marked in (a) and (b), correspond to different stages of the spectral propagations shown in Figs. 2(b) and 3(b), respectively.

Fig. 2.
Fig. 2.

Radiation emission by a fundamental soliton in a uniform fiber. Propagation distance is z85m and γ0.072/W/m at the pump λ0=800nm. (a) Time domain and (b) spectral dynamics. The zero GVD wavelength, λzGVD=790nm, is marked by the black line, and the fiber radius is r1.29μm [see dispersion in Fig. 4(a)]. Power levels are in logarithmic scale between 0 and 40dB.

Fig. 3.
Fig. 3.

Radiation emission by a fundamental soliton in a tapered fiber. Initial conditions and fiber length are identical to those of Fig. 2. The final radius is r1.53μm, and the zero GVD wavelength is marked by the black line [see also Figs. 4(b)4(d)].

Fig. 4.
Fig. 4.

(a) Dispersion parameter for several fiber radii. The smallest one corresponds to the initial conditions of Figs. 2, 3, and 5, and the other two, in increasing order, correspond to the final cross sections of Figs. 3 and 6(b), respectively. (b) and (c) show the variation of the zero GVD wavelength and radius along z corresponding to the tapers shown in the figures with labels as specified in (c), respectively. Variation of the nonlinear coefficient is shown in (d).

Fig. 5.
Fig. 5.

Fundamental soliton along 17m of several tapered fibers. The fiber in (a) keeps constant in average the soliton detuning with the zero GVD wavelength (as in Fig. 3), whereas those in (b) and (c) increase λzGVD and r faster [see Figs. 4(b) and 4(c)], showing single pulse emission. The detuning in frequency is monitored in (d) for the three cases, corresponding the bottom line to (a) and the top one to (c).

Fig. 6.
Fig. 6.

Fifth-order solitons propagating in (a) nontapered and (b) tapered fibers along z4m. Black lines mark the zero GVD wavelengths, which start in both cases at λzGVD=795nm.

Fig. 7.
Fig. 7.

(a) Radius and (b) γ of the taper in Fig. 6(b).

Equations (4)

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

izA(z,t)=q2Qβq(z,ω0)q!(it)qA(z,t)+γ(z)A(z,t)+dtR(t)|A(z,tt)|2,
β(z)=β0+β1δ+q=2Qβq(z)δq/q!,
γ=ϵ02ω0cϵdxdyn2(x,y)23[|E|4+12|E2|2][dxdyRe{E×H*}u^z]2,
HR(t)τ12+τ22τ1τ22Θ(t)et/τ2sin(t/τ1)

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