Abstract

We predict existence and study properties of the coupled core-surface solitons in hollow-core photonic crystal fibers. These solitons exist in the spectral proximity of the avoided crossings of the propagation constants of the modes guided in the air core and at the interface between the core and photonic crystal cladding.

© 2004 Optical Society of America

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References

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JETP Lett. (1)

V.M. Agranovich, V.I. Rupasov, and V.Y. Chernyak, "Self-induced transparency of surface-polaritons,�?? JETP Lett. 33, 185-188 (1981).

Nature (1)

C.M. Smith, N. Venkataraman, M.T. Gallagher, D. Müller, J.A. West, N.F. Borrelli, D.C. Alan, and K.W. Koch, "Low-loss hollow-core silica/air photonic bandgap fiber,�?? Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

V.M. Agranovich, D.M. Basko, A.D. Boardman, A.M. Kamchatnov, T.A. Leskova, �??Surface solitons due to second order cascaded nonlinearity,�?? Opt. Commun. 160, 114-118 (1999).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. A (1)

C.M. de Sterke and J.E. Sipe, "Coupled modes and the nonlinear Schrodinger-equation,�?? Phys. Rev. A 42, 550-555 (1990).
[CrossRef]

Phys. Rev. E (1)

F. Biancalana, D.V. Skryabin, A.V. Yulin, "Theory of the soliton self-frequency shift compensation by the resonant radiation in photonic crystal fibers,�?? Phys. Rev. E 70, 016615 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

G. Van Simaes, S. Coen, M. Haelterman and S. Trillo, "Observation of resonance soliton trapping due to a photoinduced gap in wave number,�?? Phys. Rev. Lett. 92, 223902 (2004).
[CrossRef]

Proc. of SPIE (1)

D.C. Alan, N.F. Borrelli, M.T. Gallagher, D. Müller, C.M. Smith, N. Venkataraman, J.A. West, P. Zhang, and K.W. Koch, "Surface modes and loss in air-core photonic band-gap fibers,�?? Proc. of SPIE 5000, 161-174 (2003).
[CrossRef]

Science (3)

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

F. Benabid, J.C. Knight, G. Antonopoulos G, P.S.J. Russell, "Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,�?? Science 298, 399-402 (2002).
[CrossRef] [PubMed]

P. St.J. Russell, "Photonic crystal fibers,�?? Science 299, 358-362 (2003).
[CrossRef] [PubMed]

Other (2)

D.L. Miles, Nonlinear Optics (Springer, Berlin, 1998).
[CrossRef]

G.P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2001).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Black lines (full and dashed) show the effective refractive indices of the two supermodes undergoing avoided crossing at 1580nm. Straight red, blue and green lines show effective refractive indices of the Fourier components of the coupled core-surface soliton for q = 0 and different values of w. (b) Group velocity dispersion parameter β 2 as function of the wavelength for the same supermodes.

Fig. 2.
Fig. 2.

(a) Temporal profiles of the amplitudes of the core (full line) and surface (dashed line) components of the coupled core-surface soliton for q = -0.7 and w = -0.5. (b) Dependencies of the peak power vs FWHM for the core surface solitons calculated for q = 0 and different values of w. Full green lines correspond to the core and dashed red lines to the surface components, respectively. For q = w = 0 the amplitude profiles of the core and surface components are identical, which explains overlap of the two lines.

Fig. 3.
Fig. 3.

Results of the numerical modelling of Eqs. (3,6) showing z evolution of the squared amplitudes of the core (a) and surface (b) modes resulting in formation of the coupled core-surface soliton. Only the core mode is excited initially. Initial conditions are shown by the red lines in (a) and (b). Peak pump power is 100kW, pump wavelength is 1580nm and pulse duration is 1ps.

Fig. 4.
Fig. 4.

The same as Fig. 3, but with 5ps pump pulse.

Equations (6)

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Z A c + α c T A c A s = i D c ( i T ) A c + i 𝓝 c ,
Z A s + α s T A s A c = i D s ( i T ) A s + i 𝓝 s Γ A s .
z F c sgn ( v ) t F c i F s = 0 ,
z F s + sgn ( v ) t F s i F c = i F s 2 F s Γ ˜ F s .
i [ w + 1 ] ξ f c = f s q f c , i [ w 1 ] ξ f s = f c q f s + f s 2 f s .
z F s + sgn ( v ) t F s i F c = i F s + R ( t ) F s ( t t , z ) 2 dt Γ ˜ F s ,

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