Abstract

We study nonlinear modes of dual-core photonic crystal fiber couplers made of a material with the focusing Kerr nonlinearity. We find numerically the profiles of symmetric, antisymmetric, and asymmetric nonlinear modes and analyze all-optical switching generated by the instability of the symmetric mode. We also describe elliptic spatial solitons controlled by the waveguide boundaries.

© 2005 Optical Society of America

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References

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2004

2003

2002

2001

S. F. Mingaleev and Yu. S. Kivshar, Phys. Rev. Lett. 86, 5474 (2001).
[CrossRef] [PubMed]

1991

1986

Agrawal, G. P.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

Akhmediev, N. N.

N. N. Akhmediev and A. Ankiewicz, Solitons (Chapman & Hall, 1997).

Ankiewicz, A.

N. N. Akhmediev and A. Ankiewicz, Solitons (Chapman & Hall, 1997).

Bang, O.

Bassi, P.

Bellanca, G.

Binosi, D.

Bjarklev, A.

Fernandez de Córdoba, P.

Ferrando, A.

Fogli, F.

Kim, H.

Kim, J.

Kim, K. T.

Kivshar, Yu. S.

S. F. Mingaleev and Yu. S. Kivshar, Phys. Rev. Lett. 86, 5474 (2001).
[CrossRef] [PubMed]

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

Koshiba, M.

Lagsgaard, J.

Lee, B. H.

Li, Q. Y.

Mingaleev, S. F.

S. F. Mingaleev and Yu. S. Kivshar, Phys. Rev. Lett. 86, 5474 (2001).
[CrossRef] [PubMed]

Moloney, J. V.

Monsoriu, J. A.

Paek, U.-C.

Pask, C.

Russell, Ph.

Ph. Russell, Science 299, 358 (2003).
[CrossRef] [PubMed]

Saccomandi, L.

Saitoh, K.

Sammut, R. A.

Sato, Y.

Seaton, C. T.

Stegeman, G. I.

Thylen, L.

Trillo, S.

Wright, E. M.

Yang, Ch.

Zacarés, M.

Zhang, L.

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Figures (5)

Fig. 1
Fig. 1

Schematic of three studied designs of a nonlinear dual-core PCF. The coupler is created by two missing neighboring holes in a nonlinear material.

Fig. 2
Fig. 2

(a)–(c) Light distribution between the two PCF cores in Fig. 1(b) for three distinct nonlinear modes: A, symmetric; B, antisymmetric; and C, asymmetric. (d) Transverse profiles of the nonlinear modes ( β = 3.95 ) .

Fig. 3
Fig. 3

Bifurcation diagram of the coupler modes. Inset, enlarged part near the bifurcation point. Asymmetric mode C bifurcates from symmetric mode A at point O 1 above a certain threshold in the mode power.

Fig. 4
Fig. 4

Switching curve calculated for the PCF nonlinear coupler of Fig. 1(b). Due to the stability of the asymmetric mode and the instability of the symmetric one, the light launched into one core only does not switch to the second core but remains in the same core.

Fig. 5
Fig. 5

Transformation of the elliptic guided modes to circular solitons for the growing mode power. Three examples on the top mark three points of the eccentricity curve for β = 4.2 , β = 6 , and β = 15 , respectively. Inset, the corresponding beam cross sections at y = 0 .

Equations (2)

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i E z = Δ E + W ( x , y ) E + V ( x , y ) E 2 E ,
β u = Δ u + W ( x , y ) u + V ( x , y ) u 2 u .

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