Abstract

It is shown that pairs of solitary pulses (SPs) in a linearly coupled system with opposite group velocity dispersions form robust breathing bound states. The system can be realized by temporal-modulation coupling of SPs with different carrier frequencies propagating in the same medium, or by coupling of SPs in a dual-core waveguide. Broad SP pairs are produced in a virtually exact form by means of the variational approximation. Strong nonlinearity tends to destroy the periodic evolution of the SP pairs.

© 2014 Optical Society of America

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  1. D. Arbel and M. Orenstein, IEEE J. Quantum Electron. 35, 977 (1999).
    [CrossRef]
  2. D. Turaev, A. G. Vladimirov, and S. Zelik, Phys. Rev. E 75, 045601 (2007).
    [CrossRef]
  3. C. R. Menyuk, J. K. Wahlstrand, J. Willits, R. P. Smith, T. R. Schibli, and S. T. Cundiff, Opt. Express 15, 6677 (2007).
    [CrossRef]
  4. F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, Phys. Rev. E 75, 046607 (2007).
    [CrossRef]
  5. A. B. Shvartsburg, Physics-Uspekhi 48, 797 (2005).
    [CrossRef]
  6. A. Bahabad, M. M. Murnane, and H. C. Kapteyn, Nat. Photonics 4, 570 (2010).
    [CrossRef]
  7. S. Kobtsev, S. Kukarin, S. Smirnov, S. Turitsyn, and A. Latkin, Opt. Express 17, 20707 (2009).
    [CrossRef]
  8. D. Y. Tang, L. M. Zhao, X. Wu, and H. Zhang, Phys. Rev. A 80, 0236806 (2009).
  9. A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 80, 043829 (2009).
    [CrossRef]
  10. R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, Phys. Rev. A 83, 043831 (2011).
    [CrossRef]
  11. Y. F. Song, L. Li, H. Zhang, D. Y. Shen, D. Y. Tang, and K. P. Loh, Opt. Express 21, 10010 (2013).
    [CrossRef]
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    [CrossRef]
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  14. S. K. Turitsyn, B. G. Bale, and M. P. Fedoruk, Phys. Rep. 521, 135 (2012).
    [CrossRef]
  15. R. Ganapathy, Commun. Nonlinear Sci. Numer. Simul. 17, 4544 (2012).
    [CrossRef]
  16. Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
    [CrossRef]
  17. J. Scheuer and M. Orenstein, J. Opt. Soc. Am. B 19, 732 (2002).
    [CrossRef]
  18. T. C. Hernandez, V. E. Villargan, V. N. Serkin, G. M. Aguero, T. L. Belyaeva, M. R. Peña, and L. L. Morales, Quantum Electron. 35, 778 (2005).
    [CrossRef]
  19. M. J. Ablowitz and J. F. Ladik, J. Math. Phys. 17, 1011 (1976).
    [CrossRef]
  20. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communication (Oxford University, 2007).
  21. A. D. Boardman and K. Xie, Phys. Rev. A 50, 1851 (1994).
    [CrossRef]
  22. D. J. Kaup and B. A. Malomed, J. Opt. Soc. Am. B 15, 2838 (1998).
    [CrossRef]
  23. S. Arismar Cerqueira, Rep. Prog. Phys. 73, 024401 (2010).
    [CrossRef]
  24. B. Dana, L. Lobachinsky, and A. Bahabad, “Spatiotemporal coupled-mode theory in dispersive media under a dynamic modulation,” arXiv:1403.2905 (2014).
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    [CrossRef]
  27. P. L. Chu, B. A. Malomed, and G. D. Peng, J. Opt. Soc. Am. B 10, 1379 (1993).
    [CrossRef]
  28. Q. Li, Y. Xie, Y. Zhu, and S. Qian, Opt. Commun. 281, 2811 (2008).
    [CrossRef]

2013 (1)

2012 (2)

S. K. Turitsyn, B. G. Bale, and M. P. Fedoruk, Phys. Rep. 521, 135 (2012).
[CrossRef]

R. Ganapathy, Commun. Nonlinear Sci. Numer. Simul. 17, 4544 (2012).
[CrossRef]

2011 (2)

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, Phys. Rev. A 83, 043831 (2011).
[CrossRef]

2010 (2)

A. Bahabad, M. M. Murnane, and H. C. Kapteyn, Nat. Photonics 4, 570 (2010).
[CrossRef]

S. Arismar Cerqueira, Rep. Prog. Phys. 73, 024401 (2010).
[CrossRef]

2009 (3)

S. Kobtsev, S. Kukarin, S. Smirnov, S. Turitsyn, and A. Latkin, Opt. Express 17, 20707 (2009).
[CrossRef]

D. Y. Tang, L. M. Zhao, X. Wu, and H. Zhang, Phys. Rev. A 80, 0236806 (2009).

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 80, 043829 (2009).
[CrossRef]

2008 (1)

Q. Li, Y. Xie, Y. Zhu, and S. Qian, Opt. Commun. 281, 2811 (2008).
[CrossRef]

2007 (3)

D. Turaev, A. G. Vladimirov, and S. Zelik, Phys. Rev. E 75, 045601 (2007).
[CrossRef]

C. R. Menyuk, J. K. Wahlstrand, J. Willits, R. P. Smith, T. R. Schibli, and S. T. Cundiff, Opt. Express 15, 6677 (2007).
[CrossRef]

F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, Phys. Rev. E 75, 046607 (2007).
[CrossRef]

2006 (1)

J. N. Kutz, SIAM Review 48, 629 (2006).
[CrossRef]

2005 (2)

A. B. Shvartsburg, Physics-Uspekhi 48, 797 (2005).
[CrossRef]

T. C. Hernandez, V. E. Villargan, V. N. Serkin, G. M. Aguero, T. L. Belyaeva, M. R. Peña, and L. L. Morales, Quantum Electron. 35, 778 (2005).
[CrossRef]

2002 (1)

1999 (1)

D. Arbel and M. Orenstein, IEEE J. Quantum Electron. 35, 977 (1999).
[CrossRef]

1998 (1)

1994 (1)

A. D. Boardman and K. Xie, Phys. Rev. A 50, 1851 (1994).
[CrossRef]

1993 (1)

1990 (1)

C. Paré and M. Florjańczyk, Phys. Rev. A 41, 6287 (1990).
[CrossRef]

1976 (1)

M. J. Ablowitz and J. F. Ladik, J. Math. Phys. 17, 1011 (1976).
[CrossRef]

Ablowitz, M. J.

M. J. Ablowitz and J. F. Ladik, J. Math. Phys. 17, 1011 (1976).
[CrossRef]

Agrawal, G.

G. Agrawal, Applications of Nonlinear Fiber Optics (Elsevier, 2010).

Aguero, G. M.

T. C. Hernandez, V. E. Villargan, V. N. Serkin, G. M. Aguero, T. L. Belyaeva, M. R. Peña, and L. L. Morales, Quantum Electron. 35, 778 (2005).
[CrossRef]

Amann, A.

F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, Phys. Rev. E 75, 046607 (2007).
[CrossRef]

Arbel, D.

D. Arbel and M. Orenstein, IEEE J. Quantum Electron. 35, 977 (1999).
[CrossRef]

Arismar Cerqueira, S.

S. Arismar Cerqueira, Rep. Prog. Phys. 73, 024401 (2010).
[CrossRef]

Bahabad, A.

A. Bahabad, M. M. Murnane, and H. C. Kapteyn, Nat. Photonics 4, 570 (2010).
[CrossRef]

B. Dana, L. Lobachinsky, and A. Bahabad, “Spatiotemporal coupled-mode theory in dispersive media under a dynamic modulation,” arXiv:1403.2905 (2014).

Bale, B. G.

S. K. Turitsyn, B. G. Bale, and M. P. Fedoruk, Phys. Rep. 521, 135 (2012).
[CrossRef]

Bekker, A.

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, Phys. Rev. A 83, 043831 (2011).
[CrossRef]

Belyaeva, T. L.

T. C. Hernandez, V. E. Villargan, V. N. Serkin, G. M. Aguero, T. L. Belyaeva, M. R. Peña, and L. L. Morales, Quantum Electron. 35, 778 (2005).
[CrossRef]

Biancalana, F.

F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, Phys. Rev. E 75, 046607 (2007).
[CrossRef]

Boardman, A. D.

A. D. Boardman and K. Xie, Phys. Rev. A 50, 1851 (1994).
[CrossRef]

Chu, P. L.

Cundiff, S. T.

Dana, B.

B. Dana, L. Lobachinsky, and A. Bahabad, “Spatiotemporal coupled-mode theory in dispersive media under a dynamic modulation,” arXiv:1403.2905 (2014).

Egorov, O.

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 80, 043829 (2009).
[CrossRef]

Fedoruk, M. P.

S. K. Turitsyn, B. G. Bale, and M. P. Fedoruk, Phys. Rep. 521, 135 (2012).
[CrossRef]

Fischer, B.

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, Phys. Rev. A 83, 043831 (2011).
[CrossRef]

Florjanczyk, M.

C. Paré and M. Florjańczyk, Phys. Rev. A 41, 6287 (1990).
[CrossRef]

Ganapathy, R.

R. Ganapathy, Commun. Nonlinear Sci. Numer. Simul. 17, 4544 (2012).
[CrossRef]

Gat, O.

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, Phys. Rev. A 83, 043831 (2011).
[CrossRef]

Hernandez, T. C.

T. C. Hernandez, V. E. Villargan, V. N. Serkin, G. M. Aguero, T. L. Belyaeva, M. R. Peña, and L. L. Morales, Quantum Electron. 35, 778 (2005).
[CrossRef]

Iliew, R.

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 80, 043829 (2009).
[CrossRef]

Kapteyn, H. C.

A. Bahabad, M. M. Murnane, and H. C. Kapteyn, Nat. Photonics 4, 570 (2010).
[CrossRef]

Kartashov, Y. V.

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

Kaup, D. J.

Kobtsev, S.

Kukarin, S.

Kutz, J. N.

J. N. Kutz, SIAM Review 48, 629 (2006).
[CrossRef]

Ladik, J. F.

M. J. Ablowitz and J. F. Ladik, J. Math. Phys. 17, 1011 (1976).
[CrossRef]

Latkin, A.

Lederer, F.

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 80, 043829 (2009).
[CrossRef]

Li, L.

Li, Q.

Q. Li, Y. Xie, Y. Zhu, and S. Qian, Opt. Commun. 281, 2811 (2008).
[CrossRef]

Lobachinsky, L.

B. Dana, L. Lobachinsky, and A. Bahabad, “Spatiotemporal coupled-mode theory in dispersive media under a dynamic modulation,” arXiv:1403.2905 (2014).

Loh, K. P.

Malomed, B. A.

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

D. J. Kaup and B. A. Malomed, J. Opt. Soc. Am. B 15, 2838 (1998).
[CrossRef]

P. L. Chu, B. A. Malomed, and G. D. Peng, J. Opt. Soc. Am. B 10, 1379 (1993).
[CrossRef]

B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2006).

Menyuk, C. R.

Morales, L. L.

T. C. Hernandez, V. E. Villargan, V. N. Serkin, G. M. Aguero, T. L. Belyaeva, M. R. Peña, and L. L. Morales, Quantum Electron. 35, 778 (2005).
[CrossRef]

Murnane, M. M.

A. Bahabad, M. M. Murnane, and H. C. Kapteyn, Nat. Photonics 4, 570 (2010).
[CrossRef]

O’Reilly, E. P.

F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, Phys. Rev. E 75, 046607 (2007).
[CrossRef]

Orenstein, M.

J. Scheuer and M. Orenstein, J. Opt. Soc. Am. B 19, 732 (2002).
[CrossRef]

D. Arbel and M. Orenstein, IEEE J. Quantum Electron. 35, 977 (1999).
[CrossRef]

Paré, C.

C. Paré and M. Florjańczyk, Phys. Rev. A 41, 6287 (1990).
[CrossRef]

Peña, M. R.

T. C. Hernandez, V. E. Villargan, V. N. Serkin, G. M. Aguero, T. L. Belyaeva, M. R. Peña, and L. L. Morales, Quantum Electron. 35, 778 (2005).
[CrossRef]

Peng, G. D.

Qian, S.

Q. Li, Y. Xie, Y. Zhu, and S. Qian, Opt. Commun. 281, 2811 (2008).
[CrossRef]

Scheuer, J.

Schibli, T. R.

Serkin, V. N.

T. C. Hernandez, V. E. Villargan, V. N. Serkin, G. M. Aguero, T. L. Belyaeva, M. R. Peña, and L. L. Morales, Quantum Electron. 35, 778 (2005).
[CrossRef]

Shen, D. Y.

Shvartsburg, A. B.

A. B. Shvartsburg, Physics-Uspekhi 48, 797 (2005).
[CrossRef]

Smirnov, S.

Smith, R. P.

Smulakovsky, V.

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, Phys. Rev. A 83, 043831 (2011).
[CrossRef]

Song, Y. F.

Tang, D. Y.

Y. F. Song, L. Li, H. Zhang, D. Y. Shen, D. Y. Tang, and K. P. Loh, Opt. Express 21, 10010 (2013).
[CrossRef]

D. Y. Tang, L. M. Zhao, X. Wu, and H. Zhang, Phys. Rev. A 80, 0236806 (2009).

Torner, L.

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

Turaev, D.

D. Turaev, A. G. Vladimirov, and S. Zelik, Phys. Rev. E 75, 045601 (2007).
[CrossRef]

Turitsyn, S.

Turitsyn, S. K.

S. K. Turitsyn, B. G. Bale, and M. P. Fedoruk, Phys. Rep. 521, 135 (2012).
[CrossRef]

Uskov, A. V.

F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, Phys. Rev. E 75, 046607 (2007).
[CrossRef]

Villargan, V. E.

T. C. Hernandez, V. E. Villargan, V. N. Serkin, G. M. Aguero, T. L. Belyaeva, M. R. Peña, and L. L. Morales, Quantum Electron. 35, 778 (2005).
[CrossRef]

Vladimirov, A. G.

D. Turaev, A. G. Vladimirov, and S. Zelik, Phys. Rev. E 75, 045601 (2007).
[CrossRef]

Wahlstrand, J. K.

Weill, R.

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, Phys. Rev. A 83, 043831 (2011).
[CrossRef]

Willits, J.

Wu, X.

D. Y. Tang, L. M. Zhao, X. Wu, and H. Zhang, Phys. Rev. A 80, 0236806 (2009).

Xie, K.

A. D. Boardman and K. Xie, Phys. Rev. A 50, 1851 (1994).
[CrossRef]

Xie, Y.

Q. Li, Y. Xie, Y. Zhu, and S. Qian, Opt. Commun. 281, 2811 (2008).
[CrossRef]

Yariv, A.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communication (Oxford University, 2007).

Yeh, P.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communication (Oxford University, 2007).

Zavyalov, A.

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 80, 043829 (2009).
[CrossRef]

Zelik, S.

D. Turaev, A. G. Vladimirov, and S. Zelik, Phys. Rev. E 75, 045601 (2007).
[CrossRef]

Zhang, H.

Y. F. Song, L. Li, H. Zhang, D. Y. Shen, D. Y. Tang, and K. P. Loh, Opt. Express 21, 10010 (2013).
[CrossRef]

D. Y. Tang, L. M. Zhao, X. Wu, and H. Zhang, Phys. Rev. A 80, 0236806 (2009).

Zhao, L. M.

D. Y. Tang, L. M. Zhao, X. Wu, and H. Zhang, Phys. Rev. A 80, 0236806 (2009).

Zhu, Y.

Q. Li, Y. Xie, Y. Zhu, and S. Qian, Opt. Commun. 281, 2811 (2008).
[CrossRef]

Commun. Nonlinear Sci. Numer. Simul. (1)

R. Ganapathy, Commun. Nonlinear Sci. Numer. Simul. 17, 4544 (2012).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. Arbel and M. Orenstein, IEEE J. Quantum Electron. 35, 977 (1999).
[CrossRef]

J. Math. Phys. (1)

M. J. Ablowitz and J. F. Ladik, J. Math. Phys. 17, 1011 (1976).
[CrossRef]

J. Opt. Soc. Am. B (3)

Nat. Photonics (1)

A. Bahabad, M. M. Murnane, and H. C. Kapteyn, Nat. Photonics 4, 570 (2010).
[CrossRef]

Opt. Commun. (1)

Q. Li, Y. Xie, Y. Zhu, and S. Qian, Opt. Commun. 281, 2811 (2008).
[CrossRef]

Opt. Express (3)

Phys. Rep. (1)

S. K. Turitsyn, B. G. Bale, and M. P. Fedoruk, Phys. Rep. 521, 135 (2012).
[CrossRef]

Phys. Rev. A (5)

A. D. Boardman and K. Xie, Phys. Rev. A 50, 1851 (1994).
[CrossRef]

D. Y. Tang, L. M. Zhao, X. Wu, and H. Zhang, Phys. Rev. A 80, 0236806 (2009).

A. Zavyalov, R. Iliew, O. Egorov, and F. Lederer, Phys. Rev. A 80, 043829 (2009).
[CrossRef]

R. Weill, A. Bekker, V. Smulakovsky, B. Fischer, and O. Gat, Phys. Rev. A 83, 043831 (2011).
[CrossRef]

C. Paré and M. Florjańczyk, Phys. Rev. A 41, 6287 (1990).
[CrossRef]

Phys. Rev. E (2)

D. Turaev, A. G. Vladimirov, and S. Zelik, Phys. Rev. E 75, 045601 (2007).
[CrossRef]

F. Biancalana, A. Amann, A. V. Uskov, and E. P. O’Reilly, Phys. Rev. E 75, 046607 (2007).
[CrossRef]

Physics-Uspekhi (1)

A. B. Shvartsburg, Physics-Uspekhi 48, 797 (2005).
[CrossRef]

Quantum Electron. (1)

T. C. Hernandez, V. E. Villargan, V. N. Serkin, G. M. Aguero, T. L. Belyaeva, M. R. Peña, and L. L. Morales, Quantum Electron. 35, 778 (2005).
[CrossRef]

Rep. Prog. Phys. (1)

S. Arismar Cerqueira, Rep. Prog. Phys. 73, 024401 (2010).
[CrossRef]

Rev. Mod. Phys. (1)

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

SIAM Review (1)

J. N. Kutz, SIAM Review 48, 629 (2006).
[CrossRef]

Other (4)

B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2006).

B. Dana, L. Lobachinsky, and A. Bahabad, “Spatiotemporal coupled-mode theory in dispersive media under a dynamic modulation,” arXiv:1403.2905 (2014).

G. Agrawal, Applications of Nonlinear Fiber Optics (Elsevier, 2010).

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communication (Oxford University, 2007).

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Figures (5)

Fig. 1.
Fig. 1.

Field evolution in a broad SP pair, with K0=1, T02=20. (a), (b) Numerical solution of Eq. (2) for Re(A2(ξ,τ)) and Im(A1(ξ,τ)), respectively. (c), (d) Approximate analytical solution given by Eqs. (5) and (7) for the same components.

Fig. 2.
Fig. 2.

Same as in Fig. 1, but for a narrow SP pair, with T0=1.

Fig. 3.
Fig. 3.

Correlators computed in the linear system. (a) COAN(ξ) for different temporal widths T0 of the SP input. The inset: ξ(COAN=0.95) versus T02, the continuous line showing a fit to an exponential function. (b) CO2π/K0(ξ) for different T0. The inset: CO2π/K0(ξ=0) versus T02, the continuous line showing a fit to a parabola.

Fig. 4.
Fig. 4.

Evolution of the Re{A2} field in the nonlinear system with Γ=0.1 for a broad SP with T0=20: (a) numerical solution of the full system [Eq. (9)] and (b) simulations of the VA-produced single NLS equation [Eq. (10)]. (c), (d) same as in (a), (b), but for a narrow SP with T0=1.

Fig. 5.
Fig. 5.

Correlator CO2π/K0, characterizing the proximity of the SP pair to a periodically oscillating mode for different strengths of nonlinearity. The top and bottom panels pertain to narrow and broad pulses, with T0=2.5 and T0=20, respectively.

Equations (10)

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

Ajz+vgj1Ajtiβj22Ajt2=iκ0A3j,
Ajξi2(1)j2Ajτ2=iK0A3j.
L=(i/2)(A1*A1ξA1A1ξ*+A2*A2ξA2A2ξ*)+(i/2)(|A1τ|2|A2τ|2)+K0(A1*A2+A2*A1).
Q2=K02+Ω4/4,
{A1(ξ,τ),A2(ξ,τ)}=A(ξ,τ){isin(K0ξ),cos(K0ξ)},
iAξ+(1/2)Aττcos(2K0ξ)=0.
A(ξ,τ)=A0T02T02+K01sin(2K0ξ)exp(τ22T02+iK01sin(2K0ξ)),
CO({f1,f2},{g1,g2},ξ)=|f1|g1τ|+|f2|g2τ|f1τg1τ+f2τg2τ,
Ajξi2(1)j2Ajτ2=iK0A3j+iΓ|Aj|2Aj,
iAξ+(1/2)Aττcos(2K0ξ)+(Γ/4)[cos(4K0ξ)+3]|A|2A=0.

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