Abstract

We present modulation instability analysis including azimuthal perturbations of steady-state continuous wave (CW) propagation in multicore-fiber configurations with a central core. In systems with a central core, a steady CW evolution regime requires power-controlled phase matching, which offers interesting spatial-division applications. Our results have general applicability and are relevant to a range of physical and engineering systems, including high-power fiber lasers, optical transmission in multicore fiber, and systems of coupled nonlinear waveguides.

© 2013 Optical Society of America

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  1. F. Y. M. Chan, A. P. T. Lau, and H.-Ya. Tam, Opt. Express 20, 4548 (2012).
    [CrossRef]
  2. B. Zhu, T. F. Taunay, M. F. Yan, J. M. Fini, M. Fishteyn, E. M. Monberg, and F. V. Dimarcello, Opt. Express 18, 11117 (2010).
    [CrossRef]
  3. B. M. Shalaby, V. Kermene, D. Pagnoux, A. Desfarges-Berthelemot, A. Barthelemy, A. Popp, M. Abdou Ahmed, A. Voss, and T. Graf, Appl. Phys. B 100, 859 (2010).
    [CrossRef]
  4. S. K. Turitsyn, A. M. Rubenchik, M. P. Fedoruk, and E. Tkachenko, Phys. Rev. A 86, 031804(R) (2012).
    [CrossRef]
  5. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef]
  6. C. Schmidt-Hattenberger, U. Truschel, and F. Lederer, Opt. Lett. 16, 294 (1991).
    [CrossRef]
  7. Yu. S. Kivshar and M. Peyard, Phys. Rev. A 46, 3198 (1992).
    [CrossRef]
  8. A. B. Aceves, C. De Angelis, G. G. Luther, and A. M. Rubenchik, Opt. Lett. 19, 1186 (1994).
    [CrossRef]
  9. A. B. Aceves, G. Luther, C. De Angelis, A. Rubenchik, and S. K. Turitsyn, Phys. Rev. Lett. 75, 73 (1995).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012 (2)

F. Y. M. Chan, A. P. T. Lau, and H.-Ya. Tam, Opt. Express 20, 4548 (2012).
[CrossRef]

S. K. Turitsyn, A. M. Rubenchik, M. P. Fedoruk, and E. Tkachenko, Phys. Rev. A 86, 031804(R) (2012).
[CrossRef]

2011 (1)

2010 (2)

B. Zhu, T. F. Taunay, M. F. Yan, J. M. Fini, M. Fishteyn, E. M. Monberg, and F. V. Dimarcello, Opt. Express 18, 11117 (2010).
[CrossRef]

B. M. Shalaby, V. Kermene, D. Pagnoux, A. Desfarges-Berthelemot, A. Barthelemy, A. Popp, M. Abdou Ahmed, A. Voss, and T. Graf, Appl. Phys. B 100, 859 (2010).
[CrossRef]

2009 (2)

V. E. Zakharov and L. A. Ostrovsky, Physica D 238, 540 (2009).
[CrossRef]

C. Huang, Y. Lai, S. Cheng, and W. Hsieh, Opt. Express 17, 1299 (2009).
[CrossRef]

2006 (1)

K. Hizaidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, Int. J. Bifurcation Chaos 16, 1739 (2006).

2005 (1)

2003 (1)

L. Hadžievski, M. Stepić, and M. M. Škorich, Phys. Rev. B 68, 014305 (2003).
[CrossRef]

2001 (1)

P. G. Kevrekidis, K. O. Rasmussen, and A. R. Bishop, Int. J. Mod. Phys. B 15, 2833 (2001).
[CrossRef]

1999 (1)

R. Morandotti, H. Eisenberg, U. Peschel, Y. Silberberg, and J. S. Aitchison, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

1996 (1)

A. A. Maier, Phys. Usp. 39, 1109 (1996).
[CrossRef]

1995 (4)

A. A. Maier, Phys. Usp. 38, 991 (1995).
[CrossRef]

E. W. Laedke, K. H. Spatschek, V. K. Mezentsev, S. L. Musher, I. V. Ryzhenkova, and S. K. Turitsyn, J. Exp. Theor. Phys. Lett. 62, 677 (1995).

E. W. Laedke, K.-H. Spatschek, S. K. Turitsyn, and V. K. Mezentsev, Phys. Rev. E 52, 5549 (1995).
[CrossRef]

A. B. Aceves, G. Luther, C. De Angelis, A. Rubenchik, and S. K. Turitsyn, Phys. Rev. Lett. 75, 73 (1995).
[CrossRef]

1994 (2)

A. B. Aceves, C. De Angelis, G. G. Luther, and A. M. Rubenchik, Opt. Lett. 19, 1186 (1994).
[CrossRef]

E. W. Laedke, K. H. Spatschek, and S. K. Turitsyn, Phys. Rev. Lett. 73, 1055 (1994).
[CrossRef]

1992 (1)

Yu. S. Kivshar and M. Peyard, Phys. Rev. A 46, 3198 (1992).
[CrossRef]

1991 (1)

1988 (1)

Abdou Ahmed, M.

B. M. Shalaby, V. Kermene, D. Pagnoux, A. Desfarges-Berthelemot, A. Barthelemy, A. Popp, M. Abdou Ahmed, A. Voss, and T. Graf, Appl. Phys. B 100, 859 (2010).
[CrossRef]

Abdullaev, F.

F. Abdullaev, S. Darmanyan, and J. Garnier, in Progress in Optics, E. Wolf, ed. (Elsevier, 2002), 44, p. 303.

Aceves, A. B.

A. B. Aceves, G. Luther, C. De Angelis, A. Rubenchik, and S. K. Turitsyn, Phys. Rev. Lett. 75, 73 (1995).
[CrossRef]

A. B. Aceves, C. De Angelis, G. G. Luther, and A. M. Rubenchik, Opt. Lett. 19, 1186 (1994).
[CrossRef]

Agger, C.

Aitchison, J. S.

R. Morandotti, H. Eisenberg, U. Peschel, Y. Silberberg, and J. S. Aitchison, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

Bang, O.

Bartal, G.

Barthelemy, A.

B. M. Shalaby, V. Kermene, D. Pagnoux, A. Desfarges-Berthelemot, A. Barthelemy, A. Popp, M. Abdou Ahmed, A. Voss, and T. Graf, Appl. Phys. B 100, 859 (2010).
[CrossRef]

Bishop, A. R.

P. G. Kevrekidis, K. O. Rasmussen, and A. R. Bishop, Int. J. Mod. Phys. B 15, 2833 (2001).
[CrossRef]

Buljan, H.

Chan, F. Y. M.

Cheng, S.

Christodoulides, D. N.

K. Hizaidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, Int. J. Bifurcation Chaos 16, 1739 (2006).

D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
[CrossRef]

Cohen, O.

Darmanyan, S.

F. Abdullaev, S. Darmanyan, and J. Garnier, in Progress in Optics, E. Wolf, ed. (Elsevier, 2002), 44, p. 303.

De Angelis, C.

A. B. Aceves, G. Luther, C. De Angelis, A. Rubenchik, and S. K. Turitsyn, Phys. Rev. Lett. 75, 73 (1995).
[CrossRef]

A. B. Aceves, C. De Angelis, G. G. Luther, and A. M. Rubenchik, Opt. Lett. 19, 1186 (1994).
[CrossRef]

Desfarges-Berthelemot, A.

B. M. Shalaby, V. Kermene, D. Pagnoux, A. Desfarges-Berthelemot, A. Barthelemy, A. Popp, M. Abdou Ahmed, A. Voss, and T. Graf, Appl. Phys. B 100, 859 (2010).
[CrossRef]

Dimarcello, F. V.

Droulias, S.

K. Hizaidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, Int. J. Bifurcation Chaos 16, 1739 (2006).

Efremidis, N.

Efremidis, N. K.

K. Hizaidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, Int. J. Bifurcation Chaos 16, 1739 (2006).

Eisenberg, H.

R. Morandotti, H. Eisenberg, U. Peschel, Y. Silberberg, and J. S. Aitchison, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

Fedoruk, M. P.

S. K. Turitsyn, A. M. Rubenchik, M. P. Fedoruk, and E. Tkachenko, Phys. Rev. A 86, 031804(R) (2012).
[CrossRef]

Fini, J. M.

Fishteyn, M.

Fleischer, J.

Freedman, B.

Garnier, J.

F. Abdullaev, S. Darmanyan, and J. Garnier, in Progress in Optics, E. Wolf, ed. (Elsevier, 2002), 44, p. 303.

Graf, T.

B. M. Shalaby, V. Kermene, D. Pagnoux, A. Desfarges-Berthelemot, A. Barthelemy, A. Popp, M. Abdou Ahmed, A. Voss, and T. Graf, Appl. Phys. B 100, 859 (2010).
[CrossRef]

Hadžievski, L.

L. Hadžievski, M. Stepić, and M. M. Škorich, Phys. Rev. B 68, 014305 (2003).
[CrossRef]

Hizaidis, K.

K. Hizaidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, Int. J. Bifurcation Chaos 16, 1739 (2006).

Hsieh, W.

Huang, C.

Joseph, R. I.

Keiding, S. R.

Kermene, V.

B. M. Shalaby, V. Kermene, D. Pagnoux, A. Desfarges-Berthelemot, A. Barthelemy, A. Popp, M. Abdou Ahmed, A. Voss, and T. Graf, Appl. Phys. B 100, 859 (2010).
[CrossRef]

Kevrekidis, P. G.

P. G. Kevrekidis, K. O. Rasmussen, and A. R. Bishop, Int. J. Mod. Phys. B 15, 2833 (2001).
[CrossRef]

Kivshar, Yu. S.

Yu. S. Kivshar and M. Peyard, Phys. Rev. A 46, 3198 (1992).
[CrossRef]

Laedke, E. W.

E. W. Laedke, K. H. Spatschek, V. K. Mezentsev, S. L. Musher, I. V. Ryzhenkova, and S. K. Turitsyn, J. Exp. Theor. Phys. Lett. 62, 677 (1995).

E. W. Laedke, K.-H. Spatschek, S. K. Turitsyn, and V. K. Mezentsev, Phys. Rev. E 52, 5549 (1995).
[CrossRef]

E. W. Laedke, K. H. Spatschek, and S. K. Turitsyn, Phys. Rev. Lett. 73, 1055 (1994).
[CrossRef]

Lai, Y.

Lau, A. P. T.

Lederer, F.

Luther, G.

A. B. Aceves, G. Luther, C. De Angelis, A. Rubenchik, and S. K. Turitsyn, Phys. Rev. Lett. 75, 73 (1995).
[CrossRef]

Luther, G. G.

Maier, A. A.

A. A. Maier, Phys. Usp. 39, 1109 (1996).
[CrossRef]

A. A. Maier, Phys. Usp. 38, 991 (1995).
[CrossRef]

Manela, O.

Mezentsev, V. K.

E. W. Laedke, K.-H. Spatschek, S. K. Turitsyn, and V. K. Mezentsev, Phys. Rev. E 52, 5549 (1995).
[CrossRef]

E. W. Laedke, K. H. Spatschek, V. K. Mezentsev, S. L. Musher, I. V. Ryzhenkova, and S. K. Turitsyn, J. Exp. Theor. Phys. Lett. 62, 677 (1995).

Monberg, E. M.

Morandotti, R.

R. Morandotti, H. Eisenberg, U. Peschel, Y. Silberberg, and J. S. Aitchison, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

Musher, S. L.

E. W. Laedke, K. H. Spatschek, V. K. Mezentsev, S. L. Musher, I. V. Ryzhenkova, and S. K. Turitsyn, J. Exp. Theor. Phys. Lett. 62, 677 (1995).

Ostrovsky, L. A.

V. E. Zakharov and L. A. Ostrovsky, Physica D 238, 540 (2009).
[CrossRef]

Pagnoux, D.

B. M. Shalaby, V. Kermene, D. Pagnoux, A. Desfarges-Berthelemot, A. Barthelemy, A. Popp, M. Abdou Ahmed, A. Voss, and T. Graf, Appl. Phys. B 100, 859 (2010).
[CrossRef]

Peschel, U.

R. Morandotti, H. Eisenberg, U. Peschel, Y. Silberberg, and J. S. Aitchison, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

Peyard, M.

Yu. S. Kivshar and M. Peyard, Phys. Rev. A 46, 3198 (1992).
[CrossRef]

Popp, A.

B. M. Shalaby, V. Kermene, D. Pagnoux, A. Desfarges-Berthelemot, A. Barthelemy, A. Popp, M. Abdou Ahmed, A. Voss, and T. Graf, Appl. Phys. B 100, 859 (2010).
[CrossRef]

Rasmussen, K. O.

P. G. Kevrekidis, K. O. Rasmussen, and A. R. Bishop, Int. J. Mod. Phys. B 15, 2833 (2001).
[CrossRef]

Rubenchik, A.

A. B. Aceves, G. Luther, C. De Angelis, A. Rubenchik, and S. K. Turitsyn, Phys. Rev. Lett. 75, 73 (1995).
[CrossRef]

Rubenchik, A. M.

S. K. Turitsyn, A. M. Rubenchik, M. P. Fedoruk, and E. Tkachenko, Phys. Rev. A 86, 031804(R) (2012).
[CrossRef]

A. B. Aceves, C. De Angelis, G. G. Luther, and A. M. Rubenchik, Opt. Lett. 19, 1186 (1994).
[CrossRef]

Ryzhenkova, I. V.

E. W. Laedke, K. H. Spatschek, V. K. Mezentsev, S. L. Musher, I. V. Ryzhenkova, and S. K. Turitsyn, J. Exp. Theor. Phys. Lett. 62, 677 (1995).

Schmidt-Hattenberger, C.

Schwartz, T.

Segev, M.

Shalaby, B. M.

B. M. Shalaby, V. Kermene, D. Pagnoux, A. Desfarges-Berthelemot, A. Barthelemy, A. Popp, M. Abdou Ahmed, A. Voss, and T. Graf, Appl. Phys. B 100, 859 (2010).
[CrossRef]

Silberberg, Y.

R. Morandotti, H. Eisenberg, U. Peschel, Y. Silberberg, and J. S. Aitchison, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

Škorich, M. M.

L. Hadžievski, M. Stepić, and M. M. Škorich, Phys. Rev. B 68, 014305 (2003).
[CrossRef]

Spatschek, K. H.

E. W. Laedke, K. H. Spatschek, V. K. Mezentsev, S. L. Musher, I. V. Ryzhenkova, and S. K. Turitsyn, J. Exp. Theor. Phys. Lett. 62, 677 (1995).

E. W. Laedke, K. H. Spatschek, and S. K. Turitsyn, Phys. Rev. Lett. 73, 1055 (1994).
[CrossRef]

Spatschek, K.-H.

E. W. Laedke, K.-H. Spatschek, S. K. Turitsyn, and V. K. Mezentsev, Phys. Rev. E 52, 5549 (1995).
[CrossRef]

Srensen, S. T.

Stepic, M.

L. Hadžievski, M. Stepić, and M. M. Škorich, Phys. Rev. B 68, 014305 (2003).
[CrossRef]

Tam, H.-Ya.

Taunay, T. F.

Thomsen, C. L.

Tkachenko, E.

S. K. Turitsyn, A. M. Rubenchik, M. P. Fedoruk, and E. Tkachenko, Phys. Rev. A 86, 031804(R) (2012).
[CrossRef]

Truschel, U.

Tsopelas, I.

K. Hizaidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, Int. J. Bifurcation Chaos 16, 1739 (2006).

Turitsyn, S. K.

S. K. Turitsyn, A. M. Rubenchik, M. P. Fedoruk, and E. Tkachenko, Phys. Rev. A 86, 031804(R) (2012).
[CrossRef]

A. B. Aceves, G. Luther, C. De Angelis, A. Rubenchik, and S. K. Turitsyn, Phys. Rev. Lett. 75, 73 (1995).
[CrossRef]

E. W. Laedke, K.-H. Spatschek, S. K. Turitsyn, and V. K. Mezentsev, Phys. Rev. E 52, 5549 (1995).
[CrossRef]

E. W. Laedke, K. H. Spatschek, V. K. Mezentsev, S. L. Musher, I. V. Ryzhenkova, and S. K. Turitsyn, J. Exp. Theor. Phys. Lett. 62, 677 (1995).

E. W. Laedke, K. H. Spatschek, and S. K. Turitsyn, Phys. Rev. Lett. 73, 1055 (1994).
[CrossRef]

Voss, A.

B. M. Shalaby, V. Kermene, D. Pagnoux, A. Desfarges-Berthelemot, A. Barthelemy, A. Popp, M. Abdou Ahmed, A. Voss, and T. Graf, Appl. Phys. B 100, 859 (2010).
[CrossRef]

Yan, M. F.

Zakharov, V. E.

V. E. Zakharov and L. A. Ostrovsky, Physica D 238, 540 (2009).
[CrossRef]

Zhu, B.

Appl. Phys. B (1)

B. M. Shalaby, V. Kermene, D. Pagnoux, A. Desfarges-Berthelemot, A. Barthelemy, A. Popp, M. Abdou Ahmed, A. Voss, and T. Graf, Appl. Phys. B 100, 859 (2010).
[CrossRef]

Int. J. Bifurcation Chaos (1)

K. Hizaidis, S. Droulias, I. Tsopelas, N. K. Efremidis, and D. N. Christodoulides, Int. J. Bifurcation Chaos 16, 1739 (2006).

Int. J. Mod. Phys. B (1)

P. G. Kevrekidis, K. O. Rasmussen, and A. R. Bishop, Int. J. Mod. Phys. B 15, 2833 (2001).
[CrossRef]

J. Exp. Theor. Phys. Lett. (1)

E. W. Laedke, K. H. Spatschek, V. K. Mezentsev, S. L. Musher, I. V. Ryzhenkova, and S. K. Turitsyn, J. Exp. Theor. Phys. Lett. 62, 677 (1995).

Opt. Express (4)

Opt. Lett. (4)

Phys. Rev. A (2)

Yu. S. Kivshar and M. Peyard, Phys. Rev. A 46, 3198 (1992).
[CrossRef]

S. K. Turitsyn, A. M. Rubenchik, M. P. Fedoruk, and E. Tkachenko, Phys. Rev. A 86, 031804(R) (2012).
[CrossRef]

Phys. Rev. B (1)

L. Hadžievski, M. Stepić, and M. M. Škorich, Phys. Rev. B 68, 014305 (2003).
[CrossRef]

Phys. Rev. E (1)

E. W. Laedke, K.-H. Spatschek, S. K. Turitsyn, and V. K. Mezentsev, Phys. Rev. E 52, 5549 (1995).
[CrossRef]

Phys. Rev. Lett. (3)

E. W. Laedke, K. H. Spatschek, and S. K. Turitsyn, Phys. Rev. Lett. 73, 1055 (1994).
[CrossRef]

A. B. Aceves, G. Luther, C. De Angelis, A. Rubenchik, and S. K. Turitsyn, Phys. Rev. Lett. 75, 73 (1995).
[CrossRef]

R. Morandotti, H. Eisenberg, U. Peschel, Y. Silberberg, and J. S. Aitchison, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

Phys. Usp. (2)

A. A. Maier, Phys. Usp. 38, 991 (1995).
[CrossRef]

A. A. Maier, Phys. Usp. 39, 1109 (1996).
[CrossRef]

Physica D (1)

V. E. Zakharov and L. A. Ostrovsky, Physica D 238, 540 (2009).
[CrossRef]

Other (1)

F. Abdullaev, S. Darmanyan, and J. Garnier, in Progress in Optics, E. Wolf, ed. (Elsevier, 2002), 44, p. 303.

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Figures (4)

Fig. 1.
Fig. 1.

Schematic depiction of the MCF and power exchanges between cores.

Fig. 2.
Fig. 2.

Four values of Γ corresponding to different power splits between cores as functions of total input power; here γ0/γ1=0.5 and κ=1. Here different curves for each branch correspond to N varying from 3 to 12 (from the bottom to the top, from left to right for green curve).

Fig. 3.
Fig. 3.

Angular stability area (shown by color) of Γ3 (Γ1, Γ2, and Γ4 are unstable) corresponding to different values of the total power Pt and N; here γ0/γ1=1 and κ=1.

Fig. 4.
Fig. 4.

Increment of instability p2 as a function of s for Γ2 and Γ4 corresponding to different Pt and N (red dashed line: N=6; solid blue: N=12; solid-dotted black: N=24).

Equations (9)

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

iAkz+m=0NCkmAm+2γk|Ak|2Ak=0;k=0,,N.
iU0z+1Nk=1NUk+2Nγ0γ1|U0|2U0=0,
iUkz+(κ2C)Uk+C(Uk+1+Uk1)+U0+2|Uk|2Uk=0.
{U0,Uk}={A,B}×eiλz,Γ=BA,
|A|2=PtN(1+Γ2),λ=Γ+2γ0Ptγ1(1+Γ2),
Γ4(κ+2PtN)Γ3(κ2γ0Ptγ1)Γ1=0.
pl2=(1Γl+4Csin2[s2])(4Γl2PtN(1+Γl2)1Γl4Csin2[s2]),
4Γl2PtN(1+Γl2)<1Γl+4Csin2[πN].
2Γl2PtN(1+Γl2)=1Γl+4Csin2[πm/N],

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