Abstract

We show that when spatially localized gain landscape performs accelerated motion in the transverse plane, i.e., when it rotates or oscillates around the light propagation axis, the effective gain experienced by the light beam considerably reduces with an increase of the amplitude of oscillations or frequency of rotation of the localized gain. In the presence of uniform background losses and defocusing nonlinearity, such gain landscapes may support dynamically oscillating gain-managed solitons, but if the amplitude of oscillations or the frequency of rotation of the localized gain exceeds a threshold, stable attractors disappear and any input beam decays.

© 2013 Optical Society of America

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References

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  1. N. Akhmediev and A. Ankiewicz, eds., Dissipative Solitons: From Optics to Biology and Medicine (Springer, 2008).
  2. N. N. Rosanov, Spatial Hysteresis and Optical Patterns (Springer, 2002).
  3. A. M. Sergeev and V. I. Petviashvili, Sov. Phys. Dokl. 29, 493 (1984).
  4. W. van Saarloos and P. C. Hohenberg, Phys. Rev. Lett. 64, 749 (1990).
    [CrossRef]
  5. N. N. Akhmediev and V. V. Afanasjev, Phys. Rev. Lett. 75, 2320 (1995).
    [CrossRef]
  6. E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, Phys. Rev. Lett. 90, 253903 (2003).
    [CrossRef]
  7. C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. 173, 233 (2009).
    [CrossRef]
  8. C. H. Tsang, B. A. Malomed, C. K. Lam, and K. W. Chow, Eur. Phys. J. 59, 81 (2010).
    [CrossRef]
  9. M. O. Williams, C. W. McGrath, and J. N. Kutz, Opt. Express 18, 11671 (2010).
    [CrossRef]
  10. Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, Opt. Lett. 36, 82 (2011).
    [CrossRef]
  11. V. E. Lobanov, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 36, 85 (2011).
    [CrossRef]
  12. V. Skarka, N. B. Aleksic, H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. Lett. 105, 213901 (2010).
    [CrossRef]
  13. A. E. Siegman, J. Opt. Soc. Am. A 20, 1617 (2003).
    [CrossRef]
  14. D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, Opt. Lett. 36, 1200 (2011).
    [CrossRef]
  15. G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, Nat. Commun. 3, 1243 (2012).
    [CrossRef]
  16. A. Hasegawa and Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
    [CrossRef]

2012 (1)

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, Nat. Commun. 3, 1243 (2012).
[CrossRef]

2011 (3)

2010 (3)

V. Skarka, N. B. Aleksic, H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

C. H. Tsang, B. A. Malomed, C. K. Lam, and K. W. Chow, Eur. Phys. J. 59, 81 (2010).
[CrossRef]

M. O. Williams, C. W. McGrath, and J. N. Kutz, Opt. Express 18, 11671 (2010).
[CrossRef]

2009 (1)

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. 173, 233 (2009).
[CrossRef]

2003 (2)

A. E. Siegman, J. Opt. Soc. Am. A 20, 1617 (2003).
[CrossRef]

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef]

1995 (1)

N. N. Akhmediev and V. V. Afanasjev, Phys. Rev. Lett. 75, 2320 (1995).
[CrossRef]

1991 (1)

A. Hasegawa and Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[CrossRef]

1990 (1)

W. van Saarloos and P. C. Hohenberg, Phys. Rev. Lett. 64, 749 (1990).
[CrossRef]

1984 (1)

A. M. Sergeev and V. I. Petviashvili, Sov. Phys. Dokl. 29, 493 (1984).

Afanasjev, V. V.

N. N. Akhmediev and V. V. Afanasjev, Phys. Rev. Lett. 75, 2320 (1995).
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev and V. V. Afanasjev, Phys. Rev. Lett. 75, 2320 (1995).
[CrossRef]

Aleksic, N. B.

V. Skarka, N. B. Aleksic, H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

Baumberg, J. J.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, Nat. Commun. 3, 1243 (2012).
[CrossRef]

Berloff, N. G.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, Nat. Commun. 3, 1243 (2012).
[CrossRef]

Chow, K. W.

C. H. Tsang, B. A. Malomed, C. K. Lam, and K. W. Chow, Eur. Phys. J. 59, 81 (2010).
[CrossRef]

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. 173, 233 (2009).
[CrossRef]

Christmann, G.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, Nat. Commun. 3, 1243 (2012).
[CrossRef]

Gao, T.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, Nat. Commun. 3, 1243 (2012).
[CrossRef]

Hasegawa, A.

A. Hasegawa and Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[CrossRef]

Hatzopoulos, Z.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, Nat. Commun. 3, 1243 (2012).
[CrossRef]

Hohenberg, P. C.

W. van Saarloos and P. C. Hohenberg, Phys. Rev. Lett. 64, 749 (1990).
[CrossRef]

Kartashov, Y. V.

Kodama, Y.

A. Hasegawa and Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[CrossRef]

Konotop, V. V.

Kutz, J. N.

Lam, C. K.

C. H. Tsang, B. A. Malomed, C. K. Lam, and K. W. Chow, Eur. Phys. J. 59, 81 (2010).
[CrossRef]

Lam, C.-K.

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. 173, 233 (2009).
[CrossRef]

Lange, C. H.

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef]

Leblond, H.

V. Skarka, N. B. Aleksic, H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

Lederer, F.

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef]

Lobanov, V. E.

Malomed, B. A.

V. Skarka, N. B. Aleksic, H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

C. H. Tsang, B. A. Malomed, C. K. Lam, and K. W. Chow, Eur. Phys. J. 59, 81 (2010).
[CrossRef]

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. 173, 233 (2009).
[CrossRef]

McGrath, C. W.

Michaelis, D.

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef]

Mihalache, D.

V. Skarka, N. B. Aleksic, H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

Petviashvili, V. I.

A. M. Sergeev and V. I. Petviashvili, Sov. Phys. Dokl. 29, 493 (1984).

Rosanov, N. N.

N. N. Rosanov, Spatial Hysteresis and Optical Patterns (Springer, 2002).

Savvidis, P. G.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, Nat. Commun. 3, 1243 (2012).
[CrossRef]

Sergeev, A. M.

A. M. Sergeev and V. I. Petviashvili, Sov. Phys. Dokl. 29, 493 (1984).

Siegman, A. E.

Skarka, V.

V. Skarka, N. B. Aleksic, H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

Stegeman, G. I.

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef]

Torner, L.

Tosi, G.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, Nat. Commun. 3, 1243 (2012).
[CrossRef]

Tsang, C. H.

C. H. Tsang, B. A. Malomed, C. K. Lam, and K. W. Chow, Eur. Phys. J. 59, 81 (2010).
[CrossRef]

Tsotsis, P.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, Nat. Commun. 3, 1243 (2012).
[CrossRef]

Ultanir, E. A.

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef]

van Saarloos, W.

W. van Saarloos and P. C. Hohenberg, Phys. Rev. Lett. 64, 749 (1990).
[CrossRef]

Vysloukh, V. A.

Wai, P. K. A.

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. 173, 233 (2009).
[CrossRef]

Williams, M. O.

Zezyulin, D. A.

Eur. Phys. J. (2)

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. 173, 233 (2009).
[CrossRef]

C. H. Tsang, B. A. Malomed, C. K. Lam, and K. W. Chow, Eur. Phys. J. 59, 81 (2010).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nat. Commun. (1)

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, Nat. Commun. 3, 1243 (2012).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. Lett. (5)

A. Hasegawa and Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[CrossRef]

V. Skarka, N. B. Aleksic, H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

W. van Saarloos and P. C. Hohenberg, Phys. Rev. Lett. 64, 749 (1990).
[CrossRef]

N. N. Akhmediev and V. V. Afanasjev, Phys. Rev. Lett. 75, 2320 (1995).
[CrossRef]

E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, Phys. Rev. Lett. 90, 253903 (2003).
[CrossRef]

Sov. Phys. Dokl. (1)

A. M. Sergeev and V. I. Petviashvili, Sov. Phys. Dokl. 29, 493 (1984).

Other (2)

N. Akhmediev and A. Ankiewicz, eds., Dissipative Solitons: From Optics to Biology and Medicine (Springer, 2008).

N. N. Rosanov, Spatial Hysteresis and Optical Patterns (Springer, 2002).

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Figures (5)

Fig. 1.
Fig. 1.

(a) and (b) Instantaneous field modulus distributions and current profiles in a dynamically oscillating soliton corresponding to the points marked by arrows in panel (c) that shows propagation dynamics at a=0.5, pi=1.8, Ω=π. The current in (a) and (b) is divided by 50 for illustrative purposes.

Fig. 2.
Fig. 2.

Soliton energy flow U and propagation constant b versus amplitude of gain oscillations a at Ω=2π for gain strength pi=1.8 (a) and pi=2.5 (b). U(a) dependence obtained with the effective gain model is shown by the line with circles. (c) U(pi) and b(pi) dependencies at Ω=2π, a=0.8. Solid lines—stable branches, dashed lines—unstable ones. (d) The domain of existence and stability on the plane (pi,a) at Ω=π. The line with circles shows acr obtained with the effective gain model. The dashed line shows the border of the stability domain in the static gain landscape.

Fig. 3.
Fig. 3.

Same as in Fig. 1 but for a two-channel gain landscape. The current in (a) and (b) is divided by 150 for illustrative purposes.

Fig. 4.
Fig. 4.

Field modulus distributions for solitons supported by the rotating gain landscapes with one (a), two (b), and three (c) amplifying channels. Arrows show the rotation direction of the amplifying channels. In all cases pi=2.8.

Fig. 5.
Fig. 5.

(a) Energy flow versus rotation frequency in one- and two-channel gain landscapes at pi=2.8. The circles correspond to solitons shown in Fig. 4. (b) Critical rotation frequency versus gain parameter for one-channel gain landscape. The dashed line indicates gain-guiding point for nonrotating gain.

Equations (2)

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iqξ=12Δq+q|q|2+i(piRγ)q.
Reff(η)=[1+(η21/2)a2]exp(η2),

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