## Continuous emission of fundamental solitons from vortices in dissipative media by a radial-azimuthal potential |

Optics Express, Vol. 21, Issue 5, pp. 5561-5566 (2013)

http://dx.doi.org/10.1364/OE.21.005561

Enhanced HTML Acrobat PDF (2573 KB)

### Abstract

We report novel dynamical regimes of dissipative vortices supported by a radial-azimuthal potential (RAP) in the 2D complex Ginzburg-Landau (CGL) equation with the cubic-quintic nonlinearity. First, the stable solutions of vortices with intrinsic vorticity *S* = 1 and 2 are obtained in the CGL equation without potential. The RAP is a model of an active optical medium with respective expanding anti-waveguiding structures with *m* (integer) annularly periodic modulation. If the potential is strong enough, *m* jets fundamental of solitons are continuously emitted from the vortices. The influence of *m*, diffusivity term (viscosity) *β*, and cubic-gain coefficient *ε* on the dynamic region is studied. For a weak potential, the shape of vortices are stretched into the polygon, such as square for *m* = 4. But for a stronger potential, the vortices will be broke into *m* fundamental solitons.

© 2013 OSA

**OCIS Codes**

(190.0190) Nonlinear optics : Nonlinear optics

(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: December 4, 2012

Revised Manuscript: January 14, 2013

Manuscript Accepted: January 14, 2013

Published: February 27, 2013

**Citation**

Bin Liu, Xing-Dao He, and Shu-Jing Li, "Continuous emission of fundamental solitons from vortices in dissipative media by a radial-azimuthal potential," Opt. Express **21**, 5561-5566 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-5561

Sort: Year | Journal | Reset

### References

- C. López-Mariscal and J. C. Gutiérrez-Vega, “In your phase: all about optical vortices,” Opt. Photonics News20(5), 10–13 (2009).
- I. S. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys.74(1), 99–143 (2002). [CrossRef]
- N. Rosanov, “Solitons in laser systems with absorption,” in Dissipative Solitons, N. Akhmediev and A. Ankievicz, eds. (Springer-Verlag, Berlin, 2005).
- B. A. Malomed, “Complex Ginzburg–Landau equation,” in Encyclopedia of Nonlinear Science, A. Scott, ed. (Routledge, New York, 2005), p. 157.
- N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Stable soliton pairs in optical transmission lines and fiber lasers,” J. Opt. Soc. Am. B15(2), 515–522 (1998). [CrossRef]
- L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.63(1 Pt 2), 016605 (2001). [PubMed]
- J. M. Soto-Crespo, N. Akhmediev, C. Mejia-Cortés, and N. Devine, “Dissipative ring solitons with vorticity,” Opt. Express17(6), 4236–4250 (2009). [CrossRef] [PubMed]
- D. V. Skryabin and A. G. Vladimirov, “Vortex induced rotation of clusters of localized states in the complex Ginzburg-Landau equation,” Phys. Rev. Lett.89(4), 044101 (2002). [CrossRef] [PubMed]
- J. M. Soto-Crespo, P. Grelu, and N. Akhmediev, “Optical bullets and “rockets” in nonlinear dissipative systems and their transformations and interactions,” Opt. Express14(9), 4013–4025 (2006). [CrossRef] [PubMed]
- 10D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. A75, 033811 (2007).
- D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. A77(3), 033817 (2008). [CrossRef]
- B. Liu, Y. J. He, Z. R. Qiu, and H. Z. Wang, “Annularly and radially phase-modulated spatiotemporal necklace-ring patterns in the Ginzburg-Landau and Swift-Hohenberg equations,” Opt. Express17(15), 12203–12209 (2009). [CrossRef] [PubMed]
- B. Liu, X. D. He, and S. J. Li, “Phase controlling of collisions between solitons in the two-dimensional complex Ginzburg-Landau equation without viscosity,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.84(5), 056607 (2011). [CrossRef] [PubMed]
- D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stablevotex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett.97, 073904 (2006).
- D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability limits for three-dimensional vortex solitons in the Ginzburg-Landau equation with the cubic-quintic nonlinearity,” Phys. Rev. A76, 045803 (2007).
- H. Leblond, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the Ginzburg-Landau model of two-dimensional lasing medium with a transverse grating,” Phys. Rev. A80(3), 033835 (2009). [CrossRef]
- H. Sakaguchi and B. A. Malomed, “Two-dimensional dissipative gap solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.80(2), 026606 (2009). [CrossRef] [PubMed]
- Y. J. He, B. A. Malomed, D. Mihalache, B. Liu, H. C. Huang, H. Yang, and H. Z. Wang, “Bound states of one-, two-, and three-dimensional solitons in complex Ginzburg-Landau equations with a linear potential,” Opt. Lett.34(19), 2976–2978 (2009). [CrossRef] [PubMed]
- B. Liu, Y. J. He, B. A. Malomed, X. S. Wang, P. G. Kevrekidis, T. B. Wang, F. C. Leng, Z. R. Qiu, and H. Z. Wang, “Continuous generation of soliton patterns in two-dimensional dissipative media by razor, dagger, and needle potentials,” Opt. Lett.35(12), 1974–1976 (2010). [CrossRef] [PubMed]
- D. Mihalache, “Three-dimensional Ginzburg-Landau dissipative solitons supported by a two-dimensional transverse grating,” Proc. Romanian Acad. Ser. A11(2), 142–147 (2010).
- B. Liu and X. D. He, “Continuous generation of “light bullets” in dissipative media by an annularly periodic potential,” Opt. Express19(21), 20009–20014 (2011). [CrossRef] [PubMed]
- Y. J. He, B. A. Malomed, F. Ye, J. Dong, Z. Qiu, H. Z. Wang, and B. Hu, “Splitting broad beams into arrays of dissipative satial solitns by material and virtual gratings,” Phys. Scr.82(6), 065404 (2010). [CrossRef]
- C. P. Yin, D. Mihalache, and Y. J. He, “Dynamics of two-dimensional dissipative spatial solitons interacting with an umbrella-shaped potential,” J. Opt. Soc. Am. B28(2), 342–346 (2011).
- Y. J. He, D. Mihalache, B. A. Malomed, Y. Qiu, Z. Chen, and Y. Li, “Generation of polygonal soliton clusters and fundamental solitons in dissipative systems by necklace-ring beams with radial-azimuthal phase modulation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.85(6), 066206 (2012). [CrossRef] [PubMed]
- D. Mihalache, D. Mazilu, V. Skarka, B. Malomed, H. Leblond, N. Aleksić, and F. Lederer, “Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials,” Phys. Rev. A82(2), 023813 (2010). [CrossRef]
- V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, “Varieties of Stable Vortical Solitons in Ginzburg-Landau Media with Radially Inhomogeneous Losses,” Phys. Rev. Lett.105(21), 213901 (2010). [CrossRef] [PubMed]
- D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Solitons in a medium with linear dissipation and localized gain,” Opt. Lett.36(7), 1200–1202 (2011). [CrossRef] [PubMed]
- C. Cleff, B. Gütlich, and C. Denz, “Gradient Induced Motion Control of Drifting Solitary Structures in a Nonlinear Optical Single Feedback Experiment,” Phys. Rev. Lett.100(23), 233902 (2008). [CrossRef] [PubMed]
- A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica,” Opt. Express14(13), 6055–6062 (2006). [CrossRef] [PubMed]
- J. Lega, J. V. Moloney, and A. C. Newell, “Swift-Hohenberg equation for Lasers,” Phys. Rev. Lett.73(22), 2978–2981 (1994). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.