TY - JOUR
T1 - Localized modes in dissipative lattice media
T2 - An overview
AU - He, Yingji
AU - Malomed, Boris A.
AU - Mihalache, Dumitru
N1 - Publisher Copyright:
© 2014 The Author(s) Published by the Royal Society.
PY - 2014/10/28
Y1 - 2014/10/28
N2 - We give an overview of recent theoretical studies of the dynamics of one- and two-dimensional spatial dissipative solitons in models based on the complex Ginzburg-Landau equations with the cubic-quintic combination of loss and gain terms, which include imaginary, real or complex spatially periodic potentials. The imaginary potential represents periodic modulation of the local loss and gain. It is shown that the effective gradient force, induced by the inhomogeneous loss distribution, gives rise to three generic propagation scenarios for one-dimensional dissipative solitons: transverse drift, persistent swing motion, and damped oscillations. When the lattice-average loss/gain value is zero, and the real potential has spatial parity opposite to that of the imaginary component, the respective complex potential is a realization of the parity-time symmetry. Under the action of lattice potentials of the latter type, one-dimensional solitons feature motion regimes in the form of the transverse drift and persistent swing. In the two-dimensional geometry, three types of axisymmetric radial lattices are considered, namely those based solely on the refractive-index modulation, or solely on the linear-loss modulation, or on a combination of both. The rotary motion of solitons in such axisymmetric potentials can be effectively controlled by varying the strength of the initial tangential kick.
AB - We give an overview of recent theoretical studies of the dynamics of one- and two-dimensional spatial dissipative solitons in models based on the complex Ginzburg-Landau equations with the cubic-quintic combination of loss and gain terms, which include imaginary, real or complex spatially periodic potentials. The imaginary potential represents periodic modulation of the local loss and gain. It is shown that the effective gradient force, induced by the inhomogeneous loss distribution, gives rise to three generic propagation scenarios for one-dimensional dissipative solitons: transverse drift, persistent swing motion, and damped oscillations. When the lattice-average loss/gain value is zero, and the real potential has spatial parity opposite to that of the imaginary component, the respective complex potential is a realization of the parity-time symmetry. Under the action of lattice potentials of the latter type, one-dimensional solitons feature motion regimes in the form of the transverse drift and persistent swing. In the two-dimensional geometry, three types of axisymmetric radial lattices are considered, namely those based solely on the refractive-index modulation, or solely on the linear-loss modulation, or on a combination of both. The rotary motion of solitons in such axisymmetric potentials can be effectively controlled by varying the strength of the initial tangential kick.
KW - Complex Ginzburg-Landau equation
KW - Dissipative lattices
KW - Localized nonlinear modes
KW - Parity-time symmetry
UR - http://www.scopus.com/inward/record.url?scp=84908099599&partnerID=8YFLogxK
U2 - 10.1098/rsta.2014.0017
DO - 10.1098/rsta.2014.0017
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C2 - 25246672
AN - SCOPUS:84908099599
SN - 1364-503X
VL - 372
JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2027
M1 - 0017
ER -