Articleshttp://nur.nu.edu.kz:80/handle/123456789/9042021-06-15T19:42:12Z2021-06-15T19:42:12ZThe Asymmetric Active Coupler: Stable Nonlinear Supermodes and Directed TransportKominis, YannisBountis, TassosFlach, Sergejhttp://nur.nu.edu.kz:80/handle/123456789/34012018-08-23T21:00:40Z2016-09-19T00:00:00ZThe Asymmetric Active Coupler: Stable Nonlinear Supermodes and Directed Transport
Kominis, Yannis; Bountis, Tassos; Flach, Sergej
We consider the asymmetric active coupler (AAC) consisting of two coupled dissimilar waveguides with
gain and loss. We show that under generic conditions, not restricted by parity-time symmetry, there
exist finite-power, constant-intensity nonlinear supermodes (NS), resulting from the balance between
gain, loss, nonlinearity, coupling and dissimilarity. The system is shown to possess non-reciprocal
dynamics enabling directed power transport functionality.
2016-09-19T00:00:00ZThe effect of long–range interactions on the dynamics and statistics of 1D Hamiltonian lattices with on–site potentialChristodoulidi, H.Bountis, TassosDrossos, L.http://nur.nu.edu.kz:80/handle/123456789/34002018-08-23T21:00:43Z2018-04-01T00:00:00ZThe effect of long–range interactions on the dynamics and statistics of 1D Hamiltonian lattices with on–site potential
Christodoulidi, H.; Bountis, Tassos; Drossos, L.
We examine the role of long–range interactions on the dynamical and statistical properties of two
1D lattices with on–site potentials that are known to support discrete breathers: the Klein–Gordon
(KG) lattice which includes linear dispersion and the Gorbach–Flach (GF) lattice, which shares the
same on–site potential but its dispersion is purely nonlinear. In both models under the implementation
of long–range interactions (LRI) we find that single–site excitations lead to special low–dimensional
solutions, which are well described by the undamped Duffing oscillator. For random initial conditions
we observe that the maximal Lyapunov exponent scales as N−0.12 in the KG model and as N−0.27 in
the GF with LRI, suggesting in that case an approach to integrable behavior towards the thermodynamic
limit. Furthermore, under LRI, their non-Gaussian momentum distributions are distinctly different from
those of the FPU model.
2018-04-01T00:00:00ZStability through asymmetry: Modulationally stable nonlinear supermodes of asymmetric non-Hermitian optical couplersKominis, YannisBountis, TassosFlach, Sergejhttp://nur.nu.edu.kz:80/handle/123456789/33992018-08-23T21:00:38Z2017-06-21T00:00:00ZStability through asymmetry: Modulationally stable nonlinear supermodes of asymmetric non-Hermitian optical couplers
Kominis, Yannis; Bountis, Tassos; Flach, Sergej
We analyze the stability of a non-Hermitian coupler with respect to modulational inhomogeneous perturbations
in the presence of unbalanced gain and loss. At the parity-time (PT ) symmetry point the coupler is unstable.
Suitable symmetry breakings lead to an asymmetric coupler, which hosts nonlinear supermodes. A subset of these
broken symmetry cases finally yields nonlinear supermodes which are stable against modulational perturbations.
The lack of symmetry requirements is expected to facilitate experimental implementations and relevant photonics
applications.
2017-06-21T00:00:00ZSpectral Signatures of Exceptional Points and Bifurcations in the Fundamental Active Photonic DimerKominis, YannisKovanis, VassiliosBountis, Tassoshttp://nur.nu.edu.kz:80/handle/123456789/33982018-08-23T21:00:33Z2018-08-01T00:00:00ZSpectral Signatures of Exceptional Points and Bifurcations in the Fundamental Active Photonic Dimer
Kominis, Yannis; Kovanis, Vassilios; Bountis, Tassos
The fundamental active photonic dimer consisting of two coupled quantum well lasers is inves-
tigated in the context of the rate equation model. Spectral transition properties and exceptional
points are shown to occur under general conditions, not restricted by PT-symmetry as in coupled
mode models, suggesting a paradigm shift in the field of non-Hermitian photonics. The opti-
cal spectral signatures of system bifurcations and exceptional points are manifested in terms of
self-termination effects and observable drastic variations of the spectral line shape that can be
controlled in terms of optical detuning and inhomogeneous pumping.
2018-08-01T00:00:00ZLotka–Volterra systems satisfying a strong Painlevé propertyBountis, TassosVanhaecke, Polhttp://nur.nu.edu.kz:80/handle/123456789/33972018-08-23T21:00:37Z2016-09-01T00:00:00ZLotka–Volterra systems satisfying a strong Painlevé property
Bountis, Tassos; Vanhaecke, Pol
We use a strong version of the Painlevé property to discover and characterize a new class of n-dimensional Hamiltonian Lotka–Volterra systems, which turn out to be Liouville integrable as well as superintegrable. These systems are in fact Nambu systems, they posses Lax equations and they can be explicitly integrated in terms of elementary functions. We apply our analysis to systems containing only quadratic nonlinearities of the form aijxixj, i =j, and require that all variables diverge as t−1. We also require that the leading terms depend on n −2free parameters. We thus discover a cocycle relation among the coefficients aijof the equations of motion and by integrating the cocycle equations we show that they are equivalent to the above strong version of the Painlevé property. We also show that these systems remain explicitly solvable even if a linear term bixiis added to the i-th equation, even though this violates the Painlevé property, as logarithmic singularities are introduced in the Laurent solutions, at the first terms following the leading order pole.
2016-09-01T00:00:00ZHomoclinic Points of 2-D and 4-D Maps via the Parametrization MethodAnastassiou, StavrosBountis, TassosB¨acker, Arndhttp://nur.nu.edu.kz:80/handle/123456789/33962018-08-23T21:00:30Z2017-09-01T00:00:00ZHomoclinic Points of 2-D and 4-D Maps via the Parametrization Method
Anastassiou, Stavros; Bountis, Tassos; B¨acker, Arnd
An interesting problem in solid state physics is to compute discrete breather
solutions in N coupled 1–dimensional Hamiltonian particle chains and investigate
the richness of their interactions. One way to do this is to compute the homoclinic
intersections of invariant manifolds of a saddle point located at the origin of a class
of 2N–dimensional invertible maps. In this paper we apply the parametrization
method to express these manifolds analytically as series expansions and compute
their intersections numerically to high precision. We first carry out this procedure
for a 2–dimensional (2–D) family of generalized H´enon maps (N = 1), prove the
existence of a hyperbolic set in the non-dissipative case and show that it is directly
connected to the existence of a homoclinic orbit at the origin. Introducing dissipation
we demonstrate that a homoclinic tangency occurs beyond which the homoclinic
intersection disappears. Proceeding to N = 2, we use the same approach to accurately
determine the homoclinic intersections of the invariant manifolds of a saddle point at
the origin of a 4–D map consisting of two coupled 2–D cubic H´enon maps. For small
values of the coupling we determine the homoclinic intersection, which ceases to exist
once a certain amount of dissipation is present. We discuss an application of our results
to the study of discrete breathers in two linearly coupled 1–dimensional particle chains
with nearest–neighbor interactions and a Klein–Gordon on site potential.
2017-09-01T00:00:00Z