8,543 research outputs found
Topological Photonic Phase in Chiral Hyperbolic Metamaterials
Recently the possibility of achieving one-way backscatter immune
transportation of light by mimicking the topological order present within
certain solid state systems, such as topological insulators, has received much
attention. Thus far however, demonstrations of non-trivial topology in
photonics have relied on photonic crystals with precisely engineered lattice
structures, periodic on the scale of the operational wavelength and composed of
finely tuned, complex materials. Here we propose a novel effective medium
approach towards achieving topologically protected photonic surface states
robust against disorder on all length scales and for a wide range of material
parameters. Remarkably, the non-trivial topology of our metamaterial design
results from the Berry curvature arising from the transversality of
electromagnetic waves in a homogeneous medium. Our investigation therefore acts
to bridge the gap between the advancing field of topological band theory and
classical optical phenomena such as the Spin Hall effect of light. The
effective medium route to topological phases will pave the way for highly
compact one-way transportation of electromagnetic waves in integrated photonic
circuits.Comment: 11 pages, 3 figures. To appear in PR
Lattice symmetry breaking perturbations for spiral waves
Spiral waves in two-dimensional excitable media have been observed
experimentally and studied extensively. It is now well-known that the symmetry
properties of the medium of propagation drives many of the dynamics and
bifurcations which are experimentally observed for these waves. Also,
symmetry-breaking induced by boundaries, inhomogeneities and anisotropy have
all been shown to lead to different dynamical regimes as to that which is
predicted for mathematical models which assume infinite homogeneous and
isotropic planar geometry. Recent mathematical analyses incorporating the
concept of forced symmetry-breaking from the Euclidean group of all planar
translations and rotations have given model-independent descriptions of the
effects of media imperfections on spiral wave dynamics. In this paper, we
continue this program by considering rotating waves in dynamical systems which
are small perturbations of a Euclidean-equivariant dynamical system, but for
which the perturbation preserves only the symmetry of a regular square lattice
Forced Symmetry Breaking from SO(3) to SO(2) for Rotating Waves on the Sphere
We consider a small SO(2)-equivariant perturbation of a reaction-diffusion
system on the sphere, which is equivariant with respect to the group SO(3) of
all rigid rotations. We consider a normally hyperbolic SO(3)-group orbit of a
rotating wave on the sphere that persists to a normally hyperbolic
SO(2)-invariant manifold . We investigate the effects of this
forced symmetry breaking by studying the perturbed dynamics induced on
by the above reaction-diffusion system. We prove that depending
on the frequency vectors of the rotating waves that form the relative
equilibrium SO(3)u_{0}, these rotating waves will give SO(2)-orbits of rotating
waves or SO(2)-orbits of modulated rotating waves (if some transversality
conditions hold). The orbital stability of these solutions is established as
well. Our main tools are the orbit space reduction, Poincare map and implicit
function theorem
Unidirectional and diffractionless surface plasmon-polaritons on three-dimensional nonreciprocal plasmonic platforms
Light-matter interactions in conventional nanophotonic structures typically
lack directionality. Furthermore, surface waves supported by conventional
material substrates do not usually have a preferential direction of
propagation, and their wavefront tends to spread as it propagates along the
surface, unless the surface or the excitation are properly engineered and
structured. In this article, we theoretically demonstrate the possibility of
realizing \emph{unidirectional and diffractionless surface-plasmon-polariton
modes} on a nonreciprocal platform, namely, a gyrotropic magnetized plasma.
Based on a rigorous Green function approach, we provide a comprehensive and
systematic analysis of all the available physical mechanisms that may bestow
the system with directionality, both in the sense of one-way excitation of
surface waves, and in the sense of directive diffractionless propagation along
the surface. The considered mechanisms include (i) the effect of strong and
weak forms of nonreciprocity, (ii) the elliptic-like or hyperbolic-like
topology of the modal dispersion surfaces, and (iii) the source polarization
state, with the associated possibility of chiral surface-wave excitation
governed by angular-momentum matching. We find that three-dimensional
gyrotropic plasmonic platforms support a previously-unnoticed wave-propagation
regime that exhibit several of these physical mechanisms simultaneously,
allowing us to theoretically demonstrate, for the first time, unidirectional
surface-plasmon-polariton modes that propagate as a single ultra-narrow
diffractionless beam. We also assess the impact of dissipation and nonlocal
effects. Our theoretical findings may enable a new generation of plasmonic
structures and devices with highly directional response
Multidimensional simple waves in fully relativistic fluids
A special version of multi--dimensional simple waves given in [G. Boillat,
{\it J. Math. Phys.} {\bf 11}, 1482-3 (1970)] and [G.M. Webb, R. Ratkiewicz, M.
Brio and G.P. Zank, {\it J. Plasma Phys.} {\bf 59}, 417-460 (1998)] is employed
for fully relativistic fluid and plasma flows. Three essential modes: vortex,
entropy and sound modes are derived where each of them is different from its
nonrelativistic analogue. Vortex and entropy modes are formally solved in both
the laboratory frame and the wave frame (co-moving with the wave front) while
the sound mode is formally solved only in the wave frame at ultra-relativistic
temperatures. In addition, the surface which is the boundary between the
permitted and forbidden regions of the solution is introduced and determined.
Finally a symmetry analysis is performed for the vortex mode equation up to
both point and contact transformations. Fundamental invariants and a form of
general solutions of point transformations along with some specific examples
are also derived.Comment: 21 page
Dam break problem for the focusing nonlinear Schr\"odinger equation and the generation of rogue waves
We propose a novel, analytically tractable, scenario of the rogue wave
formation in the framework of the small-dispersion focusing nonlinear
Schr\"odinger (NLS) equation with the initial condition in the form of a
rectangular barrier (a "box"). We use the Whitham modulation theory combined
with the nonlinear steepest descent for the semi-classical inverse scattering
transform, to describe the evolution and interaction of two counter-propagating
nonlinear wave trains --- the dispersive dam break flows --- generated in the
NLS box problem. We show that the interaction dynamics results in the emergence
of modulated large-amplitude quasi-periodic breather lattices whose amplitude
profiles are closely approximated by the Akhmediev and Peregrine breathers
within certain space-time domain. Our semi-classical analytical results are
shown to be in excellent agreement with the results of direct numerical
simulations of the small-dispersion focusing NLS equation.Comment: 29 pages, 15 figures, major revisio
Dynamics of a hyperbolic system that applies at the onset of the oscillatory instability
A real hyperbolic system is considered that applies near the onset of the oscillatory instability in large spatial domains. The validity of that system requires that some intermediate scales (large compared with the basic wavelength of the unstable modes but small compared with the size of the system) remain inhibited; that condition is analysed in some detail. The dynamics associated with the hyperbolic system is fully analysed to conclude that it is very simple if the coefficient of the cross-nonlinearity is such that , while the system exhibits increasing complexity (including period-doubling sequences, quasiperiodic transitions, crises) as the bifurcation parameter grows if ; if then the system behaves subcritically. Our results are seen to compare well, both qualitatively and quantitatively, with the experimentally obtained ones for the oscillatory instability of straight rolls in pure Rayleigh - Bénard convection
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