808 research outputs found
Edge waves and localisation in lattices containing tilted resonators
The paper presents the study of waves in a structured geometrically chiral
solid. A special attention is given to the analysis of the Bloch-Floquet waves
in a doubly periodic high-contrast lattice containing tilted resonators.
Dirac-like dispersion of Bloch waves in the structure is identified, studied
and applied to wave-guiding and wave-defect interaction problems. The work is
extended to the transmission problems and models of fracture, where
localisation and edge waves occur. The theoretical derivations are accompanied
with numerical simulations and illustrations
Anderson localization in metamaterials and other complex media
We review some recent (mostly ours) results on the Anderson localization of
light and electron waves in complex disordered systems, including: (i)
left-handed metamaterials, (ii) magneto-active optical structures, (iii)
graphene superlattices, and (iv) nonlinear dielectric media. First, we
demonstrate that left-handed metamaterials can significantly suppress
localization of light and lead to an anomalously enhanced transmission. This
suppression is essential at the long-wavelength limit in the case of normal
incidence, at specific angles of oblique incidence (Brewster anomaly), and in
the vicinity of the zero-epsilon or zero-mu frequencies for dispersive
metamaterials. Remarkably, in disordered samples comprised of alternating
normal and left-handed metamaterials, the reciprocal Lyapunov exponent and
reciprocal transmittance increment can differ from each other. Second, we study
magneto-active multilayered structures, which exhibit nonreciprocal
localization of light depending on the direction of propagation and on the
polarization. At resonant frequencies or realizations, such nonreciprocity
results in effectively unidirectional transport of light. Third, we discuss the
analogy between the wave propagation through multilayered samples with
metamaterials and the charge transport in graphene, which enables a simple
physical explanation of unusual conductive properties of disordered graphene
superlatices. We predict disorder-induced resonances of the transmission
coefficient at oblique incidence of the Dirac quasiparticles. Finally, we
demonstrate that an interplay of nonlinearity and disorder in dielectric media
can lead to bistability of individual localized states excited inside the
medium at resonant frequencies. This results in nonreciprocity of the wave
transmission and unidirectional transport of light.Comment: 37 pages, 30 figures, Review pape
Asymptotic theory of microstructured surfaces: An asymptotic theory for waves guided by diffraction gratings or along microstructured surfaces
An effective surface equation, that encapsulates the detail of a
microstructure, is developed to model microstructured surfaces. The equations
deduced accurately reproduce a key feature of surface wave phenomena, created
by periodic geometry, that are commonly called Rayleigh-Bloch waves, but which
also go under other names such as Spoof Surface Plasmon Polaritons in
photonics. Several illustrative examples are considered and it is shown that
the theory extends to similar waves that propagate along gratings. Line source
excitation is considered and an implicit long-scale wavelength is identified
and compared to full numerical simulations. We also investigate non-periodic
situations where a long-scale geometric variation in the structure is
introduced and show that localised defect states emerge which the asymptotic
theory explains
Spoof surface plasmons guided by narrow grooves
An approximate description of surface waves propagating along periodically
grooved surfaces is intuitively developed in the limit where the grooves are
narrow relative to the period. Considering acoustic and electromagnetic waves
guided by rigid and perfectly conducting gratings, respectively, the wave field
is obtained by interrelating elementary approximations obtained in three
overlapping spatial domains. Specifically, above the grating and on the scale
of the period the grooves are effectively reduced to point resonators
characterised by their dimensions as well as the geometry of their apertures.
Along with this descriptive physical picture emerges an analytical dispersion
relation, which agrees remarkably well with exact calculations and improves on
preceding approximations. Scalings and explicit formulae are obtained by
simplifying the theory in three distinguished propagation regimes, namely where
the Bloch wavenumber is respectively smaller than, close to, or larger than
that corresponding to a groove resonance. Of particular interest is the latter
regime where the field within the grooves is resonantly enhanced and the field
above the grating is maximally localised, attenuating on a length scale
comparable with the period
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Instabilities in free-surface electroosmotic flows
This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.With the recent development of novel microfluidic devices electroosmotic flows with fluid/fluid interfaces have emerged as very important subjects of investigation. Two immiscible fluids may need to be
transported in a microchannel, or one side of a channel may be open to air for various purposes, including adsorption of airborne molecules to liquid for high-sensitivity substance detection. The liquid/liquid or
liquid/gas interface in these cases can deform, resulting in significant corrugations followed sometimes by incipient rupture of liquid layers. For electroosmotic flow the rupture, leading to shortcircuit, can cause overall failure of the device. It is thus imperative to know the conditions for the rupture as well as the initial interfacial instability. Studies based on the Debye-Huckle approximation reveal that all free-surface electroosmotic flows of thickness larger than the Debye screening length are unstable and selectively lead to
rupture. Layers of the order of Debye screening length, however, are not properly described by the Debye-Huckle approximation. Even for micro-scale layers, the rupture phenomenon can make local layer
thickness to be nanoscale. A fully coupled system of hydrodynamics, electric field, and ionic distribution need to be analyzed. In this paper linear instability and subsequent nonlinear developments of a nanoscale free-surface electroosmotic flow are reported.This study is sponsored by the Ministry of Education, Science and Technology of Korea through the World Class University Grant
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