33 research outputs found
Optimization in the Natural Sciences: 30th Euro Mini-Conference, EmC-ONS 2014, Aveiro, Portugal, February 5-9, 2014: revised selected papers
This book constitutes the refereed proceedings of the 30th Euro Mini-Conference, EmC-ONS 2014, held in Aveiro, Portugal, in February 2014. The 13 revised full papers presented were carefully reviewed and selected from 70 submissions. The papers are organized in topical sections on dynamical systems; optimization and applications; modeling and statistical techniques for data analysis
Focusing: coming to the point in metamaterials
The point of the paper is to show some limitations of geometrical optics in
the analysis of subwavelength focusing. We analyze the resolution of the image
of a line source radiating in the Maxwell fisheye and the Veselago-Pendry slab
lens. The former optical medium is deduced from the stereographic projection of
a virtual sphere and displays a heterogeneous refractive index n(r) which is
proportional to the inverse of 1+r^2. The latter is described by a homogeneous,
but negative, refractive index. It has been suggested that the fisheye makes a
perfect lens without negative refraction [Leonhardt, Philbin
arxiv:0805.4778v2]. However, we point out that the definition of
super-resolution in such a heterogeneous medium should be computed with respect
to the wavelength in a homogenized medium, and it is perhaps more adequate to
talk about a conjugate image rather than a perfect image (the former does not
necessarily contains the evanescent components of the source). We numerically
find that both the Maxwell fisheye and a thick silver slab lens lead to a
resolution close to lambda/3 in transverse magnetic polarization (electric
field pointing orthogonal to the plane). We note a shift of the image plane in
the latter lens. We also observe that two sources lead to multiple secondary
images in the former lens, as confirmed from light rays travelling along
geodesics of the virtual sphere. We further observe resolutions ranging from
lambda/2 to nearly lambda/4 for magnetic dipoles of varying orientations of
dipole moments within the fisheye in transverse electric polarization (magnetic
field pointing orthogonal to the plane). Finally, we analyse the Eaton lens for
which the source and its image are either located within a unit disc of air, or
within a corona 1<r<2 with refractive index . In both cases,
the image resolution is about lambda/2.Comment: Version 2: 22 pages, 11 figures. More figures added, additional cases
discussed. Misprints corrected. Keywords: Maxwell fisheye, Eaton lens;
Non-Euclidean geometry; Stereographic projection; Transformation optics;
Metamaterials; Perfect lens. The last version appears at J. Modern Opt. 57
(2010), no. 7, 511-52
Controlling surface plasmon polaritons in transformed coordinates
Transformational optics allow for a markedly enhanced control of the
electromagnetic wave trajectories within metamaterials with interesting
applications ranging from perfect lenses to invisibility cloaks, carpets,
concentrators and rotators. Here, we present a review of curved anisotropic
heterogeneous meta-surfaces designed using the tool of transformational
plasmonics, in order to achieve a similar control for surface plasmon
polaritons in cylindrical and conical carpets, as well as cylindrical cloaks,
concentrators and rotators of a non-convex cross-section. Finally, we provide
an asymptotic form of the geometric potential for surface plasmon polaritons on
such surfaces in the limit of small curvature.Comment: 14 pages, 9 figure
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A demonstration of 'broken' visual space
It has long been assumed that there is a distorted mapping between real and âperceivedâ space, based on demonstrations of systematic errors in judgements of slant, curvature, direction and separation. Here, we have applied a direct test to the notion of a coherent visual space. In an immersive virtual environment, participants judged the relative distance of two squares displayed in separate intervals. On some trials, the virtual scene expanded by a factor of four between intervals although, in line with recent results, participants did not report any noticeable change in the scene. We found that there was no consistent depth ordering of objects that can explain the distance matches participants made in this environment (e.g. A > B > D yet also A < C < D) and hence no single one-to-one mapping between participantsâ perceived space and any real 3D environment. Instead, factors that affect pairwise comparisons of distances dictate participantsâ performance. These data contradict, more directly than previous experiments, the idea that the visual system builds and uses a coherent 3D internal representation of a scene
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Modelling human visual navigation using multi-view scene reconstruction
It is often assumed that humans generate a 3D reconstruction of the environment, either in egocentric or world-based coordinates, but the steps involved are unknown. Here, we propose two reconstruction-based models, evaluated using data from two tasks in immersive virtual reality. We model the observerâs prediction of landmark location based on standard photogrammetric methods and then combine location predictions to compute likelihood maps of navigation behaviour. In one model, each scene point is treated independently in the reconstruction; in the other, the pertinent variable is the spatial relationship between pairs of points. Participants viewed a simple environment from one location, were transported (virtually) to another part of the scene and were asked to navigate back. Error distributions varied substantially with changes in scene layout; we compared these directly with the likelihood maps to quantify the success of the models. We also measured error distributions when participants manipulated the location of a landmark to match the preceding interval, providing a direct test of the landmark-location stage of the navigation models. Models such as this, which start with scenes and end with a probabilistic prediction of behaviour, are likely to be increasingly useful for understanding 3D vision