305 research outputs found
Diffraction by a small aperture in conical geometry: Application to metal coated tips used in near-field scanning optical microscopy
Light diffraction through a subwavelength aperture located at the apex of a
metallic screen with conical geometry is investigated theoretically. A method
based on a multipole field expansion is developed to solve Maxwell's equations
analytically using boundary conditions adapted both for the conical geometry
and for the finite conductivity of a real metal. The topological properties of
the diffracted field are discussed in detail and compared to those of the field
diffracted through a small aperture in a flat screen, i. e. the Bethe problem.
The model is applied to coated, conically tapered optical fiber tips that are
used in Near-Field Scanning Optical Microscopy. It is demonstrated that such
tips behave over a large portion of space like a simple combination of two
effective dipoles located in the apex plane (an electric dipole and a magnetic
dipole parallel to the incident fields at the apex) whose exact expressions are
determined. However, the large "backward" emission in the P plane - a salient
experimental fact that remained unexplained so far - is recovered in our
analysis which goes beyond the two-dipole approximation.Comment: 21 pages, 6 figures, published in PRE in 200
Dynamics of light propagation in spatiotemporal dielectric structures
Propagation, transmission and reflection properties of linearly polarized
plane waves and arbitrarily short electromagnetic pulses in one-dimensional
dispersionless dielectric media possessing an arbitrary space-time dependence
of the refractive index are studied by using a two-component, highly symmetric
version of Maxwell's equations. The use of any slow varying amplitude
approximation is avoided. Transfer matrices of sharp nonstationary interfaces
are calculated explicitly, together with the amplitudes of all secondary waves
produced in the scattering. Time-varying multilayer structures and
spatiotemporal lenses in various configurations are investigated analytically
and numerically in a unified approach. Several new effects are reported, such
as pulse compression, broadening and spectral manipulation of pulses by a
spatiotemporal lens, and the closure of the forbidden frequency gaps with the
subsequent opening of wavenumber bandgaps in a generalized Bragg reflector
Modal Analysis and Coupling in Metal-Insulator-Metal Waveguides
This paper shows how to analyze plasmonic metal-insulator-metal waveguides
using the full modal structure of these guides. The analysis applies to all
frequencies, particularly including the near infrared and visible spectrum, and
to a wide range of sizes, including nanometallic structures. We use the
approach here specifically to analyze waveguide junctions. We show that the
full modal structure of the metal-insulator-metal (MIM) waveguides--which
consists of real and complex discrete eigenvalue spectra, as well as the
continuous spectrum--forms a complete basis set. We provide the derivation of
these modes using the techniques developed for Sturm-Liouville and generalized
eigenvalue equations. We demonstrate the need to include all parts of the
spectrum to have a complete set of basis vectors to describe scattering within
MIM waveguides with the mode-matching technique. We numerically compare the
mode-matching formulation with finite-difference frequency-domain analysis and
find very good agreement between the two for modal scattering at symmetric MIM
waveguide junctions. We touch upon the similarities between the underlying
mathematical structure of the MIM waveguide and the PT symmetric quantum
mechanical pseudo-Hermitian Hamiltonians. The rich set of modes that the MIM
waveguide supports forms a canonical example against which other more
complicated geometries can be compared. Our work here encompasses the microwave
results, but extends also to waveguides with real metals even at infrared and
optical frequencies.Comment: 17 pages, 13 figures, 2 tables, references expanded, typos fixed,
figures slightly modifie
Behavioral Responses to a Repetitive Visual Threat Stimulus Express a Persistent State of Defensive Arousal in Drosophila
The neural circuit mechanisms underlying emotion states remain poorly understood. Drosophila offers powerful genetic approaches for dissecting neural circuit function, but whether flies exhibit emotion-like behaviors has not been clear. We recently proposed that model organisms may express internal states displaying “emotion primitives,” which are general characteristics common to different emotions, rather than specific anthropomorphic emotions such as “fear” or “anxiety.” These emotion primitives include scalability, persistence, valence, and generalization to multiple contexts. Here, we have applied this approach to determine whether flies’ defensive responses to moving overhead translational stimuli (“shadows”) are purely reflexive or may express underlying emotion states. We describe a new behavioral assay in which flies confined in an enclosed arena are repeatedly exposed to an overhead translational stimulus. Repetitive stimuli promoted graded (scalable) and persistent increases in locomotor velocity and hopping, and occasional freezing. The stimulus also dispersed feeding flies from a food resource, suggesting both negative valence and context generalization. Strikingly, there was a significant delay before the flies returned to the food following stimulus-induced dispersal, suggestive of a slowly decaying internal defensive state. The length of this delay was increased when more stimuli were delivered for initial dispersal. These responses can be mathematically modeled by assuming an internal state that behaves as a leaky integrator of stimulus exposure. Our results suggest that flies’ responses to repetitive visual threat stimuli express an internal state exhibiting canonical emotion primitives, possibly analogous to fear in mammals. The mechanistic basis of this state can now be investigated in a genetically tractable insect species
Adaptive Filtering Enhances Information Transmission in Visual Cortex
Sensory neuroscience seeks to understand how the brain encodes natural
environments. However, neural coding has largely been studied using simplified
stimuli. In order to assess whether the brain's coding strategy depend on the
stimulus ensemble, we apply a new information-theoretic method that allows
unbiased calculation of neural filters (receptive fields) from responses to
natural scenes or other complex signals with strong multipoint correlations. In
the cat primary visual cortex we compare responses to natural inputs with those
to noise inputs matched for luminance and contrast. We find that neural filters
adaptively change with the input ensemble so as to increase the information
carried by the neural response about the filtered stimulus. Adaptation affects
the spatial frequency composition of the filter, enhancing sensitivity to
under-represented frequencies in agreement with optimal encoding arguments.
Adaptation occurs over 40 s to many minutes, longer than most previously
reported forms of adaptation.Comment: 20 pages, 11 figures, includes supplementary informatio
Generalized Huygens principle with pulsed-beam wavelets
Huygens' principle has a well-known problem with back-propagation due to the
spherical nature of the secondary wavelets. We solve this by analytically
continuing the surface of integration. If the surface is a sphere of radius
, this is done by complexifying to . The resulting complex sphere
is shown to be a real bundle of disks with radius tangent to the sphere.
Huygens' "secondary source points" are thus replaced by disks, and his
spherical wavelets by well-focused pulsed beams propagating outward. This
solves the back-propagation problem. The extended Huygens principle is a
completeness relation for pulsed beams, giving a representation of a general
radiation field as a superposition of such beams. Furthermore, it naturally
yields a very efficient way to compute radiation fields because all pulsed
beams missing a given observer can be ignored. Increasing sharpens the
focus of the pulsed beams, which in turn raises the compression of the
representation.Comment: 49 pages, 14 figure
Neural Decision Boundaries for Maximal Information Transmission
We consider here how to separate multidimensional signals into two
categories, such that the binary decision transmits the maximum possible
information transmitted about those signals. Our motivation comes from the
nervous system, where neurons process multidimensional signals into a binary
sequence of responses (spikes). In a small noise limit, we derive a general
equation for the decision boundary that locally relates its curvature to the
probability distribution of inputs. We show that for Gaussian inputs the
optimal boundaries are planar, but for non-Gaussian inputs the curvature is
nonzero. As an example, we consider exponentially distributed inputs, which are
known to approximate a variety of signals from natural environment.Comment: 5 pages, 3 figure
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