339 research outputs found
Neural substrates of sensory-guided locomotor decisions in the rat superior colliculus
Deciding in which direction to move is a ubiquitous feature of animal behavior, but the neural substrates of locomotor choices are not well understood. The superior colliculus (SC) is a midbrain structure known to be important for controlling the direction of gaze, particularly when guided by visual or auditory cues, but which may play a more general role in behavior involving spatial orienting. To test this idea, we recorded and manipulated activity in the SC of freely moving rats performing an odor-guided spatial choice task. In this context, not only did a substantial majority of SC neurons encode choice direction during goal-directed locomotion, but many also predicted the upcoming choice and maintained selectivity for it after movement completion. Unilateral inactivation of SC activity profoundly altered spatial choices. These results indicate that the SC processes information necessary for spatial locomotion, suggesting a broad role for this structure in sensory-guided orienting and navigation
Radiation from elementary sources in a uniaxial wire medium
We investigate the radiation properties of two types of elementary sources
embedded in a uniaxial wire medium: a short dipole parallel to the wires and a
lumped voltage source connected across a gap in a generic metallic wire. It is
demonstrated that the radiation pattern of these elementary sources have quite
anomalous and unusual properties. Specifically, the radiation pattern of a
short vertical dipole resembles that of an isotropic radiator close to the
effective plasma frequency of the wire medium, whereas the radiation from the
lumped voltage generator is characterized by an infinite directivity and a
non-diffractive far-field distribution.Comment: 10 pages, 4 figure
On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree
In our recent works [R. Szmytkowski, J. Phys. A 39 (2006) 15147; corrigendum:
40 (2007) 7819; addendum: 40 (2007) 14887], we have investigated the derivative
of the Legendre function of the first kind, , with respect to its
degree . In the present work, we extend these studies and construct
several representations of the derivative of the associated Legendre function
of the first kind, , with respect to the degree , for
. At first, we establish several contour-integral
representations of . They are then
used to derive Rodrigues-type formulas for with . Next, some closed-form
expressions for are
obtained. These results are applied to find several representations, both
explicit and of the Rodrigues type, for the associated Legendre function of the
second kind of integer degree and order, ; the explicit
representations are suitable for use for numerical purposes in various regions
of the complex -plane. Finally, the derivatives
, and , all with , are evaluated in terms
of .Comment: LateX, 40 pages, 1 figure, extensive referencin
Analytical Study of Sub-Wavelength Imaging by Uniaxial Epsilon-Near-Zero Metamaterial Slabs
We discuss the imaging properties of uniaxial epsilon-near-zero metamaterial
slabs with possibly tilted optical axis, analyzing their sub-wavelength
focusing properties as a function of the design parameters. We derive in closed
analytical form the associated two-dimensional Green's function in terms of
special cylindrical functions. For the near-field parameter ranges of interest,
we are also able to derive a small-argument approximation in terms of simpler
analytical functions. Our results, validated and calibrated against a full-wave
reference solution, expand the analytical tools available for
computationally-efficient and physically-incisive modeling and design of
metamaterial-based sub-wavelength imaging systems.Comment: 25 pages, 9 figures (modifications in the text; two figures and
several references added
Spontaneous radiation of a finite-size dipole emitter in hyperbolic media
We study the radiative decay rate and Purcell effect for a finite-size dipole
emitter placed in a homogeneous uniaxial medium. We demonstrate that the
radiative rate is strongly enhanced when the signs of the longitudinal and
transverse dielectric constants of the medium are opposite, and the
isofrequency contour has a hyperbolic shape. We reveal that the Purcell
enhancement factor remains finite even in the absence of losses, and it depends
on the emitter size.Comment: 6 pages, 3 figure
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
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
In the diffraction shadow: Norton waves versus surface plasmon-polaritons in the optical region
Surface electromagnetic modes supported by metal surfaces have a great
potential for uses in miniaturised detectors and optical circuits. For many
applications these modes are excited locally. In the optical regime, Surface
Plasmon Polaritons (SPPs) have been thought to dominate the fields at the
surface, beyond a transition region comprising 3-4 wavelengths from the source.
In this work we demonstrate that at sufficiently long distances SPPs are not
the main contribution to the field. Instead, for all metals, a different type
of wave prevails, which we term Norton waves for their reminiscence to those
found in the radio-wave regime at the surface of the Earth. Our results show
that Norton Waves are stronger at the surface than SPPs at distances larger
than 6-9 SPP's absorption lengths, the precise value depending on wavelength
and metal. Moreover, Norton waves decay more slowly than SPPs in the direction
normal to the surface.Comment: 8 pages, 8 figure
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
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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