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

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

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, $P_{\nu}(z)$, with respect to its degree $\nu$. In the present work, we extend these studies and construct several representations of the derivative of the associated Legendre function of the first kind, $P_{\nu}^{\pm m}(z)$, with respect to the degree $\nu$, for $m\in\mathbb{N}$. At first, we establish several contour-integral representations of $\partial P_{\nu}^{\pm m}(z)/\partial\nu$. They are then used to derive Rodrigues-type formulas for $[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}$ with $n\in\mathbb{N}$. Next, some closed-form expressions for $[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}$ 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, $Q_{n}^{\pm m}(z)$; the explicit representations are suitable for use for numerical purposes in various regions of the complex $z$-plane. Finally, the derivatives $[\partial^{2}P_{\nu}^{m}(z)/\partial\nu^{2}]_{\nu=n}$, $[\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=n}$ and $[\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=-n-1}$, all with $m>n$, are evaluated in terms of $[\partial P_{\nu}^{-m}(\pm z)/\partial\nu]_{\nu=n}$.Comment: LateX, 40 pages, 1 figure, extensive referencin

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

Parametric study of EEG sensitivity to phase noise during face processing

<b>Background: </b> The present paper examines the visual processing speed of complex objects, here faces, by mapping the relationship between object physical properties and single-trial brain responses. Measuring visual processing speed is challenging because uncontrolled physical differences that co-vary with object categories might affect brain measurements, thus biasing our speed estimates. Recently, we demonstrated that early event-related potential (ERP) differences between faces and objects are preserved even when images differ only in phase information, and amplitude spectra are equated across image categories. Here, we use a parametric design to study how early ERP to faces are shaped by phase information. Subjects performed a two-alternative force choice discrimination between two faces (Experiment 1) or textures (two control experiments). All stimuli had the same amplitude spectrum and were presented at 11 phase noise levels, varying from 0% to 100% in 10% increments, using a linear phase interpolation technique. Single-trial ERP data from each subject were analysed using a multiple linear regression model. <b>Results: </b> Our results show that sensitivity to phase noise in faces emerges progressively in a short time window between the P1 and the N170 ERP visual components. The sensitivity to phase noise starts at about 120–130 ms after stimulus onset and continues for another 25–40 ms. This result was robust both within and across subjects. A control experiment using pink noise textures, which had the same second-order statistics as the faces used in Experiment 1, demonstrated that the sensitivity to phase noise observed for faces cannot be explained by the presence of global image structure alone. A second control experiment used wavelet textures that were matched to the face stimuli in terms of second- and higher-order image statistics. Results from this experiment suggest that higher-order statistics of faces are necessary but not sufficient to obtain the sensitivity to phase noise function observed in response to faces. <b>Conclusion: </b> Our results constitute the first quantitative assessment of the time course of phase information processing by the human visual brain. We interpret our results in a framework that focuses on image statistics and single-trial analyses

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

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

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

Multisensory information facilitates reaction speed by enlarging activity difference between superior colliculus hemispheres in rats

Animals can make faster behavioral responses to multisensory stimuli than to unisensory stimuli. The superior colliculus (SC), which receives multiple inputs from different sensory modalities, is considered to be involved in the initiation of motor responses. However, the mechanism by which multisensory information facilitates motor responses is not yet understood. Here, we demonstrate that multisensory information modulates competition among SC neurons to elicit faster responses. We conducted multiunit recordings from the SC of rats performing a two-alternative spatial discrimination task using auditory and/or visual stimuli. We found that a large population of SC neurons showed direction-selective activity before the onset of movement in response to the stimuli irrespective of stimulation modality. Trial-by-trial correlation analysis showed that the premovement activity of many SC neurons increased with faster reaction speed for the contraversive movement, whereas the premovement activity of another population of neurons decreased with faster reaction speed for the ipsiversive movement. When visual and auditory stimuli were presented simultaneously, the premovement activity of a population of neurons for the contraversive movement was enhanced, whereas the premovement activity of another population of neurons for the ipsiversive movement was depressed. Unilateral inactivation of SC using muscimol prolonged reaction times of contraversive movements, but it shortened those of ipsiversive movements. These findings suggest that the difference in activity between the SC hemispheres regulates the reaction speed of motor responses, and multisensory information enlarges the activity difference resulting in faster responses