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

Oblique launching of optical surface waves by a subwavelength slit

The electromagnetic field on the metal surface launched by a subwavelength slit is analytically studied, for the case when the fundamental mode inside the slit has a wavevector component along the slit axis (conical mount). Both near-field and far-field regions are discussed, and the role of surface plasmon-polaritons and Norton waves is revealed. It is shown that the distance from the slit at which NW are more intense than surface plasmons decrease with parallel wavevector, which could help experimental studies on Norton waves. Additionally, it is found that the s-polarization component, while present for any non-zero parallel wavevector, only weakly contributes to the NWs.Comment: 8 pages, 5 figure

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

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

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 $R$, this is done by complexifying $R$ to $R+ia$. The resulting complex sphere is shown to be a real bundle of disks with radius $a$ 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 $a$ sharpens the focus of the pulsed beams, which in turn raises the compression of the representation.Comment: 49 pages, 14 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

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

Transmutations and spectral parameter power series in eigenvalue problems

We give an overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS). The possibility to write down the dispersion (characteristic) equations corresponding to a variety of spectral problems related to Sturm-Liouville equations in an analytic form is an attractive feature of the SPPS method. It is based on a computation of certain systems of recursive integrals. Considered as families of functions these systems are complete in the $L_{2}$-space and result to be the images of the nonnegative integer powers of the independent variable under the action of a corresponding transmutation operator. This recently revealed property of the Delsarte transmutations opens the way to apply the transmutation operator even when its integral kernel is unknown and gives the possibility to obtain further interesting properties concerning the Darboux transformed Schr\"{o}dinger operators. We introduce the systems of recursive integrals and the SPPS approach, explain some of its applications to spectral problems with numerical illustrations, give the definition and basic properties of transmutation operators, introduce a parametrized family of transmutation operators, study their mapping properties and construct the transmutation operators for Darboux transformed Schr\"{o}dinger operators.Comment: 30 pages, 4 figures. arXiv admin note: text overlap with arXiv:1111.444

From Gaussian beam to complex-source-point spherical wave

It is shown that the paraxial Gaussian beam becomes the complex-source-point spherical wave when all-order corrections are made according to the method of Lax, Louisell, and McKnight. Apparent contradictions between previously published first-order corrections are also discussed