Giant radiation heat transfer through the micron gaps

Near-field heat transfer between two closely spaced radiating media can exceed in orders radiation through the interface of a single black body. This effect is caused by exponentially decaying (evanescent) waves which form the photon tunnel between two transparent boundaries. However, in the mid-infrared range it holds when the gap between two media is as small as few tens of nanometers. We propose a new paradigm of the radiation heat transfer which makes possible the strong photon tunneling for micron thick gaps. For it the air gap between two media should be modified, so that evanescent waves are transformed inside it into propagating ones. This modification is achievable using a metamaterial so that the direct thermal conductance through the metamaterial is practically absent and the photovoltaic conversion of the transferred heat is not altered by the metamaterial.Comment: 4 pages, 3 figure

Second-order calculation of the local density of states above a nanostructured surface

We have numerically implemented a perturbation series for the scattered electromagnetic fields above rough surfaces, due to Greffet, allowing us to evaluate the local density of states to second order in the surface profile function. We present typical results for thermal near fields of surfaces with regular nanostructures, investigating the relative magnitude of the contributions appearing in successive orders. The method is then employed for estimating the resolution limit of an idealized Near-Field Scanning Thermal Microscope (NSThM).Comment: 10 pages, 7 figure

Microscopic model of Purcell enhancement in hyperbolic metamaterials

We study theoretically a dramatic enhancement of spontaneous emission in metamaterials with the hyperbolic dispersion modeled as a cubic lattice of anisotropic resonant dipoles. We analyze the dependence of the Purcell factor on the source position in the lattice unit cell and demonstrate that the optimal emitter position to achieve large Purcell factors and Lamb shifts are in the local field maxima. We show that the calculated Green function has a characteristic cross-like shape, spatially modulated due to structure discreteness. Our basic microscopic theory provides fundamental insights into the rapidly developing field of hyperbolic metamaterials.Comment: 9 pages, 11 figure

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

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

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

At Wisdom’s Table: How Narrative Shapes the Biblical Food Laws and Their Social Function

This second part of a two-paper sequence deals with the physical interpretation of the rigorously derived high-frequency asymptotic wave-field solution in Part I, pertaining to a semi-infinite phased array of parallel dipole radiators. The asymptotic solution contains two parts that represent contributions due to truncated Floquet waves (FW's) and to the corresponding edge diffractions, respectively. The phenomenology of the FW-excited diffracted fields is discussed in detail. All possible combinations of propagating (radiating) and evanescent (nonradiating) FW and diffracted contributions are considered. The format is a generalization of the conventional geometrical theory of diffraction (GTD) for smooth truncated aperture distributions to the truncated periodicity-induced FW distributions with their corresponding FW-modulated edge diffractions. Ray paths for propagating diffracted waves are defined according to a generalized Fermât principle, which is also valid by analytic continuation for evanescent diffracted ray fields. The mechanism of uniform compensation for the FW-field discontinuities (across their truncation shadow boundaries) by the diffracted waves is explored for propagating and evanescent FW's, including the cutoff transition from the propagating to the evanescent regime for both the FW and diffracted constituents. Illustrative examples demonstrate: 1) the accuracy and efficiency of the high-frequency algorithm under conditions that involve the various wave processes outlined above and 2) the cogent interpretation of the results in terms of the uniform FW-modulated GTD. ©2000 IEEE

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

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