Abstract:
An efficient and compact coupler—a device that matches a microwaveguide and a nanowaveguide—is an essential component for practical applications of nanophotonic systems. The number of coupling approaches has been rapidly increasing in the past ten years with the help of plasmonic structures and metamaterials. In this paper we overview recent as well as common solutions for nanocoupling. More specifically we consider the physical principles of operation of the devices based on a tapered waveguide section, a direct coupler, a lens, and a scatterer and support them with a number of examples. 1. Introduction Photonic components have advantages comparing to the electronic ones. Infrared and optical frequencies 1014-1015？Hz provide much broader operational bandwidth than the fastest electronic circuits. The losses in optical waveguides are smaller than in metallic wires. This is why, as D. Miller wrote, “the optical interconnects are progressively replacing wires” [1]. To achieve larger functionality on an integrated optical chip the optical components have to be miniaturized. A natural limitation, however, comes into play: the diffraction limit claims that we cannot focus light in a spot less than a half of the wavelength. The transverse size of conventional dielectric waveguides (e.g., silicon waveguides) is also limited to a half of the wavelength. Only employment of metals allows to overcome the diffraction limit and to confine a wave to a smaller area, very often at the cost of increased propagation losses. Nevertheless, the problem is not only to create efficient waveguides that provide subwavelength mode confinement, but also to make an efficient interface between free space or an optical fiber and a subwavelength nanowaveguide, that is, to focus light and launch it efficiently into the waveguide. The artistic view of the situation is depicted in Figure 1. Trying to pour water from a big bowl into a bottle with a narrow bottleneck, one would waste a lot. However, usage of a funnel simplifies the task and increases the efficiency significantly. An optical coupler plays the role of a funnel for light. Figure 1: An artistic view of the problem of coupling light from a wide microscopic fiber to a nanoscopic waveguide. Employment of a coupler, which is represented by a funnel on the figure, minimizes the losses and simplifies optical alignment. The problem of optical coupling originates from the pronounced modal mismatch between an optical fiber (a conventional single-mode telecommunication fiber has the core of 8？μm in diameter) and a nanosized waveguide,

Abstract:
All-dielectric metamaterials consisting of high-dielectric inclusions in a low-dielectric matrix are considered as a low-loss alternative to resonant metal-based metamaterials. In this contribution we investigate the applicability of the point electric and magnetic dipoles approximation to dielectric meta-atoms on the example of a dielectric ring metamaterial. Despite the large electrical size of high-dielectric meta-atoms, the dipole approximation allows for accurate prediction of the metamaterials properties for the rings with diameters up to ~0.8 of the lattice constant. The results provide important guidelines for design and optimization of all-dielectric metamaterials.

Abstract:
We investigate the lasing action in coupled multi-row nanopillar waveguides of periodic or fractal structure using the finite difference time domain (FDTD) method, coupled to the laser rate equations. Such devices exhibit band splitting with distinct and controllable supermode formation. We demonstrate that selective lasing into each of the supermodes is possible. The structure acts as a microlaser with selectable wavelength. Lasing mode selection is achieved by means of coaxial injection seeding with a Gaussian signal of appropriate transverse amplitude and phase profiles. Based on this we propose the concept of switchable lasing as an alternative to conventional laser tuning by means of external cavity control.

Abstract:
We show that under certain conditions one-dimensional dielectric lattice possesses total omnidirectional reflection of incident light. The predictions are verified experimentally using Na3AlF6/ZnSe multilayer structure developed by means of standard optical technology. The structure was found to exhibit reflection coefficient more then 99% in the range of incident angles 0-86 (degree) at the wavelength of 632.8 nm for s-polarization. The results are believed to stimulate new experiments on photonic crystals and controlled spontaneous emission.

Abstract:
A remarkable property of one-dimensional all-dielectric periodic structures has recently been reported, namely a one-dimensional lattice can totally reflect electromagnetic wave of any polarization at all angles within a prescribed frequency region. Unlike their metallic counterpart, such all-dielectric omnidirectional mirrors are nearly free of loss at optical frequencies. Here we discuss the physics, design criteria and applications of the thin-film all-dielectric omnidirectional mirror. The experimental demonstration of the mirror is presented at optical frequencies.

Abstract:
We show that the full global symmetry groups of all the D-dimensional maximal supergravities can be described in terms of the closure of the internal general coordinate transformations of the toroidal compactifications of D=11 supergravity and of type IIB supergravity, with type IIA/IIB T-duality providing an intertwining between the two pictures. At the quantum level, the part of the U-duality group that corresponds to the surviving discretised internal general coordinate transformations in a given picture leaves the internal torus invariant, while the part that is not described by internal general coordinate transformations can have the effect of altering the size or shape of the internal torus. For example, M-theory compactified on a large torus T^n can be related by duality to a compactification on a small torus, if and only if n\ge 3. We also discuss related issues in the toroidal compactification of the self-dual string to D=4. An appendix includes the complete results for the toroidal reduction of the bosonic sector of type IIB supergravity to arbitrary dimensions D\ge3.

Abstract:
The plot of allowed p and D values for p-brane solitons in D-dimensional supergravity is the same whether the solitons are extremal or non-extremal. One of the useful tools for relating different points on the plot is vertical dimensional reduction, which is possible if periodic arrays of p-brane solitons can be constructed. This is straightforward for extremal p-branes, since the no-force condition allows arbitrary multi-centre solutions to be constructed in terms of a general harmonic function on the transverse space. This has also been shown to be possible in the special case of non-extremal black holes in D=4 arrayed along an axis. In this paper, we extend previous results to include multi-scalar black holes, and dyonic black holes. We also consider their oxidation to higher dimensions, and we discuss general procedures for constructing the solutions, and studying their symmetries.

Abstract:
We study the Euclidean-signature supergravities that arise by compactifying D=11 supergravity or type IIB supergravity on a torus that includes the time direction. We show that the usual T-duality relation between type IIA and type IIB supergravities compactified on a spatial circle no longer holds if the reduction is performed on the time direction. Thus there are two inequivalent Euclidean-signature nine-dimensional maximal supergravities. They become equivalent upon further spatial compactification to D=8. We also show that duality symmetries of Euclidean-signature supergravities allow the harmonic functions of any single-charge or multi-charge instanton to be rescaled and shifted by constant factors. Combined with the usual diagonal dimensional reduction and oxidation procedures, this allows us to use the duality symmetries to map any single-charge or multi-charge p-brane soliton, or any intersection, into its near-horizon regime. Similar transformations can also be made on non-extremal p-branes. We also study the structures of duality multiplets of instanton and (D-3)-brane solutions.

Abstract:
We introduce a new approach for retrieving effective parameters of metamaterials based on the Bloch-mode analysis of quasi-periodic composite structures. We demonstrate that, in the case of single-mode propagation, a complex effective refractive index can be assigned to the structure, being restored by our method with a high accuracy. We employ both surface and volume averaging of the electromagnetic fields of the dominating (fundamental) Bloch modes to determine the Bloch and wave impedances, respectively. We discuss how this method works for several characteristic examples, and demonstrate that this approach can be useful for retrieval of both material and wave effective parameters of a broad range of metamaterials.

Abstract:
We establish a direct correspondence between certain higher-rank p-form Chern-Simons topological type theories in the bulk of a manifold with boundary and particular sectors of supergravity models on the boundary, provided that certain boundary conditions are satisfied. The cases we investigate include eleven-dimensional supergravity and both of the type II theories in ten dimensions.