Design of specific gratings operating under surface plasmon-polariton resonance.

We present a productive method of designing specific diffraction gratings that ensure some predetermined energy redistributions between outgoing waves. It is based on the analytical solution of the direct and reverse diffraction problems under surface plasmon-polariton resonance and is supported by strict numerical calculations.

[Morphometric characteristics of lumbar vertebrae of adult individuals and the feasibility of their body volume prediction in percutaneous vertebroplasty].

Using the material obtained from 96 human corpses (480 skeletal vertebra), the linear parameters of vertebra were studied. The research objective was to study morphometric characteristics of lumbar vertebra of an adult person taking into consideration the individual and sexual variability, and to estimate the feasibility of calculation of a vertebra body volume with reference to percutaneous vertebroplasty. The results of research have demonstrated the general patterns of modification of linear and volumetric parameters of L(I)-L(V) vertebra; it was shown that the values of linear parameters for the male samples were bigger than those for the female samples. The length of an axis of operational action, the linear and angular sizes of pedicles of vertebral arch were independent on gender factor, but, as a rule, gradually changed from L(I) to L(V). On the basis of comparison of the calculated and measured volumes of lumbar vertebra bodies, it is concluded that the mathematical model proposed by us has sufficiently high accuracy.

Extraordinary optical transmission through hole arrays in optically thin metal films.

A theoretical study is presented on the optical transmission through square hole arrays drilled in optically thin films, where transmission may occur through both the holes and the metal layer. It is shown that, as the thickness of the metal film decreases, the coupling of light with short-range surface plasmons redshifts the extraordinary optical transmission peak to longer wavelengths. At the same time, the maximum-to-minimum transmittance ratio is kept high even for metal thicknesses as small as one skin depth.

Left-handed interfaces for electromagnetic surface waves.

We show that surface electromagnetic waves (SEMWs) propagating along two-dimensional (2D) interfaces separating different metamaterials can behave analogously to 3D electromagnetic waves in either usual or left-handed media, depending on the permeabilities and/or permittivities of the two materials forming the interface. We derive the conditions when SEMWs carry energy opposite to the phase velocity. In analogy to three-dimensional (3D) left-handed media, we derive both an anomalous Cherenkov emission and a reversed Doppler effect. We also predict a negative refraction at the boundary between two different interfaces, which can be useful for perfect 2D lensing.

Canonical description of ideal magnetohydrodynamic flows and integrals of motion.

In the framework of the variational principle the canonical variables describing magnetohydrodynamic (MHD) flows of general type (i.e., with spatially varying entropy and nonzero values of all topological invariants) are introduced. It is shown that the velocity representation of the Clebsch type following from the variational principle with constraints is equivalent to that resulting from the generalization of the Weber transformation performed in the paper for the case of arbitrary MHD flows. Using such complete velocity representation enables us not only to describe the general type flows in terms of single-valued functions, but also to solve the intriguing problem of the "missing" MHD integrals of motion. The set of hitherto known MHD local invariants and integrals of motion appears to be incomplete: for the vanishing magnetic field it does not reduce to the set of the conventional hydrodynamic invariants. And if the analogs of the vorticity and helicity were discussed earlier for the particular cases, the analog of Ertel invariant has been so far unknown. It is shown that all "missing" invariants are expressed in terms of the decomposition of the velocity representation into the "hydrodynamic" and "magnetic" parts. In spite of the nonunique character of such representation it is shown that there exists a natural restriction of the gauge transformations set allowing one to make the invariants gauge independent. It is found that on the basis of the new invariants introduced a wide set of high-order invariants can be constructed. The new invariants are relevant both for the deeper insight into the problem of the topological structure of the MHD flows as a whole and for the examination of the stability problems. The additional advantage of the proposed approach is that it enables one to deal with discontinuous flows, including all types of possible breaks.