We consider the family of operator matrices H(K), K ∈ T3 := (−π; π]3 acting in the direct sum of zero-, one- and two-particle subspaces of the bosonic Fock space. We find a finite set Λ ⊂ T3 to establish the existence of infinitely many eigenvalues of H(K) for all K ∈ Λ when the associated Friedrichs model has a zero energy resonance. It is found that for every K ∈ Λ, the number N (K, z) of eigenvalues of H(K) lying on the left of z, z < 0, satisfies the asymptotic relation lim z→−0 N (K, z)| log |z||−1 = U0 with 0 < U0 < ∞, independently on the cardinality of Λ. Moreover, we show that for any K ∈ Λ the operator H(K) has a finite number of negative eigenvalues if the associated Friedrichs model has a zero eigenvalue or a zero is the regular type point for positive definite Friedrichs model.

We consider the one-dimensional photonic crystal composed of an infinite number of parallel alternating layers filled with a metamaterial and vacuum. We assume the metamaterial is an isotropic, homogeneous, dispersive and non-absorptive medium. We use a single Lorentz contribution and assume the permittivity and permeability are equal. Using the time and coordinate Fourier transforms and the Floquet-Bloch theorem, we obtain systems of equations for TE and TM modes, which ones are identical. We consider radiative and evanescent regimes for the metamaterial and vacuum layers and find sets of frequencies, where the metamaterial has the positive or negative refractive index. We use a numerical approach. As a result, we obtained the photonic band gap structure for different frequency intervals and ascertain how it changes with modification of the system parameters. We observe the non-reflection effect for any directions for a certain frequency but this fails with the layer width modification.

One of the basic problems of modern optics is medium creation, thanks to which, we can process and control a signal. Among such media, the Bragg media (in which the refractive index is periodically spatially-modulated) is of great interest [1–3]. As much as the medium has a periodically variable refractive index, the light pulse propagates more slowly in it, than in a medium with any fixed refractive index. This makes it possible to construct optical delay lines based on such media, which are useful for femtosecond spectroscopy for example. Such behavior can be understood in essence, providing that the light pulse is reflected and then interferes at the interface of media with different refractive indices. Additional introduction of nonlinearity into that sort of media leads to qualitatively new effects [4–6]. Particularly, Bragg solitons can be formed in such systems. They are revealed as a specified counter assembly of waves, banded in such a manner to move collectively with reduced speed. At the same time, rising interest in carbon nanotube (CNT) physics and particularly heightened attention to the study of CNT nonlinear properties leads to the conclusion that carbon nanotubes, with their characteristic nonlinear optical properties, can be non-conventional material for the nonlinear Bragg media formation [7–9]. Note that carbon nanotube usage perspectives in nonlinear optics in particular for optical bullet formation have been mentioned in some research accounts. All the above-mentioned facts gave impetus for this investigation.

The technique of optical micro-structuring of metal films based on processes of metal atoms adsorption on the surface of crystalline substrate and simultaneous controllable photo-stimulated desorption of atoms by non-uniform laser beam illumination is presented. The experiments were performed for sodium atom deposition on a sapphire substrate. The sapphire substrate was illuminated through a commercial linear mire with a pitch of 10 µm by a 440 nm laser beam with 1W/cm2 intensity. This provides the nonuniform spatial distribution of the illumination intensity over the sapphire surface and optical control of sodium atom deposition on the sapphire substrate, preventing the nucleation and growth of the granular film in the illuminated areas. Experiments showed that the mire pattern was well reproduced in the sodium deposits, thus creating the microstructured metallic film with few tens nm thickness. The novel suggestion to use nondiffracting optical beams for high contrast microstructuring of surface metal film is presented.

New concept of shungite carbon exhibits this raw material as a multi-level fractal structure of nanosize fragments of reduced graphene oxide (rGO) (Int. J. Smart Nano Mat. 1, 1, 2014). The natural rGO deposits turn out to be quite challenging for the current graphene technology. Once consistent with all the block of the available geological and physicochemical data obtained during the last few decades, the concept nonetheless needs a direct confirmation in terms of the current graphene science. The first such acknowledgement has been received just recently when studying photoluminescence (PL) of shungite dispersions (JETP 118, 735, 2014). A close similarity of PL spectra of aqueous dispersion of shungite and those of synthetic graphene quantum dots of the rGO origin has been established. The current paper presents the next direct confirmation provided with neutron scattering. Elastic neutron diffraction and inelastic neutron scattering have left no doubts concerning both graphene-like configuration and chemical composition of basic structural elements of shungite attributing the latter to rGO nanosize sheets with an average ∼6:0.1:2 (C:O:H) atomic content ratio per one benzenoid unit. The experimental data are supplemented with quantum chemical calculations that allowed suggesting a clear vision of the shungite structure at its first fractal levels.

This paper provides a new design for a gold tip optical antenna based on a specific geometry, and then, the change of electric field enhancement for plane wave laser excitation with 400 to 700 nm in the vicinity of optical antenna are simulated. Progressions of geometry incorporate the change of period of circular grating from 200–300 nm, on the shaft of antenna. In addition, the distribution of enhancement of the electric field in a plane perpendicular to the shaft has been acquired. Finally, the optimal value for the maximum enhancement at the period of 208.843 nm is calculated.

The solution of the radiative transfer equation in the layer of a diffusing medium with Frenel fronts was observed by the example of light transfer in a dielectric medium containing nickel nanoparticles. The method of spherical harmonics was used. A scattering indicatrix was calculated for 532 nm light for 140 nm nickel nanoparticles in a pentaerythriol tetranitrate matrix. The angular distribution of illumination on the sample’s fronts was calculated for reflected and transmitted light. The maximum of the scattering indicatrix is observed for the diffusion in the opposite direction. The minimum of the illumination on the front in direction of the sample’s bulk is a result of using the Frenel’s boundary conditions and the asymmetric property of the scattering indicatrix of the nickel nanoparticles. The possibility of using of the composites explosives – nickel nanoparticles as a cap of the optical detonator is considered.

The goal of this study was the sol-gel synthesis of nanocrystals La1-xSrxFeO3 (x=0.0, 0.1, 0.2, 0.3) and an examination of their magnetic properties. An aqueous solution of ammonia and 5% ammonium carbonate solution were used as precipitating agents. It was established that the crystallization of LaFeO3 is completed at 750◦C (annealing for 1 h). The average diameter of the synthesized particles was 80–100 nm. Investigation of the magnetic properties showed non-monotonic changes of saturation magnetic moment and increase of coercive force with increased Sr content in the sample.

Yttrium orthoferrite nanocrystals with an average crystallite size of 55 – 60 nm have been obtained under hydrothermal conditions. The influence of the hydrothermal synthesis temperature on the structure and crystallite size has been investigated. Mechanism of the YFeO3 formation under the hydrothermal conditions has been proposed.

Studies of the concentration dependence of electric conductivity and pH for aqueous solutions of the light fullerene – C60[=C(COOH)2]3 tris-malonate were performed at 25 ◦C. From both data (from the equivalent electric conductivity and pH), the apparent degree of dissociation and concentration dissociation constants of C60[=C(COOH)2]3 in aqueous solutions were calculated. Thermodynamic dissociation constants of C60[=C(COOH)2]3 in aqueous solutions, calculated for infinitely dilute solutions by the both methods, were reasonably similar.

The method of the electrochemical and chemical treatment of an aluminum surface to obtain selective coloration of the anodic aluminum oxide films (AAOF) with high index of the reflection and wide range of the color tones was developed. AAOF were formed and both Ag and Au were chemically deposited. The physical and chemical properties of the obtained color AAOF were studied. It was shown that the additional chemical deposition of the noble metal leads to the enhancement of the selective reflection ability and the interference contrast. Silver nanoparticle formation on the surface of the pores after chemical deposition was shown by electron microscopy. The optical reflection spectra at different angles (10◦ – 85◦) of metalized AAOF were measured and the effective refractive index (n ≈ 1.6) and thickness were calculated. The spectral shift of the reflection peaks of nanoporous metalized AAOF was shown to depend on the nature of the marked solvents.