Mode mixing in asymmetric double trench photonic crystal waveguides

e investigate both experimentally and theoretically the waveguiding properties of a novel double trench waveguide where a conventional single-mode strip waveguide is embedded in a two dimensional photonic crystal (PhC) slab formed in silicon on insulator (SOI) wafers. We demonstrate that the bandwidth for relatively low-loss (50dB/cm) waveguiding is significantly expanded to 250nm covering almost all the photonic band gap owing to nearly linear dispersion of the TE-like waveguiding mode. The flat transmission spectrum however is interrupted by numerous narrow stop bands. We found that these stop bands can be attributed to anti-crossing between TE-like (positive parity) and TM-like (negative parity) modes. This effect is a direct result of the strong asymmetry of the waveguides that have an upper cladding of air and lower cladding of oxide. To our knowledge this is the first demonstration of the effects of cladding asymmetry on the transmission characteristics of the PhC slab waveguides.Comment: 7 pages, 6 figure

Derivation of the particle dynamics from kinetic equations

We consider the microscopic solutions of the Boltzmann-Enskog equation discovered by Bogolyubov. The fact that the time-irreversible kinetic equation has time-reversible microscopic solutions is rather surprising. We analyze this paradox and show that the reversibility or irreversibility property of the Boltzmann-Enskog equation depends on the considered class of solutions. If the considered solutions have the form of sums of delta-functions, then the equation is reversible. If the considered solutions belong to the class of continuously differentiable functions, then the equation is irreversible. Also, we construct the so called approximate microscopic solutions. These solutions are continuously differentiable and they are reversible on bounded time intervals. This analysis suggests a way to reconcile the time-irreversible kinetic equations with the time-reversible particle dynamics. Usually one tries to derive the kinetic equations from the particle dynamics. On the contrary, we postulate the Boltzmann-Enskog equation or another kinetic equation and treat their microscopic solutions as the particle dynamics. So, instead of the derivation of the kinetic equations from the microdynamics we suggest a kind of derivation of the microdynamics from the kinetic equations.Comment: 18 pages; some misprints have been corrected, some references have been adde

Quantum gates and quantum algorithms with Clifford algebra technique

We use our Clifford algebra technique, that is nilpotents and projectors which are binomials of the Clifford algebra objects $\gamma^a$ with the property $\{\gamma^a,\gamma^b\}_+ = 2 \eta^{ab}$, for representing quantum gates and quantum algorithms needed in quantum computers in an elegant way. We identify $n$-qubits with spinor representations of the group SO(1,3) for a system of $n$ spinors. Representations are expressed in terms of products of projectors and nilpotents. An algorithm for extracting a particular information out of a general superposition of $2^n$ qubit states is presented. It reproduces for a particular choice of the initial state the Grover's algorithm.Comment: 9 pages, revte

Simulation of non-stationary processes in centrifugal cascades

The model of nonstationary hydraulic and dividing processes in rectangular symmetrical counterstream centrifugal cascades is considered. The calculation technique of centrifugal cascade parameters of transition processes has been developed. The results of numerical computation are presented

Increasing Fatigue LIfe of 09Mn2Si Steel by means of High-Temperature Multistep Helical Rolling

The effect of high temperature helical rolling (HR) on structure and fatigue life of 09Mn2Si pipe steel has been studied. With the use of transmission electron microscopy there was revealed that rolling gives rise to refinement of ferrite grains and cracking (fracturing) of cementite plates within the pearlite phase. The effect manifests itself to the greatest extent in the surface layer where due to the rolling the level of plastic deformation was the highest. Data of microhardness measurements confirms the gradient pattern of strain hardening over the cross section during the HR occurs while the most intensive microhardness increasing take place at the depth of up to 3 mm. According to the mechanical testing results the helical rolling of 09Mn2Si steel gives rise to increasing the level of deforming stress at the yield plateau as well as the proportionality limit with a general decrease in the relative elongation. At the same time, despite the strain hardening resulting from the helical rolling the mechanisms of plastic deformation which manifest themselves in the form of parabolic hardening with a smooth decrease in the flow stress level after neck formation are preserved in the steel. During the cyclic tension the number of cycles prior to failure increases from 2.5 to 3.8 times that depends on the location of specimens' cutting from the rolled rod. The highest improvement in fatigue fracture resistance is registered for specimens cut out from the core of the rolled rods

Electronic correlations on a metallic nanosphere

We consider the correlation functions in a gas of electrons moving within a thin layer on the surface of nanosize sphere. A closed form of expressions for the RKKY indirect exchange, superconducting Cooper loop and `density-density' correlation function is obtained. The systematic comparison with planar results is made, the effects of spherical geometry are outlined. The quantum coherence of electrons leads to the enhancement of all correlations for the points--antipodes on the sphere. This effect is lost when the radius of the sphere exceeds the temperature coherence length.Comment: 5 pages, no figures, to appear in PRB (RC