Vladimir Sergeevich Anashin

On the occasion of the 60th birthday of Professor Vladimir Sergeevich Anashin, we present a review of his significant scientific research and related activities.     

Some Quantum Gate Operators for Continuum Variables in <Emphasis Type="Italic">q</Emphasis>-Deformed Coordinate Representation

By virtue of deformation quantization methods we introduce the q-deformed coordinate representation. A new set of completeness and orthogonality relations composed of the ket and bra which are not mutually Hermitian conjugates are derived. Further, using the eigenket and eigenbra for q-deformed coordinate some important quantum gate operators for continuum variables are realized and their properties are discussed.     

Modeling Fraunhofer diffractive characteristics for modulation transfer function analysis of tilted ring metallic mesh

In order to analyze the Fraunhofer diffractive characteristics and modulation transfer function (MTF) of a tilted ring metallic mesh, an optical intensity distribution model of Fraunhofer diffraction is built using Huygens–Fresnel diffraction theory and the diffraction integral is carried out directly in the tilted mesh plane. The diffraction characteristics of the tilted ring metallic mesh are in good agreement with experimental results, which proves the correctness of the model established. MTF of an optical system with metallic mesh is calculated based on the model established and Fourier transform. Analysis shows that the degradation of MTF caused by diffraction of a ring mesh is much less than that of a square mesh whether they are vertical or tilted to the optical axis. Therefore, ring mesh can provide higher imaging quality than square mesh when they are used as high-pass filters in optical windows. A tilted array diffraction modulating factor is abstracted and believed useful in the analysis of diffractive characteristics of tilted square mesh and ring mesh, and it can be extended to Fraunhofer diffractive characteristics analysis of other tilted diffraction arrays.     

Generation of radially polarized mode using an active cylindrically symmetric birefringence fiber

A class of active fiber is presented as gain mediums of fiber lasers, where a silica layer with spoke-like air slits is introduced between the active core and cladding to obtain birefringence. With an appropriate choice of the design parameters, the fiber can support only the HE₁₁ and TM₀₁ modes. Furthermore, the numerical results show that, corresponding to the optimal rare earth doping profile, the fiber lasers can output a pure TM₀₁ mode with about 79% slope efficiency without using other mode-selective elements.     

Spontaneous quantum Hall states in chirally stacked few-layer graphene systems

Chirally stacked N-layer graphene systems with N≥2 exhibit a variety of distinct broken symmetry states in which charge density contributions from different spins and valleys are spontaneously transferred between layers. We explain how these states are distinguished by their charge, spin, and valley Hall conductivities, by their orbital magnetizations, and by their edge state properties. We argue that valley Hall states have [N/2] edge channels per spin valley.     

Cavity phase matching via an optical parametric oscillator consisting of a dielectric nonlinear crystal sheet

We experimentally demonstrate cavity phase matching for the first time using a sheet optical parametric oscillator which is made of an x-cut KTiOPO(4) crystal sheet. This microcavity presents 220 kW peak power capability for near-frequency-degenerate parametric outputs with up to 23.8% slope efficiency. It also features unique spectral characteristics such as single-longitudinal-mode and narrow linewidth. These attractive properties predict broad applications of such a mini-device, such as terahertz generation, photonic integration, spectroscopy, and quantum information, etc.     

Phase transitions in shear-induced segregation of granular materials

We computationally study shear-induced segregation of different-sized particles in vertical chute flow. We find that, for low solid fractions, large particles segregate toward regions of low shear rates where the granular temperature (velocity variance) is low. As the solid fraction increases, this trend reverses, and large particles segregate toward regions of high shear rates and temperatures. We find that this is a global phenomenon: local segregation trends reverse at high system solid fractions even where local solid fractions are small. The reversal corresponds to the growth of a single enduring cluster of 30%-60% of the particles that we propose changes the segregation dynamics.     

Application of the two-mode squeezed coherent state representation in deriving generalized optical Collins formula

We propose a new two-mode squeezed coherent state representation |z₁, z₂〉_g which is characteristic of the correlation between the squeezing and the displacement. Based on it and using the technique of integration within an ordered product of operators we obtain a generalized two-mode Fresnel operator (GTFO), which is an image of the mapping from (z₁, z₂) to in |z₁, z₂〉_g representation. The matrix element of GTFO in the coordinate representation leads to a generalized two-dimensional Collins formula (Huygens-Fresnel integration transformation describing optical diffraction) in entangled form.     

Design of different bandwidth dispersive mirrors

Dispersive mirrors in the wavelength range of 960–1110 nm, 700–900 nm, 950–1150 nm, 600–900 nm, 900–1200 nm, 600–1000 nm and 550–1050 nm are designed, respectively. From the design results, we analyse the choice of material and the approach to dispersion compensation. Furthermore, along with the increase of bandwidth, interaction between group delay dispersion (GDD) oscillation and high reflectivity, and influence of bandwidth on both GDD ripple and reflectivity are discussed.