On the Entangled Fractional Fourier Transform in Tripartite Entangled State Representation

Based on the newly constructed two mutually conjugate 3-mode entangled states of continuum variablesin three-mode Fock space we introduce entangled fractional Fourier transform (EFFT) for the tripartite entangled staterepresentations, which are not a direct product of three 1-dimensional FFTs. The eigenmodes of EFFT are obtained,which is different from the usual Hermite polynomials. The EFFT of the three-mode squeezed state is derived.     

Material-Adapted Design of Textile-Reinforced Composite Structures with Optimized Vibro-Acoustic and Damping Properties Including Shear Effects

Advanced analytical models have been developed at the ILK, which offer a possibility of calculating the vibro-acoustic and damping behavior of textile-reinforced composite shells and plates with account of shear effects. The simulation models elaborated have been verified on selected examples, and the analytical results were fully corroborated by accompanying numerical calculations for typical lay-ups.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 3, pp. 289–302, May–June, 2005.     

Full-wave analysis of dielectric waveguides at a given frequency

New variational formulation to compute propagation constants is proposed. Based on it, vector finite element method is proved to exclude spurious modes provided finite elements possess discrete compactness property. Convergence analysis is conducted in the framework of collectively compact operators. Reported theoretical results apply to a wide class of vector finite elements including two families of Nedelec and their generalization, the -edge elements. Numerical experiments fully support theoretical estimates for convergence rates.

     

Vector potential–vorticity relationship for the Stokes flows: application to the Stokes eigenmodes in 2D/3D closed domain

The unsteady dynamics of the Stokes flows, where , is shown to verify the vector potential–vorticity ( ) correlation , where the field is the pressure-gradient vector potential defined by . This correlation is analyzed for the Stokes eigenmodes, , subjected to no-slip boundary conditions on any two-dimensional (2D) closed contour or three-dimensional (3D) surface. It is established that an asymptotic linear relationship appears, verified in the core part of the domain, between the vector potential and vorticity, , where is a constant offset field, possibly zero.     

Effect of the surface free energy on the behaviour of surface and guided waves

The aim of this paper is to evaluate the influence of the surface free energy upon the propagation of the eigenmodes of structures, by studying successively (a) the Rayleigh wave for an elastic half-space, (b) the Lamb waves for an elastic layer, and (c) the guided modes for a tri-layer structure (e.g., metal/adhesive/metal). The surface free energy is a parameter which appears in the jump conditions of stresses and displacements at each interface, and which consequently modifies the eigenmodes, solutions of the boundary conditions system. As expected, the Rayleigh wave is dispersive and its velocity increases when the surface free energy increases. In the same way, the velocity of Lamb waves also increases except at normal angle of propagation where the surface free energy does not arise. Moreover, near the Rayleigh angle, the behaviour of the A₀ and S₀ Lamb modes varies strongly according to the surface free energy. Similar results are observed for the tri-layer structure.     

Correspondence between quantum-optical transform and classical-optical transform explored by developing Dirac’s symbolic method

By virtue of the new technique of performing integration over Dirac’s ket–bra operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel–Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We cannot only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. For examples, we find the generalized Fresnel operator (GFO) to correspond to the generalized Fresnel transform (GFT) in classical optics. We derive GFO’s normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area in finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used. All these have confirmed Dirac’s assertion: “...for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory”.     

Temperature gradient driven Alfvén instability producing inward energy flux in stellarators

Destabilizing influence of plasma inhomogeneity on Alfvén eigenmodes in stellarators is considered. It is found that the diamagnetic frequency can strongly increase due to the resonance interaction of particles and Alfvén eigenmodes. This occurs when the particle resonance velocity exceeds the thermal velocity, in which case the role of superthermal particles enlarges. Then Alfvén eigenmodes can be destabilized even in the absence of the energetic ion population. It is shown that in the case of the temperature distribution with a large gradient at the periphery, the destabilized mode can channel the energy from the peripheral plasma region to the inner region. A stability analysis employing a model temperature profile of the ions was carried out for the Wendelstein 7-X stellarator. It indicates that the considered mechanism could lead to an Alfvén instability accompanied with the inward energy flux in the first W7-X experiments where long-lasting high-frequency oscillations were observed.     

Ohmic quality of resonators shaped by corrugated guide sections at frequencies near bragg stop bands

The effect of ohmic loss decrease in corrugated waveguide is studied for the case of period, equal to half of longitudinal wave length (so called π-type oscillations). As demonstrated, in periodical guide there are π-type waves with ohmic quality growing approximatelly as a cube of guide radius, which looks very attractive for different applications.     

Discrete Alfven eigenmodes in international thermonuclear experimental reactor operations with negative magnetic shear

Discrete Alfven eigenmodes in steady-state operation scenarios with negative magnetic shear in the international thermonuclear experimental reactor are investigated in this paper. These magnetohydrodynamic eigenmodes are trapped by the s-induced potential wells along the magnetic field line. Here α = -q2Rdβ/dr with q being the safety factor, the ratio between plasma and magnetic pressures, and R the major radius, and r the minor radius. Due to negligible continuum damping via wave energy tunneling, these Alfven eigenmodes could be readily destabilized by energetic particles.     

A fully vectorial technique for scattering and propagation in three-dimensional stratified photonic structures

We present a three-dimensional (3D) technique for computing light scattering and propagation in complex structures formed by scatterers embedded in a stratified background. This approach relies on the Green's tensor associated with the background and requires only the discretization of the scatterers, the entire stratified background being accounted for in the Green's tensor. Further, the boundary conditions at the edges of the computation window and at the different material interfaces in the stratified background are automatically fulfilled. Different examples illustrate the application of the technique to the modeling of photonic integrated circuits: waveguides with protrusions (single element grating) and notches. Subtle effects, like polarization crosstalks in an integrated optics device are also investigated.