Characterization of non-Gaussian mid-infrared free-electron laser beams by the knife-edge method

We report the characterization of mid-infrared free-electron laser (FEL) beams at the wavelength of 11 $\mathrm{\mu }$m by the knife-edge method. From the knife-edge data we find that the FEL beam has a non-Gaussian shape. To represent the non-Gaussian beam shape we employ two methods: fitting the knife-edge data to some analytical functions with a few free parameters and numerical smoothing of the knife-edge data. Both methods work equally well. Using those data we can reconstruct the two-dimensional (2D) beam profiles at different positions around the focus by assuming that the 2D intensity distribution function is separable in x (horizontal) and y (vertical) directions. Using the 2D beam profiles at different positions around the focus, we find that the beam propagation factor ($M^2$ factor) is $\sim$1.1 in both x and y directions. As a cross-check, we also carry out the burn pattern experiment to find that the behavior of the focused FEL beam along the propagation is consistent with the results obtained by the knife-edge method.     

Evidence for structural damping in a high-stress silicon nitride nanobeam and its implications for quantum optomechanics

We resolve the thermal motion of a high-stress silicon nitride nanobeam at frequencies far below its fundamental flexural resonance (3.4 MHz) using cavity-enhanced optical interferometry. Over two decades, the displacement spectrum is well-modeled by that of a damped harmonic oscillator driven by a $1/f$ thermal force, suggesting that the loss angle of the beam material is frequency-independent. The inferred loss angle at 3.4 MHz, $?=4.5?{10}^{?6}$, agrees well with the quality factor (Q) of the fundamental beam mode ($?=Q^{?1}$). In conjunction with Q measurements made on higher order flexural modes, and accounting for the mode dependence of stress-induced loss dilution, we find that the intrinsic (undiluted) loss angle of the beam changes by less than a factor of 2 between 50 kHz and 50 MHz. We discuss the impact of such “structural damping” on experiments in quantum optomechanics, in which the thermal force acting on a mechanical oscillator coupled to an optical cavity is overwhelmed by radiation pressure shot noise. As an illustration, we show that structural damping reduces the bandwidth of ponderomotive squeezing.     

Exact PsTd invariant and PsTd symmetric breaking solutions,symmetry reductions and Bäcklund transformations for an AB–KdV system

In natural and social science, many events happened at different space–times may be closely correlated. Two events, A (Alice) and B (Bob) are defined as correlated if one event is determined by another, say, $B=\stackrel{?}{f}A$ for suitable $\stackrel{?}{f}$ operators. A nonlocal AB–KdV system with shifted-parity ($P_s$, parity with a shift), delayed time reversal ($T_d$, time reversal with a delay) symmetry where $B=\stackrel{?}{P_s}\stackrel{?}{T_d}A$ is constructed directly from the normal KdV equation to describe two-area physical event. The exact solutions of the AB–KdV system, including $P_s{T}_d$ invariant and $P_s{T}_d$ symmetric breaking solutions are shown by different methods. The $P_s{T}_d$ invariant solution show that the event happened at A will happen also at B. These solutions, such as single soliton solutions, infinitely many singular soliton solutions, soliton–cnoidal wave interaction solutions, and symmetry reduction solutions etc., show the AB–KdV system possesses rich structures. Also, a special Bäcklund transformation related to residual symmetry is presented via the localization of the residual symmetry to find interaction solutions between the solitons and other types of the AB–KdV system.     

On spacelike hypersurfaces of constant sectional curvature lorentz manifolds

Let $x:M^n\to {\overline{M}}^{n+1}$ be an n-dimensional spacelike hypersurface of a constant sectional curvature Lorentz manifold $\overline{M}$. Based on previous work of S. Montiel, L. Alías, A. Brasil and G. Colares studied what can be said about the geometry of M when $\overline{M}$ is a conformally stationary spacetime, with timelike conformal vector field K. For example, if $M^n$ has constant higher order mean curvatures $H_r$ and $H_{r+1}$, they concluded that $M^n$ is totally umbilical, provided $H_{r+1}\ne 0$ on it. If div($K$) does not vanish on $M^n$ they also proved that $M^n$ is totally umbilical, provided it has, a priori, just one constant higher order mean curvature.In this paper, we compute $L_r(S_r)$ for such an immersion, and use the resulting formula to study both r-maximal spacelike hypersurfaces of $\overline{M}$, as well as, in the presence of a constant higher order mean curvature, constraints on the sectional curvature of M that also suffice to guarantee the umbilicity of M. Here, by $L_r$ we mean the linearization of the second order differential operator associated to the r-th elementary symmetric function $S_r$ on the eigenvalues of the second fundamental form of x.     

Influence of the deGennes extrapolation parameter on the resistive state of a superconducting strip

We studied the resistive state of a mesoscopic superconducting strip (bridge) at zero external applied magnetic field under a transport electric current, $J_a$, subjected to different types of boundary conditions. The current is applied through a metallic contact (electrode) and the boundary conditions are simulated via the deGennes extrapolation length b. It will be shown that the characteristic current–voltage curve follows a scaling law for different values of b. We also show that the value of $J_a$ at which the first vortex–antivortex (V–Av) pair penetrates the sample, as well as their average velocities and dynamics, strongly depend on the b values. Our investigation was carried out by solving the two-dimensional generalized time dependent Ginzburg–Landau (GTDGL) equation.     

EPR and optical absorption studies of vanadyl impurity in lithium hydrogen oxalate single crystal

Electron paramagnetic resonance (EPR) and optical absorption studies of vanadyl ions in lithium hydrogen oxalate monohydrate single crystal and powder are reported at room temperature. Single crystal rotations in each of the three mutually orthogonal crystalline planes, $a{b}^1$, $b^1{c}^1$ and $a{c}^1$ indicate four different vanadyl complexes. The detailed investigation of EPR spectra indicates that one of the VO^{2 +} sites (the intense one) may enter the lattice substitutionally and the other three occupy the interstitial positions. From the angular variation, the spin Hamiltonian parameters are evaluated and discussed. The optical absorption spectrum shows four bands. From the optical and EPR data, various bonding parameters are determined and the nature of bonding in the crystal is discussed.     

Exchange integrals and magnetic short range order in the system CdCr2−xGaxSe4(0⩽x⩽0.06)

High-temperature series expansions are derived for the magnetic susceptibility and two-spin correlation functions for a Heisenberg ferromagnetic model on the B-spinel lattice. The calculations are developed in the framework of the random phase approximation and are given for both nearest and next-nearest neighbour exchange integrals $J_1$ and $J_2$, respectively. Our results are given up to order 6 in $\beta =(k_{\mathrm{B}}T{)}^{-1}$and are used to study the paramagnetic region of the ferromagnetic spinel CdCr_2−xGa_xSe₄. The critical temperature $T_{\mathrm{c}}$ and the critical exponents $\gamma$ and $\nu$ associated with the magnetic susceptibility $\chi (T)$ and the correlation length $\xi (T)$, respectively are deduced by applying the Padé approximate methods. The results as a function of the dilution x obtained by the present approach are found to be in agreement with the experimental ones.