The analysis of the vector wave equation was conducted. The class of self-similar solutions with inhomogeneous polarization corresponding to the resonator modes is deduced. The modes with inhomogeneous polarization can be selected by a diffraction element with polarization selectivity used as one of the resonator mirrors. Diffraction elements with high polarization selectivity about 100% are ne...

Axially symmetric equilibrium configurations of the conformally invariant Willmore energy are shown to satisfy an equation that is two orders lower in derivatives of the embedding functions than the equilibrium shape equation, not one as would be expected on the basis of axial symmetry. Modulo a translation along the axis, this equation involves a single free parameter c. If c 6= 0, a geometry ...

We present a numerical and analytic assessment of the transport in two quasi-axially symmetric stellarators, including one variant of the MHH2 class[l] of such devices, and a configuration we refer t o as NHH2, closely related t o MHH2. Monte Carlo simulation results are compared with expectations from established stellarator neoclassical theory, and with some empirical stellarator scalings, us...

Stabilizing controllers are developed for a 3D pendulum assuming that the pendulum has a single axis of symmetry and that the center of mass lies on the axis of symmetry. This assumption allows development of a reducedmodel that forms the basis for controller design and global closed-loop analysis; this reduced model is parameterized by the constant angular velocity component of the 3D pendulum...

Flattened Gaussian beams are characterized by a waist profile that passes in a continuous way from a nearly flat illuminated region to darkness. The steepness of the transition region is controlled by an integer parameter N representing the order of the beam. Being expressible as a sum of N Laguerre–Gauss modes, a flattened Gaussian beam turns out to be very simple to study as far as propagatio...