Related papers: Localized lasing modes of triangular organic micro…
We evaluate the Lienard-Wiechert field of a rotating superluminal point source numerically and show that this radiation field has the following intrinsic characteristics. (i) It is sharply focused along a narrow, rigidly rotating…
Recently, the existence of robust three-dimensional light bullets (LBs) was predicted theoretically in the output of a laser coupled to a distant saturable absorber. In this manuscript, we analyze the stability and the range of existence of…
Single and double-slit experiments are performed with two microwave billiards with the shapes of a rectangle, respectively, a quarter stadium. The classical dynamics of the former is regular, that of the latter is chaotic. Microwaves can…
We consider the class of dispersing billiard systems in the plane formed by removing three convex analytic scatterers satisfying the non-eclipse condition. The collision map in this system is conjugated to a subshift, providing a natural…
We describe the possibility for topologically robust edge states existing on interfaces of triangular lattices which are supported by rotational symmetries that are sensitive to boundary conditions. Such states are trivial from the…
We present numerical and experimental results for the development of islands of stability in atom-optics billiards with soft walls. As the walls are soften, stable regions appear near singular periodic trajectories in converging (focusing)…
The goal of this paper is an analysis of the geometry of billiards in ellipses, based on properties of confocal central conics. The extended sides of the billiards meet at points which are located on confocal ellipses and hyperbolas. They…
We describe results of measurements of the orientational motion of glass microrods in a microchannel flow, following the orientational motion of particles with different shapes. We determine how the orientational dynamics depends on the…
The optical properties of PT-symmetric periodic stack of the layers with balanced loss and gain are examined. We demonstrate that tunnelling phenomenon in periodic structures is connected with excitation of surface waves at the boundaries…
We demonstrate lasing in arrays of microring resonators with underlying para-Fermi symmetry. The properties of the algebra allow the analytic prediction of propagation constants and normal modes of an array of passive resonators that show…
The behavior of a parity-time (PT) symmetric coupled microring system is studied when operating in the vicinity of an exceptional point. Using the abrupt phase transition around this point, stable single-mode lasing is demonstrated in…
We give an explicit sub-exponential estimate on the growth rate of periodic orbits and generalized diagonals for typical triangle billiards.
We study the geometry of billiard orbits on rectangular billiards. A truncated billiard orbit induces a partition of the rectangle into polygons. We prove that thirteen is a sharp upper bound for the number of different areas of these…
We investigate a rotated, orthogonal gravitational wedge billiard - a special case of the asymmetric wedge billiard - in which the dynamics are integrable. We derive equations and conditions under which periodic orbits may be constructed…
Although controversial, the scenario of microlensing as the dominant mechanism for the long-term optical variability of quasars does provide a natural explanation for both the statistical symmetry, achromaticity and lack of cosmological…
In this thesis, we use normal surface theory to understand certain properties of minimal triangulations of compact orientable 3-manifolds. We describe the collapsing process of normal 2-spheres and disks. Using some geometrical…
We construct a highly-symmetric periodic orbit of six bodies in three dimensions. In this orbit, binary collisions occur at the origin in a regular periodic fashion, rotating between pairs of bodies located on the coordinate axes.…
A correspondence between the orbits of a system of 2 complex, homogeneous, polynomial ordinary differential equations with real coefficients and those of a polygonal billiard is displayed. This correspondence is general, in the sense that…
We define billiards in the context of sub-Finsler Geometry. We provide symplectic and variational (or rather, control theoretical) descriptions of the problem and show that they coincide. We then discuss several phenomena in this setting,…
A general formula for the linearized Poincar\'e map of a billiard with a potential is derived. The stability of periodic orbits is given by the trace of a product of matrices describing the piecewise free motion between reflections and the…