Polarization-based control of spin-orbit vector modes of light in biphoton interference.

We report the experimental generation of a class of spin-orbit vector modes of light via an asymmetric Mach-Zehnder interferometer, obtained from an input beam prepared in a product state of its spin and orbital degrees of freedom. These modes contain a spatially varying polarization structure which may be controllably propagated about the beam axis by varying the retardance between the vertical and horizontal polarization components of the light. Additionally, their transverse spatial intensity distributions may be continuously manipulated by tuning the input polarization parameters. In the case of an analogous biphoton input, we predict that this device will exhibit biphoton (Hong-Ou-Mandel) interference in conjunction with the aforementioned tunable mode transformations.

Order and chaos in the rotation and revolution of two massive line segments.

As a generalization of Newton's two body problem, we explore the dynamics of two massive line segments interacting gravitationally. The extension of each line segment or slash (/) provides extra degrees of freedom that enable the interplay between rotation and revolution in an especially simple example. This slash-slash (//) body problem can thereby elucidate the dynamics of nonspherical space structures, from asteroids to space stations. Fortunately, as we show, Newton's laws imply exact algebraic expressions for the force and torque between the slashes, and this greatly facilitates analysis. The diverse dynamics include a stable synchronous orbit, families of unstable periodic orbits, generic chaotic orbits, and spin-orbit coupling that can unbind the slashes. In particular, retrograde orbits where the slashes spin opposite to their orbits are stable, with regular dynamics and smooth parameter spaces, while prograde orbits are unstable, with chaotic dynamics and fractal parameter spaces.