Tunable Spin dependent beam shift by simultaneously tailoring geometric and dynamical phases of light in inhomogeneous anisotropic medium

Two-dimensional beam scanning by tunable photonic spin Hall effect

To the best of our knowledge, a novel tunable photonic spin Hall effect is proposed based on a pair of liquid crystal Pancharatnam-Berry (PB) lenses. Owing to the spin-dependent geometric phases, a PB lens focus or defocus the incident light field according to its spin angular momentum. By cascading two PB lenses with a small gap, the focus and defocus effects can be suppressed, and the transmitted light fields with opposite spin will be deflected toward opposite directions when the two PB lenses have a relative lateral displacement. The deflection angles vary linearly with the displacements, thus double-lines two-dimensional continuous beam scanning is achieved with a scanning angle of 39o × 39° and a beam diverging angle of 0.028o × 0.028°. The scanning beam is used to write different patterns on a 200 nm thick gold film. We believe this beam scanning system can find wide applications ranging from laser processing, Lidar, particle manipulation, to free space optical communications.

Wave-Vector-Varying Pancharatnam-Berry Phase Photonic Spin Hall Effect

The geometric Pancharatnam-Berry (PB) phase not only is of physical interest but also has wide applications ranging from condensed-matter physics to photonics. Space-varying PB phases based on inhomogeneously anisotropic media have previously been used effectively for spin photon manipulation. Here we demonstrate a novel wave-vector-varying PB phase that arises naturally in the transmission and reflection processes in homogeneous media for paraxial beams with small incident angles. The eigenpolarization states of the transmission and reflection processes are determined by the local wave vectors of the incident beam. The small incident angle breaks the rotational symmetry and induces a PB phase that varies linearly with the transverse wave vector, resulting in the photonic spin Hall effect (PSHE). This new PSHE can address the contradiction between spin separation and energy efficiency in the conventional PSHE associated with the Rytov-Vladimirskii-Berry phase, allowing spin photons to be separated completely with a spin separation up to 2.2 times beam waist and a highest energy efficiency of 86%. The spin separation dynamics is visualized by wave coupling equations in a uniaxial crystal, where the centroid positions of the spin photons can be doubled due to the conservation of the angular momentum. Our findings can greatly deepen the understanding in the geometric phase and spin-orbit coupling, paving the way for practical applications of the PSHE.

Quadrature Squeezing and Geometric-Phase Oscillations in Nano-Optics

The geometric phase, as well as the familiar dynamical phase, occurs in the evolution of a squeezed state in nano-optics as an extra phase. The outcome of the geometric phase in that state is somewhat intricate: its time behavior exhibits a combination of a linear increase and periodic oscillations. We focus in this work on the periodic oscillations of the geometric phase, which are novel and interesting. We confirm that such oscillations are due purely to the effects of squeezing in the quantum states, whereas the oscillation disappears when we remove the squeezing. As the degree of squeezing increases in q-quadrature, the amplitude of the geometric-phase oscillation becomes large. This implies that we can adjust the strength of such an oscillation by tuning the squeezing parameters. We also investigate geometric-phase oscillations for the case of a more general optical phenomenon where the squeezed state undergoes one-photon processes. It is shown that the geometric phase in this case exhibits additional intricate oscillations with small amplitudes, besides the principal oscillation. Such a sub-oscillation exhibits a beating-like behavior in time. The effects of geometric-phase oscillations are crucial in a wide range of wave interferences which are accompanied by rich physical phenomena such as Aharonov–Bohm oscillations, conductance fluctuations, antilocalizations, and nondissipative current flows.

Laguerre-Gaussian modal q-plates

We propose space-variant uniaxial flat optical elements designed to generate pure Laguerre-Gaussian modes with arbitrary azimuthal and radial indices l and p from an incident Gaussian beam. This is done via the combined use of the dynamic and the geometric phases. Optimal design protocol for the mode conversion efficiency is derived, and the corresponding characteristics are given for -6≤l≤6 and 0≤p≤5. The obtained "modal q-plates" may find many applications whenever the radial degree of freedom of a light field is at play.