Optical vortices of light in planar geometries attract large interest due to their influence on light-matter interactions , enabling forbidden electronic transitions, and creating topological memory. These arise from the nature of vortices being a phase singularity at the near field – defining an integer quantity (charge) of orbital angular momentum (OAM). Most investigations of optical vortices in planar systems were concentrated in the frequency domain, showing charge and location engineering , as well as revealing the topological rules of charge . However, the temporal dynamics of planar optical vortices, from creation and motion to annihilation, has largely remained unexplored. Intriguingly, the conservation of charge implies that vortices can only be created or annihilated in pairs, and yet, the dynamics of vortex creation\annihilation has not been observed experimentally.
Here, we show a first observation of the dynamics of optical vortices: their motion, creation, and annihilation. The measurements utilize an ultrafast transmission electron microscope that measures the dynamics of the Phonon-polaritons (PhP) electric field profile in the 2D material hexagonal boron nitride (hBN). Our results also provide the first observation of PhP vortices, and of optical vortices in any 2D material.
We measure the dynamics of PhP vortices by changing the time delay between an excitation laser pump and a free-electron probe (as in ) and infer events of vortex creation\annihilation and their continuous movement inside the sample. The planar optical vortices in 2D materials appear as points of zero field amplitude in the out-of-plane direction (Fig. 1). Our simulations of the dynamics of the PhPs verify that the points of zero field amplitude are connected to phase singularities in the field and how the features of the field profile are determined by the relations between multiple vortices. As a result, we can allocate and determine the charge of the moving vortices. The results promote the control over the vortex dynamics via boundary engineering and the vast freedoms of 2D materials.
Fig. 1: PhP optical vortex dynamics in hBN. (a) The simulated PhP electric field amplitude, , at a specific time in a 6×6 μm2 hBN sample (dashed gray) as a result of a temporal excitation. (b) The phase of the field from (a) from which we can determine the locations of the vortices (denoted in blue and red dots). These locations match the amplitude nodal points since the phase is ill-defined at the vortex locations. (c-d) The blue and red dots denote the location of a unity-charge vortex of left-handed and right-handed orientation, respectively. (e) The electric field amplitude for different timestamps, including several vortex trajectories (blue and red curves), and several events of vortex creation an annihilation (stars). The dynamics of the PhP field inside the sample creates the vortex dynamics. Using these simulations, we infer the vortex creation and annihilation rules. (f) The experimental measurement of the PhP field for time delay of ps between the IR laser excitation and the free-electron probe (sample edges in dashed gray). (g) The areas where optical vortices may appear in (f) are denoted in yellow. From the field distribution and the comparison with measurements in different times-delays we determine the vortex locations and charge. (h) The measured PhP field for several timestamps, including the location of the vortices. Few vortex trajectories are shown through the blue and red curves, which include a process of creation an annihilation. In this panel we show only the measurement and vortex locations inside the cyan dashed square in (f).
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