Exploiting the Momentum Distribution in Atomically Confined Plasmonic Fields by Inelastic Scatterings.

The utilization of atomically confined plasmonic fields has revolutionized the imaging technique. According to the fundamental position-momentum uncertainty principle, such a narrow spatial distribution certainly leads to a broad momentum distribution in the fields, which has however been overlooked. Here we propose a novel exploitation for the momentum distribution by adaptively satisfying the conservation law of momentum in inelastic Raman scatterings in periodic systems, providing a unique optical means of directly measuring the whole phonon dispersions. The proposed technique is particularly useful for measuring phonon dispersions of low-dimensional hydrogen-rich materials, which are completely inaccessible via other techniques. The numerical results for a single all- trans polyacetylene chain demonstrate that all phonon dispersion branches can be conclusively measured from their Raman images for the first time. Our findings highlight a unique advantage of the emerging momentum-based nanophotonics and open the door for exploiting highly confined plasmonic fields in another dimension.