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.