Sub-nanometer displacement sensing via a nanoparticle probe in tightly focused optical field

Résumé fourni par la source

Abstract This study theoretically proposes a highly sensitive displacement measurement method based on the interaction between a cylindrical silicon nanoparticle and a tightly focused azimuthally polarized beam. Instead of focusing solely on the scattered field, this work systematically analyzes the complete optical field information at the back-focal-plane (BFP), including the incident, scattered, extinction, and total fields. By combining the T -matrix method with vector diffraction theory, we establish a rigorous scattering model for nanoparticles under different lateral displacement states and quantitatively analyze the relationship between BFP image asymmetry and displacement. Using the displacement sensitivity as the optimization target, we optimize both the geometric dimensions of the nanoparticle and the parameters of the incident beam. During this process, a distinct dark mode is identified, which originates from destructive interference between the multi-order Mie resonances of the nanoparticle and the tailored incident field. This dark mode suppresses the total BFP background and makes the displacement-induced asymmetric redistribution of the optical field more prominent. We further quantify the dark-mode condition and compare it with a non-dark-mode reference, providing a physical criterion for the enhanced displacement response. In addition, BFP spatial filtering is introduced to further improve the sensitivity, and the optimized configuration exhibits a highly linear displacement response. Through the co-design of nanoparticle geometry, incident optical field, and BFP detection strategy, this work provides theoretical guidance for compact nanophotonic displacement sensors with high sensitivity.

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