Far-Field Super-Resolution via Longitudinal Nano-Optical Field: A Combined Theoretical and Numerical Investigation

We present a theoretical and numerical investigation of a far-field super-resolution dark-field microscopy technique based on longitudinal nano-optical field excitation and detection. This method is implemented by integrating vector optical field modulation into a back-scattering confocal laser scanning microscope. A complete forward theoretical imaging framework that rigorously accounts for light–matter interactions is adopted and validated. The weak interaction model and general model are both considered. For the weak interaction model, e.g., multiple discrete dipole sources with a uniform or modulated responding intensity are utilized to fundamentally demonstrate the relationship between the sample and the imaging information. For continuous nanostructures, the finite-difference time-domain simulation results of the interaction-induced optical fields in the imaging model show that the captured image information is not determined solely by system resolution and sample geometry, but also arises from a combination of sample-dependent factors, including material composition, the local density of optical states, and intrinsic physical properties such as the complex refractive index. Unlike existing studies, which predominantly focus on system design or rely on simplified assumptions of weak interactions, this paper achieves quantitative characterization and precise regulation of nanoscale vector optical fields and samples under strong interactions through a comprehensive analytical–numerical imaging model based on rigorous vector diffraction theory and strong near-field coupling interactions, thereby overcoming the limitations of traditional methods.