Theoretical and practical guide for an axial superresolved focus via Gouy phase steering

Abstract

Achieving an axial superresolved focus with a single lens by simply inserting a modulation mask in the pupil plane is preferred due to its compact configuration and general applicability. However, lack of a universal theoretical model to manifest the superresolved focusing mechanism vastly complicates the mask design and hinders optimal resolution. Here we establish an interference model and find out that the axial resolution closely relates to the Gouy phase gradient (GPG) at the focal point. Using a GPG tuning-based optimization approach, the axial resolution of a ring-mask-modulated beam is readily improved to attain superresolved focal depth for multiple types of pupil function and polarization. In experiment, a focus with an axial resolution of 27% improved from the diffraction limit and 11% finer than the previously reported record is demonstrated for the radially polarized beam. In simulations, a spherical focus with 3D isotropic resolution and a superoscillation-like axial modulation behavior toward extremely high axial resolution is also presented. This approach can be applied for varied types of pupil function, wavelength, and polarization, and can be easily transferred to other traditional or superresolution microscopes to upgrade their axial resolution.