Longitudinal-differential phase distribution near the focus of a high numerical aperture lens: Study of wavefront spacing and Gouy phase

We present a longitudinal-differential (LD) phase distribution near the focus of a high numerical aperture (NA=0.9) aplanatic lens illuminated with a linearly polarized monochromatic plane wave. The Richards and Wolf method is used to compute field distributions. The LD phase map is obtained by analyzing the deviation of the phase of the simulated wave to the phase of a referential plane wave. We discuss the irregular wavefront spacing that is linked to the Guoy phase and disclose subtle details of the phase features with respect to the spatial domain relative to the focal point. The LD phase is used to revisit different definitions of the focal region. We eventually identify the definition that is in agreement with the Gouy phase in the focal region. Our work paves the way towards a coherent notion to quantify the optical action of high NA optical elements that are increasingly important for many applications.