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

Abstract

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.

Manifestation of Gouy phase anomaly in a coaxial focus array generated by a Dammann zone plate

“…This phenomenon of duplication of Gouy phase into every order can be explained by Eq. (11). In addition, besides the Gouy phase shifts at the locations of those diffraction orders, it can be seen that there is an extra irregular phase shift between the zeroth and first orders and another extra phase shift between the zeroth and first orders.…”

“…Furthermore, they pointed out that, similar to focus engineering, it is also possible to engineer this Gouy phase by modification of discontinuities in the angular spectrum of the pupil aperture. More recently, Kim et al [11] studied the Gouy phase by investigating the irregular wavefront spacing in the neighborhood of focus for a tightly focused field, which indicated a new perspective of the physical picture behind the evolution of Gouy phase. Moreover, they investigated the subtle phase evolution beyond the focus by studying the longitudinal-differential (LD) phase maps.…”