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

Gouy phase anomaly of the coaxial focus array generated by a Dammann zone plate (DZP) was investigated. Based on Debye vectorial diffraction theory, the longitudinal-differential (LD) phase profile was presented in the focal region of a high numerical aperture aplanatic objective with a DZP located before as the pupil filter. The numerical simulations show that there is a Gouy phase shift exactly located at the position of every diffraction order along the axial direction. Besides the well-known Gouy phase, a type of extra irregular phase shift among some diffraction orders is demonstrated. This interesting phenomenon of the extra phase shift, physically, is attributed to transversal confinement inside the pupil aperture of the focusing system, which is induced by the discontinuities in phase retardation between any two adjacent zones of DZPs. These extra irregular phase shifts are very different for different kinds of DZPs, and thus this extra phase shift effect can be seen as a characteristic of certain DZPs. In addition, the 3D differential phase maps are presented for investigation of the subtle phase evolution in the off-axis volume.