Validation of vectorial theories for the focusing of high numerical aperture Fresnel zone plates

To study the applicability of vectorial angular spectrum (VAS) theory and vectorial Debye–Wolf diffraction integral for the focusing of high numerical aperture (NA) Fresnel Zone Plates (FZPs), these two vectorial methods have been rigorously examined by the three-dimensional finite-difference time-domain (FDTD) method under general and specific conditions. It is found that for a low total annulus number and when the wavelength dispersion or obstruction are existing, Debye–Wolf diffraction integral has failed to describe the light field distribution in the focal region. On the contrary, VAS theory can generally predict the focusing properties. However, when a FZP only contains one or two transparent annuli, both VAS and Debye–Wolf diffraction theories are invalid. Wavelength dispersion and purpose obstruction can produce the multi-focus or focal shift, which can be used for the axial wavelength scanning, the precise measurement of laser wavelength, or optical trapping.