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.