Vertical Diffraction Theory Of Multi-step Hybrid Fresnel Zone Plates

The Fresnel zone plate (FZP) is an important diffractiveoptical element. With the development of binary optics andmicroelectronics processing technology, the multi-step phasegrating already can be made up by overlaying, laser direct writingand electron beam direct writing. Comparing with the binaryFresnel zone plate, multi-step hybrid Fresnel zone plate canconcentrate the incident light of high angle effectively, so itsdiffraction efficiency is higher. When the annuluses of zone plateare fewer and the focal length is longer, its diffraction fielddistribution can be analyzed with scalar diffraction theory. Whenthe number of ring is more and the focal length is short, the widthof the ring closed to the edge of the zone plate is smaller,subwavelength structures will be generated, thus, we have toadopt vector diffraction analysis instead of scalar diffraction theory which is no longer valid.In this paper, the vertical Rayleigh-Sommerfeld (VRS)diffraction theory is proposed for calculating and analyzing thefocused field distributions of high-numerical-aperture (NA)multi-step hybrid Fresnel zone plates (M-SHFZP). The maincontents include the following aspects:(1) Some basic knowledge,diffraction theory and research status at home and abroad of thezone plate are introduced.(2) VRS diffraction integral formulasare obtain by solving the Maxwell equations. Specific expressionsof VRS diffraction integral in different polarized light are given inthis paper.(3) VRS diffraction theory is used to calculate anddiscuss the diffraction field distribution of ideal thin and real thickM-SHFZP. Comparing the results discovers that M-SHFZP caninhibit other focus light effectively, and the more the number ofsteps, the higher the numerical aperture, the stronger the ability ofM-SHFZP to suppressed high-order foci. The focused intensity ofreal thick M-SHFZP is smaller than that of ideal thin M-SHFZPcaused by transmission coefficient of the film, shielding effect ofsteps and so on. So the transmittance of the film and thediffraction inside the body of FZP cannot be ignored for ahigh-NA M-SHFZP. When the diffraction distance is less than fivewavelength, the results obtained by the VRS diffraction theory agree with the results obtained from the FDTD simulationbasically.