The Focusing Properties Of Deep Etching Subwavelength Fresnel Zone Plate

The binary phase and amplitude Fresnel zone plate(FZP) is an important planar optical element which accomplishes focusing and imaging function through diffraction and interference, rather than refraction. FZP is superior in many areas of applications such as optical antenna, nanolithography, spectroscopy and optical microscopy in near-field or far-field region. Phase Fresnel zone plate has been found to be advantageous in variety of applications such as confocal microscopy and high resolution lithography in visible regime, which is due to higher diffraction of phase FZPs than that of amplitude FZPs.An analytical model of vector formalism is proposed to investigate the diffraction of high numerical aperture sub-wavelength circular binary phase Fresnel zone plate(FZP). In the proposed model, the scattering on the FZP’s surface, reflection and refraction within groove zones are considered and diffraction fields are calculated using the vector Rayleigh–Sommerfeld integral. The numerical results obtained by the proposed phase thick FZP(TFZP) model show a good agreement with those obtained by the finite-difference time-domain(FDTD) method within the effective extent of etch depth. The optimal etch depths predicted by both methods are approximately equal. The analytical TFZP model is very useful for designing a phase FZP with high-NA and short focal length.Besides, the dependence of focusing characteristics on the incident direction of light illuminating a binary phase sub-wavelength FZP with a substrate film are studied using the finite-different time-domain method. The simulation results show that, in the range of effective etch depth, the intensity and size of FZP’s focusing spot in the far-field region are insensitive to the incident direction of whether light is incident onto the FZP from the substrate film side or from the etched structure side. However, the focal length for the incident beam from the etched structure side of the FZP is larger than that from the substrate film side of the FZP. For two different directions of incidence, focal length decreases as the increase of etch depth. For some special etch depths, for example, the etch depth of 700 nm for the studied FZP structure, the depth of focus is quite great when light is incident onto the FZP from the etched structure side and the reduce of focusing intensity and resolution of spot is within an acceptable range. The simulation results in this paper is useful for the FZP’s applications in microscopy and photolithography.