Chromatic analysis of harmonic Fresnel lenses by FDTD and angular spectrum methods

In this paper, we present a detailed and rigorous study of cylindrical harmonic Fresnel lenses (HFLs) using the finite difference time domain method (FDTD) and angular spectrum method (ASM). The HFL is a kind of diffractive lens that can have maximum diffraction efficiency at several discrete harmonic wavelengths, which is suitable for some broadband applications. Previous studies on HFLs were investigated mainly in the domain of paraxial approximation. By using our proposed calculation method, we have determined the efficiency, focal length, maximum focus intensity, and full width at half maximum (FWHM) of the focal spot for several harmonic numbers and for F-numbers of 0.5, 1, and 3. To compare with the paraxial approximation, we have presented the response to both s-polarized and p-polarized light with constant refractive index and real dispersive material, BK7. Moreover, we have also analyzed the cases with oblique illumination. We have shown that the harmonic wavelengths do not change with F/# and that the diffraction efficiency and FWHM of the focus increase as F/# increases. New results on harmonic wavelengths shift and oblique angle of incidence response have been detailed.