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To extended the effective focusing length (f) and narrowing lateral full width at half maxima (FWHM) of photonic nanojets (PNJs) formed by microlenses with wavelength-scale size, in this paper, we study focusing characteristics of dielectric hemisphere. Refractive index (RI) of hemisphere, radius of covering Au disks on flat-surface of hemisphere and immersed materials effect on focusing characteristics are studied. Simulation study show that hemisphere with radius 4.5 μm, shows narrower focusing beam waist, and shorter f when RI of hemisphere gets bigger. When RI reaches 2.5, lateral FWHM of PNJ and f are 177nm, 324nm, respectively, under illumination of a plane wave with a 365nm wavelength. Comparing with normal hemisphere, hemisphere (RI 1.52, radius 4.5μm and illumination wavelength 365nm) with Au disk covering its flat-surface center, shows obvious smaller FWHM of PNJ and shorter f (still longer than 2 μm). it is because that the engineered hemisphere is like a lens with high numerical aperture, and it only allows incident beam far away from the axis participate in the formation of PNJ. With increasing of Au disk radius, the equivalent numerical aperture gets bigger and thus FWHM of PNJ gets smaller. FWHM of PNJ small than half of illumination wavelength when radius of Au disk gets bigger than 1800nm. The length of PNJ in above study is short, less than 2μm. When the engineered hemisphere (RI 1.52, radius of hemisphere and Au disk 4.5μm and 1800nm, respectively) is immersed in water, MgF2, et al, the f and L get longer than 11μm, 5μm, respectively. Although lateral FWHM of PNJ at this time is bigger than 400nm, it can be narrowed by replacing it with bigger Au disk, optimizing immersed material, et al. Due to low manufacture cost of these hemisphere lenses and lenses array, we believe they have potential in near-field and far-field application with resolution small than 0.5λ.
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