Photonic nanojets with ultralong working distance and narrowed beam waist by immersed engineered dielectric hemisphere.

Engineered spherical micro-lens can manipulate light at sub-wavelength scale and emerges as a promising candidate to extend the focal length and narrow the focal spot size. Here, we report the generation of photonic nanojets (PNJs) with an ultralong working distance and narrowed beam waist by an immersed engineered hemisphere. Simulations show that a two-layer hemisphere of 4.5 µm radius exhibits a PNJ with the working distance of 9.6 µm, full width at half maximum of 287 nm, and length of 23.37 λ, under illumination of a plane wave with a 365 nm wavelength. A geometrical optics analysis indicated that the formed PNJ behind the immersed two-layer hemisphere results from the convergence of light of the outer-hemisphere fringe area, which refracts into and passes through the outer hemisphere and then directly leaves the outer-hemisphere flat surface. Thus the embedded hemisphere is comparable to an immersed focusing lens with high numerical aperture, which can promise both long working distance and narrowed beam waist. This is further demonstrated with the corresponding embedded-engineered single-layer hemisphere, whose spherical face is partly cut parallel to the hemispherical flat surface. In addition, the hemisphere is compatible with adjacent laser wavelengths. Finally, a spot size smaller than 0.5 λ is demonstrated in the lithography simulation. Due to these hemispheres low cost, they have potential in far-field lithography for pattern arrays with line width less than 0.5 λ.