Sub-50 nm focusing of a 405 nm laser by hemispherical silicon nanolens

In this work, we study the light focusing behaviors of sub-micron Si hemispherical nanolens in theory. Results show that the width and depth of the focus spot light at 405 nm can reach 42 nm (approximately {\lambda}/10) and 20 nm ({\lambda}/20), respectively. Theoretical analysis indicates that this nano-focusing phenomenon comes from two reasons, the high refractive index of Si and the sub-micro size of the lens which considerably decrease the influence of material losses. The focusing capability of Si nanolens is comparable with current EUV technique but with a low cost, providing an alternative approach towards super-resolution photolithography and optical microscopy.