  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.
