Spectrum analysis of liquid immersion to transparent microsphere based optical nanoscopy

Recently, it was experimentally shown that barium titanate (BaTiO3) glass microsphere immersed in the liquid can be used for super-resolution imaging. However the inherent physical mechanism is still not clear. In this paper, spectrum analysis method is adopted to investigate the effect of liquid immersion to microsphere based optical super-resolution imaging. By tracking the propagation of part of the evanescent wave of the object's spectrum, the range of immersed-liquid's refractive index to achieve super resolution can be derived. To verify this analysis, we theoretically model the imaging process with finite-difference time-domain (FDTD) and angular spectrum propagation method. The result shows that only the BaTiO3 microsphere immersed in the liquid with moderate refractive index, the super-resolution can be achieved. And the lower refractive index of liquid corresponds to larger magnification.