Focusing light for subsurface imaging

Focusing light through a boundary between two media is a topic of interest in studying and developing different microscopies. In this paper, we use plane wave (PW) expansions and multipole expansions of an electromagnetic field for deriving the transmitted and reflected field for a focused field incident onto different interfaces. We present an approximate model and a rigorous model for calculating the focal field. We also show that the locally-flat approximation of a spherical interface (SI) is not always appropriate, even for a large radius. Our results are helpful in modeling subsurface imaging and sensing.