An exact solution to Maxwell’s equations including an evanescent field for a gapped three layered optical system

We have investigated the electromagnetic characteristics of an optical configuration consisting of two dielectric regions of the same n>1 with a thin flat gap of air/vacuum of width d between them. Based on an analytical and exact solution to Maxwell’s equations including an evanescent field in the vacuum gap, we have obtained the transmission property of a four terminal optical circuit that consists of two input lights aimed toward the gap from both sides of the dielectric regions and two output lights from the gap, where all of the four terminals have the same angle to a plane that is vertical to the boundary plane between the dielectric and the vacuum. The results show several unique possible applications of the optical circuit elements such as a variable ratio power splitter, phase to amplitude field modulator, and optical mode selector.