Reflectionless Transmission through Dielectrics and Scattering Potentials

Abstract

A complete solution is given for the problem of constructing a plane stratified dielectric medium having that the property that at a fixed frequency and polarization a plane wave at any angle of incidence will be transmitted without reflection by the medium. This problem can also be interpreted quantum-mechanically. The dielectric medium of the first interpretation becomes, in the second interpretation, a potential for the one-dimensional Schrödinger equation such that a particle which is sent in from - ∞ is transmitted with probability one of getting through to + ∞, no matter what the initial kinetic energy of the particle may be. In addition, the results can be applied to the problem of finding perfectly matched nonuniform transmission lines.