Locally finite free space as limiting case of PT-symmetric medium

Abstract

We explicitly prove that the transfer matrix of a finite layered P T -symmetric system of fix length L consisting of N units of the potential system '+iV ' and '−iV ' of equal thickness becomes a unit matrix in the limit N → ∞. This result is true for waves of arbitrary wave vector k. This shows that in this limit, the transmission coefficient is always unity while the reflection amplitude is zero for all waves traversing this length L. Therefore, a free space of finite length L can be represented as a P T -symmetric medium.