What is a phase transition? Generally speaking, a phase transition is a dis-continuous change of certain properties of a medium as a result of a change of some external condition.
In the field of quantum mechanics, it is well known that Hermiticity of an operator guarantees a real eigenvalue spectrum, but an operator is not necessary to be Hermitian in order to give real eigenvalues. If an operator is PT symmetric, its eigenvalues are real in PT symmetric phase and are imaginary in broken PT symmetric phase. However, such a PT symmetric system is hard to realize in quantum system, but it is relatively easy to realize in optics because a PT symmetric potential can be achieved by carefully designed regions of refractive indexes with balanced loss and gain. A passive PT symmetric system can also be archived if the refractive indexes have different loss and no gain medium is required.
Recently, a PT symmetric system is realized experimentally using coupled and balanced loss and gain waveguides, and a passive PT symmetric system is realized experimentally using a metasurface. However, their experimental detection often relies on observing the interference pattern with a reference beam or relies on measurement of complex transmission coefficients. These are either not real time detection or not feasibly measureable at the optical frequency
In this thesis, we propose to use a passive waveplate (without gain medium) to observe the phase transition due to PT symmetry breaking manifested by a sudden jump of cross-polarization intensity pattern. Through different numerical calculations, we identified the necessary design principle for a sharp observation of phase transition. Different methods for achieving a passive waveplate and their consequence is also discussed. Neither interference with a reference beam nor measurement of complex transmission coefficients are required in our proposal, and the observation is real time.
Given the recent development of tunable metasurface, we believe the proposal in this thesis should provide a fertile ground for exploring the exotic behavior from a PT symmetric system in the future.