Visualization of Branch Points inPT-Symmetric Waveguides

Abstract

The visualization of an exceptional point in a $\mathcal{P}\mathcal{T}$-symmetric directional coupler (DC) is demonstrated. In such a system the exceptional point can be probed by varying only a single parameter. Using the Rayleigh-Schrödinger perturbation theory we prove that the spectrum of a $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian is real as long as the radius of convergence has not been reached. We also show how one can use a $\mathcal{P}\mathcal{T}$-symmetric directional coupler to measure the radius of convergence for non-$\mathcal{P}\mathcal{T}$-symmetric structures. For such systems the physical meaning of the rather mathematical term radius of convergence is exemplified.