Visualization of branch points in PT-symmetric waveguides

The visualization of an exceptional point in a PT-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 is real as long as the radius of convergence has not been reached. We also show how one can use a PT-symmetric DC to measure the radius of convergence for non PT-symmetric structures. For such systems the physical meaning of the rather mathematical term `radius of convergence´ is exemplified.