Phase transitions in Wick-rotated $\mathcal{PT}$-symmetric optics

Abstract: $\mathcal{PT}$-symmetric models with a Wick rotation of time ($ t \rightarrow \pm i t$) show spectral phase transitions that are similar to those of dissipative systems driven out of equilibrium. Optics can provide an accessible test bed to explore spectral phase transitions of Wick-rotated $\mathcal{PT}$-symmetric models. This is shown by considering the transverse dynamics of laser light in optical cavities with variable reflectivity and tilted mirrors. As examples, we discuss in details the optical analogue of the hydrodynamic Squire model of vorticity and the Wick-rotated $\mathcal{PT}$-symmetric nonlinear dimer model.