Anti-PT symmetry in dissipatively coupled optical systems

We show that anti-$\mathcal{PT}$ symmetry can be realized in dissipatively coupled optical systems. Its emergence gives rise to spontaneous phase transitions for the guided and localized photonic eigenmodes in the waveguide and cavity systems studied, respectively. As a ubiquitous feature we demonstrate that constant refraction [analogous to unit refraction in [Nat. Phys. 12, 1139 (2016)]] occurs in the $\mathcal{PT}$-symmetric phase, which leads to several interesting properties for the photonic system, such as flat broadband light transport and dispersion-induced dissipation.