Kerr Cavity Solitons in Active $\mathcal{PT}$-Symmetric Dimers

A
$\mathcal{PT}$
-symmetric photonic dimer consists of two identical coupled cavities, one with loss and the other with overall gain [1]. While exact
$\mathcal{PT}$
-symmetry is only achieved when the gain-to-loss ratio is
$\rho=+1$
, hidden
$\mathcal{PT}$
, leading to similar dynamics, occurs for
$(\rho\neq 1)$
. Recently, (hidden)
$\mathcal{PT}$
-symmetric systems attracted attention in the context of frequency combs as Kerr cavity solitons (CS) have been shown to exist in driven gain-loss ring resonators [2], as well as on each side of the exceptional point in loss-loss coupled microrings [3]. In this work, we analyze the existence region and the stability of CSs in the
$\mathcal{PT}$
-symmetric regime (strong coupling), when unequal resonator detunings are considered. The dynamics in the coupled gain-loss Kerr cavities [Fig. 1(a)] are described by the following set of normalized equations: