Phase-dependent stability and interconversion of dissipative defect solitons in non-Hermitian lattices with even gain and loss

We investigate dissipative defect solitons in a one-dimensional non-Hermitian lattice featuring an even spatial distribution of linear gain and loss and a central defect. We investigate two families of dissipative defect solitons, namely, in-phase (IP) and out-of-phase (OOP) solitons, under both focusing and defocusing nonlinearities. Their linear origins, existence domains, stability properties, and propagation dynamics are systematically analyzed. In the defocusing medium, the nonlinear branches bifurcate from the corresponding linear defect modes and exist within a finite parameter region. By contrast, the focusing solitons have no linear limit and require a finite power threshold. For a given nonlinearity, the IP and OOP branches exhibit coincident power and propagation-constant curves and nearly identical effective widths, yet their stability properties differ substantially. Under defocusing nonlinearity, the IP solitons remain stable in their existence domain, whereas the OOP solitons are unstable. Under focusing nonlinearity, the IP solitons possess a narrow stability window in the middle parameter region, whereas the OOP solitons remain stable over a broader region near the lower cutoff. Direct propagation simulations combined with normalized modal projections reveal two instability outcomes: destruction of the localized structure and conversion between the IP and OOP phase configurations. These results demonstrate that the relative phase structure provides essential stability information that cannot be inferred from the field amplitude or power alone.