Parity-Induced Exceptional Points with Localized Loss

We explore the existence and stability of exceptional points (EPs) in finite waveguide arrays subject to single-site dissipation using an exact Laplace-transform framework. We show that the EP landscape is governed by a parameter-free Wronskian condition and a geometry-dependent parity effect, yielding strictly distinct spectral behaviors for even versus odd numbers of waveguides. Specifically, odd chains with edge loss suppress coalescence via a protected central mode, whereas even chains with central loss feature a universal threshold that gives rise to imaginary zero modes. These findings clarify the fundamental rules of non-Hermitian symmetry breaking in finite systems, offering a deterministic framework to predict, engineer, or avoid spectral singularities in integrated photonic lattices.