Spectral Distribution of Exceptional Points in Lattices with Localized Loss

Abstract

We explore the existence and stability of exceptional points (EPs) in finite waveguide arrays subject to single-site dissipation. We show that the EP landscape is dictated by a geometry-dependent parity effect, leading to strictly distinct spectral behaviors for arrays with even versus odd numbers of waveguides. Through analytical derivation and numerical analysis, we define the conditions under which these singularities emerge and evolve. Our findings clarify the mechanisms of symmetry breaking in finite non-Hermitian lattices, offering new guidelines for the design of robust optical structures that exploit or avoid exceptional points.

Figures (5)

• Figure 1: Sequence with $N$ coupling waveguides, with coupling constant $\kappa$, where the waveguide $G_j$ has Markovian loss indicated by the dashed arrows.
• Figure 2: Critical loss parameter $\sigma/\kappa$ for a sequence of $N$ guides with loss in guide $G_j$, with $j\le\lceil N/2\rceil$.
• Figure 3: Eigenvalue trajectories versus the loss ratio $\sigma/\kappa$ for a chain with $N=6$ and loss at site $j=3$. Panels (A) and (B) display the real and imaginary parts of the spectrum, respectively.
• Figure 4: Eigenvalue trajectories versus the loss ratio $\sigma/\kappa$ for a chain with $N=4$ and loss at site $j=2$. Panels (A) and (B) display the real and imaginary parts of the spectrum, respectively.
• Figure 5: Regions delineating the eigenvalue spectrum's nature. The purple shaded region denotes the environment with some purely imaginary eigenvalues.