Exponentially Sensitive Lattices: Scaling and Pseudospectra

It is well established that non-Hermitian systems operating in the vicinity of exceptional points [1] demonstrate ultrasensitive behavior, amplifying even minimal perturbations, that make them ideal for sensing applications [2]. Alternatively, ultrasensitivity also appears in lattices with asymmetric couplings, where the non-Hermitian skin effect occurs [3]. It has been shown that the spectra of such asymmetric lattices exhibit exponential sensitivity with respect to the lattice size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> when the boundary conditions are varied, due to the lattice's topological properties [4]. In this study, we examine the exponential sensitivity of asymmetric photonic lattices based on pseudospectra theory [5], [6]. Our analysis reveals the connections between pseudospectra scalings with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> and/or perturbation strength, and physical obeservables that characterize the underlying non-normality and thus exponential sensitivity.