Gauge-Engineered Tunable Mode Selection in Non-Hermitian Directed-Graph Networks

Abstract

Programmable mode selection is essential for integrated photonic networks, yet selectively isolating individual modes without delicate balancing of gain and loss remains challenging. Here we introduce a gauge-engineering method in non-Hermitian directed-graph networks that support geometry-protected pure decay modes:eigenstates exhibiting smooth exponential amplitude decay along directed paths. In fully connected configurations, a single dominant mode emerges naturally, separated from the remaining modes by a large, tunable energy gap. By introducing synthetic gauge fields through phase-compensated non-reciprocal hopping, any desired pure decay mode can be promoted to the dominant position while its amplitude profile is preserved, which can be naturally interpreted by spectral graph theory. The approach further extends to simultaneous selection of paired modes in half-connected graphs and customizable multi-mode distributions in higher dimensions via orthogonal folding. Our method enables robust, loss/gain-free control over mode profiles, advancing applications in single-mode lasers, sensors, and quantum processing.