Title: Enhanced Robustness via Loss Engineering in Detuned Non-Hermitian Scattering Systems

Abstract: Non-Hermitian optics has revealed a series of counterintuitive phenomena with profound implications for sensing, lasing, and light manipulation. While the non-Hermiticity of Hamitonians is well-recognized, recent advancements in non-Hermitian physics have broadened to include scattering matrices, uncovering phenomena such as simultaneous lasing and coherent perfect absorption (CPA), reflectionless scattering modes (RSMs), and coherent chaos control. Despite these developments, the investigation has predominantly focused on static and symmetric configurations, leaving the dynamic properties of non-Hermitian scattering in detuned systems largely unexplored. Bridging this gap, we extend certain stationary non-Hermitian scattering phenomena to detuned systems. We delve into the interplay between bi-directional RSMs and RSM exceptional points (EPs), and elucidate the global existence conditions for RSMs under detuning. Moreover, we introduces a novel category of EPs, characterized by the coalescence of transmission peaks, emerging independent with the presence of Hamiltonian EPs. The transmission EPs (TEPs) exhibit flat-top lineshape and can be extended to a square-shaped spectrum when detuning is involved, accompanied by a distinctive phase transition. Significantly, we demonstrate the applications of the TEPs in a one-dimensional coupled cavity system, engineered to enhance sensing robustness against environmental instabilities such as laser frequency drifts, which can exceed 10 MHz. This capability represents a substantial improvement over traditional sensing methods and an important improvement of fragile EP sensors. Our findings not only contribute to the broader understanding of non-Hermitian scattering phenomena but also paves the way for future advancements in non-Hermitian sensing technologies.