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  1. In a reciprocal system, all the wave travels in the same way backward as forward. When the exchange between the source and detectors result in different transmittance, non-Hermiticity is granted but the nonreciprocity needs to be carefully evaluated. Although most of the integrated circuits are reciprocal, unexpected nonreciprocal response may emerge in the system, especially the tunable components containing asymmetrically coupled resonators, traveling wave electrodes and hysteresis response. The nonreciprocity may result in unexpected signal distribution, distortion and errors in analogue circuits of electrical and photonic networks. With proper engineering, the nonreciprocity can be leveraged and optimized for suppressing the laser noise in photonic systems as isolators, reducing the circuits duplication as circulators. The radio-frequency nonreciprocity can be used for protecting the high power amplifiers from oscillation and damage. Asymmetric coupling can also be useful in simplifying the circuit complexity and reducing crosstalk in the optical interconnect transceiver circuits. 
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    Free, publicly-accessible full text available November 13, 2025