Nonlinear isolators have attracted significant attention for their ability to break reciprocity and provide isolation without the need of an external bias. A popular approach for the design of such devices is based on Fano resonators, which, due to their sharp frequency response, can lead to very large isolation for moderate input intensities. Here, we show that, independent of their specific implementation, these devices are subject to fundamental bounds on the transmission coefficient in the forward direction versus their quality factor, input power, and nonreciprocal intensity range. Our analysis quantifies a general tradeoff between forward transmission and these metrics, stemming directly from time-reversal symmetry, and that unitary transmission is only possible for vanishing nonreciprocity. Our results also shed light on the operation of resonant nonlinear isolators, reveal their fundamental limitations, and provide indications on how it is possible to design nonlinear isolators with optimal performance.

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Fano非线性隔离器的基本原理

非线性隔离器具有打破互易性且无需外部偏置即可提供隔离的能力，因此备受关注。设计此类设备的一种流行方法是基于Fano谐振器，由于其尖锐的频率响应，对于中等强度的输入，它可能导致非常大的隔离度。在这里，我们表明，与它们的特定实现方式无关，这些设备在正向传输系数与其质量因数，输入功率和不可逆强度范围之间受到基本限制。我们的分析量化了正向传输和这些度量之间的一般权衡，这直接源于时间反转对称性，并且单一传输仅对于消除不可逆性是可能的。