Reciprocity is a fundamental symmetry of Maxwell’s equations. It is known that reciprocity imposes constraints on transmission, absorption, and emission. Here, we reveal reciprocity constraints on reflection. We determine the sets of all attainable reflection coefficients of $n$-port scattering matrices with prescribed singular values, both with and without assuming reciprocity. Their difference establishes reciprocity constraints and nonreciprocal behaviors. As an application, we examine the conditions for all-zero reflections. Our results deepen the understanding of reciprocity in optics.

中文翻译：

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反射的互惠约束

互易性是麦克斯韦方程组的基本对称性。众所周知，互易性对传输、吸收和发射施加了限制。在这里，我们揭示了反射的互惠约束。我们确定所有可达到的反射系数的集合$n$具有规定奇异值的端口散射矩阵，无论是否假设互易性。它们的差异建立了互惠约束和非互惠行为。作为一个应用程序，我们检查了全零反射的条件。我们的研究结果加深了对光学互易性的理解。