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We explore the scattering of waves in designed asymmetric one-dimensionalwaveguide networks. We show that the reflection between two ports of anasymmetric network can be identical over a broad frequency range, as if thenetwork was mirror-symmetric, under the condition of so-called latent symmetrybetween the ports. This broadband equireflectionality is validated numericallyfor acoustic waveguides and experimentally through measurements on microwavetransmission-line networks. In addition, introducing a generalization of latentsymmetry, we study the properties of an $N$-port scattering matrix $S$. Whenthe powers of $S$ fulfill certain relations, which we coin scaledcospectrality, the setup is guaranteed to possess at least one zero eigenvalueof $S$, so that the setup features coherent perfect absorption. Moreimportantly, scaled cospectrality introduces a scaling factor which controlsthe asymmetry of the incoming wave to be absorbed. Our findings introduce anovel approach for designing tunable wave manipulation devices in asymmetricsetups. As evidenced by our acoustic simulations and microwave experiments, thegenerality of our approach extends its potential applications to a wide rangeof physical systems.

Equireflectionality and customized unbalanced coherent perfect absorption in asymmetric waveguide networks