Enabling infinite $Q$ factors in absorbing optical systems

Resonant optical systems have widespread applications in science and technology. However, their quality ($Q$) factors can be significantly deteriorated, if some of their parts exhibit optical absorption. Here, we show that by coupling a lossy mode of such a structure to two independent lossless modes, one can create a nonradiating and absorption-free bound state in the continuum (BIC). The $Q$ factor of such a BIC is theoretically unlimited despite interaction with an absorbing structure. We use this mechanism to design a plasmonic metasurface with $Q$ factors that are close to $10^7$ in the visible spectral range. The proposed mechanism is general and can be used to engineer ultrahigh-$Q$ resonances in various absorbing structures.