Photonics is crucial for communication and computing, as it involves controlling how light scatters. Recent breakthroughs like bound states in the continuum (BICs) and parity-time-symmetric systems are linked to the scattering matrix, governed by passivity and causality. However, using complex-frequency excitations overcomes these limitations, allowing us to study systems with losses or gains and discover phenomena like virtual critical coupling and virtual gain. Applying complex-frequency-excitation concepts to more complicated systems is challenging. In this work, we extend the lumped-element model from circuit theory to analyze light-scattering anomalies in the complex-frequency domain. This approach helps us design and understand effects such as virtual perfect absorption, BICs, real and virtual critical coupling, exceptional points, and anisotropic transmission resonances. These insights broaden our knowledge of electromagnetic wave phenomena and open possibilities in photonics, offering innovative ways to create and optimize optical devices and systems for various applications.
