Theory of superlensing with complex frequency illuminations

Abstract: Recent experiments have demonstrated that the resolution of superlensing slabs can be significantly enhanced with complex frequency illuminations. In this study, we introduce a novel theoretical framework for analyzing superlensing effects with flat lenses. The framework yields a simple and transparent expression for the steady-state transfer function of lossy superlensing slabs and offers clear criteria for selecting complex frequencies that maximize resolution. It also clarifies the conditions under which the steady-state response dominates over the transient response, highlighting key advantages of synthesized complex frequency excitations compared to direct approaches involving exponentially damped illuminations with an initial time step.