Analytic theory of complex-frequency-aided virtual absorption

Complex-frequency excitations have recently attracted a lot of attention owing to their ability to solve a number of extraordinary challenges in photonics, such as overcoming losses without gain in metalenses and plasmonic waveguides and achieving virtual absorption. However, the totality of the works so far has been mainly computational or experimental, and a full theory of the complex dynamics enabled by these excitations is still missing. Here, we develop a fully analytical, exact time-domain theory for the dynamical scattering of these excitations by both sides of dielectric plates, which have been used to achieve virtual absorption. Our precise theoretical analysis confirms previous observations and, in addition, reveals a number of intriguing phenomena that were previously missed, such as discontinuities in the scattering of the outgoing electromagnetic field and release of the stored energy in distinct packets.