Coupled non-Hermitian systems can be tuned to an absorbing exceptional point (EP) at which both the eigenfrequencies and the eigenmodes associated with perfect capture of an input wave coalesce. We find that a time-domain signature of absorbing EPs is that a class of dispersionless waveforms can be perfectly captured. We show that such systems have improved performance for storage or transduction of energy and that they can be used to convert between waveforms within this class. Finally, we demonstrate that these waveforms can be naturally generated at high frequencies. If time permits, we will explore the possibility of exciting high-order atomic and molecular multipoles in the far field with potential to achieve subatomic resolution, and vibrational modes of helical structures and their coupling to electromagnetic fields.