Complex-frequency excitations in photonics and wave physics

Closed, lossless optical cavities are characterized by a Hamiltonian that obeys Hermiticity, resulting in strictly real-valued resonance frequencies. By contrast, non-Hermitian wave systems are characterized by Hamiltonians with poles and zeros at complex frequencies, whose control through precise engineering of material loss and gain can lead to exotic scattering phenomena. Notably, excitation signals that oscillate at complex-valued frequencies can mimic the emergence of gain and loss, facilitating access to these non-Hermitian responses without material modifications. These findings have been advancing the fundamental understanding of wave-matter interactions and are enabling breakthroughs in metamaterials, imaging, sensing, and computing. This Review examines theoretical advances and experimental discoveries in this emerging field, demonstrating how tailored time-domain excitations offer new opportunities for wave manipulation and control.