Complex-frequency calculation in acoustics with real-frequency solvers

Complex-frequency calculation enables the characterization of open wave systems in the complex frequency plane as well as the evaluation of wave behaviors under virtual gain and/or loss, which has widespread applications in the investigations of wave scattering and non-Hermitian physics. The corresponding calculation approaches, however, have not been well developed and are usually limited to simple analytical models. Here, we report an efficient numerical method for calculating complex-frequency acoustic wave fields, in which the imaginary part of the frequency is equivalently converted into the variation in material parameters. In this way, the complex-frequency problem becomes a real-frequency one which can then be readily implemented with most existing numerical solvers of the Helmholtz equation. The proposed method is validated by considering two representative examples: the scattering of a one-port lossy acoustic resonator and the imaging of a lossy acoustic superlens under complex frequency excitation. Our work provides a practical and general solution for complex-frequency calculation, in principle, applicable to any complex, dispersive wave systems, which could serve as a powerful tool for fundamental and applied research related to wave scattering and non-Hermiticity.