Loss Compensation and Coherent Virtual Absorption via Virtual Complex Frequency Wave Excitation

Complex frequency waves (CFWs), exhibiting extraordinary propagation properties including virtual gain/loss, have attracted increasing research attention. However, the experimental excitation of CFWs at high frequencies, especially in microwave and optical regimes, remains a big challenge. Here, by establishing a mathematical bridge between real and complex frequencies, this work presents a general method for CFW excitation, termed virtual CFW excitation, enabling us to obtain all electromagnetic responses for complex frequencies, including wavevector, electric/magnetic field, and transmission/reflection coefficient, even in the presence of intrinsic noise. Specifically, using virtual CFW excitation can offset the effect caused by material losses and the lost field information of both a point source and surface plasmon polaritons can be successfully recovered. Moreover, coherent virtual absorption is verified by proof-of-principle microwave transmission-line experiments. Our finding provides an effective tool to explore phenomena of complex frequencies, mitigating experimental difficulties and promoting the future development of optical devices.