Overcoming losses in superlenses with synthetic waves of complex frequency

Superlenses made of plasmonic materials and metamaterials can image features at the subdiffraction scale. However, intrinsic losses impose a serious restriction on imaging resolution, a problem that has hindered widespread applications of superlenses. Optical waves of complex frequency that exhibit a temporally attenuating behavior have been proposed to offset the intrinsic losses in superlenses through the introduction of virtual gain, but experimental realization has been lacking because of the difficulty of imaging measurements with temporal decay. In this work, we present a multifrequency approach to constructing synthetic excitation waves of complex frequency based on measurements at real frequencies. This approach allows us to implement virtual gain experimentally and observe deep-subwavelength images. Our work offers a practical solution to overcome the intrinsic losses of plasmonic systems for imaging and sensing applications.