Nature Materials

Surface plasmon polaritons and phonon polaritons offer a means of surpassing the diffraction limit of conventional optics and facilitate efficient energy storage, local field enhancement and highsensitivity sensing, benefiting from their subwavelength confinement of light. Unfortunately, losses severely limit the propagation decay length, thus restricting the practical use of polaritons. While optimizing the fabrication technique can help circumvent the scattering loss of imperfect structures, the intrinsic absorption channel leading to heat production cannot be eliminated. Here, we utilize synthetic optical excitation of complex frequency with virtual gain, synthesized by combining the measurements made at multiple real frequencies, to compensate losses in the propagations of phonon polaritons with dramatically enhanced propagation distance. The concept of synthetic complex frequency excitation represents a viable solution to the loss problem for various applications including photonic circuits, waveguiding and plasmonic/phononic structured illumination microscopy.