  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, high sensitivities, benefitting 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 taken at multiple real frequencies, to restore the lossless
propagations of phonon polaritons with significantly reduced intrinsic losses.
The concept of synthetic complex frequency excitation represents a viable
solution to compensate for loss and would benefit applications including
photonic circuits, waveguiding and plasmonic/phononic structured illumination
microscopy.
