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While conventional surface waves propagate along the surface and decay perpendicularly from the interface, the ghost surface polaritons show oblique propagation direction with respect to the interface. Here, we have discovered topologically protected ghost surface polaritons by applying the lattice transformation optics method to gyromagnetic photonic crystals. By introducing the transformation optics method to periodic systems, we develop the lattice transformation optics method to engineer the band structures and propagation directions of the surface polaritons. We show that a simple shear transformation on the square lattice can tailor the propagation directions with ease. The reversed ghost surface polariton is discovered by setting a negative shear factor. Interestingly, we find the topological invariant Chern number will change sign when the orientation of the Brillouin zone flipped during the transformation. Our findings open up new avenues for studying ghost surface polaritons and provide a general engineering method for periodic systems., Comment: 8 pages, 6 figures

Negative reflection and negative refraction are exotic phenomena that can be achieved by platforms such as double-negative metamaterial, hyperbolic metamaterial, and phase-discontinuity metasurface. Recently, natural biaxial van der Waals (vdW) materials, which support extremely anisotropic, low-loss, and highly confined polaritons from infrared to visible regime, are emerging as promising candidates for planar reflective and refractive optics. Here, we introduce three degrees of freedom, namely interface, crystal direction, and electric tunability to manipulate the reflection and refraction of the polaritons. With broken in-plane symmetry contributed by the interface and crystal direction, distinguished reflection and refraction such as negative and backward reflection, positive and negative refraction could exist simultaneously and exhibit high tunability. The numerical simulations show good consistency with the theoretical analysis. Our findings provide a robust recipe for the realization of negative reflection and refraction in biaxial vdW materials, paving the way for the polaritonics and interface nano-optics., Comment: 15 pages, 4 figures

Polaritons in polar biaxial crystals with extreme anisotropy offer a promising route to manipulate nanoscale light-matter interactions. The dynamical modulation of their dispersion is great significance for future integrated nano-optics but remains challenging. Here, we report a momentum-directed strategy, a coupling between the modes with extra momentum supported by the interface and in-plane hyperbolic polaritons, to tailor topological transitions of anisotropic polaritons in biaxial crystals. We experimentally demonstrate such tailored polaritons at the interface of heterostructures between graphene and {\alpha}-phase molybdenum trioxide ({\alpha}-MoO3). The interlayer coupling can be electrically modulated by changing the Fermi level in graphene, enabling a dynamic topological transition. More interestingly, we found that the topological transition occurs at a constant Fermi level when tuning the thickness of {\alpha}-MoO3. The momentum-directed strategy implemented by interface engineering offers new insights for optical topological transitions, which may shed new light for programmable polaritonics, energy transfer and neuromorphic photonics.