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The electrodynamics of Weyl semimetals (WSMs) is an extension of Maxwell'stheory where in addition to field strength tensor $F_{\mu\nu}$, an axion fieldenters the theory which is parameterized by a four-vector $b^\mu=(b_0,\bf b)$.In the tilted Weyl matter (TWM) an additional set of parameters${\bf\zeta}=(\zeta_x,\zeta_y,\zeta_z)$ enter the theory that can be encodedinto the metric of the spacetime felt by electrons in TWM. This allows anextension of Maxwell's electrodynamics that describes electric and magneticfields in TWMs and tilted Dirac material (TDM) when $b^\mu=0$. The tiltparameter $\bf\zeta$ appearing as off-diagonal metric entries mixing time andspace components mingles $\bf E$ and $\bf B$ fields whereby modifies theinhomogeneous Maxwell's equations. Surface plasmon polariton (SPP) in thesesystems describes the propagation of electromagnetic waves at the {\itinterface of two different spacetime geometries}. In the case of TDM, we find acharacteristic dependence of SPP spectrum on the tilt parameter $\zeta$ whichcan be used map $\zeta$ from SPP measurements. In the case of TWM, depending onwhether the interface with vacuum supports a Fermi arc or not, and whether thepropagation direction is along the Fermi arc or transverse to it, we find manyunusual spectral features for SPP modes. Our detailed study of the dependenceof SPP spectra on the arrangements of three vectors $(\bf b, q,\zeta)$, thefirst two of which are at our control, can be utilized to map the tiltcharacteristics and Fermi arc characteristics from SPP measurements.

Electrodynamics of tilted Dirac/Weyl materials: A unique platform for unusual surface plasmon polaritons