  The electrodynamics of Weyl semimetals (WSMs) is an extension of Maxwell's
theory where in addition to field strength tensor $F_{\mu\nu}$, an axion field
enters 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 encoded
into the metric of the spacetime felt by electrons in TWM. This allows an
extension of Maxwell's electrodynamics that describes electric and magnetic
fields in TWMs and tilted Dirac material (TDM) when $b^\mu=0$. The tilt
parameter $\bf\zeta$ appearing as off-diagonal metric entries mixing time and
space components mingles $\bf E$ and $\bf B$ fields whereby modifies the
inhomogeneous Maxwell's equations. Surface plasmon polariton (SPP) in these
systems describes the propagation of electromagnetic waves at the {\it
interface of two different spacetime geometries}. In the case of TDM, we find a
characteristic dependence of SPP spectrum on the tilt parameter $\zeta$ which
can be used map $\zeta$ from SPP measurements. In the case of TWM, depending on
whether the interface with vacuum supports a Fermi arc or not, and whether the
propagation direction is along the Fermi arc or transverse to it, we find many
unusual spectral features for SPP modes. Our detailed study of the dependence
of SPP spectra on the arrangements of three vectors $(\bf b, q,\zeta)$, the
first two of which are at our control, can be utilized to map the tilt
characteristics and Fermi arc characteristics from SPP measurements.
