Matter with topological order [1] (topological matter for short) has gained considerable attention lately. They are thoroughly studied in condensed matter physics [2], but evermore also from the context of high-energy physics. One of the interesting and peculiar characteristics of topological matter is that as far as their interaction with the electromagnetic field is concerned, they exhibit a unique macroscopic magnetoelectric response associated with its topological nature. This response is described by including the so-called $\theta$-term to Maxwell’s electrodynamics. The $\theta$ parameter can be understood as a macroscopic one that encodes its topological properties that underlie their microscopic structure and lends itself to study many “topo-optical effects” [3, 4]. In this talk I will describe the interaction between a plane monochromatic electromagnetic wave incident obliquely onto the surface of topological matter. The surface will be considered as almost planar with an albeit small periodic spatial variation. The $\theta$-term modifies the boundary conditions and in this particular case, this introduces a modification of the “drift” superficial field component that rises slightly above the surface and in direction parallel to the periodic spatial distribution. In the context of perfect conductors, this is known to provide a mechanism for charged particles' acceleration. Here we aim to study the modifications to such charged particle acceleration mechanism by the inclusion of the $\theta$-term. Topological insulators and Weyl semimetals will be considered as particular kinds of topological matter at the surface.