  Motivated by the recent proposal of giant Kerr rotation in WSMs, we
investigate the Kerr and Faraday rotations in time-reversal broken multi-Weyl
semimetals (mWSMs) in the absence of an external magnetic field. Using the
framework of Kubo response theory, we find that both the longitudinal and
transverse components of the optical conductivity in mWSMs are modified by the
topological charge ($n$). Engendered by the optical Hall conductivity, we show
in the thin film limit that, while the giant Kerr rotation and corresponding
ellipticity are independent of $n$, the Faraday rotation and its ellipticity
angle scale as $n$ and $n^2$, respectively. In contrast, the polarization
rotation in semi-infinite mWSMs is dominated by the axion field showing $n$
dependence. In particular, the magnitude of Kerr (Faraday) angle decreases
(increases) with increasing $n$ in Faraday geometry, whereas in Voigt geometry,
it depicts different $n$-dependencies in different frequency regimes. The
obtained results on the behavior of polarization rotations in mWSMs could be
used in experiments as a probe to distinguish single, double, and triple WSMs,
as well as discriminate the surfaces of mWSMs with and without hosting Fermi
arcs.
