  Polarization modulators have a broad range of applications in optics. The
acceptance angle of a free-space polarization modulator is crucial for many
applications. Polarization modulators that can achieve a wide acceptance angle
are constructed by attaching a piezoelectric transducer to an isotropic
material, and utilize a resonant transverse interaction between light and
acoustic waves. Since their demonstration in the 1960s, the design of these
modulators has essentially remained the same with minor improvements in the
following decades. In this work, we show that a suitable single crystal with
the correct crystal orientation, functioning as both the piezoelectric
transducer and the acousto-optic interaction medium, could be used for
constructing a highly efficient free-space resonant polarization modulator
operating at megahertz frequencies and exhibiting a wide acceptance angle. We
construct the modulator using gallium arsenide, an optically isotropic and
piezoelectric crystal, and demonstrate polarization modulation at 6 MHz with an
input aperture of 1 cm in diameter, acceptance angle reaching $\pm30^\circ$,
and modulation efficiency exceeding 50%. Compared to state-of-the-art resonant
photoelastic modulators, the modulator reported in this work exhibits greater
than 50 fold improvement in modulation frequency for the same input aperture,
while simultaneously reducing the thickness by approximately a factor of 80.
Increasing the modulation frequency of photoelastic modulators from the
kilohertz to the megahertz regime and substantially reducing their thickness
lead to significant performance improvements for various use cases. This
technological advancement also creates opportunities for utilizing these
devices in new applications.
