  We present an infrared magneto-optical study of the highly thermoelectric
narrow-gap semiconductor Bi$_2$Se$_3$. Far-infrared and mid-infrared (IR)
reflectance and transmission measurements have been performed in magnetic
fields oriented both parallel and perpendicular to the trigonal $c$ axis of
this layered material, and supplemented with UV-visible ellipsometry to obtain
the optical conductivity $\sigma_1(\omega)$. With lowering of temperature we
observe narrowing of the Drude conductivity due to reduced quasiparticle
scattering, as well as the increase in the absorption edge due to direct
electronic transitions. Magnetic fields $H \parallel c$ dramatically
renormalize and asymmetrically broaden the strongest far-IR optical phonon,
indicating interaction of the phonon with the continuum free-carrier spectrum
and significant magnetoelectric coupling. For the perpendicular field
orientation, electronic absorption is enhanced, and the plasma edge is slightly
shifted to higher energies. In both cases the direct transition energy is
softened in magnetic field.
