  While scattering of light by atoms and molecules yields large amount of
polarization at the B-band of both T- and L-dwarfs, scattering by dust grains
in cloudy atmosphere of L-dwarfs gives rise to significant polarization at the
far-optical and infra-red wavelengths where these objects are much brighter.
However, the observable disk averaged polarization should be zero if the clouds
are uniformly distributed and the object is spherically symmetric. Therefore,
in order to explain the observed large polarization of several L-dwarfs,
rotation-induced oblateness or horizontally inhomogeneous cloud distribution in
the atmosphere is invoked. On the other hand, when an extra-solar planet of
Earth-size or larger transits the brown dwarf along the line of sight, the
asymmetry induced during the transit gives rise to a net non-zero, time
dependent polarization. Employing atmospheric models for a range of effective
temperature and surface gravity appropriate for T- and L-dwarfs, I derive the
time dependent polarization profiles of these objects during transit phase and
estimate the peak amplitude of polarization that occurs during the inner
contact points of the transit ingress/egress phase. It is found that peak
polarization in the range of 0.2-1.0 % at I- and J-band may arise of cloudy L
dwarfs occulted by Earth-size or larger exoplanets. Such an amount of
polarization is higher than that can be produced by rotation-induced oblateness
of even the rapidly rotating L-dwarfs. Hence, I suggest that time resolved
imaging polarization should be a potential technique to detect transiting
exoplanets around L-dwarfs.
