  Propagation and scattering of lasers present new phenomena and applications
when the plasma medium becomes strongly magnetized. With mega-Gauss magnetic
fields, scattering of optical lasers already becomes manifestly anisotropic.
Special angles exist where coherent laser scattering is either enhanced or
suppressed, as we demonstrate using a cold-fluid model. Consequently, by aiming
laser beams at special angles, one may be able to optimize laser-plasma
coupling in magnetized implosion experiments. In addition, magnetized
scattering can be exploited to improve the performance of plasma-based laser
pulse amplifiers. Using the magnetic field as an extra control variable, it is
possible to produce optical pulses of higher intensity, as well as compress UV
and soft x-ray pulses beyond the reach of other methods. In even stronger
giga-Gauss magnetic fields, laser-plasma interactions begin to enter the
relativistic-quantum regime. Using quantum electrodynamics, we compute modified
wave dispersion relation, which enables correct interpretation of Faraday
rotation measurements of strong magnetic fields.
