Propagation of intense circularly polarized laser pulses in strongly magnetized inhomogeneous plasmas is investigated. It is shown that a left-hand circularly polarized laser pulse propagating up the density gradient of the plasma along the magnetic field is reflected at the left-cutoff density. However, a right-hand circularly polarized laser can penetrate up the density gradient deep into the plasma without cutoff or resonance and turbulently heat the electrons trapped in its wake. Results from particle-in-cell simulations are in good agreement with that from the theory. (c) 2015 AIP Publishing LLC.