  We analyse the effect of a strong perpendicular magnetic field on an
intersubband transition in a disordered doped quantum well strongly coupled to
an optical cavity. The magnetic field changes the lineshape of the intersubband
optical transition due to the interface roughness of the quantum well from a
Lorentzian to a Gaussian one. In this regime, a novel form of
magnetic-field-induced cavity protection sets in, which strongly reduces the
polariton linewidth to the cavity contribution only. Implications of our
results for fundamental studies of nonlinear polariton dynamics and for
technological applications to polariton lasers are finally highlighted.
