We analyze the waveguiding properties of a semiconductor slab waveguide amplifier in which the gain (i.e., the permittivity) in the quantum well (QW) is taken to be anisotropic. Losses may be present simultaneously in the cladding layers. Using scattering theory, a rigorous integral equation is derived. Our model incorporates the two main causes of polarization sensitivity of the amplification, viz., 1) waveguiding and 2) the anisotropic light-matter interaction in the QW. It is determined how much anisotropy is needed in the QW to get a polarization-insensitive amplification. Also, reflection coefficients and TE/TM mixing are studied. A comparison between the exact results and the Born approximation is made. A Green's tensor for a layered structure with losses is derived.