A brightness-and power-scalable polarization beam combining scheme for high-power, broadarea semiconductor laser diodes is investigated numerically and experimentally. To achieve the beam combining, we employ Lyot-filtered optical reinjection from an external cavity, which forces lasing of the individual diodes on interleaved frequency combs with overlapping envelopes and enables a high optical coupling efficiency. Unlike conventional spectral beam combining schemes with diffraction gratings, the optical coupling efficiency is insensitive to thermal drifts of laser wavelengths. This scheme can be used for efficient coupling of a large number of laser diodes and paves the way towards using broad-area laser diode arrays for cost-efficient material processing, which requires high-brilliance emission and optical powers in the kW-regime.