Angled-distributed-feedback semiconductor lasers have demonstrated 1-W diffraction-limited collimated output from a broad-area aperture. We present the first theoretical analysis of the modes of these devices, explaining their principle of operation and the reasons for their high spatial mode quality. A transfer matrix analysis is presented that can describe the general class of grating-guided waveguides with either finite and/or infinite grating boundaries. Lateral grating-confined broad-area waveguides are shown to have extremely high spatial mode selectivity. The theory is applied to describe the new angled-grating distributed feedback laser (α-DFB), predicting a broad near-Gaussian near field and a collimated diffraction-limited far field, in good agreement with experiment.