A new time-domain Fourier-Galerkin (TDFG) theory is developed to simulate the near-field, far-field and spectral characteristics of surface-emitting photonic-crystal distributed-feedback (SE PCDFB) lasers. It is found that a properly-designed two-dimensional hexagonal or square-lattice grating should efficiently couple the output into a single SE mode that retains coherence for aperture diameters of up to ≈1 mm. We identify lattice structures and precise conditions under which all components of the transverse electric or transverse magnetic polarized optical fields constructively interfere to produce a single-lobed, near-diffraction-limited circular output beam. The TDFG simulations predict that quantum efficiencies as high as 30% (60% if reflectors are built into the waveguide structure) should be attainable. A surprising conclusion is that diffractive coupling into the surface-emitting direction must be relatively weak, in order to assure selection of the desired symmetric in-phase mode. Furthermore, gain media with a moderate linewidth enhancement factor should produce the best SE PCDFB performance, whereas edge emitters nearly always benefit from a very small value.