Photonic-crystal distributed-feedback (PCDFB) lasers, in which the DFB grating is defined on a two-dimensional lattice, have the potential to provide near-diffraction-limited, spectrally pure sources of radiation. The conventional 1D DFB laser and also the angled-grating DFB (a-DFB) laser are special cases of the PCDFB geometry. For a first proof-of-principle demonstration, optical lithography and dry etching were used to pattern a 2nd-order two-dimensional rectangular lattice whose grating was tilted by 20 degree(s) relative to the facet normal. The antimonide type-II W active region emitted at (lambda) = 4.6-4.7 micrometers . For pulsed optical pumping, the emission line was much narrower (7-10 nm) than those of Fabry-Perot and (alpha) -DFB lasers fabricated from the same wafer, and the beam quality was enhanced by as much as a factor of 5 compared with the (alpha) -DFB. The observation of two distinct lines in the PCDFB spectrum is attributed to a near-degeneracy of grating resonances at two different symmetry points of the Brillouin zone for the rectangular lattice. Quantum-cascade (QC) PCDFB lasers are shown to be particularly attractive in the mid-IR spectral range since their linewidth enhancement factor, which governs the carrier-induced refractive index change, is close to zero. Using a time-domain Fourier-transform algorithm, we estimate that rectangular-lattice QC lasers should emit in a single mode up to a stripe width of approximately equals may be employed to maintain spectral and spatial coherence over stripes as wide as 3 mm.