We optimized the far-field emission pattern of one-dimensional photonic crystal nanobeams by modulating the nanobeam width, forming a sidewall Bragg cross-grating far-field coupler. By setting the period of the cross-grating to twice the photonic crystal period, we showed using three-dimensional finite-difference time-domain simulations that the intensity extracted to the far-field could be improved by more than three orders of magnitude compared to the unmodified ideal cavity geometry. We then experimentally studied the evolution of the quality factor and far-field intensity as a function of cross-grating coupler amplitude. High quality factor (>4000) blue (lambda = 455 nm) nanobeam photonic crystals were fabricated out of GaN thin films on silicon incorporating a single InGaN quantum well gain medium. Micro-photoluminescence spectroscopy of sets of twelve identical nanobeams revealed a nine-fold average increase in integrated far-field emission intensity and no change in average quality factor for the optimized structure compared to the unmodulated reference. These results are useful for research environments and future nanophotonic light-emitting applications where vertical in-and out-coupling of light to nanocavities is required. Published by AIP Publishing.