  Directional lasing, with a low threshold and high quality factor, in active
dielectric nanoantenna arrays is demonstrated. This is achieved through a leaky
resonance excited in coupled gallium arsenide (GaAs) nanopillars. The leaky
resonance is formed by partially breaking a bound state in the continuum (BIC)
generated by the collective, vertical electric dipole resonances excited in the
nanopillars for sub-diffractive arrays. By opening an unprotected, diffractive
channel along one of the periods of the array one can control the
directionality of the emitted light without sacrificing the high Q associated
with the BIC mode, thus achieving directional lasing. A quality factor Q = 2750
is achieved at a controlled angle of emission of ~ 3 degrees with respect to
the normal of the array with a pumping fluence as low as 10 uJ/cm^2. We
demonstrate the possibility to control the lasing directivity and wavelength by
changing the geometrical parameters of the nanoantenna array, and by tuning the
gain spectrum of GaAs with temperature. Lasing action is demonstrated at
different wavelengths and emission at different angles, which can be as large
as 25 degrees to the normal. The obtained results provide guidelines for
achieving surface emitting laser devices based on active dielectric
nanoantennas that are compact and highly transparent.
