  The optical vortices carrying orbital angular momentum (OAM) are commonly
generated by modulating the available conventional light beam. This article
shows that a micro-laser operates at the exceptional point (EP) of the
non-Hermitian quantum system can directly emit vortex laser with well-defined
OAM at will. Two gratings (the refractive index modulation and along azimuthal
direction and the grating protruding from the micro-ring cavity) modulate the
eigenmode of a micro-ring cavity to be a vortex laser mode. The phase-matching
condition ensures that we can tune the OAM of the vortex beam to be arbitrary
orders by changing the grating protruding from the micro-ring cavity while the
system is kept at EP. The results are obtained by analytical analysis and
confirmed by 3D full wave simulations.

Optics