  As an attractive degree of freedom in electromagnetic (EM) waves, the orbital
angular momentum (OAM) enables infinite communication channels for both
classical and quantum communications. The exploration of OAM generation
inspires various designs involving spiral phase plates, antenna arrays,
metasurfaces, and computer-generated holograms. In this work, we theoretically
and experimentally demonstrate an approach to producing OAM carrying EM waves
by a point defect in three-dimensional (3D) photonic crystals (PCs).
Simultaneous excitation of two vibrational-defect states with an elaborately
engineered phase retardation generates a rotational state carrying OAM. Through
converting guided waves in a line defect to localized waves in a point defect
and then to radiated vortex waves in free space, the lowest four OAM-mode
emitters, i.e., OAM indices of 1, -1, 2, and -2, are successfully realized.
This work offers a physical mechanism to generate OAM by PCs, especially when
the OAM generation is to be integrated with other designs.
