Unique handedness of a circularly polarized plane wave in simulation

While the circular polarization of electromagnetic waves is well known from its poplar definition, its handedness is not uniquely defined, even with given phase convention, observer location and phase difference. For example a circular polarization Ex+jEz (j=sqrt(-1)) traveling along y axis has opposite handedness of the polarization to Ex+jEy traveling in z axis, counter-intuitively. This cannot be explained by the conventional definition, due to the lack of clarity of the definition. In general, when there are two orthogonally linearly-polarized plane waves, say E1 and E2, choice of the reference wave to be E1 or E2 and application of the phase difference to the other wave are ambiguous. This causes confusions and sometimes contradictory results at least in simulations. This paper suggests the necessary and sufficient conditions with the help of the propagation vector and magnetic fields to define uniquely the handedness of a circular or elliptical polarization and thus a desired handedness can be correctly injected in a simulation. The newly proposed triad is added to the conventional definition for easy determining the handedness. The unique handedness of a circular polarization is critical in design, simulation, quantification of polarization-sensitive nanophotonics devices where wave can travel in 4π space along any arbitrary direction.