Canonical basis for structured light.

If the analytic signal (AS) of an optical field is treated as a vector, the trigonometric components of its real part can be regarded as the canonical basis (CB) that is independent of laboratory frames and, in general, not orthogonal. This stands in sharp contrast to the conventional approach employing laboratory frames with mutually orthogonal axes. We show that by invoking the CB for either 2D or 3D polarization, or LD orbital angular momentum (OAM) states, or both, four Stokes parameters and a 3D Poincaré sphere can be uniquely and universally defined, regardless of the nature and dimensionality of the AS vector. The CB is shown to retain the information about metric properties and helicity of the polarization/orbitalization ellipse of the beam but not about its tilt in RL, L>2. An illustrating example with a multi-mode OAM beam is provided.