Fig. 2: Characteristics of non-orthogonal meta-atoms.

A Topological configuration of proposed non-orthogonal meta-atom with periodicity a = 0.33λ0, distinct rotation angles of rectangular patches θn (n = 1, 2, 3) are the dominant factor for the non-orthogonal eigen-states implementation (other specific geometric parameters are explained in SI). B Independent profiles of Jones variables αi and βi (i = 1, 2) in two eigen-states of meta-atom against variable θ2 and θ3 with fixed θ1 = 0°. C Evolution trends of Σαi = α1 + α2 and Δβi = β1 – β2 for meta-atom with variable θ2 and θ3 when θ1 = 0°, 30°, 60° and 90°, indicating the non-orthogonality between eigen-state pairs. Gray and black dotted lines separately present orthogonal requirements Σαi = π/2 and Δβi = π. Conventional orthogonal states occur at the overlapping point, indicated by the red stars. D Degree of inhomogeneity with separately variable θi as a function of the frequency, insets present the evolution of the trajectories of corresponding eigen-state pair on Poincaré sphere with frequency (5 GHz to 15 GHz) for the meta-atoms with (θ1, θ2, θ3) = (60°, 0°, 0°), (0°, 90°, 0°), and (0°, 0°, 120°), respectively. E Amplitude and phase profiles of two non-orthogonal eigen-values of meta-atom with variable θ1 as the function of frequency, where gray dashed lines show the baselines of |κ | = 0 and ∠κ = 0.