Fig. 1. Various 3D IFCs for (a) a closed ellipsoid and (b) an open hyperboloid when the frequency increases from ω to ω+δω. The energy flows in the x, y, and z directions are marked using red, pink, and yellow arrows, respectively.

Fig. 2. (a) Radiation patterns for a simple point dipole in air, where the EM waves can propagate along all directions. (b)–(e) Unidirectional propagation from the Huygens metasource in air. (f) Radiation patterns for a simple point dipole in HMM, where the EM waves propagate mainly along the four channels with high-k modes. Panels (g)–(j) are similar to (b)–(e) but for unidirectional propagation of the Huygens metasources in an HMM.

Fig. 3. The |Fk| of the Huygens metasources as functions of the propagation direction θ in different settings. The Huygens metasources are shown in the purple boxes with numbers that indicate the phase delay (degree unit) of each excitation source. The |Fk| functions (normalized by their maximum values) in the HMM and air are denoted by blue and orange lines, respectively. The dashed red and black lines indicate the HMM dispersion ω(kx,kz) and the maximum value of |Fk|. Here, d=0.1λ, where λ is the wavelength in vacuum, and p0=1.

Fig. 4. (a) Schematic of a TL-based HMM structure with p=12mm, w=2mm, and C=1pF. (b) Prototype of a 2D TL with 21×21 unit cells and the related anisotropic 2D-circuit model. The source is near the center of the sample. The inset shows the amplified lumped capacitors, which are loaded in the x direction. (c) The effective anisotropic EM parameters are based on the TLs, where μz=0 is marked using a green dotted line. (d) The IFC of a circuit-based HMM with μz=−1.47, μx=1, and ε=3.57 at f=1.5GHz. The asymptote is represented by purple dashed lines.

Fig. 5. (a) Simulated point dipole radiation patterns in the circuit-based normal medium. The EM waves can propagate along all directions. (b)–(e) Unidirectional propagation of the Huygens metasources in a circuit-based normal medium. Panels (f)–(j) correspond, respectively, to (a)–(e) but for the simulated radiation patterns in the circuit-based HMM. Panels (k)–(o) correspond, respectively, to (a)–(e) but for the measured radiation patterns in the circuit-based HMM.

Fig. 6. (a), (b) Structure and related anisotropic 2D-circuit model of the TL-based DPS medium. Panels (c) and (d) are similar to (a) and (b) but for MNG media. Here, p=12mm, w=2.8mm, and C=5pF. (e) Dispersion relations of guided modes in a hyperbolic waveguide that is composed of a core HMM layer and two DPS-medium cladding layers. The structure is shown in the inset. Panel (f) is similar to (e), but for a normal waveguide, which is composed of a core layer of DPS medium and two MNG-medium cladding layers.

Fig. 7. Schematics of (a) anomalous PSHE in an HMM waveguide and (b) normal PSHE in a DPS waveguide. A source with specific handedness excites only a single-guided mode with a specific propagation direction. Anomalous unidirectional excitation occurs in the HMM waveguide. For a counterclockwise-spin metasource, only the guided modes that propagate from right to left and left to right are excited in the (c) HMM and (d) DPS waveguides, respectively. However, for a clockwise-spin metasource, only the guided modes that propagate from left to right and right to left are excited in the (e) HMM and (f) DPS waveguides, respectively.

Fig. 8. (a) Experimental schematic of a circuit-based hyperbolic waveguide. Measured near-field distributions of |Ey| for (c) counterclockwise and (e) clockwise spin metasources. Panels (b), (d), and (f) are similar to (a), (c), and (e), but for the circuit-based normal waveguide.