Fig. 1. Schematic diagram of the active DCZIM structure. (a) The structure of an active DCZIM based on a gyromagnetic photonic crystal. (b) Schematic diagram of a unit cell. The YIG pillars were placed in a parallel-plate copper-clad waveguide with height h1=4  mm. The thickness of the waveguide plates was h2=2  mm. Permanent magnets with 5 mm diameter and height h3=5  mm were placed in an acrylic matrix underneath the waveguide and were aligned with the YIG pillars.

Fig. 2. Theoretical and experimental demonstration of an active ZIM. (a) Measured and calculated (gray dots) photonic bands of the active ZIM using Fourier transform field scan (FTFS) of the TM modes corresponding to applied magnetic fields of 0 (left panel) and 430 Oe (right panel). (b), (c) Simulated three-dimensional dispersion surfaces near the Dirac-point frequency, depicting the relationship between the frequency and the wave vectors (kx and ky). (d) COMSOL-computed Re(Ez) on the cross section of a ZIM unit cell at the frequencies indicated by dashed arrows, depicting an electric monopole mode, a transverse magnetic dipole mode, and a longitudinal magnetic dipole. The black circles indicate the boundaries of the YIG pillars.

Fig. 3. Magnetic field-induced phase transition of active ZIM. Real and imaginary parts of the effective permittivity (εeff) and permeability tensor elements (μ and κ) (a) under an applied magnetic field of 0, and under an applied magnetic field of 430 Oe in (b) the bandgap frequency range of 8.95–9.60 GHz and (c) the bandgap frequency range of 10.24–11.04 GHz.

Fig. 4. Structure and characterization of a microwave switch based on active DCZIM. (a) Photograph of the microwave switch sample. (b) The measured transmissions in the absence and presence of an applied magnetic field of 430 Oe. (c) The real part of the Ez distribution observed at 9 GHz inside the metamaterial (each pillar is indicated in gray) in the absence of a magnetic field. (d) The real part of the Ez distribution observed at 9 GHz inside the metamaterial (each pillar is indicated in gray) in the presence of a 430 Oe magnetic field.

Fig. 5. Schematic diagram depicting the Cotton–Mouton effect.

Fig. 6. Magnetic hysteresis loop of a YIG pillar measured using a vibrating sample magnetometer (VSM) at room temperature (300 K). The sample was magnetically saturated under a small applied magnetic field of ∼0.04  T, with negligible remanence of ∼10  Gauss and saturation magnetization of 1780 Gauss.

Fig. 7. Real and imaginary parts of the permeability tensor of YIG under the applied 430 Oe magnetic field.

Fig. 8. Measurement of the photonic band structure via FTFS. (a) Electric fields measured across the photonic crystal at 2.70 GHz. The source was placed at one corner of the sample, and the field was measured across the sample. Owing to the C4z symmetry of the photonic crystal, fields in the other three quadrants could be obtained based on symmetry considerations. The fields were then stitched together to obtain a larger effective sampling area. (b) Field intensity in the reciprocal lattice space obtained via Fourier transform of (a). The first Brillouin zone is denoted by the square region. (c) Isofrequency contours of the Brillouin zone at different frequencies. (d) The 2D photonic band structure of the DCZIM structure. The FTFS data corresponding to high-symmetry points were obtained via interpolation.

Fig. 9. (a) Simulated band structures of the DCZIM under different applied magnetic fields. (b) The band edges of the bandgap, 10.24–11.04 GHz, at M as a function of the applied magnetic field.

Fig. 10. Effective constitutive parameters of the DCZIM under (a), (b) 600 Oe field and (c), (d) 800 Oe field, as calculated using BEMA.

Fig. 11. Magnetic field-induced phase transition of active DCZIM under different applied magnetic fields.

Fig. 12. Device structure of the microwave switch.

Fig. 13. (a) Electric field intensity and (b) phase distributions of 90 deg bent waveguide without YIG pillars.

Fig. 14. Observation of topologically protected unidirectional boundary state in the metamaterial. (a) The structure of the active metamaterial sample with a boundary formed by a copper bar. (b) Numerically simulated projected band structure of the metamaterial with a strip with 20 unit cells in the y direction. (c) Transmission spectra measured by antennas located at the boundary. (d) Simulated real part of Ez field distribution at 10.6 GHz inside the sample [Fig. 4(a)] under a 430 Oe magnetic field. (e) The real part of the Ez field distribution measured at 10.6 GHz inside the sample [Fig. 4(a), each pillar represented in gray] under a 430 Oe magnetic field.

Fig. 15. Observation of a much larger extinction ratio in the ultra-compact spiral magnetically tunable ZIM switch staircase structure. (a) The structure of the spiral magnetically tunable ZIM switch staircase structure. Each layer in the structure is 1.5 mm high which contains 1 mm high metal waveguides and 0.5 mm interlayer air gaps. (b) Transmission spectra of the magnetically tunable ZIM switch’s on state and off state. (c) The real part of the Ez field distribution at 9 GHz inside the sample. Upper panel: on state (without magnetic field applied) with −2.02  dB insertion loss. Lower panel: off state (with 430 Oe magnetic field applied) with −104.53  dB extinction ratio. (d) The simulated transmissions spectra of the proposed structure of Fig. 15 in the absence and presence of an applied magnetic field of 430 Oe.