We proposed and fabricated a magnet-free nonreciprocal metasurface platform for on-demand bidirectional phase modulation. Owing to the strong magneto-optical effect and strong magnetocrystalline anisotropy of La:BaM, we achieved nonreciprocal and arbitrary intensity and phase profiles for both forward and backward propagation with subwavelength-scale Mie resonators. For the intensity-modulated NRM, we demonstrated one-way transmission in a wide angular range of 0° to ±64° at 15.7 GHz frequency. For phase-gradient NRMs, we demonstrated three functional devices: a nonreciprocal deflector, a nonreciprocal metalens, and nonreciprocal holography at the Ku band. This technology can be potentially extended to cover the MHz to the optical frequency range by choosing appropriate self-biased magnetic materials. Magnet-free, low-profile, passive, linear, and broadband NRMs are poised to find broad applications in devices such as free-space isolators, nonreciprocal antennas, radomes, and full-duplex wireless communication links.
The platform demonstrated in this study overcomes several barriers that hamper the practical applications of NRMs. Self-biased magnetic meta-atoms eliminate the need for an external field, thereby resolving a major roadblock in the deployment of magnetic metasurfaces. Our approach also circumvents the challenges encountered in other nonreciprocal metasurfaces, such as the sensitivity to incident wave intensity, large active power consumption, high harmonic generation, low signal-to-noise ratio, poor power handling capability, and bandwidth limitations. Our metasurface designs are also insensitive to incidence angles, potentially enabling their application as omnidirectional antennas, for example, for wireless communications or integration on curved surfaces such as antenna radomes. The transmission efficiency of the metasurfaces reaches 30%–77% in the Ku band, ranking among the best values in nonreciprocal metasurfaces reported so far14, 35. This is particularly remarkable considering that no gain elements were used. Even though the experiments were carried out only in the Ku band, NRMs can be constructed in the V band (40 GHz to 75 GHz) or W band (75 GHz to 110 GHz) using the same La:BaM material by observing the nontrivial off-diagonal component at these frequencies in Fig. S2c. Furthermore, the operating frequency of such metasurfaces can be extended to cover the MHz to optical frequencies by choosing different self-biased magnetic materials. For example, in the MHz frequency range, cobalt or nickel spinel ferrites are ideal materials36-39; in the GHz to THz range, hexaferrites with tunable magnetic anisotropies are good candidates40; at optical frequency, self-biased garnet thin films using magnetoelastic effects are promising materials41, 42. Therefore, a variety of bias-free magnetic nonreciprocal metasurfaces are envisioned for future studies.
There is also considerable room for further improvement in device performance. First, reflection at the air-metasurface interface and optical absorption in the meta-atoms, on average, account for 15% and 40% efficiency losses, respectively, in the devices. Impedance-matching structures can be incorporated into meta-atoms to reduce the reflection loss. With optimized doping or growth protocols, the imaginary parts of ε and μ in hexaferrite materials can be diminished43. Moreover, the large off-diagonal μ element implies a “non-perturbative” design scheme in which forward and backward waves yield different modal overlaps with meta-atoms, thereby suppressing the insertion loss to a level well beyond the material’s figure-of-merit limit44. This effect is illustrated in Figs. S3i and S3j, where the scattering cross-section is different for forward and backward propagation in the same meta-atom, leading to a low insertion loss of only 1.1 dB in the one-way transmission metasurface. Second, polarization-independent nonreciprocal metasurfaces can be developed by leveraging different magneto-optical effects, such as transverse magneto-optical Kerr effects (TMOKE) for linearly polarized waves or the Faraday effect for circularly polarized waves. Third, the bandwidth of metasurfaces can be further extended. This is because the gyromagnetic property of the magnetic material is broadband, as shown in Fig. S2c. Dispersion engineering on both the forward and backward propagating modes can be performed on the meta-atoms, analogous to the design of an achromatic metalens, except for the bidirectional nature. These considerations will aid development of nonreciprocal metasurfaces for high-efficiency, broadband, and on-demand nonreciprocal control of electromagnetic radiation in the future.