Magnet-free nonreciprocal metasurface for on-demand bi-directional phase modulation

doi:10.21203/rs.3.rs-1528665/v1

PDF

Article

Magnet-free nonreciprocal metasurface for on-demand bi-directional phase modulation

https://doi.org/10.21203/rs.3.rs-1528665/v1

This work is licensed under a CC BY 4.0 License

Version 1

posted 28 Apr, 2022

You are reading this latest preprint version

Unconstrained by Lorentz reciprocity, nonreciprocal metasurfaces are uniquely capable of encoding distinctive optical functions on forward- and backward-propagating waves. The nonreciprocal metasurfaces reported to date require external electric or magnetic field biasing or rely on nonlinear effects, both of which are challenging to practically implement. Here, we propose and experimentally realize a magnet-free, linear, and passive nonreciprocal metasurface based on self-biased magnetic meta-atoms. Record transmittance up to 77% and operation angle reaching ±64˚ are experimentally demonstrated. Moreover, on-demand bidirectional phase modulation in a “LEGO-like” manner is theoretically proposed and experimentally demonstrated, enabling a cohort of nonreciprocal functionalities such as microwave isolation, nonreciprocal beam steering, nonreciprocal focusing, and nonreciprocal holography. The design can also be extended to MHz and optical frequencies, taking advantage of the wide variety of self-biased gyrotropic materials available. We foresee that the nonreciprocal metasurfaces demonstrated in this work will have a significant practical impact for applications ranging from nonreciprocal antennas and radomes to full-duplex wireless communication and radar systems.

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 K_u 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 K_u band, ranking among the best values in nonreciprocal metasurfaces reported so far^{14, 35}. This is particularly remarkable considering that no gain elements were used. Even though the experiments were carried out only in the K_u 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 materials^36-39; 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 materials^{41, 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.

Metasurface fabrication. Metasurface fabrication involved the fabrication of La:BaM elements and their attachment onto a Teflon substrate. La:BaM bulk crystals were cut using an ultrahigh-precision computer numerical control (CNC) machine to fabricate square nanopillars with a dimensional accuracy better than 0.05 mm. Subsequently, the nanopillars were placed in an electromagnet with a maximum magnetic field of 2.3 T. The easy magnetization axis was saturated by gradually applying the voltage and current of the electromagnet, and the external magnetic field was gradually removed to maintain the remanent magnetization of the ferrite. The Teflon substrates were 18 cm × 18 cm sheets with a thickness of 0.5 cm. A double-sided adhesive was applied and the acrylic plate was covered with an array of pockets to facilitate meta-atom fixture. The magnetized meta-atoms were placed in predefined pockets and laminated with double-sided adhesive. After all elements were arranged in the substrate, the acrylic plate and unused double-sided adhesive were removed.

Metasurface characterization. All experimental results were measured using a vector network analyzer (VNA, Agilent E8363C) to obtain the K_u-band complex scattering parameters S₂₁ and S₁₂ in a microwave darkroom. To obtain the transmittance spectra of the metasurfaces, two identical circularly polarized antennas were placed on each side of the sample and connected to the two ports of the VNA via cables. Each antenna could function either as a source or detector to obtain the S-parameters. A Teflon lens with a focal length of 30 cm was placed between the metasurface and antennas on both sides to better focus energy on the sample. Calibration was first performed by eliminating the path loss without the sample using a two-port-through calibration. The sample was then placed to obtain the complex S-parameters. For circularly polarized antennas, only microwaves with the same handedness as the antennas could be detected. Because the reflected microwave possesses opposite handedness to the incident wave, the S₁₁ and S₂₂ parameters vanish. Therefore, only two-port-through calibration was used instead of through-reflect-line calibration. To eliminate the multipath effect, the time-domain gate was activated in the VNA to smoothen the spectra.

For the transmittance spectra measurement under oblique incidence, the sample holder was replaced by a scaled rotatable platform (scale accuracy of 1°), and the scattering matrix under oblique incidence was obtained by rotating the sample.

For the beam deflector measurement, the sample and transceiver antenna were fixed on the same rotating platform with the rotation axis located at the center of the sample holder. The rotation angle was measured using an electronic angle ruler with 0.05° accuracy. The beam deflector sample was placed toward or opposite the transceiver antenna to obtain the intensity of the transmitted microwave. To fully characterize the radiation pattern, measurements were performed at angles ranging from 0° to 180°.

For the metalens and hologram measurements, only one Teflon lens was used in front of the source antenna to focus the incident microwave. The transceiver antenna (with a field resolution of 5 mm) was fixed on a linear translation stage driven by a stepper motor in the horizontal and vertical directions. The maximum moving range was 30 cm in both the horizontal and vertical directions. In our measurements, the moving speed of the receiving antenna was 5 mm/s. The custom-built motor scanning program communicated with the VNA to execute point-by-point measurements, and the energy/phase distribution on a specific plane was obtained.

Metasurface simulation. Simulations were performed using the commercial software COMSOL Multiphysics based on the finite element method. Periodic boundary conditions were employed in both transverse directions around each unit cell, whereas the polarization and incident angle of the microwave were defined in the incident port along the z- (longitudinal) axis. A perfectly matched layer was imposed on the incident port to absorb scattered waves. The phase and transmission spectra were inferred from the S-parameters in COMSOL. Home-made Python codes based on the Kirchhoff diffraction integral and Gerchberg–Saxton algorithm were used to calculate the nonreciprocal focusing characteristics and holographic patterns, respectively.

Data availability

Source data are provided with this paper. All other data from this study are available from the corresponding authors upon reasonable request.

Wu, C., Arju, N., Kelp, G., et al. Spectrally selective chiral silicon metasurfaces based on infrared Fano resonances. Nat. Commun. 5, 1–9 (2014).
Park, J., Kang, J.-H., Kim, S. J., et al. Dynamic reflection phase and polarization control in metasurfaces. Nano Lett. 17, 407–413 (2017).
Frese, D., Wei, Q., Wang, Y., et al. Nonreciprocal asymmetric polarization encryption by layered plasmonic metasurfaces. Nano Lett. 19, 3976–3980 (2019).
Liu, H., Wang, Z.-H., Li, L., et al. Vanadium dioxide-assisted broadband tunable terahertz metamaterial absorber. Sci. Rep. 9, 1–10 (2019).
Yao, Y., Shankar, R., Kats, M. A., et al. Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators. Nano Lett. 14, 6526–6532 (2014).
Arbabi, A., Horie, Y., Bagheri, M., et al. Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission. Nat. Nanotechnol. 10, 937 (2015).
Lin, J., Genevet, P., Kats, M. A., et al. Nanostructured holograms for broadband manipulation of vector beams. Nano Lett. 13, 4269–4274 (2013).
Yin, X., Ye, Z., Rho, J., et al. Photonic spin Hall effect at metasurfaces. Science 339, 1405–1407 (2013).
Pfeiffer, C. & Grbic, A. Controlling vector Bessel beams with metasurfaces. Phys. Rev. Appl. 2, 044012 (2014).
Yu, P., Chen, S., Li, J., et al. Generation of vector beams with arbitrary spatial variation of phase and linear polarization using plasmonic metasurfaces. Opt. Lett. 40, 3229–3232 (2015).
Mahmoud, A. M., Davoyan, A. R. & Engheta, N. All-passive nonreciprocal metastructure. Nat. Commun. 6, 1–7 (2015).
Shaltout, A. M., Shalaev, V. M. & Brongersma, M. L. Spatiotemporal light control with active metasurfaces. Science 364, eaat3100 (2019).
Guo, X., Ding, Y., Duan, Y., et al. Nonreciprocal metasurface with space-time phase modulation. Light Sci. Appl. 8, 123 (2019).
Zhang, L., Chen, X. Q., Shao, R. W., et al. Breaking reciprocity with space-time-coding digital metasurfaces. Adv. Mater. 31, 1904069 (2019).
Mazor, Y. & Alù, A. Nonreciprocal hyperbolic propagation over moving metasurfaces. Phys. Rev. B 99, 045407 (2019).
Hadad, Y., Soric, J. C. & Alù, A. Breaking temporal symmetries for emission and absorption. Proc. Natl. Acad. Sci. U. S. A. 113, 3471–3475 (2016).
Kord, A., Sounas, D. L. & Alù, A. Microwave nonreciprocity. Proc. IEEE 108, 1728–1758 (2020).
Jalas, D., Petrov, A., Eich, M., et al. What is-and what is not-an optical isolator. Nat. Photonics 7, 579–582 (2013).
Tanaka, S., Shimomura, N. & Ohtake, K. Active circulators-the realization of circulators using transistors. Proc. IEEE 53, 260–267 (1965).
Kodera, T., Sounas, D. L. & Caloz, C. Artificial Faraday rotation using a ring metamaterial structure without static magnetic field. Appl. Phys. Lett. 99, 031114 (2011).
Carchon, G. & Nanwelaers, B. Power and noise limitations of active circulators. IEEE Trans. Microw. Theory Techn. 48, 316–319 (2000).
Dinc, T., Tymchenko, M., Nagulu, A., et al. Synchronized conductivity modulation to realize broadband lossless magnetic-free non-reciprocity. Nat. Commun. 8, 795 (2017).
Shi, Y., Yu, Z. & Fan, S. Limitations of nonlinear optical isolators due to dynamic reciprocity. Nat. Photonics 9, 388 (2015).
Hofstrand, A., Cotrufo, M. & Alù, A. Nonreciprocal pulse shaping and chaotic modulation with asymmetric noninstantaneous nonlinear resonators. Phys. Rev. A 104, 053529 (2021).
Wang, X., Han, J., Tian, S., et al. Amplification and manipulation of nonlinear electromagnetic waves and enhanced nonreciprocity using transmissive space-time-coding metasurface. Adv. Sci., 2105960 (2022).
Shalaginov, M. Y., Campbell, S. D., An, S., et al. Design for quality: reconfigurable flat optics based on active metasurfaces. Nanophotonics 9, 3505–3534 (2020).
Shalaginov, M. Y., An, S., Zhang, Y., et al. Reconfigurable all-dielectric metalens with diffraction-limited performance. Nat. Commun. 12, 1225 (2021).
Chen, W. T., Zhu, A. Y. & Capasso, F. Flat optics with dispersion-engineered metasurfaces. Nat. Rev. Mater. 5, 604–620 (2020).
Chen, K., Feng, Y., Monticone, F., et al. A reconfigurable active Huygens' metalens. Adv. Mater. 29, 1606422 (2017).
Tay, S., Blanche, P. A., Voorakaranam, R., et al. An updatable holographic three-dimensional display. Nature 451, 694–698 (2008).
Wang, Z., Liu, J., Ding, X., et al. Three-dimensional microwave holography based on broadband Huygens' metasurface. Phys. Rev. Appl. 13, 014033 (2020).
Lin, X., Rivenson, Y., Yardimci Nezih, T., et al. All-optical machine learning using diffractive deep neural networks. Science 361, 1004–1008 (2018).
Ni, X., Kildishev, A. V. & Shalaev, V. M. Metasurface holograms for visible light. Nat. Commun. 4, 2807 (2013).
Wu, J. W., Wang, Z. X., Zhang, L., et al. Anisotropic metasurface holography in 3-D space with high resolution and efficiency. IEEE Trans. Antennas Propag. 69, 302–316 (2021).
Cardin, A. E., Silva, S. R., Vardeny, S. R., et al. Surface-wave-assisted nonreciprocity in spatio-temporally modulated metasurfaces. Nat. Commun. 11, 1469 (2020).
Yang, G., Xing, X., Daigle, A., et al. Planar annular ring antennas with multilayer self-biased NiCo-ferrite films loading. IEEE Trans. Antennas Propag. 58, 648–655 (2010).
Hannour, A., Vincent, D., Kahlouche, F., et al. Self-biased cobalt ferrite nanocomposites for microwave applications. J. Magn. Magn. Mater. 353, 29–33 (2014).
Zhang, J., Chen, D., Li, K., et al. Self-biased magnetoelectric gyrators in composite of samarium substituted nickel zinc ferrites and piezoelectric ceramics. AIP Advances 9, 035137 (2019).
Wu, R., Zhang, D., Maity, T., et al. Self-biased magnetoelectric switching at room temperature in three-phase ferroelectric-antiferromagnetic-ferrimagnetic nanocomposites. Nat. Electron. 4, 333–341 (2021).
Harris, V. G. & Sokolov, A. S. The self-biased circulator: ferrite materials design and process considerations. J. Supercond. Novel Magn. 32, 97–108 (2019).
Avci, C. O., Quindeau, A., Pai, C.-F., et al. Current-induced switching in a magnetic insulator. Nat. Mater. 16, 309–314 (2017).
Zhang, Y., Du, Q., Wang, C., et al. Dysprosium substituted Ce:YIG thin films with perpendicular magnetic anisotropy for silicon integrated optical isolator applications. APL Mater. 7, 081119 (2019).
Joseph, S. D., Huang, Y., Schuchinsky, A., et al. Self-biased CPW circulator with low insertion loss. In: 2020 IEEE MTT-S International Microwave Workshop Series on Advanced Materials and Processes for RF and THz Applications (IMWS-AMP)) (2020).
Zhang, Q., Zhang, Y., Li, J., et al. Broadband nonvolatile photonic switching based on optical phase change materials: beyond the classical figure-of-merit. Opt. Lett. 43, 94–97 (2018).

Acknowledgements

The authors are grateful for the support from the Ministry of Science and Technology of the People’s Republic of China (MOST) (Grant Nos. 2018YFE0109200, 2021YFB2801600), National Natural Science Foundation of China (NSFC) (Grant Nos. 51972044, 52021001, 52102357), Sichuan Provincial Science and Technology Department (Grant Nos. 2019YFH0154, 2021YFSY0016), Fundamental Research Funds for the Central Universities (Grant No. ZYGX2020J005), Open Foundation of Key Laboratory of Laser Device Technology, China North Industries Group Corporation Limited (KLLDT202102).

Author contributions

L.B. and J.Q. conceived the idea. W.Y. (Weihao Yang) performed the device design, metasurface fabrication, and characterization. J.L., W.Y. (Wei Yan) and Y.Y. conducted the device characterization. C.L., E.L., L.D., and J.H. analyzed the data and wrote the manuscript. J.Q., L.D., Q.D., J.H., and L.B. supervised the study. All authors contributed to the technical discussions and writing of the manuscript.

Competing financial interests

The authors declare no competing financial interests.

There is NO Competing Interest.

lensbwd.mp4
metalens backward
lensfwd.mp4
metalens forward
deflectorfwd.gif
deflector forward
deflectorbwd.gif
deflector backward
Supportinginformation.docx

PDF

Version 1

posted 28 Apr, 2022

You are reading this latest preprint version

Magnet-free nonreciprocal metasurface for on-demand bi-directional phase modulation

Status:

Version 1

Abstract

Figures

Full Text

Conclusion

Methods

References

Declarations

Competing Interests

Supplementary Files

Status:

Version 1