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1

Xu, Zhu-Long, Shi-Bo Yu, Junjie Liu und Kuo-Chih Chuang. „A Tunable Zig-Zag Reflective Elastic Metasurface“. Crystals 12, Nr. 8 (20.08.2022): 1170. http://dx.doi.org/10.3390/cryst12081170.

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In this paper, inspired by origami structures, we offer a very simple tuning method to overcome the limitations of general elastic metasurfaces, where only a certain functionality at a certain frequency range can be achieved, by designing a reflective metasurface based on foldable/deployable zig-zag structures. By utilizing peg/screw connections, the folding angles of the zig-zag structures can be easily tuned while also being fixable. By tuning the folding angle, the subunit of the zig-zag metasurface can cover a 2π phase shift span and the phase shift can be tuned continuously, and almost linearly, with respect to the folding angle. With a simple folding motion, the tunable reflective metasurface can steer reflected flexural waves in different directions and focus-reflected flexural waves with different focal distances. In addition to demonstrating tunable performance, the mechanism that associates the changing speed of the phase shift is explained. The proposed tunable zig-zag elastic metasurface provides a new way to design reconfigurable metamaterials/metasurfaces.
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2

Yang, Jingyi, Sudip Gurung, Subhajit Bej, Peinan Ni und Ho Wai Howard Lee. „Active optical metasurfaces: comprehensive review on physics, mechanisms, and prospective applications“. Reports on Progress in Physics 85, Nr. 3 (01.03.2022): 036101. http://dx.doi.org/10.1088/1361-6633/ac2aaf.

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Abstract Optical metasurfaces with subwavelength thickness hold considerable promise for future advances in fundamental optics and novel optical applications due to their unprecedented ability to control the phase, amplitude, and polarization of transmitted, reflected, and diffracted light. Introducing active functionalities to optical metasurfaces is an essential step to the development of next-generation flat optical components and devices. During the last few years, many attempts have been made to develop tunable optical metasurfaces with dynamic control of optical properties (e.g., amplitude, phase, polarization, spatial/spectral/temporal responses) and early-stage device functions (e.g., beam steering, tunable focusing, tunable color filters/absorber, dynamic hologram, etc) based on a variety of novel active materials and tunable mechanisms. These recently-developed active metasurfaces show significant promise for practical applications, but significant challenges still remain. In this review, a comprehensive overview of recently-reported tunable metasurfaces is provided which focuses on the ten major tunable metasurface mechanisms. For each type of mechanism, the performance metrics on the reported tunable metasurface are outlined, and the capabilities/limitations of each mechanism and its potential for various photonic applications are compared and summarized. This review concludes with discussion of several prospective applications, emerging technologies, and research directions based on the use of tunable optical metasurfaces. We anticipate significant new advances when the tunable mechanisms are further developed in the coming years.
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3

Peng, Yao-Yin, Jin-Heng Chen, Zhang-Zhao Yang, Xin-Ye Zou, Chao Tao und Jian-Chun Cheng. „Broadband tunable acoustic metasurface based on piezoelectric composite structure with two resonant modes“. Applied Physics Express 15, Nr. 1 (01.01.2022): 014004. http://dx.doi.org/10.35848/1882-0786/ac444a.

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Abstract In this letter, we propose a deep-wavelength tunable acoustic metasurface composed of a fixed piezoelectric composite structure with a broad operating frequency range. The metasurface unit has two tunable resonant frequencies determined by specific external inductors and can continuously modulate the phase of the transmitted wave. The influence of the inductors on resonant frequencies are studied by simulation and experiment. Moreover, the functions of acoustic beam steering and focusing by the designed metasurface at three arbitrarily chosen frequencies are verified in simulation. This work may have good potential in the design of acoustic metasurfaces with broadband operating frequencies.
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4

He, Shaowei, Huimin Yang, Yunhui Jiang, Wenjun Deng und Weiming Zhu. „Recent Advances in MEMS Metasurfaces and Their Applications on Tunable Lens“. Micromachines 10, Nr. 8 (31.07.2019): 505. http://dx.doi.org/10.3390/mi10080505.

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The electromagnetic (EM) properties of metasurfaces depend on both structural design and material properties. microelectromechanical systems (MEMS) technology offers an approach for tuning metasurface EM properties by structural reconfiguration. In the past 10 years, vast applications have been demonstrated based on MEMS metasurfaces, which proved to have merits including, large tunability, fast speed, small size, light weight, capability of dense integration, and compatibility of cost-effective fabrication process. Here, recent advances in MEMS metasurface applications are reviewed and categorized based on the tuning mechanisms, operation band and tuning speed. As an example, the pros and cons of MEMS metasurfaces for tunable lens applications are discussed and compared with traditional tunable lens technologies followed by the summary and outlook.
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5

Chen, Yankai, und Yi Wang. „Electrically tunable toroidal Fano resonances of symmetry-breaking dielectric metasurfaces using graphene in the infrared region“. Journal of Optics 24, Nr. 4 (09.03.2022): 044012. http://dx.doi.org/10.1088/2040-8986/ac5836.

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Abstract The magnitudes of coupling strength play an important role in various resonant phenomena such as Fano resonances (FRs). However, the coupling strength within the FRs using dielectric metasurfaces cannot be easily manipulated once they have been made. In this paper, toroidal FR is excited using the silicon metasurface with symmetry-breaking nanocylinders. Inserting a graphene layer with an ion-gel top gate onto the silicon metasurface, actively tunable response of a toroidal FR resulting from the manipulated coupling strength and the phase shift between two states. The hybrid graphene-silicon metasurface realize tunable Fano parameter (q) from −1.38 to −1.85 with applied voltage ranging from 0 to 2 v. Theoretical results predicted that higher q values are reachable relying on the hybrid graphene-silicon metasurface. The high-quality(Q)-factor (∼444) tunable FR of metasurface in the near-infrared region is observed. By applying a bias voltage to graphene obtain a blueshift of resonant wavelength (∼4 nm) with a maximum change of transmission spectrum peak up to 30%. These results have potential in high-efficient tunable electro-optic modulators, near-infrared optical switches, etc.
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6

Li, Jing, Hongjie Fan, Han Ye, Tiesheng Wu, Yuhang Sun, Xueyu Wang und Yumin Liu. „Design of Multifunctional Tunable Metasurface Assisted by Elastic Substrate“. Nanomaterials 12, Nr. 14 (13.07.2022): 2387. http://dx.doi.org/10.3390/nano12142387.

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Metasurfaces with both multifunctionality and tunability hold great application potential in next-generation optical devices. In this paper, we propose a stretchable metasurface composed of arrays of identical dielectric rectangular resonators embedded in the polydimethylsiloxane (PDMS) substrate. It is shown that the metasurface possesses three functions at the operating wavelength of 532 nm. The switching of functions can be implemented by changing the period Px of the metasurface, induced by stretching the PDMS substrate along the x-direction. When the period Px is less than the operating wavelength of 532 nm, the behavior of metasurface can switch between transmissive window and reflective mirror. When the period Px of the metasurface varies from 532 nm to 700 nm, the metasurface act as a dynamic equal-power beam splitter with conversion efficiency higher than 90%, and the corresponding splitting angle can be adjusted from 90° to around 49.5°. Moreover, we achieve the switching of transmissive window/reflective mirror/split-ratio-variable splitter based on the metasurface consisting of arrays of identical L-shaped resonators embedded in the PDMS substrate.
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7

Wang, Ling, Weijun Hong, Li Deng, Shufang Li, Chen Zhang, Jianfeng Zhu und Hongjun Wang. „Reconfigurable Multifunctional Metasurface Hybridized with Vanadium Dioxide at Terahertz Frequencies“. Materials 11, Nr. 10 (19.10.2018): 2040. http://dx.doi.org/10.3390/ma11102040.

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Driven by the continuous demand for system integration and device miniaturization, integrating multiple diversified functions into a single metasurface hybridized with the tunable metaparticle is highly demanding at terahertz (THz) range. However, up to now, because of the limitation of the tunable metaparticle at terahertz range, most of the metasurfaces feature a single function only or process similar functionalities at a single frequency. A reconfigurable multifunctional metasurface which can realize the switch of transmission and reflection and manipulate the linearized polarization state of electromagnetic waves simultaneously over a controllable terahertz frequency range based on the vanadium dioxide was designed for the first time in the paper. The numerical result demonstrates the validity of the appropriately designed metasurface. Simulation results show that the reconfigurable and multifunctional performance of this metasurface can be acquired over 1.59 THz to 1.74 THz without re-optimizing or re-fabricating structures, which effectively extends the operating frequencies. The proposed metasurface holds potential for electromagnetic wave manipulation and this study can motivate the realization of the wideband multifunctional metasurface and the software-driven reconfigurable metasurface at terahertz frequencies.
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8

Luo, Sisi, Jianjiao Hao, Fuju Ye, Jiaxin Li, Ying Ruan, Haoyang Cui, Wenjun Liu und Lei Chen. „Evolution of the Electromagnetic Manipulation: From Tunable to Programmable and Intelligent Metasurfaces“. Micromachines 12, Nr. 8 (20.08.2021): 988. http://dx.doi.org/10.3390/mi12080988.

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Looking back on the development of metamaterials in the past 20 years, metamaterials have gradually developed from three-dimensional complex electromagnetic structures to a two-dimensional metasurface with a low profile, during which a series of subversive achievements have been produced. The form of electromagnetic manipulation of the metasurface has evolved from passive to active tunable, programmable, and other dynamic and real-time controllable forms. In particular, the proposal of coding and programmable metasurfaces endows metasurfaces with new vitality. By describing metamaterials through binary code, the digital world and the physical world are connected, and the research of metasurfaces also steps into a new era of digitalization. However, the function switch of traditional programmable metamaterials cannot be achieved without human instruction and control. In order to achieve richer and more flexible function regulation and even higher level metasurface design, the intelligence of metamaterials is an important direction in its future development. In this paper, we review the development of tunable, programmable, and intelligent metasurfaces over the past 5 years, focusing on basic concepts, working principles, design methods, manufacturing, and experimental validation. Firstly, several manipulation modes of tunable metasurfaces are discussed; in particular, the metasurfaces based on temperature control, mechanical control, and electrical control are described in detail. It is demonstrated that the amplitude and phase responses can be flexibly manipulated by the tunable metasurfaces. Then, the concept, working principle, and design method of digital coding metasurfaces are briefly introduced. At the same time, we introduce the active programmable metasurfaces from the following aspects, such as structure, coding method, and three-dimensional far-field results, to show the excellent electromagnetic manipulation ability of programmable metasurfaces. Finally, the basic concepts and research status of intelligent metasurfaces are discussed in detail. Different from the previous programmable metamaterials, which must be controlled by human intervention, the new intelligent metamaterials control system will realize autonomous perception, autonomous decision-making, and even adaptive functional manipulation to a certain extent.
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9

Si, Wenrong, Chenzhao Fu, Fengyuan Gan, Dun Lan und Wei Li. „Dynamic Beam Switching by the Highly Sensitive Metasurface Composed of All-Metallic Split-Ring Resonators“. Journal of Nanomaterials 2022 (14.07.2022): 1–6. http://dx.doi.org/10.1155/2022/5186069.

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The development of metasurfaces capable of arbitrarily manipulating electromagnetic waves has created new opportunities for various applications. However, most tunable metasurface devices via different modulation techniques exhibit large fabrication difficulties or narrow bandwidths. Here, we use the all-metallic split-ring resonator to design a dynamically tunable metasurface that is highly sensitive to the ambient refractive index and capable of broadband beam switching. Different from the previous optical scatters, the split-ring resonator is put on the metal substrate. Due to the existence of metallic substrate and large interaction of corner modes, the proposed resonator has small ohmic loss and high sensitivity to the ambient refractive index. By arraying the all-metallic split-ring resonators with different parameters, dynamic beam switching of anomalous reflection is demonstrated numerically. In particularly, the designed metasurface exhibits the dynamic beam switching in a broadband wavelength range of Δλ≈100 nm. Such an all-metallic metasurface with high sensitivity can greatly reduce the designing difficulty of the tunable optical devices. The dynamic metadevices may find potential applications in stealth camouflage, information encryption, and data storage.
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10

Zhang, Ming, Peng Dong, Yu Wang, Baozhu Wang, Lin Yang, Ruihong Wu, Weimin Hou und Junyao Zhang. „Tunable Terahertz Wavefront Modulation Based on Phase Change Materials Embedded in Metasurface“. Nanomaterials 12, Nr. 20 (13.10.2022): 3592. http://dx.doi.org/10.3390/nano12203592.

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In the past decades, metasurfaces have shown their extraordinary abilities on manipulating the wavefront of electromagnetic wave. Based on the ability, various kinds of metasurfaces are designed to realize new functional metadevices based on wavefront manipulations, such as anomalous beam steering, focus metalens, vortex beams generator, and holographic imaging. However, most of the previously proposed designs based on metasurfaces are fixed once design, which is limited for applications where light modulation needs to be tunable. In this paper, we proposed a design for THz tunable wavefront manipulation achieved by the combination of plasmonic metasurface and phase change materials (PCMs) in THz region. Here, we designed a metal-insulator-metal (MIM) metasurface with the typical C-shape split ring resonator (CSRR), whose polarization conversion efficiency is nearly 90% for circular polarized light (CPL) in the range of 0.95~1.15 THz when PCM is in the amorphous state, but the conversion efficiency turns to less than 10% in the same frequency range when PCM switches into the crystalline state. Then, benefiting from the high polarization conversion contrast of unit cell, we can achieve tunable wavefront manipulation by utilizing the Pancharatnam–Berry (PB) phase between the amorphous and crystalline states. As a proof-of-concept, the reflective tunable anomalous beam deflector and focusing metalens are designed and characterized, and the results further verify their capability for tunable wavefront manipulation in THz range. It is believed that the design in our work may pave the way toward the tunable wavefront manipulation of THz waves and is potential for dynamic tunable THz devices.
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11

Hu, Yunsheng, Yihua Bai, Qing Zhang und Yuanjie Yang. „Electrically controlled molecular fingerprint retrieval with van der Waals metasurface“. Applied Physics Letters 121, Nr. 14 (03.10.2022): 141701. http://dx.doi.org/10.1063/5.0111940.

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Polaritons in two-dimensional van der Waals (vdW) materials possess extreme light confinement, which have emerged as a potential platform for next-generation biosensing and infrared spectroscopy. Here, we propose an ultra-thin and electric tunable graphene/hexagonal boron nitride/graphene metasurface for detecting molecular fingerprints over a broad spectrum. The vdW metasurface supports hybrid plasmon–phonon polariton resonance with high-quality factor (Q > 120) and electrically controlled broadband spectra tunability from 6.5 to 7 μm. After coating a thin layer of bio-molecular (e.g., CBP) on top of the metasurface, the molecular absorption signatures can be readout at multiple spectral points and, thus, achieve broadband fingerprint retrieval of bio-molecules. Additionally, our electric tunable metasurface works as an integrated graphene-based field-effect transistor device, without the need of multiple resonance generators such as angle-resolved or pixelated dielectric metasurfaces for broadband spectra scanning, thereby paving the way for highly sensitive, miniaturized, and electrically addressed biosensing and infrared spectroscopy.
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12

Shen, Zhe, und Dingxin Huang. „A Review on Metasurface Beam Splitters“. Nanomanufacturing 2, Nr. 4 (01.11.2022): 194–228. http://dx.doi.org/10.3390/nanomanufacturing2040014.

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Beam splitters are widely used in various optical systems, but traditional beam splitters are bulky and heavy, which are not conducive to the integrated utilization of optical devices. Metamaterials have attracted extensive attention as a kind of miniature artificial materials, and there have been many works on the design of metasurface beam splitters. Using metasurfaces, multiple functions of traditional beam splitters can be achieved. Meanwhile, metasurface beam splitters have the advantages of small size, easy integration, flexible design of beam-splitting performance, and tunable functions. This review surveys the current work on metasurface beam splitters and provides a classification and introduction to metasurface beam splitters. Metasurface beam splitters are expected to play a huge role in interferometers, multiplexing, multi-beam communications, and more.
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13

Cui, Ying, Xiaosai Wang, Huan Jiang und Yongyuan Jiang. „High-efficiency and tunable circular dichroism in chiral graphene metasurface“. Journal of Physics D: Applied Physics 55, Nr. 13 (30.12.2021): 135102. http://dx.doi.org/10.1088/1361-6463/ac4450.

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Abstract Circular dichroism (CD) response is extremely important for dynamic polarization control, chiral molecular sensing and imaging, etc. Here, we numerically demonstrated high-efficiency and tunable CD using a symmetry broken graphene-dielectric-metal composite microstructure. By introducing slot patterns in graphene ribbons, the metasurface exhibits giant polarization-selective absorption for circularly polarized (CP) wave excitations. The maximum CD reaches 0.87 at 2.78 THz, which originates from the localized surface plasmon resonances in patterned graphene. Besides, the operating frequency and magnitude of CD are dynamically manipulated by gating graphene’s Fermi energies. The proposed chiral graphene metasurface with high-efficiency and tunable capability paves a way to the design of active CD metasurfaces.
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14

He, Qiong, Shulin Sun und Lei Zhou. „Tunable/Reconfigurable Metasurfaces: Physics and Applications“. Research 2019 (07.07.2019): 1–16. http://dx.doi.org/10.34133/2019/1849272.

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Metasurfaces, ultrathin metamaterials constructed by planar meta-atoms with tailored electromagnetic (EM) responses, have attracted tremendous attention due to their exotic abilities to freely control EM waves. With active elements incorporated into metasurface designs, one can realize tunable and/or reconfigurable metadevices with functionalities controlled by external stimuli, opening a new platform to dynamically manipulate EM waves. In this article, we briefly review recent progress on tunable/reconfigurable metasurfaces, focusing on their working mechanisms and practical applications. We first describe available approaches, categorized into different classes based on external stimuli applied, to realize homogeneous tunable/reconfigurable metasurfaces, which can offer uniform manipulations on EM waves. We next summarize recent achievements on inhomogeneous tunable/reconfigurable metasurfaces with constitutional meta-atoms locally tuned by external knobs, which can dynamically control the wave-fronts of EM waves. We conclude this review by presenting our own perspectives on possible future directions and existing challenges in this fast developing field.
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15

Meng, Qi, Xingqiao Chen, Wei Xu, Zhihong Zhu, Xiaodong Yuan und Jianfa Zhang. „High Q Resonant Sb2S3-Lithium Niobate Metasurface for Active Nanophotonics“. Nanomaterials 11, Nr. 9 (13.09.2021): 2373. http://dx.doi.org/10.3390/nano11092373.

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Phase change materials (PCMs) are attracting more and more attentions as enabling materials for tunable nanophotonics. They can be processed into functional photonic devices through customized laser writing, providing great flexibility for fabrication and reconfiguration. Lithium Niobate (LN) has excellent nonlinear and electro-optical properties, but is difficult to process, which limits its application in nanophotonic devices. In this paper, we combine the emerging low-loss phase change material Sb2S3 with LN and propose a new type of high Q resonant metasurface. Simulation results show that the Sb2S3-LN metasurface has extremely narrow linewidth of 0.096 nm and high quality (Q) factor of 15,964. With LN as the waveguide layer, strong nonlinear properties are observed in the hybrid metasurface, which can be employed for optical switches and isolators. By adding a pair of Au electrodes on both sides of the LN, we can realize dynamic electro-optical control of the resonant metasurface. The ultra-low loss of Sb2S3, and its combination with LN, makes it possible to realize a new family of high Q resonant metasurfaces for actively tunable nanophotonic devices with widespread applications including optical switching, light modulation, dynamic beam steering, optical phased array and so on.
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Stojanoska, Katerina, und Chen Shen. „Non-Hermitian planar elastic metasurface for unidirectional focusing of flexural waves“. Applied Physics Letters 120, Nr. 24 (13.06.2022): 241701. http://dx.doi.org/10.1063/5.0097177.

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Metasurfaces exhibiting spatially asymmetric inner structures have been shown to host unidirectional scattering effects, benefiting areas where directional control of waves is desired. In this work, we propose a non-Hermitian planar elastic metasurface to achieve unidirectional focusing of flexural waves. The unit cells are constructed by piezoelectric disks and metallic blocks that are asymmetrically loaded. A tunable material loss is then introduced by negative capacitance shunting. By suitably engineering the induced loss profile, a series of unit cells are designed, which can individually access the exceptional points manifested by unidirectional zero reflection. We then construct a planar metasurface by tuning the reflected phase to ensure constructive interference at one side of the metasurface. Unidirectional focusing of the incident waves is demonstrated, where the reflected wave energy is focused from one direction, and zero reflection is observed in the other direction. The proposed metasurface enriches the flexibility in asymmetric elastic wave manipulation as the loss and the reflected phase can be tailored independently in each unit cell.
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17

Wang, Yue, Yu Wang, Guohui Yang, Qingyan Li, Yu Zhang, Shiyu Yan und Chunhui Wang. „All-Solid-State Optical Phased Arrays of Mid-Infrared Based Graphene-Metal Hybrid Metasurfaces“. Nanomaterials 11, Nr. 6 (11.06.2021): 1552. http://dx.doi.org/10.3390/nano11061552.

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Optical phased arrays (OPAs) are essential optical elements in applications that require the ability to manipulate the light-wavefront, such as beam focusing and light steering. To miniaturize the optical components, active metasurfaces, especially graphene metasurfaces, are used as competent alternatives. However, the metasurface cannot achieve strong resonance effect and phase control function in the mid-infrared region only relying on a single-layer graphene. Here we present a graphene-metal hybrid metasurface that can generate a specific phase or a continuous sweep in the range of a 275°-based single-layer graphene structure. A key feature of our design is that the phase adjustment mainly depends on the combination mechanism of resonance intensity and frequency modulation. An all-solid-state, electrically tunable, and reflective OPA is designed by applying the bias voltage to a different pixel metasurface. The simulation results show that the maximum deflection angle of the OPA can reach 42.716°, and the angular resolution can reach 0.62°. This design can be widely applied to mid-infrared imaging, optical sensing, and optical communication systems.
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Hu, Yuze, Mingyu Tong, Siyang Hu, Weibao He, Xiang’ai Cheng und Tian Jiang. „Multidimensional engineered metasurface for ultrafast terahertz switching at frequency-agile channels“. Nanophotonics 11, Nr. 7 (22.02.2022): 1367–78. http://dx.doi.org/10.1515/nanoph-2021-0774.

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Abstract The ability to actively manipulate free-space optical signals by using tunable metasurfaces is extremely appealing for many device applications. However, integrating photoactive semiconductors into terahertz metamaterials still suffers from a limited functionality. The ultrafast switching in picosecond timescale can only be operated at a single frequency channel. In the hybrid metasurface proposed here, we experimentally demonstrate a dual-optically tunable metaphotonic device for ultrafast terahertz switching at frequency-agile channels. Picosecond ultrafast photoswitching with a 100% modulation depth is realized at a controllable operational frequency of either 0.55 THz or 0.86 THz. The broadband frequency agility and ultrafast amplitude modulation are independently controlled by continuous wave light and femtosecond laser pulse, respectively. The frequency-selective, temporally tunable, and multidimensionally-driven features can empower active metamaterials in advanced multiplexing of information, dual-channel wireless communication, and several other related fields.
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19

Gora, Paulina, und Przemyslaw Lopato. „Thin Dielectric Layers Evaluation Using Tunable Split-Ring Resonator Based Metasurface in THz Frequency Range“. Applied Sciences 12, Nr. 17 (26.08.2022): 8526. http://dx.doi.org/10.3390/app12178526.

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The paper presents the evaluation of thin dielectric layers using a tunable split-ring resonator-based metasurface in the THz frequency range. Tunable unit cells of a metasurface allow its resonant frequency variation using some external excitation. This can be done in various ways. In this work, the behavior of such a metasurface is investigated by monitoring the resonant frequency value when the unit cell geometry is changed. Such behavior is utilized for the quality evaluation of a thin dielectric layer placed in vicinity of a metasurface. A change in dielectric permittivity noticeably affects the resonant frequency of a metasurface. In order to examine the state of the material under test, finite element method simulations were made for a 15 µm thin layer. As a result, the approximation-based relations between resonant frequencies (obtained for various geometries of structural element—in tunability range) and dielectric parameters of the examined material were derived. These relations carry more information than in the case of just one resonant frequency (the case of a non-tunable metasurface) and can be utilized for permittivity evaluation.
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He, Liu und Fu. „Transmit-Array, Metasurface-Based Tunable Polarizer and High-Performance Biosensor in the Visible Regime“. Nanomaterials 9, Nr. 4 (11.04.2019): 603. http://dx.doi.org/10.3390/nano9040603.

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There are two types of metasurfaces, reflect-array and transmit-array,—which are classified on the basis of structural features. In this paper, we design a transmit-array metasurface for y-polarized incidence which is characterized by having a transmission spectrum with a narrow dip (i.e., less than 3 nm). Furthermore, a tunable polarizer is achieved using linear geometric configurations, realizing a transmittivity ratio between x- and y-polarized incidence ranging from 0.031% to 1%. Based on the narrow-band polarization sensitivity of our polarizer, a biosensor was designed to detect an environmental refractive index ranging from 1.30 to 1.39, with a factor of sensitivity S = 192 nm/RIU and figure of merit (FOM) = 64/RIU. In the case of a narrow-band feature and dips in transmission spectrums close to zero, FOM* can have a value as large as 92,333/RIU. This unique feature makes the novel transmit-array metasurface a potential market candidate in the field of biosensors. Moreover, transmit-array metasurfaces with lossless materials offer great convenience by means of detecting either the reflectance spectrum or the transmission spectrum.
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He, Fengyan, Jianjun Liu, Guiming Pan, Fangzhou Shu, Xufeng Jing und Zhi Hong. „Analogue of Electromagnetically Induced Transparency in an All-Dielectric Double-Layer Metasurface Based on Bound States in the Continuum“. Nanomaterials 11, Nr. 9 (09.09.2021): 2343. http://dx.doi.org/10.3390/nano11092343.

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Bound states in the continuum (BICs) have attracted much attention due to their infinite Q factor. However, the realization of the analogue of electromagnetically induced transparency (EIT) by near-field coupling with a dark BIC in metasurfaces remains challenging. Here, we propose and numerically demonstrate the realization of a high-quality factor EIT by the coupling of a bright electric dipole resonance and a dark toroidal dipole BIC in an all-dielectric double-layer metasurface. Thanks to the designed unique one-dimensional (D)–two-dimensional (2D) combination of the double-layer metasurface, the sensitivity of the EIT to the relative displacement between the two layer-structures is greatly reduced. Moreover, several designs for widely tunable EIT are proposed and discussed. We believe the proposed double-layer metasurface opens a new avenue for implementing BIC-based EIT with potential applications in filtering, sensing and other photonic devices.
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22

Cheng, Jierong, Fei Fan und Shengjiang Chang. „Recent Progress on Graphene-Functionalized Metasurfaces for Tunable Phase and Polarization Control“. Nanomaterials 9, Nr. 3 (08.03.2019): 398. http://dx.doi.org/10.3390/nano9030398.

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The combination of graphene and a metasurface holds great promise for dynamic manipulation of the electromagnetic wave from low terahertz to mid-infrared. The optical response of graphene is significantly enhanced by the highly-localized fields in the meta-atoms, and the characteristics of meta-atoms can in turn be modulated in a large dynamic range through electrical doping of graphene. Graphene metasurfaces are initially focused on intensity modulation as modulators and tunable absorbers. In this paper, we review the recent progress of graphene metasurfaces for active control of the phase and the polarization. The related applications involve, but are not limited to lenses with tunable intensity or focal length, dynamic beam scanning, wave plates with tunable frequency, switchable polarizers, and real-time generation of an arbitrary polarization state, all by tuning the gate voltage of graphene. The review is concluded with a discussion of the existing challenges and the personal perspective of future directions.
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Shih, Yi-Hong, Xin-Yu Lin, Harry Miyosi Silalahi, Chia-Rong Lee und Chia-Yi Huang. „Optically Tunable Terahertz Metasurfaces Using Liquid Crystal Cells Coated with Photoalignment Layers“. Crystals 11, Nr. 9 (10.09.2021): 1100. http://dx.doi.org/10.3390/cryst11091100.

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An optically tunable terahertz filter was fabricated using a metasurface-imbedded liquid crystal (LC) cell with photoalignment layers in this work. The LC director in the cell is aligned by a pump beam and makes angles θ of 0, 30, 60 and 90° with respect to the gaps of the split-ring resonators (SRRs) of the metasurface under various polarized directions of the pump beam. Experimental results display that the resonance frequency of the metasurface in the cell increases with an increase in θ, and the cell has a frequency tuning region of 15 GHz. Simulated results reveal that the increase in the resonance frequency arises from the birefringence of the LC, and the LC has a birefringence of 0.13 in the terahertz region. The resonance frequency of the metasurface is shifted using the pump beam, so the metasurface-imbedded LC cell with the photoalignment layers is an optically tunable terahertz filter. The optically tunable terahertz filter is promising for applications in terahertz telecommunication, biosensing and terahertz imaging.
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Yu, Bo, Hao-Wen Zhou und Qi Cheng. „Design and Simulation of Tunable Infrared Absorber Based on Flexible Metasurface“. Journal of Nanoelectronics and Optoelectronics 17, Nr. 6 (01.06.2022): 883–87. http://dx.doi.org/10.1166/jno.2022.3280.

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Tunable metasurface plays a crucial role in the modulation of infrared. And the flexible substrate realizes the possibility for mechanical tuning without additional electronic equipment. Based on the nanoscale metasurface, a tunable infrared absorber is designed and simulated with a narrow-band absorption peak of 75.6% at 18.4 THz. A silver structure is embedded in the PDMS flexible substrate. Through the simulation of CST software and the analysis of the RLC model, it is evidenced that the infrared absorption spectrum of the metasurface appears an obvious redshift, with the increase of area. When the flexible metasurface is stretched by 132%, the frequency of absorption peak moves to 16.4 THz, which still stays above 75%. Based on stretchtuned metasurface, the absorber is expected to be applied in displacement sensing, infrared detection, and other fields.
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Zhou, Hongqiang, Yongtian Wang, Xiaowei Li, Qing Wang, Qunshuo Wei, Guangzhou Geng und Lingling Huang. „Switchable active phase modulation and holography encryption based on hybrid metasurfaces“. Nanophotonics 9, Nr. 4 (11.03.2020): 905–12. http://dx.doi.org/10.1515/nanoph-2019-0519.

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AbstractMetasurfaces are planar devices containing delicately designed nanoantenna or resonator arrays that allow for beam shaping, super resolution imaging, and holography. Hybrid metasurface – by integrating with tunable materials such as two-dimensional materials and phase change materials (PCMs) – provides a potential platform for active modulation of wavefronts. Specifically, PCMs can flexibly switch between crystalline and amorphous states with nonvolatile property under external stimuli and provide a large refractive permittivity contrast. Using metasurfaces based on PCM to manipulate wavefronts may provide new opportunities for switchable functionalities. Here, we propose two types of metasurface devices based on whole PCM films to realize switchable holography and simultaneous phase and interference encryption. This feature can be used to encrypt information in a switched state and store camouflage information in the other state by simply applying external thermal stimuli to the entire metasurface. This method can be applied in areas such as beam shaping, optical encryption, and anti-counterfeiting.
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Choudhury, Sajid M., Di Wang, Krishnakali Chaudhuri, Clayton DeVault, Alexander V. Kildishev, Alexandra Boltasseva und Vladimir M. Shalaev. „Material platforms for optical metasurfaces“. Nanophotonics 7, Nr. 6 (27.06.2018): 959–87. http://dx.doi.org/10.1515/nanoph-2017-0130.

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AbstractOptical metasurfaces are judicously engineered electromagnetic interfaces that can control and manipulate many of light’s quintessential properties, such as amplitude, phase, and polarization. These artificial surfaces are composed of subwavelength arrays of optical antennas that experience resonant light-matter interaction with incoming electromagnetic radiation. Their ability to arbitrarily engineer optical interactions has generated considerable excitement and interest in recent years and is a promising methodology for miniaturizing optical components for applications in optical communication systems, imaging, sensing, and optical manipulation. However, development of optical metasurfaces requires progress and solutions to inherent challenges, namely large losses often associated with the resonant structures; large-scale, complementary metal-oxide-semiconductor-compatible nanofabrication techniques; and incorporation of active control elements. Furthermore, practical metasurface devices require robust operation in high-temperature environments, caustic chemicals, and intense electromagnetic fields. Although these challenges are substantial, optical metasurfaces remain in their infancy, and novel material platforms that offer resilient, low-loss, and tunable metasurface designs are driving new and promising routes for overcoming these hurdles. In this review, we discuss the different material platforms in the literature for various applications of metasurfaces, including refractory plasmonic materials, epitaxial noble metal, silicon, graphene, phase change materials, and metal oxides. We identify the key advantages of each material platform and review the breakthrough devices that were made possible with each material. Finally, we provide an outlook for emerging metasurface devices and the new material platforms that are enabling such devices.
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Yu, Jaeyeon, Seongjin Park, Inyong Hwang, Daeik Kim, Frederic Demmerle, Gerhard Boehm, Markus-Christian Amann, Mikhail A. Belkin und Jongwon Lee. „Electrically tunable nonlinear polaritonic metasurface“. Nature Photonics 16, Nr. 1 (23.12.2021): 72–78. http://dx.doi.org/10.1038/s41566-021-00923-7.

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28

Wang, Zehao, Dashuang Liao, Ting Zhang, Tianhang Chen, Yi Ruan und Bin Zheng. „Metasurface-based focus-tunable mirror“. Optics Express 27, Nr. 21 (07.10.2019): 30332. http://dx.doi.org/10.1364/oe.27.030332.

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29

Mao, Libang, und Tun Cao. „A tunable multiband chirped metasurface“. Journal of Science: Advanced Materials and Devices 1, Nr. 3 (September 2016): 393–99. http://dx.doi.org/10.1016/j.jsamd.2016.07.004.

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30

Ou, Jie, Xiao-Qing Luo, You-Lin Luo, Wei-Hua Zhu, Zhi-Yong Chen, Wu-Ming Liu und Xin-Lin Wang. „Near-infrared dual-wavelength plasmonic switching and digital metasurface unveiled by plasmonic Fano resonance“. Nanophotonics 10, Nr. 2 (11.11.2020): 947–57. http://dx.doi.org/10.1515/nanoph-2020-0511.

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AbstractPlasmonic Fano resonance (FR) that contributes to multitudinous potential applications in subwavelength nanostructures can facilitate the realization of tunable wavelength selectivity for controlling light–matter interactions in metasurfaces. However, the plasmonic FR can be generated in metasurfaces with simple or complex geometries, and few of them can support flexible amplitude modulation and multiwavelength information transfer and processing. Here, we study the near-infrared plasmonic FR in a hybrid metasurface composed of concentrically hybridized parabolic-hole and circular-ring-aperture unit cells, which can induce polarization-dependent dual-wavelength passive plasmonic switching (PPS) and digital metasurface (DM). It is shown that the designable plasmonic FR can be realized by changing the geometric configurations of the unit cells. In particular, owing to the polarization-dependent characteristic of FR, it is possible to fulfill a compact dual-wavelength PPS with high ON/OFF ratios in the related optical communication bands. Moreover, such PPS that manipulates the amplitude response of the transmitted spectrum is an efficient way to reveal a 1-bit DM, which can also be rationally extended to a 2-bit DM or more. Our results suggest a pathway for studying polarization-dependent PPS and programmable metasurface devices, yielding possibilities for subwavelength nanostructures in optical communication and information processing.
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Cui, Cheng, Zheng Liu, Bin Hu, Yurong Jiang und Juan Liu. „A multi-channeled vortex beam switch with moiré metasurfaces“. Journal of Optics 24, Nr. 1 (17.12.2021): 015004. http://dx.doi.org/10.1088/2040-8986/ac38c4.

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Abstract Tunable metasurface devices are considered to be an important link for metasurfaces to practical applications due to their functional diversity and high adaptability to application scenarios. Metasurfaces have unique value in the generation of vortex beams because they can realize light wavefronts of any shape. In recent years, several vortex beam generators using metasurfaces have been proposed. However, topological charge generally lacks tunability, which reduces the scope of their applications. Here, we propose an active tunable multi-channeled vortex beam switch based on a moiré structure composed of two cascaded dielectric metasurfaces. The simulation results show that when linearly polarized light with a wavelength of 810 nm is incident, the topological charge from −6 to +6 can be continuously generated by relatively rotating the two metasurfaces. Meanwhile, different topological charges are deflected to different spatial channels, realizing the function of multi-channeled signal transmission. We also study the efficiency and broadband performance of the structure. The proposed multi-channel separation method involving vortex beams that can actively tune topological charges paves the way for the compactness and functional diversity of devices in the fields of optical communications, biomedicine, and optoelectronics.
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Lynch, Jason, Ludovica Guarneri, Deep Jariwala und Jorik van de Groep. „Exciton resonances for atomically-thin optics“. Journal of Applied Physics 132, Nr. 9 (07.09.2022): 091102. http://dx.doi.org/10.1063/5.0101317.

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Metasurfaces enable flat optical elements by leveraging optical resonances in metallic or dielectric nanoparticles to obtain accurate control over the amplitude and phase of the scattered light. While highly efficient, these resonances are static and difficult to tune actively. Exciton resonances in atomically thin 2D semiconductors provide a novel and uniquely strong resonant light–matter interaction, which presents a new opportunity for optical metasurfaces. Their resonant properties are intrinsic to the band structure of the material, do not rely on nanoscale patterns, and are highly tunable using external stimuli. In this tutorial, we present the role that exciton resonances can play for atomically thin optics. We describe the essentials of metasurface physics and provide background on exciton physics and a comprehensive overview of excitonic materials. Excitons demonstrate to provide new degrees of freedom and enhanced light–matter interactions in hybrid metasurfaces through coupling with metallic and dielectric metasurfaces. Using the high sensitivity of excitons to the medium's electron density, the first demonstrations of electrically tunable nanophotonic devices and atomically thin optical elements are also discussed. The future of excitons in metasurfaces looks promising, while the main challenge lies in large-area growth and precise integration of high-quality materials.
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Li, Shi-Qiang, Xuewu Xu, Rasna Maruthiyodan Veetil, Vytautas Valuckas, Ramón Paniagua-Domínguez und Arseniy I. Kuznetsov. „Phase-only transmissive spatial light modulator based on tunable dielectric metasurface“. Science 364, Nr. 6445 (13.06.2019): 1087–90. http://dx.doi.org/10.1126/science.aaw6747.

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Rapidly developing augmented reality, solid-state light detection and ranging (LIDAR), and holographic display technologies require spatial light modulators (SLMs) with high resolution and viewing angle to satisfy increasing customer demands. Performance of currently available SLMs is limited by their large pixel sizes on the order of several micrometers. Here, we propose a concept of tunable dielectric metasurfaces modulated by liquid crystal, which can provide abrupt phase change, thus enabling pixel-size miniaturization. We present a metasurface-based transmissive SLM, configured to generate active beam steering with >35% efficiency and a large beam deflection angle of 11°. The high resolution and steering angle obtained provide opportunities to develop the next generation of LIDAR and display technologies.
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Rotshild, David, Daniel Rozban, Efi Rahamim, Asaf Barom, Rotem Yosef, Liel Bhanam und Amir Abramovich. „Steer by Image Technology for Intelligent Reflecting Surface Based on Reconfigurable Metasurface with Photodiodes as Tunable Elements“. Crystals 12, Nr. 7 (07.07.2022): 951. http://dx.doi.org/10.3390/cryst12070951.

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Lately, metasurface has become an essential and promising component in implementing Intelligent Reflecting Surface (IRS) for 5G and 6G. A novel method that simplifies the ability to reconfigure the metasurface is presented in this paper. The suggested technology uses a PIN photodiode as a tuning element. The desired image is projected on the metasurface’s backside, where the PIN photodiodes are placed and reconfigures the metasurface. The projected image’s color and intensity pattern influence the PIN photodiode’s junction capacitance, which leads to local reflection phase control. This enables the required pattern reflection phase distribution to manipulate the reflection beam, for example, 2D beam steering or focusing, and any other beam forming combination, instead of wiring many digital-to-analog converters (DACs) or FPGA outputs, which bias the standard tuning element such as PIN diode or varactor using a complex RF circuit. Using a PIN photodiode as a tunable element instead of a varactor diode, PIN diode, Liquid Crystal and MEMS allows the changing of the internal junction capacitance without direct contact and thus continuously controlling the reflection phase. In addition, an open circuit work mode with negligible energy consumption can be obtained. This technology can be used to implement metasurface based on discrete or continuous phases and is called Steer by Image (SBI). A full description of the SBI technology using PIN photodiode is presented in this paper.
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Shields, Joe, Carlota Ruiz de Galarreta, Jacopo Bertolotti und C. David Wright. „Enhanced Performance and Diffusion Robustness of Phase-Change Metasurfaces via a Hybrid Dielectric/Plasmonic Approach“. Nanomaterials 11, Nr. 2 (18.02.2021): 525. http://dx.doi.org/10.3390/nano11020525.

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Materials of which the refractive indices can be thermally tuned or switched, such as in chalcogenide phase-change alloys, offer a promising path towards the development of active optical metasurfaces for the control of the amplitude, phase, and polarization of light. However, for phase-change metasurfaces to be able to provide viable technology for active light control, in situ electrical switching via resistive heaters integral to or embedded in the metasurface itself is highly desirable. In this context, good electrical conductors (metals) with high melting points (i.e., significantly above the melting point of commonly used phase-change alloys) are required. In addition, such metals should ideally have low plasmonic losses, so as to not degrade metasurface optical performance. This essentially limits the choice to a few noble metals, namely, gold and silver, but these tend to diffuse quite readily into phase-change materials (particularly the archetypal Ge2Sb2Te5 alloy used here), and into dielectric resonators such as Si or Ge. In this work, we introduce a novel hybrid dielectric/plasmonic metasurface architecture, where we incorporated a thin Ge2Sb2Te5 layer into the body of a cubic silicon nanoresonator lying on metallic planes that simultaneously acted as high-efficiency reflectors and resistive heaters. Through systematic studies based on changing the configuration of the bottom metal plane between high-melting-point diffusive and low-melting-point nondiffusive metals (Au and Al, respectively), we explicitly show how thermally activated diffusion can catastrophically and irreversibly degrade the optical performance of chalcogenide phase-change metasurface devices, and how such degradation can be successfully overcome at the design stage via the incorporation of ultrathin Si3N4 barrier layers between the gold plane and the hybrid Si/Ge2Sb2Te5 resonators. Our work clarifies the importance of diffusion of noble metals in thermally tunable metasurfaces and how to overcome it, thus helping phase-change-based metasurface technology move a step closer towards the realization of real-world applications.
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Peng, Yao-Yin, Zhang-Zhao Yang, Zhi-Lei Zhang, Xin-Ye Zou, Chao Tao und Jian-Chun Cheng. „Tunable acoustic metasurface based on tunable piezoelectric composite structure“. Journal of the Acoustical Society of America 151, Nr. 2 (Februar 2022): 838–45. http://dx.doi.org/10.1121/10.0009379.

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37

Zhai, Shilong, Kun Song, Changlin Ding, Yuanbo Wang, Yibao Dong und Xiaopeng Zhao. „Tunable Acoustic Metasurface with High-Q Spectrum Splitting“. Materials 11, Nr. 10 (14.10.2018): 1976. http://dx.doi.org/10.3390/ma11101976.

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We propose a tunable acoustic metasurface using a nested structure as the microunit, which is constituted by two distinct resonators. Thanks to the coupling resonance for the microunit and by simply adjusting the rotation angle of the inner split cavity, this nested structure provides nearly 2π phase shift. The full-wave simulations demonstrate that the constructed metasurface can be tuned to reflect incident sound waves to different directions in the operation frequency region with a very narrow bandwidth, which is a key functionality for many applications such as filtering and imaging. Meanwhile, the reflected sound waves out of the operation frequency region always remain unchanged. As a result, a high Q-factor spectrum splitting can be realised. The presented metasurface is of importance to develop many metamaterial-based devices, such as tunable acoustic cloaks and acoustic switching devices.
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Filonov, Dmitry, Vitali Kozlov, Andrey Shmidt, Ben Z. Steinberg und Pavel Ginzburg. „Resonant metasurface with tunable asymmetric reflection“. Applied Physics Letters 113, Nr. 9 (27.08.2018): 094103. http://dx.doi.org/10.1063/1.5046948.

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39

Arroyo Huidobro, Paloma, Stefan A. Maier und John B. Pendry. „Tunable plasmonic metasurface for perfect absorption“. EPJ Applied Metamaterials 4 (2017): 6. http://dx.doi.org/10.1051/epjam/2017001.

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40

Zárate, Yair, Ilya V. Shadrivov und David A. Powell. „Tunable focusing by a flexible metasurface“. Photonics and Nanostructures - Fundamentals and Applications 26 (September 2017): 62–68. http://dx.doi.org/10.1016/j.photonics.2017.07.004.

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41

Kamali, Seyedeh Mahsa, Ehsan Arbabi, Amir Arbabi, Yu Horie und Andrei Faraon. „Highly tunable elastic dielectric metasurface lenses“. Laser & Photonics Reviews 10, Nr. 6 (November 2016): 1002–8. http://dx.doi.org/10.1002/lpor.201600144.

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42

Dong, Weiling, Yimei Qiu, Xilin Zhou, Agnieszka Banas, Krzysztof Banas, Mark B. H. Breese, Tun Cao und Robert E. Simpson. „Tunable Mid‐Infrared Phase‐Change Metasurface“. Advanced Optical Materials 6, Nr. 14 (06.05.2018): 1701346. http://dx.doi.org/10.1002/adom.201701346.

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43

Ma, Zhenhe, Xianghe Meng, Xiaodi Liu, Guangyuan Si und Yan Jun Liu. „Liquid Crystal Enabled Dynamic Nanodevices“. Nanomaterials 8, Nr. 11 (23.10.2018): 871. http://dx.doi.org/10.3390/nano8110871.

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Inspired by the anisotropic molecular shape and tunable alignment of liquid crystals (LCs), investigations on hybrid nanodevices which combine LCs with plasmonic metasurfaces have received great attention recently. Since LCs possess unique electro-optical properties, developing novel dynamic optical components by incorporating nematic LCs with nanostructures offers a variety of practical applications. Owing to the large birefringence of LCs, the optical properties of metamaterials can be electrically or optically modulated over a wide range. In this review article, we show different elegant designs of metasurface based nanodevices integrated into LCs and explore the tuning factors of transmittance/extinction/scattering spectra. Moreover, we review and classify substantial tunable devices enabled by LC-plasmonic interactions. These dynamically tunable optoelectronic nanodevices and components are of extreme importance, since they can enable a significant range of applications, including ultra-fast switching, modulating, sensing, imaging, and waveguiding. By integrating LCs with two dimensional metasurfaces, one can manipulate electromagnetic waves at the nanoscale with dramatically reduced sizes. Owing to their special electro-optical properties, recent efforts have demonstrated that more accurate manipulation of LC-displays can be engineered by precisely controlling the alignment of LCs inside small channels. In particular, device performance can be significantly improved by optimizing geometries and the surrounding environmental parameters.
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Zhang, Jihua, Jinyong Ma, Dragomir N. Neshev und Andrey A. Sukhorukov. „Photon pair generation from lithium niobate metasurface with tunable spatial entanglement“. Chinese Optics Letters 21, Nr. 1 (2023): 010005. http://dx.doi.org/10.3788/col202321.010005.

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Xu, Yuehong, Quanlong Yang, Ying Zhang, Shaoxian Li, Quan Xu, Xueqian Zhang, Yanfeng Li et al. „Quasicrystal Metasurfaces: Tunable On‐Chip Sources with Aperiodic Metasurface (Ann. Phys. 12/2019)“. Annalen der Physik 531, Nr. 12 (Dezember 2019): 1970047. http://dx.doi.org/10.1002/andp.201970047.

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46

Shah, Deesha, Zhaxylyk A. Kudyshev, Soham Saha, Vladimir M. Shalaev und Alexandra Boltasseva. „Transdimensional material platforms for tunable metasurface design“. MRS Bulletin 45, Nr. 3 (März 2020): 188–95. http://dx.doi.org/10.1557/mrs.2020.63.

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47

Jin CHENG, 程进, 周顺 Shun ZHOU, 孙雪平 Xue-ping SUN, 蒲欣欣 Xin-xin PU, 孙其梁 Qi-liang SUN, 徐英舜 Ying-shun XU und 刘卫国 Wei-guo LIU. „Laser Speckle Suppression Based on Tunable Metasurface“. ACTA PHOTONICA SINICA 49, Nr. 7 (2020): 724001. http://dx.doi.org/10.3788/gzxb20204907.0724001.

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48

Chen, Pai-Yen, Jason Soric, Yashwanth R. Padooru, Hossein M. Bernety, Alexander B. Yakovlev und Andrea Alù. „Nanostructured graphene metasurface for tunable terahertz cloaking“. New Journal of Physics 15, Nr. 12 (17.12.2013): 123029. http://dx.doi.org/10.1088/1367-2630/15/12/123029.

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49

Zhou, Hong-Tao, Shi-Wang Fan, Xiao-Shuang Li, Wen-Xiao Fu, Yan-Feng Wang und Yue-Sheng Wang. „Tunable arc-shaped acoustic metasurface carpet cloak“. Smart Materials and Structures 29, Nr. 6 (14.05.2020): 065016. http://dx.doi.org/10.1088/1361-665x/ab87e4.

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50

Odit, Mikhail, Polina Kapitanova, Andrei Andryieuski, Pavel Belov und Andrei V. Lavrinenko. „Experimental demonstration of water based tunable metasurface“. Applied Physics Letters 109, Nr. 1 (04.07.2016): 011901. http://dx.doi.org/10.1063/1.4955272.

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