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13 pages, 4389 KiB

Open AccessArticle

Reconfigurable Terahertz Metamaterials Based on the Refractive Index Change of Epitaxial Vanadium Dioxide Films Across the Metal–Insulator Transition

by Chang Lu and Weizheng Liang

Nanomaterials 2025, 15(6), 439; https://doi.org/10.3390/nano15060439 - 13 Mar 2025

Cited by 1 | Viewed by 608

Abstract

The intrinsic metal–insulator transition (MIT) of VO₂ films near room temperature presents significant potential for reconfigurable metamaterials in the terahertz (THz) frequency range. While previous designs primarily focused on changes in electrical conductivity across the MIT, the accompanying dielectric changes due to [...] Read more.

The intrinsic metal–insulator transition (MIT) of VO₂ films near room temperature presents significant potential for reconfigurable metamaterials in the terahertz (THz) frequency range. While previous designs primarily focused on changes in electrical conductivity across the MIT, the accompanying dielectric changes due to the mesoscopic carrier confinement effect have been largely unexplored. In this study, we integrate asymmetric split-ring resonators on 35 nm epitaxial VO₂ film and identify a “dielectric window” at the early stages of the MIT. This is characterized by a redshift in the resonant frequency without a significant degradation in the resonant quality. This phenomenon is attributed to an inhomogeneous phase transition in the VO₂ film, which induces a purely dielectric change at the onset of the MIT, while the electrical conductivity transition occurs later, slightly above the percolation threshold. Our findings provide deeper insights into the THz properties of VO₂ films and pave the way for dielectric-based, VO₂ hybrid reconfigurable metamaterials. Full article

(This article belongs to the Special Issue Advances and Applications of Nanomaterials in Terahertz Science and Technology)

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16 pages, 2769 KiB

Open AccessArticle

A Reflective Terahertz Point Source Meta-Sensor with Asymmetric Meta-Atoms for High-Sensitivity Bio-Sensing

by Luwei Zheng, Kazuki Hara, Hironaru Murakami, Masayoshi Tonouchi and Kazunori Serita

Biosensors 2024, 14(12), 568; https://doi.org/10.3390/bios14120568 - 23 Nov 2024

Cited by 1 | Viewed by 1021

Abstract

Biosensors operating in the terahertz (THz) region are gaining substantial interest in biomedical analysis due to their significant potential for high-sensitivity trace-amount solution detection. However, progress in compact, high-sensitivity chips and methods for simple, rapid and trace-level measurements is limited by the spatial [...] Read more.

Biosensors operating in the terahertz (THz) region are gaining substantial interest in biomedical analysis due to their significant potential for high-sensitivity trace-amount solution detection. However, progress in compact, high-sensitivity chips and methods for simple, rapid and trace-level measurements is limited by the spatial resolution of THz waves and their strong absorption in polar solvents. In this work, a compact nonlinear optical crystal (NLOC)-based reflective THz biosensor with a few arrays of asymmetrical meta-atoms was developed. A near-field point THz source was locally generated at a femtosecond-laser-irradiation spot via optical rectification, exciting only the single central meta-atom, thereby inducing Fano resonance. The reflective resonance response demonstrated dependence on several aspects, including structure asymmetricity, geometrical size, excitation point position, thickness and array-period arrangement. DNA samples were examined using 1 μL applied to an effective sensing area of 0.234 mm² (484 μm × 484 μm) for performance evaluation. The developed Fano resonance sensor exhibited nearly double sensitivity compared to that of symmetrical sensors and one-gap split ring resonators. Thus, this study advances liquid-based sensing by enabling easy, rapid and trace-level measurements while also driving the development of compact and highly sensitive THz sensors for biological samples. Full article

(This article belongs to the Section Optical and Photonic Biosensors)

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7 pages, 2272 KiB

Open AccessComment

Comment on Lu et al. Ultrathin Terahertz Dual-Band Perfect Metamaterial Absorber Using Asymmetric Double-Split Rings Resonator. Symmetry 2018, 10, 293

by Tariq Ullah and Aamir Rashid

Symmetry 2024, 16(4), 445; https://doi.org/10.3390/sym16040445 - 7 Apr 2024

Viewed by 889

Abstract

In this study, the design of a dual-band terahertz absorber, previously published by Lu et al. (Symmetry 2018, 10, 293), was re-simulated. Our findings showed significantly different absorption results from those published in the article. A detailed analysis was conducted to [...] Read more.

In this study, the design of a dual-band terahertz absorber, previously published by Lu et al. (Symmetry 2018, 10, 293), was re-simulated. Our findings showed significantly different absorption results from those published in the article. A detailed analysis was conducted to explain this discrepancy, which was attributed to the reflection of an unaccounted orthogonal component of the waves from the design, rather than absorption. The metasurface design has two resonances at 4.48 THz and 4.76 THz, respectively. It was reported that at these frequencies, the structure achieved absorption of 98.6% and 98.5%, respectively. However, in our results, it was found that at the second resonance (4.76 THz), the structure acted as a strong cross-polarization converter, reflecting a significant amount of incident energy in the cross-polarization component of the reflected wave. When this component is considered in the reflection coefficient calculations, the absorption reduces to 41% (from 98.5%), which is not an acceptable level for an absorber. In addition, the structure was simulated for both lossy and lossless (FR4) substrate cases to understand the effect of substrate losses. The results showed that the absorption response significantly deteriorates at the first resonance (4.48 THz) in the case of a lossy FR4 substrate. Full article

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16 pages, 4799 KiB

Open AccessArticle

Resonator-Loaded Waveguide Notch Filters with Broad Tuning Range and Additive-Manufacturing-Based Operating Frequency Adjustment Procedure

by Tanveerul Haq, Slawomir Koziel and Anna Pietrenko-Dabrowska

Electronics 2023, 12(21), 4486; https://doi.org/10.3390/electronics12214486 - 31 Oct 2023

Cited by 4 | Viewed by 2759

Abstract

This article presents a new class of ring-resonator-loaded waveguide notch filters with a broad tuning range, low cost, and improved performance. The proposed approach employs a complementary asymmetric split-ring resonator coupled to a microstrip transmission line and excited in a rectangular waveguide. An [...] Read more.

This article presents a new class of ring-resonator-loaded waveguide notch filters with a broad tuning range, low cost, and improved performance. The proposed approach employs a complementary asymmetric split-ring resonator coupled to a microstrip transmission line and excited in a rectangular waveguide. An equivalent circuit model is proposed to explain the working principle of the proposed notch filter. The adjustment of the operating frequency is based on the additive manufacturing of a metallic copper patch allocated on the microstrip transmission line, which enables extensive tuning capabilities and consistent performance with minimum variations across the tuning window. For demonstration purposes, a filter employing a WR-28 waveguide and photolithography-manufactured resonator is prototyped and experimentally validated. The measured results indicate a broad 8 GHz tuning range with a consistent insertion loss, ranging from 23.4 to 31.4 GHz. An inverse regression model is constructed using measurement data obtained for tuning patches of various sizes, which allows for determining the relationships between the operating frequency and the copper patch size. The resulting calibration curve enables rapid filter tuning to the required frequency by inserting metallic patches of the model-predicted size. Full article

(This article belongs to the Special Issue Advanced Waveguides Technology for Sensing and Communications)

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13 pages, 6407 KiB

Open AccessArticle

Polarization Splitting at Visible Wavelengths with the Rutile TiO₂ Ridge Waveguide

by Xinzhi Zheng, Yujie Ma, Chenxi Zhao, Bingxi Xiang, Mingyang Yu, Yanmeng Dai, Fang Xu, Jinman Lv, Fei Lu, Cangtao Zhou and Shuangchen Ruan

Nanomaterials 2023, 13(12), 1891; https://doi.org/10.3390/nano13121891 - 20 Jun 2023

Cited by 5 | Viewed by 2085

Abstract

On-chip polarization control is in high demand for novel integrated photonic applications such as polarization division multiplexing and quantum communications. However, due to the sensitive scaling of the device dimension with wavelength and the visible-light absorption properties, traditional passive silicon photonic devices with [...] Read more.

On-chip polarization control is in high demand for novel integrated photonic applications such as polarization division multiplexing and quantum communications. However, due to the sensitive scaling of the device dimension with wavelength and the visible-light absorption properties, traditional passive silicon photonic devices with asymmetric waveguide structures cannot achieve polarization control at visible wavelengths. In this paper, a new polarization-splitting mechanism based on energy distributions of the fundamental polarized modes in the r-TiO₂ ridge waveguide is investigated. The bending loss for different bending radii and the optical coupling properties of the fundamental modes in different r-TiO₂ ridge waveguide configurations are analyzed. In particular, a polarization splitter with a high extinction ratio operating at visible wavelengths based on directional couplers (DCs) in the r-TiO₂ ridge waveguide is proposed. Polarization-selective filters based on micro-ring resonators (MRRs) with resonances of only TE or TM polarizations are designed and operated. Our results show that polarization-splitters for visible wavelengths with a high extinction ratio in DC or MRR configurations can be achieved with a simple r-TiO₂ ridge waveguide structure. Full article

(This article belongs to the Special Issue Optical Properties of Nanostructured Thin Films)

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9 pages, 5982 KiB

Open AccessCommunication

Bistable Switch Based on Tunable Fano Resonance in Coupled Resonator-Cavity Structure

by Zhuofan Jiang, Lei Gao, Yaqiong Ding, Yu Fang, Xingzhi Wu, Qian Wu, Yong Sun and Yongqiang Chen

Electronics 2023, 12(9), 2023; https://doi.org/10.3390/electronics12092023 - 27 Apr 2023

Cited by 1 | Viewed by 1692

Abstract

We report a side-coupled resonator-cavity configuration with a tunable Fano-type interference effect for a novel subwavelength switch. A defective microstrip photonic crystal (PC) structure is designed to provide a continuum state, while a split ring resonator (SRR) is introduced to offer a narrow [...] Read more.

We report a side-coupled resonator-cavity configuration with a tunable Fano-type interference effect for a novel subwavelength switch. A defective microstrip photonic crystal (PC) structure is designed to provide a continuum state, while a split ring resonator (SRR) is introduced to offer a narrow discrete resonance. The SRR is conductively side-coupled with the microstrip PC cavity in a subwavelength volume. Interactions between them result in Fano-type transmitting spectra with a sharp and asymmetric spectral line profile. A varactor diode serving as the nonlinear medium inclusion is integrated into the slit of the SRR for active control of the sharp Fano resonance. The strongly localized field produced by Fano resonance plays a role in improving the nonlinear properties of the microstrip PC cavity. It is found that a significant blue shift of 94 MHz on the Fano resonance frequency can be achieved by increasing the input power levels from −25 dBm to 8 dBm. We also found that the maximum transmission contrast exceeding 15.9 dB can take place between two bistable states existing at 3.05 dBm and 4.32 dBm for a bidirectional sweep of input power under a monochromatic signal frequency of 1.27 GHz. The findings may benefit the exploitation of metamaterials-assisted active photonic nanocircuits. Full article

(This article belongs to the Section Optoelectronics)

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10 pages, 1907 KiB

Open AccessArticle

Excitation of Asymmetric Resonance with Symmetric Split-Ring Resonator

by Ibraheem Al-Naib and Ijlal Shahrukh Ateeq

Materials 2022, 15(17), 5921; https://doi.org/10.3390/ma15175921 - 26 Aug 2022

Cited by 3 | Viewed by 1936

Abstract

In this paper, a new approach to excite sharp asymmetric resonances using a single completely symmetric split-ring resonator (SRR) inside a rectangular waveguide is proposed. The method is based on an asymmetry in the excitation of a symmetric split-ring resonator by placing it [...] Read more.

In this paper, a new approach to excite sharp asymmetric resonances using a single completely symmetric split-ring resonator (SRR) inside a rectangular waveguide is proposed. The method is based on an asymmetry in the excitation of a symmetric split-ring resonator by placing it away from the center of the waveguide along its horizontal axis. In turn, a prominent asymmetric resonance was observed in the transmission amplitude of both the simulated results and the measured data. Using a single symmetric SRR with an asymmetric distance of 6 mm from the center of a rectangular waveguide led to the excitation of a sharp resonance with a Q-factor of 314 at 6.9 GHz. More importantly, a parametric study simulating different overlayer analytes with various refractive indices revealed a wavelength sensitivity of 579,710 nm/RIU for 150 μm analyte thickness. Full article

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14 pages, 3737 KiB

Open AccessArticle

Tunable Electromagnetically Induced Transparent Window of Terahertz Metamaterials and Its Sensing Performance

by Zhenlin Wu, Peiyao An, Menghan Ding, Yanan Qi, Lin Zhang, Shaoshuai Han, Di Lian, Changming Chen and Xin Yang

Appl. Sci. 2022, 12(14), 7057; https://doi.org/10.3390/app12147057 - 13 Jul 2022

Cited by 8 | Viewed by 2009

Abstract

The electromagnetically induced transparency effect of terahertz metamaterials exhibits excellent modulation and sensing properties, and it is critical to investigate the modulation effect of the transparent window by optimizing structural parameters. In this work, a unilateral symmetrical metamaterial structure based on the cut-wire [...] Read more.

The electromagnetically induced transparency effect of terahertz metamaterials exhibits excellent modulation and sensing properties, and it is critical to investigate the modulation effect of the transparent window by optimizing structural parameters. In this work, a unilateral symmetrical metamaterial structure based on the cut-wire resonator and the U-shaped split ring resonator is demonstrated to achieve electromagnetically induced transparency-like (EIT-like) effect. Based on the symmetrical structure, by changing the structural parameters of the split ring, an asymmetric structure metamaterial is also studied to obtain better tuning and sensing characteristics. The parameters for controlling the transparent window of the metamaterial are investigated in both passive and active modulation modes. In addition, the metamaterial structure based on the cut-wire resonator, unilateral symmetric and asymmetric configurations are investigated for high performance refractive index sensing purposes, and it is found that the first two metamaterial structures can achieve sensitivity responses of 63.6 GHz/RIU and 84.4 GHz/RIU, respectively, while the asymmetric metamaterial is up to 102.3 GHz/RIU. The high sensitivity frequency response of the proposed metamaterial structures makes them good candidates for various chemical and biomedical sensing applications. Full article

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14 pages, 4620 KiB

Open AccessArticle

Analysis of Asymmetry in Active Split-Ring Resonators to Design Circulating-Current Eigenmode: Demonstration of Beamsteering and Focal-Length Control toward Reconfigurable Intelligent Surface

by Daisuke Kitayama, Adam Pander and Hiroyuki Takahashi

Sensors 2022, 22(2), 681; https://doi.org/10.3390/s22020681 - 17 Jan 2022

Cited by 2 | Viewed by 3318

Abstract

In this work, toward an intelligent radio environment for 5G/6G, design methodologies of active split-ring resonators (SRRs) for more efficient dynamic control of metasurfaces are investigated. The relationship between the excitation of circulating-current eigenmode and the asymmetric structure of SRRs is numerically analyzed, [...] Read more.

In this work, toward an intelligent radio environment for 5G/6G, design methodologies of active split-ring resonators (SRRs) for more efficient dynamic control of metasurfaces are investigated. The relationship between the excitation of circulating-current eigenmode and the asymmetric structure of SRRs is numerically analyzed, and it is clarified that the excitation of the circulating-current mode is difficult when the level of asymmetry of the current path is decreased by the addition of large capacitance such as from semiconductor-based devices. To avoid change in the asymmetry, we incorporated an additional gap (slit) in the SRRs, which enabled us to excite the circulating-current mode even when a large capacitance was implemented. Prototype devices were fabricated according to this design methodology, and by the control of the intensity/phase distribution, the variable focal-length and beamsteering capabilities of the transmitted waves were demonstrated, indicating the high effectiveness of the design. The presented design methodology can be applied not only to the demonstrated case of discrete varactors, but also to various other active metamaterials, such as semiconductor-integrated types for operating in the millimeter and submillimeter frequency bands as potential candidates for future 6G systems. Full article

(This article belongs to the Special Issue Mobile Communications in 5G Networks)

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12 pages, 1934 KiB

Open AccessArticle

Glucose Level Sensing Using Single Asymmetric Split Ring Resonator

by Gameel Saleh, Ijlal Shahrukh Ateeq and Ibraheem Al-Naib

Sensors 2021, 21(9), 2945; https://doi.org/10.3390/s21092945 - 22 Apr 2021

Cited by 34 | Viewed by 4749

Abstract

In this article, a biosensor composed of a single metamaterial asymmetric resonator is specifically designed for sensing the glucose level of 1 µL of solution. The resonator has two gaps, and one of them ends with a semicircle shape on which the glucose [...] Read more.

In this article, a biosensor composed of a single metamaterial asymmetric resonator is specifically designed for sensing the glucose level of 1 µL of solution. The resonator has two gaps, and one of them ends with a semicircle shape on which the glucose solution is placed. This design helps in confining the drops of glucose solutions in a specific area where the field is maximally confined in order to enhance the electromagnetic wave-matter interaction. Six samples of glucose solutions with concentrations that cover hypoglycemia, normal and hyperglycemia conditions that vary from around 41 to 312 mg/dL were prepared and examined by this biosensor. The resonance frequency redshift was used as a measure of the changes in the glucose level of the solutions. Without glucose solution, an excellent agreement between the measured and simulated transmission amplitude was observed. The increase in glucose concentrations exhibited clear and noticeable redshifts in the resonance frequency. This biosensor revealed a 0.9997 coefficient of determination, which implies an excellent prediction fitting model. More importantly, a sensitivity of 438 kHz/(mg/dL) was observed over the range of concentrations of the aqueous solution. Full article

(This article belongs to the Special Issue Blood Glucose Sensors Based on RF, Microwave and mmWave Techniques)

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9 pages, 3259 KiB

Open AccessArticle

Multi-Band Electromagnetically-Induced-Transparency Metamaterial Based on the Near-Field Coupling of Asymmetric Split-Ring and Cut-Wire Resonators in the GHz Regime

by Man Hoai Nam, Vu Thi Hong Hanh, Nguyen Ba Tuong, Bui Son Tung, Bui Xuan Khuyen, Vu Dinh Lam, Liang Yao Chen and Young Pak Lee

Crystals 2021, 11(2), 164; https://doi.org/10.3390/cryst11020164 - 6 Feb 2021

Cited by 8 | Viewed by 2900

Abstract

A metamaterial (MM), mimicking electromagnetically-induced transparency (EIT) in the GHz regime, was demonstrated numerically and experimentally by exploiting the near-field coupling of asymmetric split-ring and cut-wire resonators. By moving the resonators towards each other, the original resonance dip was transformed to a multi-band [...] Read more.

A metamaterial (MM), mimicking electromagnetically-induced transparency (EIT) in the GHz regime, was demonstrated numerically and experimentally by exploiting the near-field coupling of asymmetric split-ring and cut-wire resonators. By moving the resonators towards each other, the original resonance dip was transformed to a multi-band EIT. The phenomenon was explained clearly through the excitation of bright and dark modes. The dispersion characteristic of the proposed MM was also investigated, which showed a strongly-dispersive behavior, leading to a high group index and a time delay of the MM. Our work is expected to contribute a simple way to develop the potential devices based on the multi-band EIT effect. Full article

(This article belongs to the Special Issue Advances in Metamaterials)

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9 pages, 3320 KiB

Open AccessArticle

Graphene Multiple Fano Resonances Based on Asymmetric Hybrid Metamaterial

by Zhendong Yan, Zhixing Zhang, Wei Du, Wenjuan Wu, Taoping Hu, Zi Yu, Ping Gu, Jing Chen and Chaojun Tang

Nanomaterials 2020, 10(12), 2408; https://doi.org/10.3390/nano10122408 - 2 Dec 2020

Cited by 11 | Viewed by 2024

Abstract

We theoretically investigate multiple Fano resonances in an asymmetric hybrid graphene–metal metamaterial. The multiple Fano resonances emerge from the coupling of the plasmonic narrow bonding and antibonding modes supported by an in-plane graphene nanoribbon dimer with the broad magnetic resonance mode supported by [...] Read more.

We theoretically investigate multiple Fano resonances in an asymmetric hybrid graphene–metal metamaterial. The multiple Fano resonances emerge from the coupling of the plasmonic narrow bonding and antibonding modes supported by an in-plane graphene nanoribbon dimer with the broad magnetic resonance mode supported by a gold split-ring resonator. It is found that the Fano resonant mode with its corresponding dark mode of the antibonding mode in the in-plane graphene nanoribbon dimer is only achieved by structural symmetry breaking. The multiple Fano resonances can be tailored by tuning the structural parameters and Fermi levels. Active control of the multiple Fano resonances enables the proposed metamaterial to be widely applied in optoelectronic devices such as tunable sensors, switches, and filters. Full article

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9 pages, 3924 KiB

Open AccessArticle

Reconfigurable Terahertz Metamaterial Using Split-Ring Meta-Atoms with Multifunctional Electromagnetic Characteristics

by Yuhang Liao and Yu-Sheng Lin

Appl. Sci. 2020, 10(15), 5267; https://doi.org/10.3390/app10155267 - 30 Jul 2020

Cited by 11 | Viewed by 3463

Abstract

We propose a reconfigurable terahertz (THz) metamaterial (RTM) to investigate its multifunctional electromagnetic characteristics by moving the meta-atoms of split-ring resonator (SRR) array. It shows the preferable and capable adjustability in the THz frequency range. The electromagnetic characteristics of the proposed RTM device [...] Read more.

We propose a reconfigurable terahertz (THz) metamaterial (RTM) to investigate its multifunctional electromagnetic characteristics by moving the meta-atoms of split-ring resonator (SRR) array. It shows the preferable and capable adjustability in the THz frequency range. The electromagnetic characteristics of the proposed RTM device are compared and analyzed by moving the meta-atoms in different polarized transverse magnetic (TM) and transverse electric (TE) modes. The symmetrical meta-atoms of RTM device exhibit a resonant tuning range of several tens of GHz and the asymmetrical meta-atoms of RTM device exhibit the better tunability. Therefore, an RTM device with reconfigurable meta-atoms possesses the resonance shifting, polarization switching, electromagnetically induced transparency (EIT) switching and multiband to single-band switching characteristics. This proposed RTM device provides the potential possibilities for the use of THz-wave optoelectronics with tunable resonance, EIT analog and tunable multiresonance characteristics. Full article

(This article belongs to the Special Issue Advances of THz Spectroscopy)

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8 pages, 2231 KiB

Open AccessArticle

Free-Standing Complementary Asymmetric Metasurface for Terahertz Sensing Applications

by Fatima Taleb, Ibraheem Al-Naib and Martin Koch

Sensors 2020, 20(8), 2265; https://doi.org/10.3390/s20082265 - 16 Apr 2020

Cited by 28 | Viewed by 4461

Abstract

We designed and tested a highly sensitive metasurface device based on free-standing complementary asymmetric split-ring resonators at terahertz frequencies. It is utilized for sensing a galactose film. We characterized the device using the induced red shift of a Fano resonance observed in the [...] Read more.

We designed and tested a highly sensitive metasurface device based on free-standing complementary asymmetric split-ring resonators at terahertz frequencies. It is utilized for sensing a galactose film. We characterized the device using the induced red shift of a Fano resonance observed in the THz transmission. The sensor has a high sensitivity of 91.7 GHz/RIU due to a significant interaction between the galactose overlayer and the metasurface. Full article

(This article belongs to the Special Issue Optical Spectroscopy, Sensing, and Imaging from UV to THz Range)

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8 pages, 2322 KiB

Open AccessArticle

Enhanced FANO Structure Based on Tip-Field-Enhancement Theory

by Tianchi Zhou, Bo Zhang, Yaxin Zhang, Chao Shu, Shixiong Liang, Lan Wang and Kaijun Song

Appl. Sci. 2019, 9(23), 5009; https://doi.org/10.3390/app9235009 - 21 Nov 2019

Viewed by 2394

Abstract

High-Q metasurfaces have attracted much interest owing to their potential application in biological sensors. FANO is a type of high-Q factor metasurface. However, it is difficult to achieve large resonant intensity and a high-Q factor at the same time. In this paper, by [...] Read more.

High-Q metasurfaces have attracted much interest owing to their potential application in biological sensors. FANO is a type of high-Q factor metasurface. However, it is difficult to achieve large resonant intensity and a high-Q factor at the same time. In this paper, by sharpening the tips of the asymmetrical split-ring FANO structure and letting more charges stack at the tips to enhance tip coupling, the Q factor was significantly improved without sacrificing too much resonant intensity. Simulation results showed that the Q factor increased up to 2.4 times, while the resonant intensity stayed higher than 20 dB, and the experiment results agreed with the simulations. This indicated that the tip-field-enhancement theory can be applied in time-harmonic electromagnetic-fields, and the method proposed here can be used to increase the sensitivity and accuracy of microfluidic sensors. Additionally, other types of research, such as on antenna design, could benefit from this theory. Full article

(This article belongs to the Special Issue Photonic Crystals for Electromagnetic Applications)

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