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Jiang Z, He W, Chen J, Jiang K, Li S, Wang L. Plasmonic direct-writing lithography via high numerical aperture objectives. OPTICS LETTERS 2023; 48:4153-4156. [PMID: 37527141 DOI: 10.1364/ol.496697] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2023] [Accepted: 07/05/2023] [Indexed: 08/03/2023]
Abstract
The exploration of light-matter interactions at the sub-wavelength scale requires advanced nano-patterning tools with low cost and high flexibility. Plasmonic lithography as a promising candidate receives much attention owing to its ability to confine ultraviolet light sources into an extremely tiny volume. To date, most plasmonic patterning schemes utilize metallic nano-structures to achieve tight focusing. The drawback is that the plasmonic structures need, however, to be pre-defined, usually accompanied with the expense of complex fabrication processes. Here we numerically and experimentally report an antenna-free plasmonic lithography technique using high numerical aperture (NA) objectives as the scanning head. Minimum feature sizes of 0.36λ/NA and 0.46λ/NA are numerically and experimentally demonstrated, respectively, under the linearly polarized continuous-wave illumination at 457 nm with no involvement of nonlinear effects. Back-focal-plane imaging is used to visualize surface-plasmon excitations, acting as a viable way of adjusting focus precisely. Our method can serve as a candidate for laser processing at the sub-wavelength scale, and offers a truly convenient and economical way of nano-patterning.
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Han D, Deng S, Ye T, Wei Y. Enhancement of pattern quality in maskless plasmonic lithography via spatial loss modulation. MICROSYSTEMS & NANOENGINEERING 2023; 9:40. [PMID: 37007604 PMCID: PMC10060221 DOI: 10.1038/s41378-023-00512-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/23/2022] [Revised: 02/08/2023] [Accepted: 02/13/2023] [Indexed: 06/19/2023]
Abstract
Plasmonic lithography, which uses the evanescent electromagnetic (EM) fields to generate image beyond the diffraction limit, has been successfully demonstrated as an alternative lithographic technology for creating sub-10 nm patterns. However, the obtained photoresist pattern contour in general exhibits a very poor fidelity due to the near-field optical proximity effect (OPE), which is far below the minimum requirement for nanofabrication. Understanding the near-field OPE formation mechanism is important to minimize its impact on nanodevice fabrication and improve its lithographic performance. In this work, a point-spread function (PSF) generated by a plasmonic bowtie-shaped nanoaperture (BNA) is employed to quantify the photon-beam deposited energy in the near-field patterning process. The achievable resolution of plasmonic lithography has successfully been enhanced to approximately 4 nm with numerical simulations. A field enhancement factor (F) as a function of gap size is defined to quantitatively evaluate the strong near-field enhancement effect excited by a plasmonic BNA, which also reveals that the high enhancement of the evanescent field is due to the strong resonant coupling between the plasmonic waveguide and the surface plasmon waves (SPWs). However, based on an investigation of the physical origin of the near-field OPE, and the theoretical calculations and simulation results indicate that the evanescent-field-induced rapid loss of high-k information is one of the main optical contributors to the near-field OPE. Furthermore, an analytic formula is introduced to quantitatively analyze the effect of the rapidly decaying feature of the evanescent field on the final exposure pattern profile. Notably, a fast and effective optimization method based on the compensation principle of the exposure dose is proposed to reduce the pattern distortion by modulating the exposure map with dose leveling. The proposed pattern quality enhancement method can open new possibilities in the manufacture of nanostructures with ultrahigh pattern quality via plasmonic lithography, which would find potentially promising applications in high density optical storage, biosensors, and plasmonic nanofocusing.
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Affiliation(s)
- Dandan Han
- University of Chinese Academy of Sciences, School of Integrated Circuits, Beijing, 100049 China
| | - Sen Deng
- University of Chinese Academy of Sciences, School of Integrated Circuits, Beijing, 100049 China
| | - Tianchun Ye
- University of Chinese Academy of Sciences, School of Integrated Circuits, Beijing, 100049 China
- Chinese Academy of Sciences, Institute of Microelectronics, Beijing, 100029 China
| | - Yayi Wei
- University of Chinese Academy of Sciences, School of Integrated Circuits, Beijing, 100049 China
- Chinese Academy of Sciences, Institute of Microelectronics, Beijing, 100029 China
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Gong J, Xiong L, Pu M, Guo Y, Wen Y, He Q, Li X, Ma X, Luo X. Simple route for high-throughput fabrication of metasurfaces using one-step UV-curable resin printing. OPTICS EXPRESS 2023; 31:8068-8080. [PMID: 36859924 DOI: 10.1364/oe.481384] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2022] [Accepted: 01/20/2023] [Indexed: 06/18/2023]
Abstract
Phase-gradient metasurfaces are two-dimensional (2D) optical elements that can manipulate light by imposing local, space-variant phase changes on an incident electromagnetic wave. These metasurfaces hold the potential and the promise to revolutionize photonics by providing ultrathin alternatives for a wide range of common optical elements such as bulky refractive optics, waveplates, polarizers, and axicons. However, the fabrication of state-of-the-art metasurfaces typically requires some time-consuming, expensive, and possibly hazardous processing steps. To overcome these limitations on conventional metasurface fabrication, a facile methodology to produce phase-gradient metasurfaces through one-step UV-curable resin printing is developed by our research group. The method dramatically reduces the required processing time and cost, as well as eliminates safety hazards. As a proof-of-concept, the advantages of the method are clearly demonstrated via a rapid reproduction of high-performance metalenses based on the Pancharatnam-Berry phase gradient concept in the visible spectrum.
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Han D, Wei Y. Achieving high aspect ratio in plasmonic lithography for practical applications with sub-20 nm half pitch. OPTICS EXPRESS 2022; 30:20589-20604. [PMID: 36224800 DOI: 10.1364/oe.457995] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2022] [Accepted: 05/15/2022] [Indexed: 06/16/2023]
Abstract
Plasmonic lithography, which exploits a bowtie nanoaperture (BNA) for the purpose of subwavelength near-field focusing, has the capability of high-resolution patterning. However, the ultra-small feature size is achieved at the price of sharply decay of the surface plasmon waves (SPWs) in the photoresist (PR) layer, which directly leads to some unfavorable patterning issues, such as non-uniformity and shallow pattern depth even over small exposure areas. In this work, a special hybrid plasmonic waveguide (HPW) patterning system, which is composed of the plasmonic BNA-PR layer-silver reflector, is designed to facilitate high spatial frequency selection and amplify the evanescent field in the PR layer. Theoretical calculations indicate that the antisymmetric coupled SPWs and plasmonic waveguide modes excited by the HPW structure can remove the exponential decay and ensure uniform exposure over the entire depth of the PR layer. Importantly, the hyperbolic decaying characteristic of the SPWs in the PR layer plays a noticeable role in the improvement of achievable resolution, depth-of-field, and line array pattern profile. It is worth to note that the uniform periodic patterns in sub-20 nm feature can be achieved with high aspect ratio. Additionally, further numerical simulation results are presented to demonstrate the achievement of spatial frequency selection of high-k mode in HPW structure by controlling the PR thickness and gap size. Our findings may provide a new perspective on the manufacture of surface nanostructures and broaden the potential promising applications of plasmonic lithography in nanoscale patterning.
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Fan Y, Zhang T, Cai Z, Li D, Yue W, Gong T, Luo Y, Gao P. Surface-enhanced Raman Scattering of Au-Ag bimetallic nanopillars fabricated using surface-plasmon lithography. NANOTECHNOLOGY 2022; 33:255301. [PMID: 35290967 DOI: 10.1088/1361-6528/ac5df8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2022] [Accepted: 03/15/2022] [Indexed: 06/14/2023]
Abstract
Arrays of gold-silver (Au-Ag) bimetallic nanopillars were fabricated by a newly developed surface-plasmon lithography (SPL) and their enhancement properties as surface-enhanced Raman scattering (SERS) substrates have been studied. We demonstrated that the SPL is a low-cost and high efficiency method for the fabrication of SERS substrates with both high sensitivity and reproducibility. The nanopillars showed a good response in the detection of methylene blue molecules at a low concentration of 1.0 × 10-11mol· l-1. The SERS enhancement factors (EFs) are on the orders of 107and the relative standard deviation of SERS intensity is <8% over an area of 50μm × 50μm. The EFs increase fast with the height increasing from 200 to 530 nm, then increase slowly when further increase the height of the nanopillars to 1100 nm. In addition, the Au-Ag bimetallic coating has shown much higher SERS enhancement than the coatings of either the pure Au or Ag. The excellent SERS enhancement and reproducibility of the Au-Ag coated nanopillars indicated that the fabricated SERS substrates can be used for the detection of biochemical molecules at trace level and the SPL is a promising method for fabrication of SERS substrates.
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Affiliation(s)
- Yimin Fan
- State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, PO Box 350, Chengdu 610209, People's Republic of China
- School of Optoelectronics, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Tao Zhang
- State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, PO Box 350, Chengdu 610209, People's Republic of China
| | - Zubo Cai
- State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, PO Box 350, Chengdu 610209, People's Republic of China
| | - Dongxian Li
- State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, PO Box 350, Chengdu 610209, People's Republic of China
| | - Weisheng Yue
- State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, PO Box 350, Chengdu 610209, People's Republic of China
- School of Optoelectronics, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Tiancheng Gong
- State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, PO Box 350, Chengdu 610209, People's Republic of China
| | - Yunfei Luo
- State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, PO Box 350, Chengdu 610209, People's Republic of China
- School of Optoelectronics, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Ping Gao
- State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, PO Box 350, Chengdu 610209, People's Republic of China
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Akbari‐Hasanjani R, Sabbaghi‐Nadooshan R. Innovation Quinary and
n
‐Value toward Fuzzy Logic QCA Cell Design. ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202100304] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Reza Akbari‐Hasanjani
- Department of Electrical Engineering Central Tehran Branch Islamic Azad University Tehran 1469669191 Iran
| | - Reza Sabbaghi‐Nadooshan
- Department of Electrical Engineering Central Tehran Branch Islamic Azad University Tehran 1469669191 Iran
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Luo S, Hoff BH, Maier SA, de Mello JC. Scalable Fabrication of Metallic Nanogaps at the Sub-10 nm Level. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2021; 8:e2102756. [PMID: 34719889 PMCID: PMC8693066 DOI: 10.1002/advs.202102756] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2021] [Revised: 08/09/2021] [Indexed: 06/01/2023]
Abstract
Metallic nanogaps with metal-metal separations of less than 10 nm have many applications in nanoscale photonics and electronics. However, their fabrication remains a considerable challenge, especially for applications that require patterning of nanoscale features over macroscopic length-scales. Here, some of the most promising techniques for nanogap fabrication are evaluated, covering established technologies such as photolithography, electron-beam lithography (EBL), and focused ion beam (FIB) milling, plus a number of newer methods that use novel electrochemical and mechanical means to effect the patterning. The physical principles behind each method are reviewed and their strengths and limitations for nanogap patterning in terms of resolution, fidelity, speed, ease of implementation, versatility, and scalability to large substrate sizes are discussed.
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Affiliation(s)
- Sihai Luo
- Department of ChemistryNorwegian University of Science and Technology (NTNU)TrondheimNO‐7491Norway
| | - Bård H. Hoff
- Department of ChemistryNorwegian University of Science and Technology (NTNU)TrondheimNO‐7491Norway
| | - Stefan A. Maier
- Nano‐Institute MunichFaculty of PhysicsLudwig‐Maximilians‐Universität MünchenMünchen80539Germany
- Blackett LaboratoryDepartment of PhysicsImperial College LondonLondonSW7 2AZUK
| | - John C. de Mello
- Department of ChemistryNorwegian University of Science and Technology (NTNU)TrondheimNO‐7491Norway
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Li T, Ma T, Li J, Chen S, Ma X, Yin J, Jiang X. Micropatterns Fabricated by Photodimerization-Induced Diffusion. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2021; 33:e2007699. [PMID: 34363250 DOI: 10.1002/adma.202007699] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Revised: 05/31/2021] [Indexed: 06/13/2023]
Abstract
Pattern technology plays an important role in the generation of microstructures with different functionalities and morphologies. In this report, a straightforward and versatile strategy is presented for spatially regulating the growth of a microstructure on a surface by the photodimerization of maleimide (MI). Upon exposure of ultraviolet (UV) light, photodimerization of MI in a film comprising furan-grafted polymer and bismaleimide (BMI) produces a chemical gradient, which can drive the diffusion of BMI from the unexposed to the exposed region and from the bottom to the surface, resulting in the growth of micropatterns. Sequential crosslinking induced by the Diels-Alder reaction between MI and furan maintains the stability of pattern shape. Theoretical modeling with reaction-diffusion equations reveal that as photodimerization moves the system far from thermodynamic equilibrium, the formation of a chemical potential gradient requires the redistribution of matter, resulting in the formation of topographies. Directional molecular motion induced by UV light can generate complex morphology, and produce materials with unique optical functions, such as charming-ordered gratings. This straightforward method of fabricating micropatterns by photodimerization-induced diffusion is successfully applied to patterned curved surfaces, microfluidic channels and encapsulation of integrated light emitting diode chips.
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Affiliation(s)
- Tiantian Li
- School of Chemistry and Chemical Engineering Frontiers Science Center for Transformative Molecules State Key Laboratory for Metal Matrix Composite Materials, Shanghai Jiao Tong University, Shanghai, 200240, P. R. China
| | - Tianjiao Ma
- School of Chemistry and Chemical Engineering Frontiers Science Center for Transformative Molecules State Key Laboratory for Metal Matrix Composite Materials, Shanghai Jiao Tong University, Shanghai, 200240, P. R. China
| | - Jin Li
- School of Chemistry and Chemical Engineering Frontiers Science Center for Transformative Molecules State Key Laboratory for Metal Matrix Composite Materials, Shanghai Jiao Tong University, Shanghai, 200240, P. R. China
| | - Shuai Chen
- School of Chemistry and Chemical Engineering Frontiers Science Center for Transformative Molecules State Key Laboratory for Metal Matrix Composite Materials, Shanghai Jiao Tong University, Shanghai, 200240, P. R. China
| | - Xiaodong Ma
- School of Chemistry and Chemical Engineering Frontiers Science Center for Transformative Molecules State Key Laboratory for Metal Matrix Composite Materials, Shanghai Jiao Tong University, Shanghai, 200240, P. R. China
| | - Jie Yin
- School of Chemistry and Chemical Engineering Frontiers Science Center for Transformative Molecules State Key Laboratory for Metal Matrix Composite Materials, Shanghai Jiao Tong University, Shanghai, 200240, P. R. China
| | - Xuesong Jiang
- School of Chemistry and Chemical Engineering Frontiers Science Center for Transformative Molecules State Key Laboratory for Metal Matrix Composite Materials, Shanghai Jiao Tong University, Shanghai, 200240, P. R. China
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Akbari‐Hasanjani R, Sabbaghi‐Nadooshan R. Design and Simulation of Innovative QCA Quaternary Logic Gates. ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202100069] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Reza Akbari‐Hasanjani
- Department of Electrical Engineering Central Tehran Branch, Islamic Azad University Tehran Iran
| | - Reza Sabbaghi‐Nadooshan
- Department of Electrical Engineering Central Tehran Branch, Islamic Azad University Tehran Iran
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10
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Oh DK, Lee T, Ko B, Badloe T, Ok JG, Rho J. Nanoimprint lithography for high-throughput fabrication of metasurfaces. FRONTIERS OF OPTOELECTRONICS 2021; 14:229-251. [PMID: 36637666 PMCID: PMC9743954 DOI: 10.1007/s12200-021-1121-8] [Citation(s) in RCA: 29] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Accepted: 02/02/2021] [Indexed: 05/27/2023]
Abstract
Metasurfaces are composed of periodic sub-wavelength nanostructures and exhibit optical properties that are not found in nature. They have been widely investigated for optical applications such as holograms, wavefront shaping, and structural color printing, however, electron-beam lithography is not suitable to produce large-area metasurfaces because of the high fabrication cost and low productivity. Although alternative optical technologies, such as holographic lithography and plasmonic lithography, can overcome these drawbacks, such methods are still constrained by the optical diffraction limit. To break through this fundamental problem, mechanical nanopatterning processes have been actively studied in many fields, with nanoimprint lithography (NIL) coming to the forefront. Since NIL replicates the nanopattern of the mold regardless of the diffraction limit, NIL can achieve sufficiently high productivity and patterning resolution, giving rise to an explosive development in the fabrication of metasurfaces. In this review, we focus on various NIL technologies for the manufacturing of metasurfaces. First, we briefly describe conventional NIL and then present various NIL methods for the scalable fabrication of metasurfaces. We also discuss recent applications of NIL in the realization of metasurfaces. Finally, we conclude with an outlook on each method and suggest perspectives for future research on the high-throughput fabrication of active metasurfaces.
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Affiliation(s)
- Dong Kyo Oh
- Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea
| | - Taejun Lee
- Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea
| | - Byoungsu Ko
- Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea
| | - Trevon Badloe
- Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea
| | - Jong G Ok
- Department of Mechanical and Automotive Engineering, Seoul National University of Science and Technology (SEOULTECH), Seoul, 01811, Republic of Korea.
| | - Junsuk Rho
- Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea.
- Department of Chemical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea.
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Gu Z, Song Q, Xiao S. Nanowire Waveguides and Lasers: Advances and Opportunities in Photonic Circuits. Front Chem 2021; 8:613504. [PMID: 33490039 PMCID: PMC7820942 DOI: 10.3389/fchem.2020.613504] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2020] [Accepted: 12/03/2020] [Indexed: 11/13/2022] Open
Abstract
Due to their single-crystalline structures, comparatively large aspect ratios, tight optical confinement and smooth surfaces, nanowires have increasingly attracted research interests for both fundamental studies and technological applications in on-chip photonic devices. This class of nanostructures typically have cross-sections of 2~200 nm and lengths upwards of several micrometers, allowing for the bridging of the nanoscopic and macroscopic world. In particular, the lasing behaviors can be established from a nanowire resonator with positive feedback via end-facet reflection, making the nanowire a promising candidate in the next generation of optoelectronics. Consequently, versatile nanowire-based devices ranging from nanoscale coherent lasers, optical sensors, waveguides, optical switching, and photonic networks have been proposed and experimentally demonstrated in the past decade. In this article, significant progresses in the nanowire fabrication, lasers, circuits, and devices are reviewed. First, we focus on the achievements of nanowire synthesis and introduce the basics of nanowire optics. Following the cavity configurations and mode categories, then the different light sources consisting of nanowires are presented. Next, we review the recent progress and current status of functional nanowire devices. Finally, we offer our perspective of nanowires regarding their challenges and future opportunities in photonic circuits.
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Affiliation(s)
- Zhiyuan Gu
- Department of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan, China
- Ministry of Industry and Information Technology Key Lab of Micro–Nano Optoelectronic Information System, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, China
| | - Qinghai Song
- Department of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan, China
| | - Shumin Xiao
- Department of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan, China
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Nanostructured Color Filters: A Review of Recent Developments. NANOMATERIALS 2020; 10:nano10081554. [PMID: 32784749 PMCID: PMC7466596 DOI: 10.3390/nano10081554] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/21/2020] [Revised: 07/22/2020] [Accepted: 07/23/2020] [Indexed: 01/22/2023]
Abstract
Color plays an important role in human life: without it life would be dull and monochromatic. Printing color with distinct characteristics, like hue, brightness and saturation, and high resolution, are the main characteristic of image sensing devices. A flexible design of color filter is also desired for angle insensitivity and independence of direction of polarization of incident light. Furthermore, it is important that the designed filter be compatible with the image sensing devices in terms of technology and size. Therefore, color filter requires special care in its design, operation and integration. In this paper, we present a comprehensive review of nanostructured color filter designs described to date and evaluate them in terms of their performance.
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