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Keywords = one dimensional photonic crystal

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28 pages, 8135 KiB  
Communication
Angle-Dispersion-Free Near-Infrared Transparent Bands in One-Dimensional Photonic Hypercrystals
by Feng Wu, Jiayi Ruan, Li He, Abinash Panda and Haitao Jiang
Photonics 2025, 12(8), 748; https://doi.org/10.3390/photonics12080748 - 24 Jul 2025
Viewed by 261
Abstract
In classic all-dielectric one-dimensional photonic crystals, transparent bands exhibit strong angular dispersion. Herein, we realize an angle-dispersion-free near-infrared transparent band in a one-dimensional photonic hypercrystal containing hyperbola-dispersion metamaterials. As the incident angle increases from 0° to 80°, the relative shifts of the wavelengths [...] Read more.
In classic all-dielectric one-dimensional photonic crystals, transparent bands exhibit strong angular dispersion. Herein, we realize an angle-dispersion-free near-infrared transparent band in a one-dimensional photonic hypercrystal containing hyperbola-dispersion metamaterials. As the incident angle increases from 0° to 80°, the relative shifts of the wavelengths of four transmittance peaks within the transparent band are smaller than 1.5% and the bandwidth of the transparent band marginally fluctuates from 1098.2 to 1132.5 nm. Particularly, the angle-dispersion-free property of the transparent band is quite robust with respect to the layer thickness disturbance. Our work not only offers a viable method of achieving angle-dispersion-free transparent bands but also facilitates the development of transparency-based optical devices. Full article
(This article belongs to the Special Issue Photonic Crystals: Physics and Devices, 2nd Edition)
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13 pages, 9483 KiB  
Article
Abnormal Angle-Dependent Multi-Channel Filtering in Photonic Crystals Containing Hyperbolic Metamaterials
by Mingyan Xie, Yuanda Huang, Haoyuan Qin and Guiqiang Du
Nanomaterials 2025, 15(14), 1122; https://doi.org/10.3390/nano15141122 - 19 Jul 2025
Viewed by 399
Abstract
Tunneling modes in all-dielectric one-dimensional photonic crystals can be utilized for multi-channel filtering. However, these tunneling modes generally blue shift upon increasing the incident angle. When hyperbolic metamaterials are introduced into one-dimensional photonic crystals, the competition between the propagation phase shifts in the [...] Read more.
Tunneling modes in all-dielectric one-dimensional photonic crystals can be utilized for multi-channel filtering. However, these tunneling modes generally blue shift upon increasing the incident angle. When hyperbolic metamaterials are introduced into one-dimensional photonic crystals, the competition between the propagation phase shifts in the dielectric materials and hyperbolic metamaterials can result in different angle dependencies, including blue shift, abnormal zero shift, and abnormal red shift. When the reduction in the propagation phase in the dielectric layer exceeds the increment in the propagation phase in the hyperbolic metamaterial, the tunneling modes are blue-shifted; conversely, when the phase increment in the hyperbolic metamaterial exceeds the phase reduction in the dielectric layer, the tunneling modes are abnormally red-shifted. When the phase changes in the two materials are the same, the tunneling modes are angle independent. In this study, we investigated the multiple filtering effects of one-dimensional photonic structures composed of hyperbolic metamaterials. These composed structures exhibited multiple tunneling modes based on one-, two-, or three-angle dependencies and can be applied in novel optical devices with different angle-dependence requirements. Full article
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22 pages, 3862 KiB  
Article
Composition-Dependent Structural, Phonon, and Thermodynamical Characteristics of Zinc-Blende BeZnO
by Devki N. Talwar and Piotr Becla
Materials 2025, 18(13), 3101; https://doi.org/10.3390/ma18133101 - 1 Jul 2025
Cited by 1 | Viewed by 296
Abstract
Both ZnO and BeO semiconductors crystallize in the hexagonal wurtzite (wz), cubic rock salt (rs), and zinc-blende (zb) phases, depending upon their growth conditions. Low-dimensional heterostructures ZnO/BexZn1-xO and BexZn1-xO ternary alloy-based devices have recently gained [...] Read more.
Both ZnO and BeO semiconductors crystallize in the hexagonal wurtzite (wz), cubic rock salt (rs), and zinc-blende (zb) phases, depending upon their growth conditions. Low-dimensional heterostructures ZnO/BexZn1-xO and BexZn1-xO ternary alloy-based devices have recently gained substantial interest to design/improve the operations of highly efficient and flexible nano- and micro-electronics. Attempts are being made to engineer different electronic devices to cover light emission over a wide range of wavelengths to meet the growing industrial needs in photonics, energy harvesting, and biomedical applications. For zb materials, both experimental and theoretical studies of lattice dynamics ωjq have played crucial roles for understanding their optical and electronic properties. Except for zb ZnO, inelastic neutron scattering measurement of ωjq for BeO is still lacking. For the BexZn1-xO ternary alloys, no experimental and/or theoretical studies exist for comprehending their structural, vibrational, and thermodynamical traits (e.g., Debye temperature ΘDT; specific heat CvT). By adopting a realistic rigid-ion model, we have meticulously simulated the results of lattice dynamics, and thermodynamic properties for both the binary zb ZnO, BeO and ternary BexZn1-xO alloys. The theoretical results are compared/contrasted against the limited experimental data and/or ab initio calculations. We strongly feel that the phonon/thermodynamic features reported here will encourage spectroscopists to perform similar measurements and check our theoretical conjectures. Full article
(This article belongs to the Special Issue Advanced Additive Manufacturing Processing of Ceramic Materials)
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8 pages, 576 KiB  
Article
Coherent Grating Transition Radiation of a Hollow Relativistic Electron Beam from a Flat 2D Photonic Crystal
by Daria Yu. Sergeeva and Alexey A. Tishchenko
Particles 2025, 8(2), 62; https://doi.org/10.3390/particles8020062 - 12 Jun 2025
Viewed by 443
Abstract
Hollow electron beams are a promising tool for generating coherent radiation in various frequency ranges. Hollow beams have unique properties, including increased stability and the ability to achieve high current densities without significant deterioration of beam quality. This paper presents the results of [...] Read more.
Hollow electron beams are a promising tool for generating coherent radiation in various frequency ranges. Hollow beams have unique properties, including increased stability and the ability to achieve high current densities without significant deterioration of beam quality. This paper presents the results of a theoretical study on coherent grating transition radiation arising during the interaction between a relativistic hollow electron beam and a flat two-dimensional photonic crystal. The radiation field is calculated using the dipole approximation. Theoretical analysis has shown that, under certain conditions, a high degree of radiation coherence can be achieved. The results open up new possibilities for the creation of new sources of coherent terahertz radiation. Full article
(This article belongs to the Special Issue Generation and Application of High-Power Radiation Sources 2025)
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9 pages, 9851 KiB  
Article
Manipulation of Topological Edge States and Realization of Zero-Dimensional Higher-Order Topological Point States
by Jiahui Ren, Wenjing Ding, Sihan Wang and Shiwei Tang
Micromachines 2025, 16(6), 686; https://doi.org/10.3390/mi16060686 - 7 Jun 2025
Viewed by 481
Abstract
Topological photonics has provided revolutionary ideas for the design of next-generation photonic devices due to its unique light transmission properties. This paper proposes a honeycomb photonic crystal structure based on a mirror-symmetric interface and numerically simulates the precise manipulation of topological edge states [...] Read more.
Topological photonics has provided revolutionary ideas for the design of next-generation photonic devices due to its unique light transmission properties. This paper proposes a honeycomb photonic crystal structure based on a mirror-symmetric interface and numerically simulates the precise manipulation of topological edge states and the robust excitation of high-order topological corner states in this structure. Specifically, two honeycomb photonic crystals with non-trivial topological properties form an interface through mirror-symmetric stitching. Continuous adjustment of the spacing between their coupling pillars can induce the closure and reopening of topological edge state energy bands, accompanied by significant band inversion, revealing the dynamic process of topological phase transitions. Furthermore, zero-dimensional high-order topological corner states are observed at the junction of boundaries with different topological properties. Their localized field strengths are strictly confined and exhibit strong robustness against structural defects. This study not only provides a new mechanism for the local symmetry manipulation of topological edge states but also lays a foundation for the design of high-order topological photonic crystals and the practical application of topological photonic devices. Full article
(This article belongs to the Special Issue Novel Electromagnetic and Acoustic Devices)
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14 pages, 2006 KiB  
Article
Design and Optimization of Optical NAND and NOR Gates Using Photonic Crystals and the ML-FOLD Algorithm
by Alireza Mohammadi, Fariborz Parandin, Pouya Karami and Saeed Olyaee
Photonics 2025, 12(6), 576; https://doi.org/10.3390/photonics12060576 - 6 Jun 2025
Viewed by 658
Abstract
The continuous demand for faster processing systems, driven by the rise of artificial intelligence, has exposed limitations in traditional transistor-based electronics, including quantum tunneling, heat dissipation, and switching delays due to challenges in further miniaturization. This study explores optical systems as a promising [...] Read more.
The continuous demand for faster processing systems, driven by the rise of artificial intelligence, has exposed limitations in traditional transistor-based electronics, including quantum tunneling, heat dissipation, and switching delays due to challenges in further miniaturization. This study explores optical systems as a promising alternative, leveraging the speed of photons over electrons. Specifically, we design and simulate optical NAND and NOR logic gates using a two-dimensional photonic crystal structure with a square lattice. Symmetrical waveguides are used for the input paths to make the structure relatively more straightforward to fabricate. A key innovation is the ability to realize both gates within a single structure by adjusting the phases of the input sources. To optimize the phase parameters efficiently, we employ the ML-FOLD (Meta-Learning and Formula Optimization for Logic Design) optimization formula, which outperforms traditional methods and machine learning approaches in terms of computational efficiency and data requirements. Through finite-difference time-domain (FDTD) simulations, the proposed optical structure demonstrates successful implementation of NAND and NOR gate logic, achieving high contrast ratios of 4.2 dB and 4.8 dB, respectively. The results validate the effectiveness of the ML-FOLD method in identifying optimal configurations, offering a streamlined approach for the design of all-optical logic devices. Full article
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17 pages, 698 KiB  
Article
Numerical Method for Band Gap Structure and Dirac Point of Photonic Crystals Based on Recurrent Neural Network
by Yakun Wang and Jianhua Yuan
Axioms 2025, 14(6), 445; https://doi.org/10.3390/axioms14060445 - 6 Jun 2025
Viewed by 483
Abstract
In this paper, we propose a recurrent neural network numerical method with the finite element method for partial differential equations to study the band gap structure and Dirac points in two-dimensional photonic crystals. Electromagnetic wave propagation is governed by Maxwell’s equations. We transform [...] Read more.
In this paper, we propose a recurrent neural network numerical method with the finite element method for partial differential equations to study the band gap structure and Dirac points in two-dimensional photonic crystals. Electromagnetic wave propagation is governed by Maxwell’s equations. We transform the partial differential equations into large-scale generalized eigenvalue problems by spatially discretising them using the finite element method. Compared with traditional numerical computation methods, neural networks can perform high-speed parallel computation. Existing neural network-based eigenvalue solvers are typically restricted to computing extremal eigenvalues of real symmetric matrix pairs. To overcome this limitation, we develop a novel RNN-based numerical scheme tailored for solving the band structure problem in photonic crystals. We validate our method by computing the dispersion relations of photonic crystals with periodic dielectric columns, achieving excellent agreement with the plane-wave expansion method. In addition, we calculate the Dirac points at the center of the Brillouin zone, which is crucial for understanding the unique optical properties of photonic crystals. We determine the precise filling ratios at which these Dirac points appear, thus providing insight into the relationship between geometrical and material parameters and the appearance of Dirac points. Full article
(This article belongs to the Topic Numerical Methods for Partial Differential Equations)
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14 pages, 3264 KiB  
Article
Thickness and Wavelength Optimizations of a High-Performance SPR Sensor Employing a Silver Layer and Black Phosphorus in Principal Directions
by Jakub Chylek, Dalibor Ciprian and Petr Hlubina
Nanomaterials 2025, 15(11), 790; https://doi.org/10.3390/nano15110790 - 24 May 2025
Viewed by 608
Abstract
In this paper, we propose an innovative approach based on the wavelength optimization of a light source for a simple, high-performance surface plasmon resonance (SPR) sensor utilizing comprehensive reflectance analysis in the angular domain. The proposed structure consists of a glass substrate, an [...] Read more.
In this paper, we propose an innovative approach based on the wavelength optimization of a light source for a simple, high-performance surface plasmon resonance (SPR) sensor utilizing comprehensive reflectance analysis in the angular domain. The proposed structure consists of a glass substrate, an adhesion layer of titanium dioxide, a silver plasmonic layer, and a 2D material. Analysis is performed in the Kretschmann configuration for liquid analyte sensing. Sensing parameters such as the refractive index (RI) sensitivity, the reflectance minimum, and the figure of merit (FOM) are investigated in the first step of this study as a function of the thickness of the silver layer together with the RI of a coupling prism. Next, utilizing the results offering a fused silica prism, the thickness of the silver layer and the wavelength of the light source are optimized for the structure with the addition of a 2D material, black phosphorus (BP), which is studied along different principal directions, the zigzag and armchair directions. In addition, a new approach of adjusting the source wavelength using a one-dimensional photonic crystal combined with an LED, is presented. Based on this analysis, for the reference structure at a wavelength of 632.8 nm, the optimized silver layer thickness is 50 nm, and the achieved RI sensitivity ranges from 193.9 to 251.5 degrees per RI unit (deg/RIU), with the highest FOM reaching 52.3 RIU−1. In addition, for the modified structure with BP, the achieved RI sensitivity varies in the range of 269.1–351.2 deg/RIU at the optimized wavelength of 628 nm, with the highest FOM reaching 44.7 RIU−1 for the zigzag direction. Due to the optimization and adjusting the wavelength of the source, the results obtained for the proposed SPR structure could have significant implications for the development of more sensitive and efficient sensors employing a simple plasmonic structure. Full article
(This article belongs to the Section 2D and Carbon Nanomaterials)
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12 pages, 3972 KiB  
Article
A Dengue Virus Detection Using Biosensor-Based Two-Dimensional Photonic Crystal Ring Resonator
by Nadhir Djeffal, Sarra Bendib and Abdallah Hedir
Photonics 2025, 12(5), 514; https://doi.org/10.3390/photonics12050514 - 21 May 2025
Cited by 1 | Viewed by 630
Abstract
This study proposes a novel two-dimensional photonic crystal ring resonator for detecting dengue-induced changes in blood components such as platelets, haemoglobin, and plasma. By monitoring shifts in the central wavelength linked to refractive index variations, the structure offers highly sensitive and accurate detection. [...] Read more.
This study proposes a novel two-dimensional photonic crystal ring resonator for detecting dengue-induced changes in blood components such as platelets, haemoglobin, and plasma. By monitoring shifts in the central wavelength linked to refractive index variations, the structure offers highly sensitive and accurate detection. The Lorentzian peak cavity exhibits a high-quality factor, achieving sensitivity up to 1800 nm/RIU, underscoring its potential as a precise diagnostic tool against dengue. Full article
(This article belongs to the Section Biophotonics and Biomedical Optics)
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16 pages, 5900 KiB  
Article
Tuning Transmission Properties of Two-Dimensional Photonic Crystal Waveguides Using Functional Dielectric Cavities
by Siqi Zhang, Feng Yang, Wenying Zhang, Wei Zhao, Luhe Yang and Hong Li
Micromachines 2025, 16(5), 597; https://doi.org/10.3390/mi16050597 - 20 May 2025
Viewed by 505
Abstract
In this study, the photonic band structure, transmissivity, and electric field distribution of a two-dimensional photonic crystal coupled waveguide structure are calculated using the supercell technique and finite element method. The waveguide consists of circular KNbO3 and functional dielectric [...] Read more.
In this study, the photonic band structure, transmissivity, and electric field distribution of a two-dimensional photonic crystal coupled waveguide structure are calculated using the supercell technique and finite element method. The waveguide consists of circular KNbO3 and functional dielectric cylinders embedded in air. The dielectric constant of a functional medium cylinder is spatially dependent, which is realized through the electro-optic and Kerr effects. The dielectric constant function is defined as εc(r)=k·r+b (0rrc), where the coefficient k and parameter b can be adjusted by an external electric field. By tuning k and b, the transmission characteristics of the waveguide, including the propagation direction and light field distribution, exhibit significant adjustability. Specifically, parameter b enhances or suppresses the transmissivity at output ports 1 and 2. By utilizing the regulatory capability of functional media on waveguide transmission characteristics, optical filters with specific filtering functions can be designed. These findings provide novel design strategies for advanced optical devices. Full article
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11 pages, 4726 KiB  
Article
Directional Excitation of Multi-Dimensional Coupled Topological Photonic States Based on Higher-Order Chiral Source
by Jiangle He, Yaxuan Li, Yangyang Fan, Xinwen Zhao, Lin Ding, Xueqi Yuan, Beijia Ji, Junzheng Hu, Lifu Liu, Guangxu Su, Peng Zhan and Fanxin Liu
Photonics 2025, 12(5), 488; https://doi.org/10.3390/photonics12050488 - 15 May 2025
Viewed by 410
Abstract
The topological phase of matter brings extra inspiration for efficient light manipulation. Here, we propose two-parameter tunable topological transitions based on distorted Kagome photonic crystals. By selecting specific splicing boundaries, we successfully visualize several diverse types of robust edge states and corner states. [...] Read more.
The topological phase of matter brings extra inspiration for efficient light manipulation. Here, we propose two-parameter tunable topological transitions based on distorted Kagome photonic crystals. By selecting specific splicing boundaries, we successfully visualize several diverse types of robust edge states and corner states. Through introducing optical vortices with tunable orbital angular momentum, we demonstrate the directional excitation of multi-dimensional topological states as needed. Furthermore, we have studied the coupling effects of multi-dimensional photonic states and the modulation of source in three typical areas. This work provides an instructive avenue for manipulating light in integrated topological photonic devices. Full article
(This article belongs to the Special Issue Polaritons Nanophotonics: Physics, Materials and Applications)
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10 pages, 2270 KiB  
Article
Highly Luminescent and Scintillating Hybrid Halide of (C13H25N)2[MnBr4] Enabled by Rigid Cation
by Renfu Li, Lulu Jiang, Qinghua Zou, Jianlong Bai, Lingkun Wu, Jianrong Li and Jinsheng Liao
Molecules 2025, 30(10), 2157; https://doi.org/10.3390/molecules30102157 - 14 May 2025
Viewed by 453
Abstract
Organic–inorganic hybrid manganese halides (OIMnHs) have attracted significant attention in the field of optoelectronics due to their outstanding optical properties and low toxicity. However, the development of crystalline compounds with scintillating properties and high light yield remains a significant challenge. In this study, [...] Read more.
Organic–inorganic hybrid manganese halides (OIMnHs) have attracted significant attention in the field of optoelectronics due to their outstanding optical properties and low toxicity. However, the development of crystalline compounds with scintillating properties and high light yield remains a significant challenge. In this study, a simple solution method was employed to successfully synthesize a new zero-dimensional (0-D) scintillation crystal, (C13H25N)2[MnBr4] (C13H25N = trimethyladamantan-1-aminium). The introduction of bulky and rigid organic cations not only spatially isolates the [MnBr4]2− tetrahedrons but also effectively expands the Mn···Mn distance, thereby suppressing the concentration quenching and self-absorption effects. This structural design achieves a high photoluminescence quantum yield of about 63.8% at room temperature and a remarkable light yield of 44,300 photons MeV−1. After multiple irradiation cycles, the material retains its stable radiative characteristics. This work highlights the key role of rigid cation engineering in improving luminescence efficiency and scintillation performance and provides new ideas for designing efficient and nontoxic OIMnH-based scintillators. Full article
(This article belongs to the Special Issue Emerging Topics in Luminescent Materials)
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17 pages, 6072 KiB  
Article
Parameter Investigations of Waveguide-Integrated Lithium Niobate Photonic Crystal Microcavity
by Sohail Muhammad, Dingwei Chen, Chengwei Xian, Jun Zhou, Zhongke Lei, Pengju Kuang, Liang Ma, Guangjun Wen, Boyu Fan and Yongjun Huang
Photonics 2025, 12(5), 475; https://doi.org/10.3390/photonics12050475 - 12 May 2025
Viewed by 671
Abstract
Despite significant progress, fabricating two-dimensional (2D) lithium niobate (LN)-based photonic crystal (PhC) cavities integrated with tapered and PhC waveguides remains challenging, due to structural imperfections. Notable, especially, are variations in hole radius (r) and inclination angle (°), which induce bandgap shifts [...] Read more.
Despite significant progress, fabricating two-dimensional (2D) lithium niobate (LN)-based photonic crystal (PhC) cavities integrated with tapered and PhC waveguides remains challenging, due to structural imperfections. Notable, especially, are variations in hole radius (r) and inclination angle (°), which induce bandgap shifts and degrade quality factors (Q-factor). These fabrication errors underscore the critical need to address nanoscale tolerances. Here, we systematically investigate the impacts of key geometric parameters on optical performance and optimize a 2D LN-based cavity integrated with taper and PhC waveguide system. Using a 3D Finite-Difference Time-Domain (FDTD) and varFDTD simulations, we identify stringent fabrication thresholds. The a must exceed 0.72 µm to sustain Q > 107; reducing a to 0.69 µm collapses Q-factors below 104, due to under-coupled modes and bandgap misalignment, which necessitates ±0.005 µm precision. When an r < 0.22 µm weakens confinement, Q plummets to 2 × 104 at r = 0.20 µm (±0.01 µm etching tolerance). Inclination angles < 70° induce 100× Q-factor losses, requiring ±2° alignment for symmetric modes. Air slot width (s) variations shift resonant wavelengths and require optimization in coordination with the inclination angle. By optimizing s and the inclination angle (at 70°), we achieve a record Q-factor of 6.21 × 106, with, in addition, C-band compatibility (1502–1581 nm). This work establishes rigorous design–fabrication guidelines, demonstrating the potential for LN-based photonic devices with high nano-fabrication robustness. Full article
(This article belongs to the Special Issue Advances in Integrated Photonics)
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17 pages, 6987 KiB  
Review
Colorimetric Visualization of Chirality: From Molecular Sensors to Hierarchical Extension
by Yuji Kubo
Molecules 2025, 30(8), 1748; https://doi.org/10.3390/molecules30081748 - 14 Apr 2025
Viewed by 630
Abstract
The optical sensing of chirality is widely used in many fields, such as pharmaceuticals, agriculture, food, and environmental materials. In this context, the color-based cascade amplification of chirality, coupled with chiral recognition for analytes, provides a low-cost and straightforward detection method that avoids [...] Read more.
The optical sensing of chirality is widely used in many fields, such as pharmaceuticals, agriculture, food, and environmental materials. In this context, the color-based cascade amplification of chirality, coupled with chiral recognition for analytes, provides a low-cost and straightforward detection method that avoids the use of expensive and sophisticated instrumentation. However, the realization of chiral detection using this approach is still challenging because the construction of a three-dimensional optical recognition site is required to easily discern differences in chirality. Therefore, considerable efforts have been dedicated to developing a hierarchical approach based on molecular organization to provide colorimetric sensors for chirality detection. This review covers function-integrated molecular sensors with colorimetric responsive sites based on absorption, fluorescence, and aggregation-induced emission enabled by molecular organization. In line with the hierarchical approach, data-driven chemometrics is a useful method for quantitative and accurate chiral pattern recognition. Finally, colorimetric nanomaterials are discussed, focusing on sensing platforms using noble-metal nanoparticles, carbon dots, and photonic crystal gels. Full article
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15 pages, 7737 KiB  
Article
The Transmission Characteristics of Novel Symmetric Photonic Crystals in Multi- and Single-Mode Configurations
by Rongkang Xuan, Dan Zhang and Na Wang
Symmetry 2025, 17(4), 576; https://doi.org/10.3390/sym17040576 - 10 Apr 2025
Viewed by 325
Abstract
By combining the Fourier series expansion method with the perfect matching layer strategy, this study provides a detailed analysis of symmetric periodic chains consisting of two-dimensional monolayer dielectric cylinders. The numerical and field distribution characteristics were systematically compared by varying the semidiameter and [...] Read more.
By combining the Fourier series expansion method with the perfect matching layer strategy, this study provides a detailed analysis of symmetric periodic chains consisting of two-dimensional monolayer dielectric cylinders. The numerical and field distribution characteristics were systematically compared by varying the semidiameter and dielectric constant of the monolayer cylindrical periodic structure. The results show that, under a constant dielectric constant, structural chains with larger radii support both odd and even modes, enabling multimode communication. Additionally, when the radius is fixed, structural chains with a lower dielectric constant exhibit more stable single-mode behavior under the same radius conditions. These findings provide valuable theoretical insights for the design of high-density optical interconnects and reconfigurable photonic networks, contributing to the advancement of next-generation optical communication systems. Full article
(This article belongs to the Section Physics)
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