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Keywords = coupling-of-modes theory

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11 pages, 1999 KiB  
Article
Optimized Quasi-Optical Mode Converter for TE33,12 in 210 GHz Gyrotron
by Hamid Sharif, Muhammad Haris Jamil and Wenlong He
Micromachines 2025, 16(3), 308; https://doi.org/10.3390/mi16030308 - 6 Mar 2025
Viewed by 135
Abstract
This article discusses the design of a high-performance quasi-optical mode converter for the TE33,12 mode at 210 GHz. The conversion process is challenging due to a caustic-to-cavity radius ratio of approximately 0.41. The mode converter employs an optimized dimpled [...] Read more.
This article discusses the design of a high-performance quasi-optical mode converter for the TE33,12 mode at 210 GHz. The conversion process is challenging due to a caustic-to-cavity radius ratio of approximately 0.41. The mode converter employs an optimized dimpled wall launcher, analyzed using coupling mode theory with twenty-five coupled modes, compared to the usual nine modes and optimized reflector systems, to effectively address the conversion challenge.Electromagnetic field analysis within the launcher wall was optimized using MATLAB R2021b. The radiation fields from the launcher were analyzed in free space using Gaussian optics and vector diffraction theory. The mirror system consists of a quasi-elliptical mirror, an elliptical mirror, and phase-corrected parabolic mirrors. Following phase correction, the output window achieved a scalar Gaussian mode content of 99.0% and a vector Gaussian mode content of 97.4%. Full article
(This article belongs to the Special Issue Optoelectronic Fusion Technology)
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Figure 1
<p>Waveguide wall disturbance curve distribution of Denisov radiator.</p>
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<p>Variation in relative power coefficients for the <math display="inline"><semantics> <mrow> <mi>T</mi> <msub> <mi>E</mi> <mrow> <mn>33</mn> <mo>,</mo> <mn>12</mn> </mrow> </msub> </mrow> </semantics></math> mode along the z-axis in the launcher, depicting coupling with 24 modes.</p>
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<p>Variation in relative power coefficients for the <math display="inline"><semantics> <mrow> <mi>T</mi> <msub> <mi>E</mi> <mrow> <mn>33</mn> <mo>,</mo> <mn>12</mn> </mrow> </msub> </mrow> </semantics></math> mode along the z-axis in the launcher, depicting coupling with 25 modes along with the main mode.</p>
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<p>Electric field distribution on the launcher wall for the <math display="inline"><semantics> <mrow> <mi>T</mi> <msub> <mi>E</mi> <mrow> <mn>33</mn> <mo>,</mo> <mn>12</mn> </mrow> </msub> </mrow> </semantics></math> mode at 210 GHz, simulated with MATLAB.</p>
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<p>Electric field distribution on the launcher wall for the <math display="inline"><semantics> <mrow> <mi>T</mi> <msub> <mi>E</mi> <mrow> <mn>33</mn> <mo>,</mo> <mn>12</mn> </mrow> </msub> </mrow> </semantics></math> mode at 210 GHz, simulated with FEKO.</p>
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<p>Optical path layout of the QO mode converter system.</p>
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<p>Surface current distribution on surface of launcher and mirror system.</p>
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<p>Beam propagation effect near the exit surface.</p>
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<p>Distribution of electric fields at the exit surface.</p>
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<p>Phases at the exit surface.</p>
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<p>The solid line represents the wave-beam mode, while the dashed lines indicate the ideal Gaussian distribution.</p>
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13 pages, 3606 KiB  
Article
A High-Sensitivity Graphene Metasurface and Four-Frequency Switch Application Based on Plasmon-Induced Transparency Effects
by Aijun Zhu, Mengyi Zhang, Weigang Hou, Lei Cheng, Cong Hu and Chuanpei Xu
Photonics 2025, 12(3), 218; https://doi.org/10.3390/photonics12030218 - 28 Feb 2025
Viewed by 235
Abstract
In this paper, we propose the use of a monolayer graphene metasurface to achieve various excellent functions, such as sensing, slow light, and optical switching through the phenomenon of plasmon-induced transparency (PIT). The designed structure of the metasurface consists of a diamond-shaped cross [...] Read more.
In this paper, we propose the use of a monolayer graphene metasurface to achieve various excellent functions, such as sensing, slow light, and optical switching through the phenomenon of plasmon-induced transparency (PIT). The designed structure of the metasurface consists of a diamond-shaped cross and a pentagon graphene resonator. We conducted an analysis of the electric field distribution and utilized Lorentz resonance theory to study the PIT window that is generated by the coupling of bright-bright modes. Additionally, by adjusting the Fermi level of graphene, we were able to achieve tunable dual frequency switching modulators. Furthermore, the metasurface also demonstrates exceptional sensing performance, with sensitivity and figure of merit (FOM) reaching values of 3.70 THz/RIU (refractive index unit) and 22.40 RIU-1, respectively. As a result, our numerical findings hold significant guiding significance for the design of outstanding terahertz sensors and photonic devices. Full article
(This article belongs to the Special Issue Photonics Metamaterials: Processing and Applications)
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Figure 1
<p>(<b>a</b>) schematic diagram of unit structure; (<b>b</b>) vertical view of cell structure.</p>
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<p>(<b>a</b>) the real parts of permittivity for graphene in different chemical potentials.; (<b>b</b>) the imaginary parts of permittivity for graphene in different chemical potentials.</p>
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<p>(<b>a</b>) transmission spectrum of graphene metasurface; (<b>b</b>–<b>d</b>) the normalized electric field distribution at the frequency of 5.3 THz, 6.0 THz, and 6.7 THz.</p>
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<p>The transmission of our proposed graphene metasurface in THz region. The black dotted line indicates numerical simulation result and the blue solid line represents the Lorentz oscillation coupling model calculation result.</p>
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<p>(<b>a</b>,<b>b</b>) transmittance spectra with different Fermi energies in the THz region.</p>
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<p>Four-frequency switching modulator modulation of the transmittance spectra when <span class="html-italic">E<sub>F</sub></span> is set as 0.9 eV and 1.2 eV.</p>
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<p>(<b>a</b>) transmission spectra with different refraction indices of the surrounding medium; (<b>b</b>) linear fit of resonant peak with different refractive indices.</p>
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<p>(<b>a</b>) transmission spectra with r1 from 2.1 μm to 2.7 μm; (<b>b</b>) transmission spectra with r2 from 0.6 μm to 1.0 μm.</p>
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<p>(<b>a</b>,<b>b</b>) transmission spectra with various incident angles.</p>
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23 pages, 7253 KiB  
Article
Study on Cross-Coupling Synchronous Control Strategy of Dual-Motor Based on Improved Active Disturbance Rejection Control–Nonsingular Fast Terminal Sliding Mode Control Strategy
by Daode Zhang, Shaofeng Yu, Enshun Lu, Qiong Wei and Zhiyong Yang
Electronics 2025, 14(3), 526; https://doi.org/10.3390/electronics14030526 - 28 Jan 2025
Viewed by 424
Abstract
This paper presents a cross-coupling control strategy that enhances sliding mode control by incorporating active disturbance rejection control. This approach effectively addresses the issue of inadequate synchronous control accuracy in a dual-motor servo system subjected to high load disturbances. Firstly, a mathematical model [...] Read more.
This paper presents a cross-coupling control strategy that enhances sliding mode control by incorporating active disturbance rejection control. This approach effectively addresses the issue of inadequate synchronous control accuracy in a dual-motor servo system subjected to high load disturbances. Firstly, a mathematical model of a single motor is established, and a discrete sliding mode controller (DSMC) is designed to enhance the motor’s response speed and dynamic performance. Secondly, the approach rate is optimized to improve the control smoothness of the single-motor controller, and the system’s stability is demonstrated using the Lyapunov theorem. In addition, to enhance the precision and stability of synchronous control when the load is unevenly distributed on both sides of the motor, a discrete nonlinear tracking differentiator (DNLTD) and a discrete nonlinear extended state observer (DNLESO) based on active disturbance rejection control (ADRC) theory are proposed, which are, in turn, combined with nonsingular fast terminal sliding mode control (NFTSMC), utilizing an optimized approach rate to form the ADRC-NFTSMC control strategy, and the cross-coupled control structure is used to achieve synchronous closed-loop control. Finally, the experimental results demonstrate that, compared to the NFTSMC strategy, the proposed control strategy improves response speed by 18.9% and synchronous control accuracy by 46.7%, which significantly enhances the quality of dual-motor servo control. Full article
(This article belongs to the Section Power Electronics)
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<p>Equivalent circuit diagram of a BLDC.</p>
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<p>Structural diagram of the BLDC control system.</p>
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<p>Structural diagram of the dual-motor synchronous control system.</p>
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<p>Structural diagram of the NFTSMC.</p>
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<p>The speed curve of motor response in simulation.</p>
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<p>The speed curve of motor tracking.</p>
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<p>The speed curve of two motors (SMC).</p>
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<p>The speed curve of two motors in simulation (NFTSMC).</p>
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<p>The speed curve of two motors in simulation (ADRC-NFTSMC).</p>
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<p>The synchronous error curve of three strategies.</p>
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<p>Dual-motor servo system experiment platform.</p>
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<p>The speed curve of motor response.</p>
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<p>The error curve of motor tracking.</p>
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<p>The speed curve of two motors (NFTSMC).</p>
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<p>The speed curve of two motors (ADRC-NFTSMC).</p>
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<p>The synchronous error curve of two strategies.</p>
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20 pages, 4916 KiB  
Article
Quaternion-Based Robust Sliding-Mode Controller for Quadrotor Operation Under Wind Disturbance
by Jung-Ju Bae and Jae-Young Kang
Aerospace 2025, 12(2), 93; https://doi.org/10.3390/aerospace12020093 - 27 Jan 2025
Viewed by 483
Abstract
This paper presents a quaternion-based robust sliding-mode controller for quadrotors operating under significant wind disturbances. The proposed control method improves the reliability and efficiency of quadrotor control by eliminating the singularity problem inherent in the Euler angle method. The quadrotor dynamics and wind [...] Read more.
This paper presents a quaternion-based robust sliding-mode controller for quadrotors operating under significant wind disturbances. The proposed control method improves the reliability and efficiency of quadrotor control by eliminating the singularity problem inherent in the Euler angle method. The quadrotor dynamics and wind environment are modeled, and dynamic analysis is performed via numerical simulation. A realistic wind model is used, similar to a combination of deterministic and statistical models. The Lyapunov stability theory is utilized to prove the convergence and stability of the proposed control system. The simulation results demonstrate that the quaternion-based controller enables the quadrotor to follow the desired path and remain stable, even under external wind disturbances. Specifically, both position and attitude converge to the desired values within 10 s, demonstrating stable performance despite the challenging wind disturbances in both scenarios. Scenario 1 features turbulence with an average wind speed of 12 m/s and changing wind directions, while Scenario 2 models an environment with wind speeds that change abruptly and discretely over time, coupled with temporal variations in wind direction. Additionally, a comparative analysis with the conventional PD controller highlights the superior performance of the proposed RSMC controller in terms of trajectory tracking, stability, and energy efficiency. The rotor speeds remain within a reasonable and hardware-feasible range, ensuring practical applicability. Full article
(This article belongs to the Special Issue Flight Dynamics, Control & Simulation (2nd Edition))
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<p>Quadrotor model system: (<b>a</b>) quadrotor configuration; (<b>b</b>) coordinate system.</p>
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<p>Definition of rotation matrices.</p>
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<p>Profile of the wind model: (<b>a</b>) Scenario 1; (<b>b</b>) Scenario 2.</p>
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<p>Desired path.</p>
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<p>Simulation results: (<b>a</b>) position; (<b>b</b>) attitude.</p>
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<p>Wind disturbance: (<b>a</b>) force; (<b>b</b>) moment.</p>
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<p>Angular velocity responses of rotor: (<b>a</b>) RSMC; (<b>b</b>) PD.</p>
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<p>Simulation results: (<b>a</b>) position; (<b>b</b>) attitude.</p>
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<p>Wind disturbance: (<b>a</b>) force; (<b>b</b>) moment.</p>
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<p>Angular velocity responses of rotor: (<b>a</b>) RSMC; (<b>b</b>) PD.</p>
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19 pages, 7892 KiB  
Article
Horizontal Refraction Effects of Sound Propagation Within Continental Shelf Slope Environment: Modeling and Theoretical Analysis
by Jinci Wang, Bo Lei, Yixin Yang and Jianbo Zhou
J. Mar. Sci. Eng. 2025, 13(2), 217; https://doi.org/10.3390/jmse13020217 - 23 Jan 2025
Viewed by 629
Abstract
Horizontal refraction notably influences propagation characteristics with the variation of the waveguide environment. In this study, the horizontal refraction phenomenon at low frequencies was investigated in a sloping sea region with an incomplete vertical sound speed profile. Using the mode coupling theory, this [...] Read more.
Horizontal refraction notably influences propagation characteristics with the variation of the waveguide environment. In this study, the horizontal refraction phenomenon at low frequencies was investigated in a sloping sea region with an incomplete vertical sound speed profile. Using the mode coupling theory, this research explores the relationship between horizontal refraction and energy exchange among modes, examining the impact of environmental conditions on the horizontal refraction angle. Theoretical derivations and numerical simulations reveal the mechanisms by which the source depth and modal order influence the horizontal refraction. The analysis indicates that the horizontal refraction angle increases with the modal order when the real part of the horizontal wavenumber km at the source position is less than the wavenumber ks. In this situation, the horizontal refraction angle corresponding to the same modal order does not vary with the source depth. However, if the real part of km is larger than ks, then the horizontal refraction angle decreases as the source depth increases. This condition is due to the extremely small eigenfunction value at source depth of the low-order mode, thereby enhancing the mode coupling effect. The mode coupling is intimately associated with the mode excited by the source. Therefore, the source depth exerts a substantial influence on the horizontal refraction. Under these conditions, the modal order has a negligible effect on the horizontal refraction angle. Full article
(This article belongs to the Special Issue Advances in Underwater Positioning and Navigation Technology)
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Figure 1
<p>The horizontal refraction scene. (<b>a</b>) Schematic of the ocean waveguide with a wedge bottom. <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mn>0</mn> </msub> </mrow> </semantics></math> denotes the slope inclination angle. The speed in the water column <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mn>1</mn> </msub> </mrow> </semantics></math> is a function of depth. (<b>b</b>) The horizontal refraction angle.</p>
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<p>An illustration of the horizontal propagation direction of a single ray after individual reactions to the sea surface and seafloor.</p>
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<p>(<b>a</b>) The sound speed profile. The data were adapted from the World Ocean Atlas database [<a href="#B35-jmse-13-00217" class="html-bibr">35</a>] (the acoustic profile remains unchanged with range, except that the depth is consistent with the sea depth); (<b>b</b>) the grazing angle corresponding to the order of the mode; (<b>c</b>) modal eigenfunctions. The red circles indicate sound depths of 50, 100, 150, and 200 m from top to bottom.</p>
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<p>The horizontal refraction angle of the ray corresponding to the modal order with a slope inclination angle of 3° after an interaction with the seabed at horizontal emergence angles of (<b>a</b>) 10° and (<b>b</b>) 80°.</p>
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<p>Inter-mode coupling coefficient <math display="inline"><semantics> <mrow> <msub> <mi>B</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> at ranges of 0–5.8 km of different slope inclination angles. The frequency is 100 Hz. The distance grid for calculating coupling coefficients is 0.2 m. (<b>a</b>) Mode 1 with 2, (<b>b</b>) mode 1 with 3, (<b>c</b>) mode 1 with 5, and (<b>d</b>) mode 1 with 13.</p>
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<p>Mode coupling coefficients with a slope inclination of 3° for the following conditions: (<b>a</b>) the frequency is 50 Hz, and the range is 2 km; (<b>b</b>) the frequency is 50 Hz, and the range is 4 km; (<b>c</b>) the frequency is 100 Hz, and the range is 2 km; and (<b>d</b>) the frequency is 100 Hz, and the range is 4 km.</p>
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<p>Imaginary parts of eigenvalues of the first 20 modes at the ranges of 2 and 4 km at a frequency of (<b>a</b>) 50 Hz and (<b>b</b>) 100 Hz.</p>
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<p>Inter-mode coupling coefficient <math display="inline"><semantics> <mrow> <msub> <mi>B</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> at ranges of 0–5.8 km for different frequencies with a slope inclination of 3°. (<b>a</b>) Mode 1 with 2; (<b>b</b>) mode 1 with 3; (<b>c</b>) mode 1 with 5; (<b>d</b>) mode 1 with 13.</p>
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<p>The amplitude of the value <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ω</mi> <mi>m</mi> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> within ranges of 0–4 km of different source depths at a frequency of 100 Hz with a slope inclination of 3°: (<b>a</b>) source depth is 50 m, (<b>b</b>) source depth is 100 m, (<b>c</b>) source depth is 150 m, and (<b>d</b>) source depth is 200 m.</p>
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<p>The absolute value of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ψ</mi> <mi>m</mi> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> within ranges of 0–4 km at a frequency of 100 Hz with a slope inclination angle of 3° at source depths of (<b>a</b>) 50 m, (<b>b</b>) 100 m, (<b>c</b>) 150 m, and (<b>d</b>) 200 m. The white curves represent the dominant excited modes of different source depths.</p>
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<p>Values of mode coupling within ranges of 0–4 km of different frequencies with a source depth of 150 m and a slope inclination angle of 3°. (<b>a</b>) The amplitude of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ω</mi> <mi>m</mi> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> at a frequency of 50 Hz. (<b>b</b>) The amplitude of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ω</mi> <mi>m</mi> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> at a frequency of 100 Hz. (<b>c</b>) The amplitude of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ψ</mi> <mi>m</mi> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> at a frequency of 50 Hz. (<b>d</b>) The amplitude of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ψ</mi> <mi>m</mi> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> at a frequency of 100 Hz.</p>
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<p>Values of mode coupling within ranges of 0–4 km of different frequencies at a source depth of 200 m and a frequency of 100 Hz. (<b>a</b>) The amplitude of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ω</mi> <mi>m</mi> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> with a slope inclination angle of 3°. (<b>b</b>) The amplitude of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ω</mi> <mi>m</mi> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> with a slope inclination angle of 5°. (<b>c</b>) The amplitude of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ψ</mi> <mi>m</mi> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> with a slope inclination angle of 3°. (<b>d</b>) The amplitude of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ψ</mi> <mi>m</mi> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> with a slope inclination angle of 5°.</p>
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<p>Analysis of the effect of the source depth on the horizontal refraction angle with a slope inclination angle of 3° and a frequency of 100 Hz. (<b>a</b>) The horizontal refraction angle at different source depths; (<b>b</b>) the amplitude of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Λ</mi> <mi>m</mi> </msub> </mrow> </semantics></math>; (<b>c</b>) the amplitude of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ψ</mi> <mi>m</mi> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>; (<b>d</b>) the normalization of the horizontal refraction angle.</p>
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<p>Analysis of the effect of the slope inclination angle and the frequency on the horizontal refraction angle. (<b>a</b>) The horizontal refraction angle with different slope inclination angles with a source depth of 200 m and a frequency of 100 Hz. (<b>b</b>) The normalization of the horizontal refraction angle with a source depth of 200 m and a frequency of 100 Hz. (<b>c</b>) The horizontal refraction angle at different frequencies with a source depth of 200 m and a slope inclination angle of 3°. (<b>d</b>) The amplitude of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Λ</mi> <mi>m</mi> </msub> </mrow> </semantics></math> with a source depth of 200 m and a slope inclination angle of 3°.</p>
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14 pages, 4162 KiB  
Article
Impact of Internal Solitary Wave on Acoustic Propagation Based on Coupled Normal Mode Theory
by Zhuolong Liu, Yongchui Zhang, Fei Gao, Yunxiang Zhang, Yang Wang and Mei Hong
J. Mar. Sci. Eng. 2025, 13(2), 189; https://doi.org/10.3390/jmse13020189 - 21 Jan 2025
Viewed by 471
Abstract
An internal solitary wave (ISW) significantly affects acoustic propagation; however, its detailed characteristics are poorly understood. Simulation experiments of sound propagation in a shallow water environment are presented to examine the effects of the source conditions and characteristics of the ISW on transmission [...] Read more.
An internal solitary wave (ISW) significantly affects acoustic propagation; however, its detailed characteristics are poorly understood. Simulation experiments of sound propagation in a shallow water environment are presented to examine the effects of the source conditions and characteristics of the ISW on transmission loss (TL). The results show that the TL decreases as the depth of the source increases and the frequency of the source decreases and that the different characteristics of the ISW are highly important for estimating sound propagation when a SONAR system is in an ISW environment. Coupled normal mode theory is further employed to analyse the variations in coupling between sound field modes in an ISW environment. Further analysis reveals that the magnitude of the TL is affected by the direction and fluctuation of energy propagation between different modes, and in different ISW environments under the deep and low-frequency source conditions, the sound field energy is mainly in lower-order modes. Full article
(This article belongs to the Section Ocean Engineering)
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Figure 1

Figure 1
<p>Schematic diagram of the sound velocity distribution under the influence of an ISW; the thermocline displacement geometries are plotted as solid black lines, and the boundaries of the bottom are plotted as dotted black lines: (<b>a</b>) Soliton wave; and (<b>b</b>) packet wave.</p>
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<p>Comparison of different source conditions on the TL when Dr = 40 m. The blue line represents a source depth of 10 m and a source frequency of 600 Hz, the red line represents a source depth of 10 m and a source frequency of 200 Hz, the black line represents a source depth of 50 m and a source frequency of 200 Hz and the green line represents a source depth of 50 m and a source frequency of 600 Hz.</p>
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<p>Comparisons of the acoustic fields with different ISWs; the thermocline displacement geometries are plotted as black lines. (<b>a</b>) LADS; (<b>b</b>) LADP; (<b>c</b>) SADS; and (<b>d</b>) LAES.</p>
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<p>Comparison of the effects of different numbers and amplitudes of ISWs on the TL with distance variations when the source frequency is 600 Hz and Ds = 50 m: (<b>a</b>) Receiver at a depth of 12 m and (<b>b</b>) receiver at a depth of 40 m.</p>
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<p>Comparison of the effects of different numbers and amplitudes of the ISW on the TL with depth variations: (<b>a</b>) TL between LADS and LADP; (<b>b</b>) difference in TL between LADS and LADP; (<b>c</b>) TL between LADS and SADS; and (<b>d</b>) difference in TL between LADS and SADS.</p>
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<p>Comparison of the effects of different ISW polarities on the TL under different source conditions: (<b>a</b>) Ds = 10 m, 200 Hz; (<b>b</b>) Ds = 10 m, 600 Hz; (<b>c</b>) Ds = 50 m, 200 Hz; and (<b>d</b>) Ds = 50 m, 600 Hz.</p>
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<p>Relationship between the TL at the receiving array and the position of the ISW: (<b>a</b>) SADS; (<b>b</b>) LADS; (<b>c</b>) SAES; and (<b>d</b>) LAES.</p>
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<p>Intensity of modes 1–6 in different ISW environments: (<b>a</b>) LADS; (<b>b</b>) LADP; (<b>c</b>) SADS; and (<b>d</b>) LAES.</p>
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<p>The sum of modal intensities in each group in different ISW environments: (<b>a</b>) Intensity of mode 1–26; (<b>b</b>) intensity of mode 1–8; (<b>c</b>) intensity of mode 9–15; and (<b>d</b>) intensity of mode 16–26.</p>
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26 pages, 3630 KiB  
Article
Tailoring Spectral Response of Grating-Assisted Co-Directional Couplers with Weighting Techniques and Rational Transfer Functions: Theory and Experiment
by Anatole Lupu
Photonics 2025, 12(1), 73; https://doi.org/10.3390/photonics12010073 - 15 Jan 2025
Viewed by 519
Abstract
This work addresses the tailoring spectral response of grating-assisted co-directional couplers (GADCs) in the context of wavelength filtering for fiber-to-the-home (FTTH) applications. Design methods for spectral response engineering by means of coupling profile apodization-type weighting techniques and also more advanced rational transfer functions [...] Read more.
This work addresses the tailoring spectral response of grating-assisted co-directional couplers (GADCs) in the context of wavelength filtering for fiber-to-the-home (FTTH) applications. Design methods for spectral response engineering by means of coupling profile apodization-type weighting techniques and also more advanced rational transfer functions fitting a predefined spectral window template are presented. Modeling results based on coupled mode theory are then applied for the design and experimental fabrication of InGaAsP/InP GADCs targeting 1.3+/1.3− µm diplexer application in FTTH access networks. The experimental results are found to be in good agreement with the modeling predictions. The design tools presented are quite general and can be easily adapted to other technology platforms, such as silicon photonics for the use of GADCs as add-drop wavelength division multiplexers. The field of parity–time symmetry is another avenue where these types of gain–loss-assisted GADCs as active components are of interest for switching applications, and the design methods presented here may find utility. Full article
(This article belongs to the Special Issue Silicon-Based Integrated Optics: From Design to Applications)
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Figure 1

Figure 1
<p>(<b>a</b>) Schematic of the integrated ONU 1.3+/1.3− µm diplexer. (<b>b</b>) Prospect view of the III-V semiconductor meander grating directional coupler. (<b>c</b>) Cross-sectional view of the InGaAsP/InP heterostructure used for the experimental realization of the GADC.</p>
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<p>(<b>a</b>) Ideal filter cross-channel spectral response. (<b>b</b>) GADC-apodized spectral response (cross-channel—blue curve; bar-channel—red curve). The green dashed lines at −3 dB and −20 dB delineate the pass band and attenuation band levels, respectively.</p>
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<p>Schematic of different types of optical network terminal configurations for 1.3+/1.3− µm diplexer application: (<b>a</b>) 1.32 µm OLT; (<b>b</b>) 1.32 µm ONU; (<b>c</b>) 1.28 µm OLT; (<b>d</b>) 1.32 µm ONU.</p>
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<p>(<b>a</b>) Asymmetrical GADCs with variable interguide distance. (<b>b</b>) Variation in the effective grating period with respect to the nominal value caused by the variation in the coupling coefficient. (<b>c</b>) Impact of the “chirp” effect on the GADC spectral response.</p>
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<p>Schematic of GADCs with the modulation of the grating geometry profile using the BDC method. The resulting variation in the coupling coefficient κ(z) is necessarily discrete. The finest variation that can be obtained is determined by the number of periods of the grating.</p>
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<p>(<b>a</b>) Schematic of GADCs with the modulation of the grating geometry profile using the SDC method. (<b>b</b>) Variation in the local grating period along the grating length. (<b>c</b>) Asymmetrical GADCs with variable interguide distance combined with the modulation of the local grating period using the SDC method.</p>
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<p>Experimental (red and blue curves) and CMT (brown and green curves) spectral response of GADCs using different apodization techniques. (<b>a</b>) Interguide distance variation. (<b>b</b>) Interguide distance variation combined with chirp compensation. (<b>c</b>) Interguide distance variation combined with SDC modulation. (<b>d</b>) Interguide distance variation combined with SDC modulation and chirp compensation.</p>
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<p>Low-pass frequency filter spectral response (blue curve) and target spectral window template (red lines indicate the delimited area).</p>
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<p>(<b>a</b>) Example of the impulse response of a filter; (<b>b</b>) coupling profile obtained from the truncated impulse response.</p>
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<p>Chebyshev polynomials of type I approximation. (<b>a</b>) Coupling profile (Chebyshev type I—blue curve; generalized cosine—green curve) The dashed black line corresponds to the zero value of the coupling coefficient. (<b>b</b>) GADC spectral response (cross-channel—blue curve; bar-channel—red curve). The lowest levels of the pass band and the highest levels of the attenuation band are delineated by green and cyan dash-dotted lines at the −3 dB and −20 dB levels, respectively.</p>
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<p>Chebyshev type II approximation. (<b>a</b>) Coupling profile (Chebyshev type II—blue curve; generalized cosine—green curve). The dashed black line corresponds to the zero value of the coupling coefficient. (<b>b</b>) GADC spectral response (cross-channel—blue curve; bar-channel—red curve). The lowest levels of the pass band and the highest levels of the attenuation band are delineated by green and cyan dash-dotted lines at the −3 dB and −20 dB levels, respectively.</p>
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<p>Elliptic approximation. (<b>a</b>) Coupling profile (elliptic—blue curve; generalized cosine—green curve). The dashed black line corresponds to the zero value of the coupling coefficient. (<b>b</b>) GADC spectral response (cross-channel—blue curve; bar-channel—red curve). The lowest levels of the pass band and the highest levels of the attenuation band are delineated by green and cyan dash-dotted lines at the −3 dB and −20 dB levels, respectively.</p>
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<p>Butterworth approximation. (<b>a</b>) Coupling profile (Butterworth—blue curve; generalized cosine—green curve). The dashed black line corresponds to the zero value of the coupling coefficient. (<b>b</b>) GADC spectral response (cross-channel—blue curve; bar-channel—red curve). The lowest levels of the pass band and the highest levels of the attenuation band are delineated by green and cyan dash-dotted lines at the −3 dB and −20 dB levels, respectively.</p>
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<p>(<b>a</b>) Coupling profile (variational optimization—blue curve; Chebyshev type I—green curve). The dashed black line corresponds to the zero value of the coupling coefficient. (<b>b</b>) GADC spectral response (cross-channel—blue curve; bar-channel—red curve). The lowest levels of the pass band and the highest levels of the attenuation band are delineated by green and cyan dash-dotted lines at the −3 dB and −20 dB levels, respectively.</p>
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<p>GADC geometry with altered polarity in the coupling profile. The red rectangles indicates the areas of 180°-phase shift sections.</p>
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<p>Square window template GADC experimental spectral response for bar (//) and cross (X) channels for the TE and TM polarizations. The lowest levels of the pass band and the highest levels of the attenuation band are delineated by green dashed lines at the −3 dB and −20 dB levels, respectively.</p>
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<p>GADC with grating waveguide ridge width of 1.9 µm experimental spectral response for bar (//) and cross (X) channels for the TE and TM polarizations. The lowest levels of the pass band and the highest levels of the attenuation band are delineated by green dashed lines at the −3 dB and −20 dB levels, respectively.</p>
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31 pages, 28202 KiB  
Article
Analysis of Acoustic Surface Wave Focused Unidirectional Interdigital Transducers Using Coupling-of-Mode Theory
by Guopeng Hui, Tinglun Ao, Haotian Liu, Minglei Li and Chen Chen
Micromachines 2025, 16(1), 3; https://doi.org/10.3390/mi16010003 - 24 Dec 2024
Viewed by 564
Abstract
In cell or droplet separation, high acoustic wave energy of a surface acoustic wave (SAW) device is required to generate sufficient acoustic radiation force. In this paper, the electrode width-control floating electrode focused unidirectional interdigital transducer (EWC-FEFUDT) is proposed due to its enhanced [...] Read more.
In cell or droplet separation, high acoustic wave energy of a surface acoustic wave (SAW) device is required to generate sufficient acoustic radiation force. In this paper, the electrode width-control floating electrode focused unidirectional interdigital transducer (EWC-FEFUDT) is proposed due to its enhanced focusing properties. The performance of the EWC-FEFUDT is investigated using the Coupling-of-Mode (COM) theory, and the COM parameter is extracted using the Finite Element Method (FEM). The four different forbidden band edge frequencies account for the unidirectionality of the proposed EWC-FEFUDT. A direction angle of ϕκϕζ=44.5° of the EWC-FEFUDT (Design 3) is obtained, being fairly close to the optimum value of 45°. The EWC-FEFUDT (Design 3) has a lower insertion loss (IL) of −5.1 dB and greater unidirectionality (20 × log10(D) = 13.8 dB). The SAW maximum amplitude of the EWC-FEFUDT (Design 3) is increased by about 1.5×104 µm compared to that of the focused interdigital transducers (FIDTs). The maximum acoustic pressure of the EWC-FEFUDT is an order of magnitude higher than that of FIDTs. The EWC-FEFUDT exhibits enhanced focusing properties. The proposed EWC-FEFUDT may provide an alternative method for cell or droplet separation in an efficient manner. Full article
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Figure 1

Figure 1
<p>Various types of IDTs. (<b>a</b>) Conventional uniform IDT; (<b>b</b>) FIDT; (<b>c</b>) EWC-UDT; (<b>d</b>) FEUDT; (<b>e</b>) SPFT; (<b>f</b>) FUDT.</p>
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<p>EWC-FEFUDT.</p>
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<p>Schematic diagram of particle separation using EWC-FEFUDT (<b>a</b>) x–y plane view; (<b>b</b>) view of y–z cross-section taken along the line AA’ of (<b>a</b>).</p>
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<p>The complete FEM model of the EWC-FEFUDT.</p>
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<p>Elements and nodes of FEM model of EWC-FEFUDT.</p>
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<p>A single-period FEM model of the EWC-FEFUDT and the mesh convergence analysis. (<b>a</b>) A single-period FEM model of the EWC-FEFUDT; (<b>b</b>) meshes of a single-period FEM model of the EWC-FEFUDT; (<b>c</b>) mesh convergence analysis.</p>
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<p>The total displacements of eigenmodes. (<b>a</b>) The lower frequency of the forbidden band in a short-circuited grating; (<b>b</b>) the upper frequency of the forbidden band in a short-circuited grating; (<b>c</b>) the lower frequency of the forbidden band in an open-circuited grating; (<b>d</b>) the upper frequency of the forbidden band in an open-circuited grating.</p>
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<p>The displacement components of <a href="#micromachines-16-00003-f007" class="html-fig">Figure 7</a>a.</p>
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<p>Admittance curves of EWC-FEFUDT on 128°Y-X LiNbO<sub>3</sub>.</p>
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<p>Two-dimensional FEM models of the SAW device. (<b>a</b>) The model for the analysis of the EWC-FEFUDT; (<b>b</b>) the model for the IL calculation of the EWC-FEFUDT.</p>
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<p>The effect of <math display="inline"><semantics> <mrow> <mi>n</mi> </mrow> </semantics></math> on the IL of the EWC-FEFUDT.</p>
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<p>The effect of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> </mrow> </semantics></math> on IL of the EWC-FEFUDT.</p>
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<p>IL of EWC-FEFUDT with different electrode thicknesses.</p>
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<p>Effect of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>L</mi> </mrow> </msub> </mrow> </semantics></math> on IL of EWC-FEFUDT.</p>
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<p>EWC-FEFUDT loss for different <math display="inline"><semantics> <mrow> <mi>L</mi> </mrow> </semantics></math>. (<b>a</b>) Insertion loss; (<b>b</b>) return loss.</p>
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<p>S parameters. (<b>a</b>) FIDT; (<b>b</b>) EWC-FEFUDT.</p>
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<p>Focus region of EWC-FEFUDT.</p>
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<p>The half-symmetry FEM model of the EWC-FEFUDT. (<b>a</b>) The model for the analysis of SAW displacement; (<b>b</b>) the model for the analysis of acoustic pressure.</p>
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<p>The effect of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> </mrow> </semantics></math> on SAW displacement and acoustic pressure. (<b>a</b>) SAW displacement for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mn>30</mn> <mo>°</mo> </mrow> </semantics></math> (Design 3); (<b>b</b>) acoustic pressure for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mn>30</mn> <mo>°</mo> </mrow> </semantics></math> (Design 3); (<b>c</b>) SAW displacement for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mn>60</mn> <mo>°</mo> </mrow> </semantics></math> (Design 4); (<b>d</b>) acoustic pressure for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mn>60</mn> <mo>°</mo> </mrow> </semantics></math> (Design 4); (<b>e</b>) SAW displacement for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mn>90</mn> <mo>°</mo> </mrow> </semantics></math> (Design 5); (<b>f</b>) acoustic pressure for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>D</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mn>90</mn> <mo>°</mo> </mrow> </semantics></math> (Design 5).</p>
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<p>Effect of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>L</mi> </mrow> </msub> </mrow> </semantics></math> on acoustic pressure and SAW displacement. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mn>45</mn> <mo> </mo> <mi>µ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> (Design 3); (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mn>65</mn> <mo> </mo> <mi>µ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> (Design 8); (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mn>85</mn> <mo> </mo> <mi>µ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> (Design 9); (<b>d</b>) x component of SAW displacement in the Design 3 (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mn>45</mn> <mo> </mo> <mi>µ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>), Design 8 (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mn>65</mn> <mo> </mo> <mi>µ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>), and Design 9 (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mn>85</mn> <mo> </mo> <mi>µ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>).</p>
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<p>Effect of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>L</mi> </mrow> </msub> </mrow> </semantics></math> on acoustic pressure and SAW displacement. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mn>45</mn> <mo> </mo> <mi>µ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> (Design 3); (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mn>65</mn> <mo> </mo> <mi>µ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> (Design 8); (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mn>85</mn> <mo> </mo> <mi>µ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> (Design 9); (<b>d</b>) x component of SAW displacement in the Design 3 (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mn>45</mn> <mo> </mo> <mi>µ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>), Design 8 (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mn>65</mn> <mo> </mo> <mi>µ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>), and Design 9 (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mn>85</mn> <mo> </mo> <mi>µ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>).</p>
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<p>Substrate displacement and acoustic pressure distribution. (<b>a</b>) FEM model for calculating displacement amplitude in FIDT; (<b>b</b>) FEM model for calculating displacement amplitude in EWC-FEFUDT; (<b>c</b>) SAW displacements generated by FIDT and EWC-FEFUD in +X direction of (<b>a</b>,<b>b</b>); (<b>d</b>) acoustic pressure generated by EWC-FEFUDT; (<b>e</b>) acoustic pressure generated by FIDT.</p>
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<p>SAW displacements generated by EWC-FEFUDT and FIDT. (<b>a</b>) Total displacement generated by EWC-FEFUDT; (<b>b</b>) SAW displacement generated by EWC-FEFUDT along red line of (<b>a</b>); (<b>c</b>) Total displacement generated by FIDT; (<b>d</b>) SAW displacement generated by FIDT along red line of (<b>c</b>).</p>
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<p>SAW standing wave distributions. (<b>a</b>) SAW standing waves under short-circuit conditions; (<b>b</b>) SAW standing waves under open circuit conditions.</p>
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<p>The relationships between COM parameters and normalized electrode thicknesses. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>v</mi> </mrow> </semantics></math> versus normalized electrode thickness; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>κ</mi> </mrow> <mrow> <mn>12</mn> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>ζ</mi> </mrow> </semantics></math> versus normalized electrode thickness; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ϕ</mi> </mrow> <mrow> <mi>κ</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ϕ</mi> </mrow> <mrow> <mi>ζ</mi> </mrow> </msub> </mrow> </semantics></math> versus normalized electrode thickness; (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ϕ</mi> </mrow> <mrow> <mi>κ</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow> <mi>ϕ</mi> </mrow> <mrow> <mi>ζ</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>D</mi> </mrow> </semantics></math> versus normalized electrode thickness.</p>
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<p>Two fibers. (<b>a</b>) Coupled fibers; (<b>b</b>) fibers without coupling.</p>
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<p>Input and output for an arbitrary section.</p>
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<p>Symmetric and anti-symmetric modes. (<b>a</b>) Symmetric modes; (<b>b</b>) anti-symmetric modes.</p>
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<p>Periodic structure.</p>
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<p>Reflection coefficient <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Γ</mi> </mrow> <mrow> <mo>±</mo> </mrow> </msub> </mrow> </semantics></math> of periodic structure.</p>
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<p>Single-periodic structure of the EWC-FEFUDT.</p>
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<p>Unit section of EWC-FEFUDT.</p>
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<p>Current on busbar of EWC-FEFUDT.</p>
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<p>(<b>a</b>) Shorted-circuited gratings; (<b>b</b>) open-circuited gratings.</p>
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11 pages, 2649 KiB  
Communication
Applications of Isosceles Triangular Coupling Structure in Optical Switching and Sensing
by Lili Zeng, Xingjiao Zhang, Qinghua Guo, Yang Fan, Yuanwen Deng, Zhengchao Ma and Boxun Li
Sensors 2024, 24(24), 8221; https://doi.org/10.3390/s24248221 - 23 Dec 2024
Viewed by 597
Abstract
In the case of waveguide-based devices, once they are fabricated, their optical properties are already determined and cannot be dynamically controlled, which limits their applications in practice. In this paper, an isosceles triangular-coupling structure which consists of an isosceles triangle coupled with a [...] Read more.
In the case of waveguide-based devices, once they are fabricated, their optical properties are already determined and cannot be dynamically controlled, which limits their applications in practice. In this paper, an isosceles triangular-coupling structure which consists of an isosceles triangle coupled with a two-bus waveguide is proposed and researched numerically and theoretically. The coupled mode theory (CMT) is introduced to verify the correctness of the simulation results, which are based on the finite difference time domain (FDTD). Due to the existence of the side mode and angular mode, the transmission spectrum presents two high transmittance peaks and two low transmittance peaks. In addition, the four transmission peaks exhibit different variation trends when the dimensions of the isosceles triangle are changed. The liquid crystal (LC) materials comprise anisotropic uniaxial crystal and exhibit a remarkable birefringence effect under the action of the external field. When the isosceles triangle coupling structure is filled with LC, the refractive index of the liquid crystal can be changed by changing the applied voltage, thereby achieving the function of an optical switch. Within a certain range, a linear relationship between refractive index and applied voltage can be obtained. Moreover, the proposed structure can be applied to biochemical sensing to detect glucose concentrations, and the sensitivity reaches as high as 0.283 nm·L/g, which is significantly higher than other values reported in the literature. The triangular coupling structure has advantages such as simple structure and ease of manufacturing, making it an ideal choice for the design of high-performance integrated plasmonic devices. Full article
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Figure 1

Figure 1
<p>The diagram of the isosceles triangular coupling structure: (<b>a</b>) 3D structure, (<b>b</b>) 2D structure (top view).</p>
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<p>(<b>a</b>) The transmission spectrum of the isosceles triangular coupling structure. (<b>b</b>–<b>e</b>) are the distributions of magnetic field with four peaks. The coordinates of the three vertices of the isosceles triangle are as follows: A (100,0), B (−500,480) and C (−500,−480).</p>
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<p>The coordinates of the three vertices of the isosceles triangle are as follows: A (100,0), B (−500,480) and C (−500,−480). The effects of structural parameters on transmission characteristics are shown here: (<b>a</b>,<b>b</b>) are the horizontal coordinates of A and B/C.</p>
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<p>(<b>a</b>) Extraordinary and ordinary refractive indices, <span class="html-italic">n<sub>e</sub></span> and <span class="html-italic">n<sub>o</sub></span>, with various wavelengths. (<b>b</b>) The refractive index of LC with different voltages.</p>
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<p>The configurations of LC molecules with different voltages: (<b>a</b>) <span class="html-italic">V</span> &lt; <span class="html-italic">V<sub>th</sub></span>, (<b>b</b>) <span class="html-italic">V</span> ≥ <span class="html-italic">V<sub>th</sub></span>. (<b>c</b>) The angle <span class="html-italic">θ</span> between the long axis of the LC molecule and the x-axis, with different voltages.</p>
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<p>(<b>a</b>) The diagram of isosceles triangular coupling structure filled with LC. (<b>b</b>,<b>c</b>) The transmission spectra with different voltages applied.</p>
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<p>(<b>a</b>) The refractive index as a function of the concentration of glucose solution. (<b>b</b>) The glucose concentration detection model.</p>
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<p>(<b>a</b>,<b>b</b>) The transmission spectra associated with glucose solutions of different concentrations. (<b>c</b>) The wavelength shifts with glucose solutions of different concentrations.</p>
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15 pages, 5488 KiB  
Article
Analysis of Vibration Energy Harvesting Performance of Thermo-Electro-Elastic Microscale Devices Based on Generalized Thermoelasticity
by Ailing He, Tianhu He, Bingdong Gu and Yuan Li
Actuators 2024, 13(12), 533; https://doi.org/10.3390/act13120533 - 23 Dec 2024
Cited by 1 | Viewed by 3906
Abstract
Piezoelectric material structures with an excellent mechatronic coupling property effectively promote self-power energy harvesting in micro-/nano-electro-mechanical systems (MEMS/NEMS). Therein, the characteristics of the microscale and multi-physical aspects effect significant influence on performance, such as attaining a fast response and high power density. It [...] Read more.
Piezoelectric material structures with an excellent mechatronic coupling property effectively promote self-power energy harvesting in micro-/nano-electro-mechanical systems (MEMS/NEMS). Therein, the characteristics of the microscale and multi-physical aspects effect significant influence on performance, such as attaining a fast response and high power density. It is difficult to use the classical mechanical and heat conduction models to effectively explain and analyze microscale physical field coupling behaviors. The purpose of this study is to develop the piezoelectric thermoelastic theoretical model, firstly considering the non-uniform physical field. The generalized equations governing thermo-electro-elastic vibration energy harvesting in a microbeam model were obtained based on Hamilton’s principle and the generalized thermoelastic theory was developed by considering thermopolarization and thermal hysteresis behavior. After that, the explicit expressions for voltage and output power were derived using the assumed-modes method; meanwhile, effects such as the piezo-flexoelectric aspect, size dependence, etc. are discussed in detail. It was found that thermal and microscale effects significantly promote the voltage and output power. The research is also helpful for the design and optimization of self-powered and high-performance micro/nano devices and systems. Full article
(This article belongs to the Section Miniaturized and Micro Actuators)
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<p>Diagram of the cantilever piezoelectric microbeam model.</p>
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<p>Variation of the (<b>a</b>) voltage and (<b>b</b>) output power with vibration frequency in piezoelectric microbeam with or without thermal effect.</p>
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<p>Variation of the (<b>a</b>) voltage and (<b>b</b>) output power with vibration frequency in piezoelectric microbeam with or without thermopolarization effect.</p>
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<p>Influence of strain gradient coefficient on the variation of the (<b>a</b>) voltage and (<b>b</b>) output power with thickness.</p>
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<p>Comparison of the (<b>a</b>) voltage and (<b>b</b>) output power against the classical theory model.</p>
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<p>Variations of the (<b>a</b>) voltage and (<b>b</b>) output power with frequency for changing load resistance in microbeam model.</p>
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14 pages, 8579 KiB  
Article
Fano and Electromagnetically Induced Transparency Resonances in Dual Side-Coupled Photonic Crystal Nanobeam Cavities
by Yong Zhao, Yuxuan Chen and Lijun Hao
Materials 2024, 17(24), 6213; https://doi.org/10.3390/ma17246213 - 19 Dec 2024
Viewed by 591
Abstract
We propose two types of structures to achieve the control of Fano and electromagnetically induced transparency (EIT) line shapes, in which dual one-dimensional (1D) photonic crystal nanobeam cavities (PCNCs) are side-coupled to a bus waveguide with different gaps. For the proposed type Ⅰ [...] Read more.
We propose two types of structures to achieve the control of Fano and electromagnetically induced transparency (EIT) line shapes, in which dual one-dimensional (1D) photonic crystal nanobeam cavities (PCNCs) are side-coupled to a bus waveguide with different gaps. For the proposed type Ⅰ and type Ⅱ systems, the phase differences between the nanobeam periodic structures of the two cavities are π and 0, respectively. The whole structures are theoretically analyzed via the coupled mode theory and numerically demonstrated using the three-dimensional finite-difference time-domain (3D FDTD) method. The simulation results show that the proposed structure can achieve several kinds of spectra, including Fano, EIT and asymmetric EIT line shapes, which is dependent on the width of the bus waveguide. Compared to the previously proposed Fano resonator with 1D PCNCs, the proposed structures have the advantages of high transmission at the resonant peak, low insertion loss at non-resonant wavelengths, a wide free spectral range (FSR) and a high roll-off rate. Therefore, we believe the proposed structure can find broad applications in optical switches, modulators and sensors. Full article
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<p>Simplified model of two side-coupled standing-wave cavities (<span class="html-italic">C</span><sub>1</sub> and <span class="html-italic">C</span><sub>2</sub>).</p>
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<p>The calculated transmission spectra of the (<b>a</b>) type Ⅰ and (<b>b</b>) type Ⅱ systems based on the temporary CMT. The coupling Q-factors are <span class="html-italic">Q<sub>w</sub></span><sub>1</sub> = 500 and <span class="html-italic">Q<sub>w</sub></span><sub>2</sub> = 2000, and the intrinsic Q-factors are <span class="html-italic">Q<sub>i</sub></span><sub>1</sub> = <span class="html-italic">Q<sub>i</sub></span><sub>2</sub> = 1 × 10<sup>5</sup>. The resonant wavelengths of <span class="html-italic">C</span><sub>1</sub> and <span class="html-italic">C</span><sub>2</sub> are <span class="html-italic">λ</span><sub>1</sub> = <span class="html-italic">λ</span><sub>2</sub> = 1550 nm in (<b>a</b>) and <span class="html-italic">λ</span><sub>1</sub> = 1550 nm and <span class="html-italic">λ</span><sub>2</sub> = 1549 nm in (<b>b</b>).</p>
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<p>Models of two side-coupled cavities with phase-shifted periodic structure under weak perturbation conditions: (<b>a</b>) Type Ⅰ system with same resonant wavelengths and grating phase difference of <span class="html-italic">π</span> between <span class="html-italic">C</span><sub>1</sub> and <span class="html-italic">C</span><sub>2</sub>. (<b>b</b>) Type Ⅱ system with different resonant wavelengths and same grating phase between <span class="html-italic">C</span><sub>1</sub> and <span class="html-italic">C</span><sub>2</sub>.</p>
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<p>The calculated transmission spectra of the (<b>a</b>) type Ⅰ and (<b>b</b>) type Ⅱ systems under weak perturbation conditions based on the coupled mode equations of Equations (6)–(8).</p>
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<p>Schematics of proposed (<b>a</b>) type Ⅰ and (<b>b</b>) type Ⅱ dual-PCNC systems on SOI platform.</p>
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<p>The reflection spectra of the designed Bragg reflector with 4 tapered holes and 9 uniform holes and the Bragg reflector with 13 uniform holes.</p>
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<p>A schematic of the calculation of the effective index of the strip waveguide with a hole.</p>
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<p>Simulated (<b>a</b>) transmission and (<b>b</b>) reflection spectra when only <span class="html-italic">C</span><sub>1</sub> or <span class="html-italic">C</span><sub>2</sub> is side-coupled to the bus waveguide.</p>
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<p>(<b>a</b>) The transmission and reflection spectra of the type Ⅰ dual-PCNC system with an EIT-like line shape, and the |<span class="html-italic">H<sub>y</sub></span>| profile at the (<b>b</b>) transmission peak point <span class="html-italic">A</span>, (<b>c</b>) transmission dip point <span class="html-italic">B</span> and (<b>d</b>) transmission dip point <span class="html-italic">C</span> calculated by the 3D FDTD method.</p>
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<p>(<b>a</b>) Transmission spectra and (<b>b</b>) phase of type Ⅰ dual-PCNC system with different bus waveguide widths calculated by 3D FDTD method. Red dot is point of maximum slope change in phase relative to wavelength.</p>
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<p>(<b>a</b>) The transmission and reflection spectra of the type Ⅰ dual-PCNC system with a Fano line shape (<span class="html-italic">w</span><sub>0</sub> = 435 nm), and the |<span class="html-italic">H<sub>y</sub></span>| profile at (<b>b</b>) point <span class="html-italic">A</span>, (<b>c</b>) point <span class="html-italic">B</span> and (<b>d</b>) point <span class="html-italic">C</span> calculated by the 3D FDTD method.</p>
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<p>(<b>a</b>) The transmission and reflection spectra of the type Ⅱ dual-PCNC system with an EIT-like line shape, and the |<span class="html-italic">H<sub>y</sub></span>| profile at the (<b>b</b>) transmission peak point <span class="html-italic">A</span>, (<b>c</b>) transmission dip point <span class="html-italic">B</span> and (<b>d</b>) transmission dip point <span class="html-italic">C</span> calculated by the 3D FDTD method.</p>
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<p>(<b>a</b>) The transmission spectra and (<b>b</b>) phase of the type Ⅱ dual-PCNC system with different bus waveguide widths calculated by the 3D FDTD method. The red dot is the point of the maximum slope change in phase relative to the wavelength.</p>
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<p>(<b>a</b>) The transmission and reflection spectra of the type Ⅱ dual-PCNC system with an asymmetric EIT line shape (<span class="html-italic">w</span><sub>0</sub> = 380) nm, and the |<span class="html-italic">H<sub>y</sub></span>| profile at (<b>b</b>) point <span class="html-italic">A</span>, (<b>c</b>) point <span class="html-italic">B</span> and (<b>d</b>) point <span class="html-italic">C</span> calculated by the 3D FDTD method.</p>
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<p>(<b>a</b>) The transmission and reflection spectra of the type Ⅱ dual-PCNC system with a Fano line shape and (<span class="html-italic">w</span><sub>0</sub> = 460), and the |<span class="html-italic">H<sub>y</sub></span>| profile at (<b>b</b>) point <span class="html-italic">A</span>, (<b>c</b>) point <span class="html-italic">B</span> and (<b>d</b>) point <span class="html-italic">C</span> calculated by the 3D FDTD method.</p>
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<p>The transmission spectra of the (<b>a</b>) type Ⅰ and (<b>b</b>) type Ⅱ dual-PCNC systems with EIT line shapes with different waveguide width deviations (∆<span class="html-italic">w</span>).</p>
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<p>The transmission spectra of the (<b>a</b>) type Ⅰ and (<b>b</b>) type Ⅱ dual-PCNC systems with EIT line shapes with different hole radius deviations (∆<span class="html-italic">r</span>).</p>
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21 pages, 2778 KiB  
Article
Research on the Mechanical Parameter Identification and Controller Performance of Permanent Magnet Motors Based on Sensorless Control
by Mingchen Luan, Yun Zhang, Jiuhong Ruan, Yongwu Guo, Long Wang and Huihui Min
Actuators 2024, 13(12), 525; https://doi.org/10.3390/act13120525 - 19 Dec 2024
Viewed by 549
Abstract
In order to improve the control performance of the position sensorless control system of permanent magnet synchronous motors and to reduce the influence of external uncertainties on the control system, such as inertia ingestion and load disturbance, this paper proposes a novel position [...] Read more.
In order to improve the control performance of the position sensorless control system of permanent magnet synchronous motors and to reduce the influence of external uncertainties on the control system, such as inertia ingestion and load disturbance, this paper proposes a novel position sensorless control algorithm for permanent magnet synchronous motors based on an interleaved parallel extended sliding mode observer. Firstly, in order to identify the time-varying moment of inertia, load torque and viscous friction coefficient of the system, a novel interleaved parallel extended sliding mode observer based on a single-observer model is proposed, and a robust activator is designed to reduce the coupling between the parameters to be measured. Then, a new predefined-time sliding mode controller is designed for the face-mounted permanent magnet synchronous motor using sliding film control theory, which improves the response speed and control accuracy of the system. Then, the proposed novel interleaved parallel extended sliding mode observer and predefined-time sliding mode controller are used to design the permanent magnet synchronous motor control system, and the stability of the system is proved using the Lyapunov stability theorem. Finally, through simulation analysis and experimental tests, it is verified that the control strategy proposed in this paper can improve the identification accuracy of the motor parameters, reduce the time of identification, and improve the control accuracy and tracking speed. Full article
(This article belongs to the Special Issue Power Electronics and Actuators—Second Edition)
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<p>Voltage equivalent circuit diagram.</p>
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<p>Block diagram of permanent magnet synchronous motor control system.</p>
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<p>Block diagram of the observer principle.</p>
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<p>Convergence of the error system for different control schemes.</p>
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<p>Curves at convergence of sliding mode surface for different control schemes.</p>
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<p>Single-state observer load torque observation results.</p>
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<p>Multi- state observer load torque observation results.</p>
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<p>Multi-state observer rotational inertia observation results.</p>
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<p>Observations of <math display="inline"><semantics> <mi mathvariant="italic">B</mi> </semantics></math> when using the IPESMO algorithm.</p>
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<p>Experimental control platform.</p>
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<p>Experimental logic diagram.</p>
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<p>Fitting of the friction coefficients on the test bench. (<b>A</b>) Motor reversal. (<b>B</b>) Motor forward.</p>
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<p>Actual and estimated motor speeds obtained using the SMC and NFTSMC algorithms, respectively, when the desired speeds are different. (<b>A</b>) 1000 rpm. (<b>B</b>) 1500 rpm. (<b>C</b>) 2000 rpm. (<b>D</b>) 3000 rpm.</p>
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<p>Comparison of estimation results with and without Coulomb friction torque compensation. (<b>A</b>) With compensation <math display="inline"><semantics> <mover accent="true"> <mi>J</mi> <mo stretchy="false">^</mo> </mover> </semantics></math>. (<b>B</b>) With compensation <math display="inline"><semantics> <msub> <mover accent="true"> <mi>T</mi> <mo stretchy="false">^</mo> </mover> <mi>L</mi> </msub> </semantics></math>. (<b>C</b>) With compensation <math display="inline"><semantics> <mover accent="true"> <mi>B</mi> <mo stretchy="false">^</mo> </mover> </semantics></math>. (<b>D</b>) Without compensation <math display="inline"><semantics> <mover accent="true"> <mi>J</mi> <mo stretchy="false">^</mo> </mover> </semantics></math>. (<b>E</b>) Without compensation <math display="inline"><semantics> <msub> <mover accent="true"> <mi>T</mi> <mo stretchy="false">^</mo> </mover> <mi>L</mi> </msub> </semantics></math>. (<b>F</b>) Without compensation <math display="inline"><semantics> <mover accent="true"> <mi>B</mi> <mo stretchy="false">^</mo> </mover> </semantics></math>.</p>
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<p>Comparison of errors with and without Cullen friction torque compensation.</p>
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<p>(<b>A</b>) IPESMO. (<b>B</b>) DESMO. (<b>C</b>) ESO.</p>
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<p>Comparison of the errors in the observations of the three algorithms.</p>
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<p>Comparison of observed values of each mechanical parameter at different times of gain. (<b>A</b>) Observation value of J. (<b>B</b>) Observation value of <math display="inline"><semantics> <msub> <mi>T</mi> <mi>L</mi> </msub> </semantics></math>. (<b>C</b>) Observation value of B.</p>
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<p>Multi-load multi-algorithm comparison experiments. (<b>A</b>) IPESMO −0.1 N·m. (<b>B</b>) ESMO −0.1 N·m. (<b>C</b>) DESMO −0.1 N·m. (<b>D</b>) IPESMO −0.2 N·m. (<b>E</b>) ESMO −0.2 N·m. (<b>F</b>) DESMO −0.2 N·m.</p>
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29 pages, 8434 KiB  
Article
Extending Generalized Explicit Terms and Applying Euler–Bernoulli Beam Theory to Enhance Dynamic Response Prediction in Receptance Coupling Method
by Behzad Hamedi and Saied Taheri
Appl. Sci. 2024, 14(24), 11841; https://doi.org/10.3390/app142411841 - 18 Dec 2024
Viewed by 630
Abstract
This paper presents a theoretical framework to enhance the prediction of dynamic responses in complex mechanical systems, such as vehicle structures, by incorporating both translational and rotational degrees of freedom. Traditional receptance coupling methods often neglect rotational effects, leading to significant inaccuracies at [...] Read more.
This paper presents a theoretical framework to enhance the prediction of dynamic responses in complex mechanical systems, such as vehicle structures, by incorporating both translational and rotational degrees of freedom. Traditional receptance coupling methods often neglect rotational effects, leading to significant inaccuracies at higher frequencies. Additionally, approaches that implicitly include full dynamics frequently result in redundancy of generalized coordinates, especially at connection points. To address these limitations, the generalized receptance coupling method using Frequency-Based Substructuring is extended to explicitly account for rotational dynamics resulting in a refined GRCFBS approach. This extension enhances both the understanding and prediction of system responses, which are represented through the receptance matrix or Frequency Response Function. Building on Jetmundsen’s foundational work, the proposed framework introduces a practical, generalized formulation that explicitly incorporates full translational and rotational dynamics at each substructure node. This explicit definition provides deeper insights into system behavior, particularly for complex interactions between substructures under weak and strong coupling scenarios at interface points. The Euler–Bernoulli beam theory is employed to model rotational behavior at critical points, yielding reduced-order and explicit receptance matrices for substructures in the coupling process. The methodology’s accuracy and applicability in capturing resonance and anti-resonance modes are validated through two case studies: the coupling of two flexible subsystems and the integration of flexible and rigid components. Results are benchmarked against numerical finite element analysis, and all limitations and potential improvements are discussed. By directly incorporating rotational dynamics directly, this approach enables more reliable dynamic response predictions under multi-directional loading conditions, particularly for vehicle and machinery system design. The GRCFBS method offers a versatile and reliable tool for dynamic system analysis, with significant potential for vibration analysis over a broad frequency range. Full article
(This article belongs to the Section Acoustics and Vibrations)
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<p>Schematic of system AB for the 1st case study.</p>
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<p>Decomposition of system AB into substructures A and B for case study 1.</p>
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<p>Excitation force and moment on substructures A for case study 1.</p>
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<p>Excitation force and moment on substructures B for case study 1.</p>
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<p>Schematic of system AC, consisting of substructures A and C.</p>
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<p>Decomposition of system AC into substructures A and C using substructuring strategy.</p>
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<p>Excitation loads (force and moment) applied to substructure C.</p>
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<p>Receptance component (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> </mrow> </semantics></math>): translational disp. at the tip due to excitation force at the same point (case study 1).</p>
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<p>Receptance component (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> </mrow> </semantics></math>): translational displacement at tip due to couple at tip (case study 1).</p>
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<p>Receptance component (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> </mrow> </semantics></math>): rotational displacement at the tip due to couple at the same point (case study 1).</p>
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<p>Comparison between direct/cross-receptance components at tip (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> <mo>,</mo> <mtext> </mtext> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> <mo>,</mo> <mtext> </mtext> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> </mrow> </semantics></math>) (case study 1).</p>
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<p>Receptance (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> </mrow> </semantics></math>): translational disp. at connection due to excitation force at same point (case study 1).</p>
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<p>Receptance (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> </mrow> </semantics></math>): translational disp. at connection point due to excitation couple at same point (case study 1).</p>
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<p>Receptance (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> </mrow> </semantics></math>): Rotational disp. at connection point due to excitation couple at the same point (case study 1).</p>
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<p>Comparison between cross-receptance at connection point (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> <mo>,</mo> <mtext> </mtext> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> <mo>,</mo> <mtext> </mtext> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> </mrow> </semantics></math>) (case study 1).</p>
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<p>Cross-receptance (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> <mo>=</mo> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> </mrow> </semantics></math>): translational disp. between tip and connection points (case study 1).</p>
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<p>Cross-receptance <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mtext> </mtext> <mo>(</mo> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> <mo>=</mo> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> </mrow> </semantics></math>): translational disp. at the connection node due to the moment excitation at the tip (case study 1).</p>
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<p>Cross-receptance (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> <mo>=</mo> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> </mrow> </semantics></math>): rotational disp. at the connection due to the excitation couple at the tip (case study 1).</p>
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<p>Comparison between cross-receptance components (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> <mo>,</mo> <mtext> </mtext> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> <mo>,</mo> <mtext> </mtext> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">d</mi> <mtext> </mtext> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </msubsup> </mrow> </semantics></math>) (case study 1).</p>
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<p>Receptance component (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msubsup> </mrow> </semantics></math>): translational displacement to excitation force (2nd case study).</p>
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<p>Receptance component <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mo>(</mo> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msubsup> <mo>)</mo> </mrow> </semantics></math>: translational displacement to excitation moment (2nd case study).</p>
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<p>Receptance component (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msubsup> </mrow> </semantics></math>): rotational disp. to excitation couple (2nd case study).</p>
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<p>Comparison between cross-receptance components (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msubsup> <mo>,</mo> <mtext> </mtext> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msubsup> <mo>,</mo> <mtext> </mtext> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">d</mi> <mtext> </mtext> <msubsup> <mrow> <mi>H</mi> </mrow> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </msubsup> </mrow> </semantics></math>) for 2nd case study.</p>
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<p>Comparison between receptance component at the tip: translational displacement to excitation force for two cases.</p>
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15 pages, 5530 KiB  
Article
Regulation and Liquid Sensing of Electromagnetically Induced Transparency-like Phenomena Implemented in a SNAP Microresonator
by Chenxiang Liu, Minggang Chai, Chenglong Zheng, Chengfeng Xie, Chuanming Sun, Jiulin Shi, Xingdao He and Mengyu Wang
Sensors 2024, 24(21), 7069; https://doi.org/10.3390/s24217069 - 2 Nov 2024
Viewed by 809
Abstract
Optical microresonators supporting whispering-gallery modes (WGMs) have become a versatile platform for achieving electromagnetically induced transparency-like (EIT-like) phenomena. We theoretically and experimentally demonstrated the tunable coupled-mode induced transparency based on the surface nanoscale axial photonics (SNAP) microresonator. Single-EIT-like and double-EIT-like (DEIT-like) effects with [...] Read more.
Optical microresonators supporting whispering-gallery modes (WGMs) have become a versatile platform for achieving electromagnetically induced transparency-like (EIT-like) phenomena. We theoretically and experimentally demonstrated the tunable coupled-mode induced transparency based on the surface nanoscale axial photonics (SNAP) microresonator. Single-EIT-like and double-EIT-like (DEIT-like) effects with one or more transparent windows are achieved due to dense mode families and tunable resonant frequencies. The experimental results can be well-fitted by the coupled mode theory. An automatically adjustable EIT-like effect is discovered by immersing the sensing region of the SNAP microresonator into an aqueous environment. The sharp lineshape and high slope of the transparent window allow us to achieve a liquid refractive index sensitivity of 2058.8 pm/RIU. Furthermore, we investigated a displacement sensing phenomenon by monitoring changes in the slope of the transparent window. We believe that the above results pave the way for multi-channel all-optical switching devices, multi-channel optical communications, and biochemical sensing processing. Full article
(This article belongs to the Special Issue Research Progress in Optical Microcavity-Based Sensing)
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Figure 1

Figure 1
<p>(<b>a</b>) Normalized electric field distribution for the fifth order axial mode. (<b>b</b>) Normalized electric field distribution for the third order radial mode. (<b>c</b>) Cross-sectional views of the normalized electric field distributions with (<span class="html-italic">p</span> = 1, <span class="html-italic">m</span> = 365, <span class="html-italic">q</span> = 0), (<span class="html-italic">p</span> = 2, <span class="html-italic">q</span> = 2, <span class="html-italic">m</span> = 337), and (<span class="html-italic">p</span> = 3, <span class="html-italic">m</span> = 319, <span class="html-italic">q</span> = 4). (<b>d</b>) Resonant wavelengths as a function of axial mode numbers <span class="html-italic">q</span> with measurement size.</p>
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<p>(<b>a</b>) Schematic diagram for the microresonator–taper coupling system. (<b>b</b>) Schematic diagram for the three-mode-coupling microcapillary system. (<b>c</b>) Illustration for the three-pathway interference effect induced by the three kinds of WGMs.</p>
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<p>(<b>a</b>) Simulation spectrum varies with <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>γ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>. The resonant frequency difference between high-<span class="html-italic">Q</span> mode and low-<span class="html-italic">Q</span> mode is not zero and induces the Fano resonance. (<b>b</b>) Transparent window spectrum varies with <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>γ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>. The resonant frequency difference between the two modes is zero and induces the standard transparent window. (<b>c</b>,<b>d</b>) show the derivatives of the spectra with respect to <math display="inline"><semantics> <mrow> <mi>ω</mi> </mrow> </semantics></math> in (<b>a</b>,<b>b</b>), respectively. (<b>e</b>) Transparent window lineshape (blue line) and Fano lineshape (red line) with <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>γ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> = 150. (<b>f</b>) Slope curves of transparent window and Fano resonance in case of (<b>e</b>).</p>
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<p>Dual-mode-coupling and the corresponding Fano/EIT–like effects realized in the SNAP microresonator. (<b>a</b>–<b>e</b>) Experimental normalized transmission spectra at different coupling positions, <math display="inline"><semantics> <mrow> <mo>∆</mo> <mi>z</mi> </mrow> </semantics></math> = 5 μm, 10 μm, 15 μm, 20 μm, and 25 μm. (<b>f</b>–<b>j</b>) Fitting experimental data corresponding to (<b>a</b>–<b>e</b>). The simulation data are set to: <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mrow> <mi>γ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>γ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>κ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>κ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>∆</mo> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>∆</mo> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>φ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>φ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>]</mo> </mrow> </semantics></math> = [783.2, 26.4, 183.2, 12.8, 295, 772.7, 0.28, 8.9], [643.2, 1, 263.2, 74.8, 195, 564.7, 0.52, 8.76], [373.2, 5, 263.2, 124.8, −15, 394.7, 0.73, 8.91], [293.2, 10, 240.2, 140.8, −75, 204.7, 0.71, 9], [153.2, 10, 290.2, 130.8, −100, −19.7, 0.69, 12.25].</p>
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<p>Multi-mode-coupling and DEIT effect realized in the SNAP microresonator. (<b>a</b>–<b>f</b>) Experimental normalized transmission spectra at different coupling positions. (<b>g</b>–<b>l</b>) Theoretical transmission lineshapes for fitting experimental data. The simulation data are set to: <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mrow> <mi>γ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>γ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <msub> <mrow> <mi>γ</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>,</mo> <mi>κ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>κ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>κ</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mo>∆</mo> <mi>ω</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>∆</mo> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>∆</mo> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>φ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo> </mo> <msub> <mrow> <mi>φ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo> </mo> <msub> <mrow> <mi>φ</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>]</mo> </mrow> </semantics></math> = [403.2, 576.4, 77.4, −3403.2, −290.8, −12, 170, −5, 740.7, 0.17, 8.82, 8.6], [1253.2, 585.4, 77.4, −3203.2, −287.8, −12, 60, −15, 690.7, 0.17, 8.82, 8.7], [1753.2, 625.4, 22.4, −4003.2, −287.8, −1, 20, −90, 590.7, 0.12, 8.82, 9.6], [1753.2, 625.4, 32.4, −4003.2, −297.8, −1, −50, −110, 565.7], [1753.2, 625.4, 32.4, −4003.2, −304.8, −5, −50, −110, 535.7, 0.12, 8.82, 8.4], [1753.2, 625.4, 32.4, −3503.2, −294.8, −5, −180, −180, 485.7, 0.12, 8.82, 8.7].</p>
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<p>(<b>a</b>) Experimental apparatus for the axial separation sensing. (<b>b</b>) Schematic diagram of the axial separation sensing technology for detecting the aqueous environment. (<b>c</b>) The physical device corresponding to (<b>a</b>). (<b>d</b>) Automatically adjustable EIT-like effect when the sensing region is immersed in deionized water. (<b>e</b>) Theoretical transmission lineshapes for fitting experimental data. The simulation data are set to: <math display="inline"><semantics> <mrow> <mo>[</mo> <msub> <mrow> <mi>γ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>γ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mo> </mo> <mi>κ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>κ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mo>∆</mo> <mi>ω</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>∆</mo> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>φ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo> </mo> <msub> <mrow> <mi>φ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>]</mo> </mrow> </semantics></math> = [94.2, 11.3, 31.4, 0.063, 375, 562, 0.24, 8.78], [94.2, 7.54, 31.4, 0.063, 187, 312, 0.24, 8.85], [94.2, 6.91, 31.4, 0.063, 62.5, 137.4, 0.44, 8.91], [94.2, 3.14, 31.4, 0, 0, 0, 0.58, 9.23], [94.2, 3.14, 31.4, 0, −50, −125, 0.52, 10.88], [94.2, 3.14, 31.4, 0, −250, −400, 0.61, 11.91], [94.2, 3.14, 31.4, 0, −324.6, −500, 0.61, 11.97].</p>
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<p>(<b>a</b>) Cross-sectional WGMs distribution with increasing air refractive indices. (<b>b</b>) The resonant wavelength shifts towards longer wavelengths as <math display="inline"><semantics> <mrow> <mi>n</mi> </mrow> </semantics></math> continues to increase. (<b>c</b>) The electric field intensity distribution decreases as <math display="inline"><semantics> <mrow> <mi>n</mi> </mrow> </semantics></math> continues to increase. (<b>d</b>) Evolution of the transmission spectrum with increasing liquid refractive index. The green arrow indicates the wavelength shift direction. (<b>e</b>) The resonant wavelength shifts as a function of the liquid refractive index.</p>
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<p>(<b>a</b>) Simulation model for the electric field distribution. One stem of the microresonator is immersed in liquid. Axial mode with <span class="html-italic">q</span> = 6 is excited in the model. The liquid surfaces are set to −10 μm, −5 μm, and 0 μm; the corresponding electric field distribution models are shown in (<b>i</b>), (<b>ii</b>), and (<b>iii</b>), respectively. The electric field intensity in liquid and air along the radial section line direction is shown in (<b>iv</b>). (<b>b</b>) Axial electric field intensity distribution with different liquid surfaces along the axial section line direction. (<b>i</b>), (<b>ii</b>), and (<b>iii</b>) are electric field distribution models as the interaction area between the liquid and the sensing region of the SNAP microresonator is increased. (<b>c</b>) Representative transmission spectra corresponding to each liquid lifting height; red (0 μm), green (100 μm), and blue (200 μm). (<b>d</b>) Localized magnification for the spectra in (<b>c</b>). (<b>e</b>) The slope values of the transparent window with MD = 0 μm, 100 μm, 200 μm, respectively. The slope data are divided with three different color intervals from left to right, corresponding to each MD. The mean values of the slopes as a function of the MD are displayed in the inset. (<b>f</b>) Probability distribution histogram of the slope values corresponding to various MD.</p>
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32 pages, 9532 KiB  
Article
Considering Carbon–Hydrogen Coupled Integrated Energy Systems: A Pathway to Sustainable Energy Transition in China Under Uncertainty
by Anjie Lu, Jianguo Zhou, Minglei Qin and Danchen Liu
Sustainability 2024, 16(21), 9256; https://doi.org/10.3390/su16219256 - 24 Oct 2024
Viewed by 1572
Abstract
The low-carbon construction of integrated energy systems is a crucial path to achieving dual carbon goals, with the power-generation side having the greatest potential for emissions reduction and the most direct means of reduction, which is a current research focus. However, existing studies [...] Read more.
The low-carbon construction of integrated energy systems is a crucial path to achieving dual carbon goals, with the power-generation side having the greatest potential for emissions reduction and the most direct means of reduction, which is a current research focus. However, existing studies lack the precise modeling of carbon capture devices and the cascaded utilization of hydrogen energy. Therefore, this paper establishes a carbon capture power plant model based on a comprehensive, flexible operational mode and a coupled model of a two-stage P2G (Power-to-Gas) device, exploring the “energy time-shift” characteristics of the coupled system. IGDT (Information Gap Decision Theory) is used to discuss the impact of uncertainties on the power generation side system. The results show that by promoting the consumption of clean energy and utilizing the high energy efficiency of hydrogen while reducing reliance on fossil fuels, the proposed system not only meets current energy demands but also achieves a more efficient emission reduction, laying a solid foundation for a sustainable future. By considering the impact of uncertainties, the system ensures resilience and adaptability under fluctuating renewable energy supply conditions, making a significant contribution to the field of sustainable energy transition. Full article
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<p>Liquid storage carbon capture power plant CO<sub>2</sub> flow diagram.</p>
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<p>Comparison of net generations from carbon capture power plants.</p>
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<p>Energy time shifting in carbon capture power plants.</p>
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<p>Two-stage energy bus diagram for Power-to-Gas.</p>
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<p>Dispatch structure of the system.</p>
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<p>Day-ahead forecast load in case studies.</p>
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<p>Carbon capture power plant outputs.</p>
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<p>Outputs of other conventional thermal power units.</p>
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<p>Scenario 3: composition of electrical power.</p>
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<p>Output power of the PV Unit.</p>
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<p>Net generation power of the carbon capture unit.</p>
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<p>Total carbon emissions of the system.</p>
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