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Keywords = optical beam shaping

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15 pages, 4886 KiB  
Article
Fabrication of Diffractive Optical Elements to Generate Square Focal Spots via Direct Laser Lithography and Machine Learning
by Hieu Tran Doan Trung, Young-Sik Ghim and Hyug-Gyo Rhee
Photonics 2025, 12(8), 794; https://doi.org/10.3390/photonics12080794 - 6 Aug 2025
Abstract
Recently, diffractive optics systems have garnered increasing attention due to their myriad benefits in various applications, such as creating vortex beams, Bessel beams, or optical traps, while refractive optics systems still exhibit some disadvantages related to materials, substrates, and intensity shapes. The manufacturing [...] Read more.
Recently, diffractive optics systems have garnered increasing attention due to their myriad benefits in various applications, such as creating vortex beams, Bessel beams, or optical traps, while refractive optics systems still exhibit some disadvantages related to materials, substrates, and intensity shapes. The manufacturing of diffractive optical elements has become easier due to the development of lithography techniques such as direct laser writing, photo lithography, and electron beam lithography. In this paper, we improve the results from previous research and propose a new methodology to design and fabricate advanced binary diffractive optical elements that achieve a square focal spot independently, reducing reliance on additional components. By integrating a binary square zone plate with an axicon zone plate of the same scale, we employ machine learning for laser path optimization and direct laser lithography for manufacturing. This streamlined approach enhances simplicity, accuracy, efficiency, and cost effectiveness. Our upgraded binary diffractive optical elements are ready for real-world applications, marking a significant improvement in optical capabilities. Full article
(This article belongs to the Section Lasers, Light Sources and Sensors)
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22 pages, 6689 KiB  
Article
Design and Implementation of a Sun Outage Simulation System with High Uniformity and Stray Light Suppression Capability
by Zhen Mao, Zhaohui Li, Yong Liu, Limin Gao and Jianke Zhao
Sensors 2025, 25(15), 4655; https://doi.org/10.3390/s25154655 - 27 Jul 2025
Viewed by 368
Abstract
To enable accurate evaluation of satellite laser communication terminals under solar outage interference, this paper presents the design and implementation of a solar radiation simulation system targeting the 1540–1560 nm communication band. The system reconstructs co-propagating interference conditions through standardized and continuously tunable [...] Read more.
To enable accurate evaluation of satellite laser communication terminals under solar outage interference, this paper presents the design and implementation of a solar radiation simulation system targeting the 1540–1560 nm communication band. The system reconstructs co-propagating interference conditions through standardized and continuously tunable output, based on high irradiance and spectral uniformity. A compound beam homogenization structure—combining a multimode fiber and an apodizator—achieves 85.8% far-field uniformity over a 200 mm aperture. A power–spectrum co-optimization strategy is introduced for filter design, achieving a spectral matching degree of 78%. The system supports a tunable output from 2.5 to 130 mW with a 50× dynamic range and maintains power control accuracy within ±0.9%. To suppress internal background interference, a BRDF-based optical scattering model is established to trace primary and secondary stray light paths. Simulation results show that by maintaining the surface roughness of key mirrors below 2 nm and incorporating a U-shaped reflective light trap, stray light levels can be reduced to 5.13 × 10−12 W, ensuring stable detection of a 10−10 W signal at a 10:1 signal-to-background ratio. Experimental validation confirms that the system can faithfully reproduce solar outage conditions within a ±3° field of view, achieving consistent performance in spectrum shaping, irradiance uniformity, and background suppression. The proposed platform provides a standardized and practical testbed for ground-based anti-interference assessment of optical communication terminals. Full article
(This article belongs to the Section Communications)
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23 pages, 9118 KiB  
Article
Scattering Characteristics of a Circularly Polarized Bessel Pincer Light-Sheet Beam Interacting with a Chiral Sphere of Arbitrary Size
by Shu Zhang, Shiguo Chen, Qun Wei, Renxian Li, Bing Wei and Ningning Song
Micromachines 2025, 16(8), 845; https://doi.org/10.3390/mi16080845 - 24 Jul 2025
Viewed by 197
Abstract
The scattering interaction between a circularly polarized Bessel pincer light-sheet beam and a chiral particle is investigated within the framework of generalized Lorenz–Mie theory (GLMT). The incident electric field distribution is rigorously derived via the vector angular spectrum decomposition method (VASDM), with subsequent [...] Read more.
The scattering interaction between a circularly polarized Bessel pincer light-sheet beam and a chiral particle is investigated within the framework of generalized Lorenz–Mie theory (GLMT). The incident electric field distribution is rigorously derived via the vector angular spectrum decomposition method (VASDM), with subsequent determination of the beam-shape coefficients (BSCs) pmnu and qmnu through multipole expansion in the basis of vector spherical wave functions (VSWFs). The expansion coefficients for the scattered field (AmnsBmns) and interior field (AmnBmn) are derived by imposing boundary conditions. Simulations highlight notable variations in the scattering field, near-surface field distribution, and far-field intensity, strongly influenced by the dimensionless size parameter ka, chirality κ, and beam parameters (beam order l and beam scaling parameter α0). These findings provide insights into the role of chirality in modulating scattering asymmetry and localization effects. The results are particularly relevant for applications in optical manipulation and super-resolution imaging in single-molecule microbiology. Full article
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12 pages, 3671 KiB  
Article
Method for Suppressing Scintillation in Up-Link Optical Communication Using Optical Pin-like Beams Propagating Through Atmospheric Turbulence
by Rong Wang, Bin Lan, Chao Liu, Kaihe Zhang, Jiaxin Zhou, Xueying Li, Tianjun Dai and Hao Xian
Photonics 2025, 12(7), 739; https://doi.org/10.3390/photonics12070739 - 20 Jul 2025
Viewed by 263
Abstract
Free space optical communication (FSOC) systems operating in the space–atmosphere channel are susceptible to severe turbulence-induced scintillation, particularly in up-link configurations where the adaptive optics (AO) pre-correction becomes ineffective due to anisoplanatic constraints. This study presents a novel scintillation suppression strategy utilizing self-focusing [...] Read more.
Free space optical communication (FSOC) systems operating in the space–atmosphere channel are susceptible to severe turbulence-induced scintillation, particularly in up-link configurations where the adaptive optics (AO) pre-correction becomes ineffective due to anisoplanatic constraints. This study presents a novel scintillation suppression strategy utilizing self-focusing optical pin-like beams (OPBs) with tailored phase modulation, combining theoretical derivation and numerical simulation. It is found that increasing the shape factor γ and modulation depth C elevates the average received power and reduces the scintillation index at the focal point. Meanwhile, quantitative evaluation of the five OPB configurations shows that the parameter set γ = 1.4 and C = 7 × 10−5 gives a peak scintillation suppression efficiency. It shows that turbulence induced scintillation is suppressed by 44% with the turbulence intensity D/r0 = 10, demonstrating exceptional effectiveness in up-link transmission. The findings demonstrate that OPB with optimized γ and C establish an approach for uplink FSOC, which is achieved through suppressed scintillation and stabilized power reception. Full article
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19 pages, 4423 KiB  
Review
Laser Active Optical Systems (LAOSs) for Material Processing
by Vladimir Chvykov
Micromachines 2025, 16(7), 792; https://doi.org/10.3390/mi16070792 - 2 Jul 2025
Viewed by 610
Abstract
The output energy of Laser Active Optical Systems (LAOSs), in which image brightness is amplified within the laser-active medium, is always higher than the input energy. This contrasts with conventional optical systems (OSs). As a result, a LAOS enables the creation of laser [...] Read more.
The output energy of Laser Active Optical Systems (LAOSs), in which image brightness is amplified within the laser-active medium, is always higher than the input energy. This contrasts with conventional optical systems (OSs). As a result, a LAOS enables the creation of laser beams with tailored energy distribution across the aperture, making them ideal for material processing applications. This concept was first successfully implemented using metal vapor lasers as the gain medium. In these systems, material processing was achieved by using a laser beam that either carried the required energy profile or the image of the object itself. Later, other laser media were utilized for LAOSs, including barium vapor, strontium vapor, excimer XeCl lasers, and solid-state media. Additionally, during the development of these systems, several modifications were introduced. For example, Space-Time Light Modulators (STLMs) and CCD cameras were incorporated, along with the use of multipass amplifiers, disk-shaped or thin-disk (TD) solid-state laser amplifiers, and other advancements. These techniques have significantly expanded the range of power, energy, pulse durations, and operating wavelengths. Currently, TD laser amplifiers and STLMs based on Digital Light Processor (DLP) technology or Digital Micromirror Devices (DMDs) enhance the potential to develop LAOS devices for Subtractive and Additive Technologies (ST, AT), applicable in both macromachining (cutting, welding, drilling) and micro-nano processing. This review presents comparable characteristics and requirements for these various LAOS applications. Full article
(This article belongs to the Special Issue Optical and Laser Material Processing, 2nd Edition)
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15 pages, 7120 KiB  
Article
A Dynamic Analysis of Toron Formation in Chiral Nematic Liquid Crystals Using a Polarization Holographic Microscope
by Tikhon V. Reztsov, Aleksey V. Chernykh, Tetiana Orlova and Nikolay V. Petrov
Polymers 2025, 17(13), 1849; https://doi.org/10.3390/polym17131849 - 2 Jul 2025
Viewed by 403
Abstract
Topological orientation structures in chiral nematic liquid crystals, such as torons, exhibit promising optical properties and are of increasing interest for applications in photonic devices. However, despite this attention, their polarization and phase dynamics during formation remain insufficiently explored. In this work, we [...] Read more.
Topological orientation structures in chiral nematic liquid crystals, such as torons, exhibit promising optical properties and are of increasing interest for applications in photonic devices. However, despite this attention, their polarization and phase dynamics during formation remain insufficiently explored. In this work, we investigate the dynamic optical response of a toron generated by focused femtosecond infrared laser pulses. A custom-designed polarization holographic microscope is employed to simultaneously record four polarization-resolved interferograms in a single exposure. This enables the real-time reconstruction of the Jones matrix, providing a complete description of the local polarization transformation introduced by the formation of the topological structure. The study demonstrates that torons can facilitate spin–orbit coupling of light in a manner analogous to q-plates, highlighting their potential for advanced vector beam shaping and topological photonics applications. Full article
(This article belongs to the Section Polymer Physics and Theory)
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18 pages, 4356 KiB  
Article
A Miniaturized Design for a Terahertz Tri-Mirror CATR with High QZ Characteristics
by Zhi Li, Yuan Yao, Haiming Xin and Daocai Xiang
Sensors 2025, 25(12), 3751; https://doi.org/10.3390/s25123751 - 15 Jun 2025
Viewed by 393
Abstract
This paper proposes a miniaturized design for a terahertz tri-mirror compact antenna test range (CATR) system, composed of a square-aperture paraboloid primary mirror with a side length of 0.2 m and two shaped mirrors with circular apertures of 0.06 m and 0.07 m [...] Read more.
This paper proposes a miniaturized design for a terahertz tri-mirror compact antenna test range (CATR) system, composed of a square-aperture paraboloid primary mirror with a side length of 0.2 m and two shaped mirrors with circular apertures of 0.06 m and 0.07 m in diameter. The design first employs the cross-polarization cancelation method based on beam mode expansion to determine the geometric configuration of the system, thereby enabling the structure to exhibit low cross-polarization characteristics. Subsequently, the shaped mirrors, with beamforming and wave-front control capabilities, are synthesized using dynamic ray tracing based on geometric optics (GO) and the dual-paraboloid expansion method. Finally, the strong edge diffraction effects induced by the small-aperture primary mirror are suppressed by optimizing the desired quiet-zone (QZ) field width, adjusting the feed-edge taper, and incorporating rolled-edge structures on the primary mirror. Numerical simulation results indicate that within the 100–500 GHz frequency band, the system’s cross-polarization level is below −40 dB, while the amplitude and phase ripples of the co-polarization in the QZ are, respectively, less than 1.6 dB and 10°, and the QZ usage ratio exceeds 70%. The designed CATR was manufactured and tested. The results show that at 183 GHz and 275 GHz, the measured co-polarization amplitude and phase ripples in the system’s QZ are within 1.8 dB and 15°, respectively. While these values deviate slightly from simulations, they still meet the CATR evaluation criteria, which specify QZ co-polarization amplitude ripple < 2 dB and phase ripple < 20°. The overall physical structure sizes of the system are 0.61 m × 0.2 m × 0.66 m. The proposed miniaturized terahertz tri-mirror CATR design methodology not only enhances the QZ characteristics but also significantly reduces the spatial footprint of the entire system, demonstrating significant potential for practical engineering applications. Full article
(This article belongs to the Section Optical Sensors)
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12 pages, 6768 KiB  
Article
Study on the Evolutionary Characteristics of Airyprime Beams in Gaussian-Type PT Symmetric Optical Lattices
by Depeng Chen, Dongchu Jiang and Zhewen Xiao
Photonics 2025, 12(6), 566; https://doi.org/10.3390/photonics12060566 - 4 Jun 2025
Viewed by 268
Abstract
The Airyprime beam, due to its adjustable focusing ability and controllable orbital angular momentum, has attracted significant attention in fields such as free-space optical communication and particle trapping. However, systematic studies on the propagation behavior of oscillating solitons in PT-symmetric optical lattices remain [...] Read more.
The Airyprime beam, due to its adjustable focusing ability and controllable orbital angular momentum, has attracted significant attention in fields such as free-space optical communication and particle trapping. However, systematic studies on the propagation behavior of oscillating solitons in PT-symmetric optical lattices remain scarce, particularly regarding their formation mechanisms and self-accelerating characteristics. In this study, the propagation characteristics of Airyprime beams in PT symmetric optical lattices are numerically studied using the split-step Fourier method, and the generation mechanism and control factors of oscillating solitons are analyzed. The influence of lattice parameters (such as the modulation depth P, modulation frequency w, and gain/loss distribution coefficient W0) and beam initial characteristics (such as the truncation coefficient a) on the dynamic behavior of the beam is revealed. The results show that the initial parameters determine the propagation characteristics of the beam and the stability of the soliton. This research provides theoretical support for beam shaping, optical path design, and nonlinear optical manipulation and has important application value. Full article
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17 pages, 1579 KiB  
Article
Closed Form Analytic Expressions for the Evanescent and Traveling Components of the Electromagnetic Green Function and for Defocused Hemispherical Focusing of Electromagnetic Waves
by Colin J. R. Sheppard
Photonics 2025, 12(6), 558; https://doi.org/10.3390/photonics12060558 - 2 Jun 2025
Viewed by 357
Abstract
Explicit analytic forms, in terms of Lommel functions of two variables, for the evanescent and traveling components of the electromagnetic Green tensor are presented. The field in the focal region, including defocus, of hemispherically focused electric dipole, magnetic dipole, and mixed-dipole waves are [...] Read more.
Explicit analytic forms, in terms of Lommel functions of two variables, for the evanescent and traveling components of the electromagnetic Green tensor are presented. The field in the focal region, including defocus, of hemispherically focused electric dipole, magnetic dipole, and mixed-dipole waves are expressed analytically in closed form. Full article
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10 pages, 1488 KiB  
Article
Influence of Lithography Process Parameters on Continuous Surface Diffractive Optical Elements for Laser Beam Shaping
by Wenjing Liu, Axiu Cao, Junbo Liu, Hui Pang, Qiling Deng, Jian Wang and Song Hu
Micromachines 2025, 16(5), 601; https://doi.org/10.3390/mi16050601 - 21 May 2025
Viewed by 455
Abstract
To address the demand for laser beam-shaping techniques, we developed a one-step exposure process based on moving-mask lithography for the fabrication of a continuous-surface diffractive optical element (DOE) for laser beam shaping. The fabrication process is described in detail, and the influence of [...] Read more.
To address the demand for laser beam-shaping techniques, we developed a one-step exposure process based on moving-mask lithography for the fabrication of a continuous-surface diffractive optical element (DOE) for laser beam shaping. The fabrication process is described in detail, and the influence of key parameters, such as pre-baking conditions, exposure gaps, development conditions, and post-baking conditions, of the lithography process on the microstructure profile of the DOE is analyzed. The reliability of the preparation method was verified through optical performance experiments. The speckle contrast, uniformity, and diffraction efficiency of the prepared linear beam-shaping element are 4.2%, 97.3%, and 87%. Full article
(This article belongs to the Section E:Engineering and Technology)
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13 pages, 4280 KiB  
Article
Performance Characteristics of the Battery-Operated Silicon PIN Diode Detector with an Integrated Preamplifier and Data Acquisition Module for Fusion Particle Detection
by Allan Xi Chen, Benjamin F. Sigal, John Martinis, Alfred YiuFai Wong, Alexander Gunn, Matthew Salazar, Nawar Abdalla and Kai-Jian Xiao
J. Nucl. Eng. 2025, 6(2), 15; https://doi.org/10.3390/jne6020015 - 15 May 2025
Viewed by 687
Abstract
We present the performance and application of a commercial off-the-shelf Si PIN diode (Hamamatsu S14605) as a charged particle detector in a compact ion beam system (IBS) capable of generating D–D and p–B fusion charged particles. This detector is inexpensive, widely available, and [...] Read more.
We present the performance and application of a commercial off-the-shelf Si PIN diode (Hamamatsu S14605) as a charged particle detector in a compact ion beam system (IBS) capable of generating D–D and p–B fusion charged particles. This detector is inexpensive, widely available, and operates in photoconductive mode under a reverse bias voltage of 12 V, supplied by an A23 battery. A charge-sensitive preamplifier (CSP) is mounted on the backside of the detector’s four-layer PCB and powered by two ±3 V lithium batteries (A123). Both the detector and CSP are housed together on the vacuum side of the IBS, facing the fusion target. The system employs a CF-2.75-flanged DB-9 connector feedthrough to supply the signal, bias voltage, and rail voltages. To mitigate the high sensitivity of the detector to optical light, a thin aluminum foil assembly is used to block optical emissions from the ion beam and target. Charged particles generate step responses at the preamplifier output, with pulse rise times in the order of 0.2 to 0.3 µs. These signals are recorded using a custom-built data acquisition unit, which features an optical fiber data link to ensure the electrical isolation of the detector electronics. Subsequent digital signal processing is employed to optimally shape the pulses using a CR-RCn filter to produce Gaussian-shaped signals, enabling the accurate extraction of energy information. Performance results indicate that the detector’s baseline RMS ripple noise can be as low as 0.24 mV. Under actual laboratory conditions, the estimated signal-to-noise ratios (S/N) for charged particles from D–D fusion—protons, tritons, and helions—are approximately 225, 75, and 41, respectively. Full article
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19 pages, 5298 KiB  
Article
Efficient Generation of Transversely and Longitudinally Truncated Chirped Gaussian Laser Pulses for Application in High-Brightness Photoinjectors
by Andreas Hoffmann, Sumaira Zeeshan, James Good, Matthias Gross, Mikhail Krasilnikov and Frank Stephan
Photonics 2025, 12(5), 460; https://doi.org/10.3390/photonics12050460 - 9 May 2025
Viewed by 437
Abstract
The optimization of photoinjector brightness is crucial for achieving the highest performance at X-ray free-electron lasers. To this end, photocathode laser pulse shaping has been identified as a key technology for enhancing photon flux and lasing efficiency at short wavelengths. Supported by beam [...] Read more.
The optimization of photoinjector brightness is crucial for achieving the highest performance at X-ray free-electron lasers. To this end, photocathode laser pulse shaping has been identified as a key technology for enhancing photon flux and lasing efficiency at short wavelengths. Supported by beam dynamics simulations, we identify transversely and longitudinally truncated Gaussian electron bunches as a beneficial bunch shape in terms of the projected emittance and 5D brightness. The realization of such pulses from chirped Gaussian pulses is studied for 514 nm and 257 nm wavelengths by inserting an amplitude mask in the symmetry plane of the pulse stretcher to achieve longitudinal shaping and an aperture for transverse beam shaping. Using this scheme, transversely and longitudinally truncated Gaussian pulses can be generated and later used for the production of up to 3 nC electron bunches in the photoinjector. The 3D pulse shape at a wavelength of 514 nm is characterized via imaging spectroscopy, and second-harmonic generation frequency-resolved optical gating (SHG FROG) measurements are also performed to analyze the shaping scheme’s efficacy. Furthermore, this pulse-shaping scheme is transferred to a UV stretcher, allowing for direct application of the shaped pulses to cesium telluride photocathodes. Full article
(This article belongs to the Special Issue Photonics: 10th Anniversary)
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17 pages, 6128 KiB  
Article
Beam Shape Control System with Cylindrical Lens Optics for Optical Wireless Power Transmission
by Kenta Moriyama, Kaoru Asaba and Tomoyuki Miyamoto
Energies 2025, 18(9), 2310; https://doi.org/10.3390/en18092310 - 30 Apr 2025
Viewed by 535
Abstract
Due to its narrow divergence, optical wireless power transmission (OWPT) is promising for long-distance transmission systems. In OWPT systems, matching the beam shape with the solar cell geometry is crucial for both efficiency and safety. When the light is incident at an oblique [...] Read more.
Due to its narrow divergence, optical wireless power transmission (OWPT) is promising for long-distance transmission systems. In OWPT systems, matching the beam shape with the solar cell geometry is crucial for both efficiency and safety. When the light is incident at an oblique angle, the beam is distorted in an axial direction, which requires appropriate beam shape control. In this study, a cylindrical lens system was designed to ensure uniform and effective light beam irradiation, even under oblique incidence conditions. A numerical model of the optical system was constructed, and it was experimentally confirmed that the beam shape could be controlled within 5% error over a transmission range of 1 m. The optical system was integrated with solar cell detection for consistent target recognition and beam irradiation, and its functionality was experimentally validated. The results are useful for expanding the application and infrastructure design in OWPT. Full article
(This article belongs to the Special Issue Energy, Electrical and Power Engineering: 4th Edition)
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11 pages, 3893 KiB  
Article
Wavefront Characterization of an Optical Parametric Oscillator as a Function of Wavelength
by Juan M. Bueno
Photonics 2025, 12(4), 347; https://doi.org/10.3390/photonics12040347 - 8 Apr 2025
Viewed by 446
Abstract
The wavefront aberrations (WAs) of a laser beam produced by an optical parametric oscillator (OPO) have been measured using a Hartmann–Shack sensor. The OPO tuning operation requires changes in the device that might affect the shape of the wavefront beam as the illumination [...] Read more.
The wavefront aberrations (WAs) of a laser beam produced by an optical parametric oscillator (OPO) have been measured using a Hartmann–Shack sensor. The OPO tuning operation requires changes in the device that might affect the shape of the wavefront beam as the illumination wavelength is being modified. Different output wavelengths in the range 550–850 nm were systematically analyzed in terms of WAs. The WA laser beam was fairly stable with time (changes of about 1%), independently of the wavelength. Moreover, WAs were non-negligible and nearly constant between 600 and 800 nm, but they noticeably increased for 550 (~90%) and 850 nm (~50%), mainly due to a higher astigmatism influence. The contributions of other higher-order terms such as coma and spherical aberration also present particular spectral dependences. To our knowledge, this is the first report of a spectral OPO laser beam characterization in terms of optical aberrations. It addresses a gap in OPO laser characterization of WAs and offers actionable insights for multi-wavelength applications. These results might be useful in applications ranging from micromachining procedures to biomedical imaging, where an optimized focal spot is required to increase the efficiency of certain physical phenomena or to enhance the quality of the acquired images. Full article
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33 pages, 12750 KiB  
Article
Experimental Study on Fiber Optic Strain Characterization of Overlying Rock Layer Movement Forms and States Using DFOS
by Tao Hu, Fengjun Wei, Jintao Wang, Yan Wang, Chunhua Song, Kuiliang Han and Kaiqiang Han
Photonics 2025, 12(4), 321; https://doi.org/10.3390/photonics12040321 - 30 Mar 2025
Viewed by 482
Abstract
Mastering the movement laws of hard overlying rock layers is the foundation of the development of coal mining technology and plays an important role in improving coal mine safety production. Therefore, an indoor similar simulation experiment was conducted based on an actual coal [...] Read more.
Mastering the movement laws of hard overlying rock layers is the foundation of the development of coal mining technology and plays an important role in improving coal mine safety production. Therefore, an indoor similar simulation experiment was conducted based on an actual coal mining face to test the strain variations of the pre-embedded optical fibers in the model using distributed fiber optic sensing. Finally, the fiber optic strain distribution curve was used to characterize the movement form and state of the overlying rock layer and fractured rock blocks. The experimental results showed the following. (1) The strain distribution of horizontally laid optical fibers is characterized by an upward trapezoidal convex platform, reflecting the evolution law of various horizontal movement forms of overlying rock layers: voussoir beam → cantilever beam → reverse cantilever beam → voussoir beam. The strain curve of vertically laid optical fibers is characterized by two levels of right-handed trapezoidal protrusions above and below, representing the motion state of the upper voussoir beam–lower cantilever beam structure of the overburden. (2) In addition, as excavation progresses, the range and height of the failure deformation of the overlying rock layers develop in a stepped shape. (3) In the end, the final vertical development heights of the cantilever beam structure and the voussoir beam structure in the overburden were 90.27 m and 24.99 m, respectively. The experimental results are highly consistent with the UDEC numerical simulation and mandatory calculation formulas, thus verifying the feasibility of the experiment. These research results provide theoretical and experimental support for safe coal mining in practical working faces. Full article
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