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Quasi-line waves represent a distinct class of propagation modes along non-complementary impedance surfaces, offering an alternative to the conventional line waves typically formed by complementary impedance surfaces. In this study, we introduce a novel design for quasi-line waves utilizing non-dual, purely inductive impedance structures. By incorporating multilayer graphene, our design achieves wide bandwidth and extended propagation lengths in the terahertz range, with field concentration localized at the edges of the inductive surfaces. This configuration enables unidirectional wave propagation, with graphene integration providing precise control over bandwidth and transmission characteristics. Unlike traditional line waves, which are constrained to specific terahertz frequency ranges, our quasi-line mode—guided by self-inductive impedance surfaces—demonstrates significantly broader bandwidth and enhanced electric field intensity. The performance of this mode is strongly influenced by capacitance variations between impedance surfaces, exceeding the singularity limitation of conventional line waves. Our proposed structure demonstrates superior performance in both bandwidth and mode singularity within the terahertz spectrum, surpassing traditional line wave designs.

Predicting the critical crack propagation length (CCPL) of sustainable additive-enhanced concrete (SAEC) is a significant challenge in structural durability analysis and fracture mechanics. Experimental and numerical techniques often face limitations of complexity, cost, and computational inefficiency. To overcome these limitations, this paper presents a comprehensive machine learning framework that integrates ensemble, kernel-based, and deep learning models. A high-quality experimental dataset of 800 SAEC samples, incorporating nine key features and controlled curing, mixing, and fracture testing, was prepared. Model performance was evaluated using different statistical indices under both hold-out and k-fold cross-validation. Among all the machine learning models, the novel Neural Tangent Kernel Gaussian Process (NTK–GP) achieved the best predictive performance with R 2  = 0.95‒0.96, RMSE = 0.74‒0.90 mm, MAPE = 0.09‒0.14, and VAF = 0.95‒0.96. The NTK–GP’s hybrid architecture, which unites the flexibility of neural representations with Bayesian uncertainty quantification, enabled accurate, smooth, and stable predictions even under nonlinear, high-dimensional data. Statistical significance tests, such as the Friedman and Nemenyi tests, confirmed that the NTK-GP is statistically comparable to several state-of-the-art models. Explainable AI analysis using SHAP revealed that fiber type (FT) and fiber volume content (FVC) are the most influential features, accounting for over 65% of the model’s variance in CCPL. SHAP interaction and dependency plots showed strong combined influences between FT and FVC, especially with steel and basalt fibers at higher volumes. This supports the idea that these fibers bridge cracks and dissipate energy. Bootstrap-based 95% confidence intervals were applied for uncertainty quantification, confirming the predictive reliability by showing consistent coverage across the dataset. This study pioneers the use of NTK–GP for fracture mechanics. It demonstrates that integrating explainable machine learning with uncertainty-aware regression provides a data-efficient, robust, and interpretable alternative to experimental and numerical methods. The proposed framework not only enhances CCPL prediction accuracy and computational efficiency but also contributes to the broader goal of designing sustainable, fracture-resistant concrete materials through intelligent and data-driven modeling.

A modulator is the core of many optoelectronic applications such as communication and sensing. However, a traditional modulator can hardly reach high modulation depth. In order to achieve the higher modulation depth, a graphene electro-optical switch modulator is proposed by adjusting propagation length in the near infrared band. The switch modulator is designed based on a hybrid plasmonic waveguide structure, which is comprised of an SiO2 substrate, graphene–Si–graphene heterostructure, Ag nanowire and SiO2 cladding. The propagation length of the hybrid plasmonic waveguide varies from 0.14 μm to 20.43 μm by the voltage tunability of graphene in 1550 nm incident light. A modulator with a length of 3 μm is designed based on the hybrid waveguide and it achieves about 100% modulation depth. The lower energy loss (~1.71 fJ/bit) and larger 3 dB bandwidth (~83.91 GHz) are attractive for its application in a photoelectric integration field. In addition, the excellent robustness (error of modulation effects lower than 8.84%) is practical in the fabrication process. Most importantly, by using the method of adjusting propagation length, other types of graphene modulators can also achieve about 100% modulation depth.

We investigate surface plasmon polaritons (SPPs) modes in palladium (Pd)-coated silver double nanowires by using the finite difference time domain (FDTD) method. Since Pd can absorb hydrogen (H 2 ) and converts to Pd-H, its permittivity is completely different from that of Pd-H, so the optical response of the system will be also change. The results of electric field distributions and propagation lengths of seven modes of the designed structure are obtained by calculations. For different modes, it is found that the propagation length increases with the increase of mode order. The propagation lengths of the same mode in the structure of Pd and Pd-H are respectively compared, and it is discovered that it is also different due to the change of dielectric constant before and after H 2 absorption. The results show that in the double nanowire structure, the propagation lengths of structures with Pd are larger than the ones of structures with Pd-H for each mode. The distance of the two nanowires impacts on the coupling between the two nanowires. By changing the radius of Ag nanowire, the propagation lengths of the fundamental mode increase, while the ones of the harmonic modes decrease. There is an optimal thickness to make the propagation length longest for each mode by changing the thickness of Pd, which shows the competition between the dissipation of the structure and the coupling between SPPs in different layers. The structure we designed can be applied to the direction of the hydrogen sensor to realize the monitoring of its state when using hydrogen energy to ensure safety.

Knowledge of surface plasmon polariton (SPP) modes in one-dimensional (1D) metallic nanostructures is essential for the development of subwavelength optical devices such as photonic circuits, integrated light sources, and photodetectors. Despite many efforts to characterize the propagation parameters of these subwavelength 1D plasmonic waveguides, such as Ag nanowires, large discrepancies exist among available reports owing to their sensitivity to the relative weights of co-existing SPP modes and the lack of a method of decoupling these modes and analyzing them separately. In this work, we develop an interference method to distinguish different SPP modes that are simultaneously excited in a Ag nanowire waveguide and measure their propagation parameters separately. By extracting information from the propagation-distancedependent intensity oscillations of the scattered light from the nanowire tip, the effective refractive indices, propagation lengths, and relative mode weights of co-existing SPP modes supported by the nanowire are derived from a mode interference model. These parameters depend strongly on the nanowire diameter and excitation wavelength. In particular, we demonstrate the possibility of selective excitation of different SPP modes by varying the nanowire diameter. This new mode analysis technique provides unique insights into the development and optimization of SPP-based applications.

Metallic nanoscale structures are capable of supporting surface plasmon polaritons (SPPs), propagating collective electron oscillations with tight spatial confinement at the metal surface. SPPs represent one of the most promising structures to beat the diffraction limit imposed by conventional dielectric optics. Ag nano wires have drawn increasing research attention due to 2D sub-100 nm mode confinement and lower losses as compared with fabricated metal structures. However, rational and versatile integration of Ag nanowires with other active and passive optical components, as well as Ag nanowire based optical routing networks, has yet to be achieved. Here, we demonstrate that SPPs can be excited simply by contacting a silver nanowire with a SnO₂ nanoribbon that serves both as an unpolarized light source and a dielectric waveguide. The efficient coupling makes it possible to measure the propagation-distance-dependent waveguide spectra and frequency-dependent propagation length on a single Ag nanowire. Furthermore, we have demonstrated prototypical photonic-plasmonic routing devices, which are essential for incorporating low-loss Ag nanowire waveguides as practical components into high-capacity photonic circuits.

Waveguide gratings are used for applications such as guided-mode resonance filters and fiber-to-chip couplers. A waveguide grating typically consists of a stack of a single-mode slab waveguide and a grating. The filling factor of the grating with respect to the mode intensity profile can be altered via changing the waveguide’s refractive index. As a result, the propagation length of the mode is slightly sensitive to refractive index changes. Here, we theoretically investigate whether this sensitivity can be increased by using alternative waveguide grating geometries. Using rigorous coupled-wave analysis (RCWA), the filling factors of the modes of waveguide gratings supporting more than one mode are simulated. It is observed that both long propagation lengths and large sensitivities with respect to refractive index changes can be achieved by using the intensity nodes of higher-order modes.

The development of the digital economy in the modern era significantly embodies a country’s comprehensive strength. This paper uses the data from China’s 2012 and 2017 input-output tables to analyze the linkage structure between the digital economy industry and other industries using the average propagation length model and social network analysis. The Weaver–Thomas model was used to obtain the industrial linkage matrix and network characteristics. An industrial chain map of the digital economy was depicted as the core. This paper is of practical significance in depicting the industrial chain structure and network characteristics, understanding the position of digital economy industry in the economic system and promoting the integrated development of the digital economy and traditional manufacturing industries, which allows them to incorporate the new generation of technology and industrial transformation with the digital technology as the core to promote their transformation and upgrading.

It is important to control grout propagation and ensure the engineering effectiveness of the advanced regional grouting process in the Middle Ordovician limestone (MOL) aquifer. In our study, we found that the physical and mechanical properties of cement grout are affected mainly by the water–cement ratio, followed by water glass content and finally by hydro-chemical type. In a horizontal grouting hole inclined single fracture, the grout spread over time depended on the water–cement ratio, grouting pressure, width of fracture and angle between fracture and grouting hole and the rate of spread increased over time. However, when the grout propagation length was hundreds of meters or more, the length in the fracture above the grouting hole was greater than that in the fracture below. The sensitivity sequence of influencing factors of grout propagation length in an inclined fracture of a horizontal grouting hole was as follows, from large to small: width of fracture, fracture angle, water–cement ratio, grouting pressure.