A calculation model to assess the crack propagation length of rock block in clastic flow

The primary cracks in the rock block undergo series of steps and finally disintegrate,during this procession,the radius affects the impact force of rock block in clastic flow.Therefore,it is essential to figure out the evolution mechanism of crack propagation for the design of engineering protection.In this study,based on fracture mechanics and Hertz contact theory,collision happened between rock block and slope surface is assumed to be elastic contact.Based on the above assumption,the critical impact force of crack propagation is obtained,and a model used to calculate the crack propagation length in a single collision is established.Besides,a rock fall site in Jiuzhai Valley was used to verify the calculation model.According to the model,several key factors were identified to influence crack propagation length including falling height,initial equivalent radius,and recovery coefficient of slope surface.Moreover,as a result of the orthogonal experiment,the influence of those factors on the crack propagation length was ranked,normal recovery coefficient>initial radius>initial falling height.In addition,the kinetic energy of the rock block in the compression stage is transformed into elastic deformation energy,angular kinetic energy,and dissipated energy of crack propagation.Due to the increase of collisions,the kinetic energy is gradually transformed into angular kinetic energy,and the dissipated energy of crack propagation weights is reduced.In conclusion,the crack propagation in rock block is a complicated progress,which is affected by multiple factors,especially falling height,initial equivalent radius,and recovery coefficient of slope surface.Our study may provide guidance for the design of protective structure of clastic flows.

Propagation of surface magnetoplasmon polaritons in a symmetric waveguide with two-dimensional electron gas

The properties of surface magnetoplasmon polaritons(SMPPs)in a symmetric structure,composed of two semi-infinite regions of high-density two-dimensional electron gas(2DEG)separated by a thin film in Voigt configuration,are investigated.The normal and absorption dispersion relations for the transverse magnetic polarization are derived by correlating Maxwell’s equation and the boundary conditions.It is demonstrated that the features of SMPPs are greatly influenced by the external magnetic field,collision frequency of 2DEG,the dielectric constant,and the thickness of the thin film,suggesting that the locations and propagation lengths of SMPPs can be governed accordingly.It is shown that the symmetry of the physical geometry preserves the symmetry of the dispersion relations of SMPPs.Furthermore,it is discovered that as the external magnetic field increases,the penetration depth of SMPPs decreases,while their energy loss reduces,implying that plasmons can propagate for longer distances.Additionally,it is observed that SMPPs in the symmetric configuration have a longer lifetime than those in the asymmetric configuration.

Long-range surface plasmon polaritons with subwavelength mode expansion in an asymmetrical system

Long-range surface plasmon polariton （LRSPP） modes in an asymmetrical system, in which the thin metal film is sandwiched between a semi-infinite substrate and a high permittivity polymer film with a finite thickness, are theoret~ ically calculated and analyzed. Due to the high permittivity of the polymer film, at proper polymer film thicknesses, the index-matching condition of the dielectrics at both sides of the metal can be satisfied for supporting LRSPP modes, and the electromagnetic field above the metal can be localized well. It is found that these LRSPP modes have both long propagation lengths and subwavelength mode expansion above the metal at the optimal polymer film thickncsses. Furthermore, the requirements on the refractive index and the thickness of the polymer film to support LRSPP modes at the optimal thicknesses are found to be not critical.

Quantitative relationship between the maximum streamer length and discharge voltage of a pulsed positive streamer discharge in water

A linear relationship has been realized between the maximum streamer length and discharge voltage of a pulsed positive streamer discharge by measuring the streamer length in water with conductivity of 100 μS cm-1using high-speed photography. Based on Ohm＇s law, a quantitative equation has been derived for the dependence of the maximum streamer length on the discharge voltage of a pulsed positive streamer discharge in water. According to the equation, our results suggest that the streamers spontaneously stop propagating through water due to the voltage at the streamer head dropping below the ignition voltage of a pulsed positive streamer discharge.

Sensitivity Dependence of Surface Plasmon Resonance Based Sensors on Prism Refractive Index

We theoretically and experimentally demonstrate that refractive index of the prism used to load metal film has significant influence on sensitivity of surface plasmon resonance based sensors. The prism with lower refractive index gives the sensors a higher sensitivity in detecting refractive index variations of a sample. We attribute this effect to the fact that a prism with low refractive index will increase coupling distance between surface plasmons and the medium under investigation.

Hybrid plasmon waveguides with metamaterial substrate and dielectric substrate:A contrastive study

Hybrid plasmon waveguides, respectively, with metamaterial substrate and dielectric substrate are investigated and analyzed contrastively with a numerical finite element method. Basic properties, including propagation length Lp, effective mode area Aeff, and energy distribution, are obtained and compared with waveguide geometric parameters at 1.55 gin. For the waveguide with metamaterial substrate, propagation length Lp increases to several tens of microns and effective mode area Aeff is reduced by more than 3 times. Moreover, the near field region is expanded, leading to potential applications in nanophotonics. Therefore, it could be very helpful for improving the integration density in optical chips and developing functional components on a nanometer scale for all optical integrated circuits.

Surface plasmon polaritons in plasma-dielectric-magnetic plasma structure

The properties of surface plasmon polaritons(SPPs) excited in the plasma-dielectric-magnetic plasma structure are investigated theoretically. Both the normal and the absorbing dispersion relations of SPPs are derived and presented for transverse-magnetic polarization. The influences of the external magnetic field, collision frequency of plasma, background material dielectric constant,and thickness on the characteristics of SPPs are explored and discussed. Results show that these factors greatly alter the properties of SPPs. The results imply that the locations and propagation length of SPPs can be tuned. In addition, the results also show that a one-way dispersion relation of SPPs can be realized in the low-frequency regions when the external magnetic field is introduced.

Decoupling co-existing surface plasmon polariton （SPP） modes in a nanowire plasmonic waveguide for quantitative mode analysis

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 photo- detectors. 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-distance- dependent 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 develop- ment and optimization of SPP-based applications.