Planar Media Research Articles

Escape Probability and Average Numbers of Photon Scattering Events. II. Monochromatic Isotropic Scattering in a One-Dimensional Medium and Plane Media

Escape Probability and Average Numbers of Photon Scattering Events. II. Monochromatic Isotropic Scattering in a One-Dimensional Medium and Plane Media

Surface plasmon polariton excitation and propagation in metal tripod systems

Through the activation of a planar gaseous medium consisting of four-level tripod atoms, our approach provides a mechanism to generate the Surface Plasmon Polariton (SPP). We investigate a three-layer structure in which the bottom layer is composed of atoms arranged in a tripod configuration, a metal film is layered in the middle, and a transparent layer of either air or vacuum resides on top. The bottom layer facilitates SPP excitation via amplification in the atom arrangement, caused by three laser beams: control, weak probe, and signal. The electromagnetically induced transparency effect, which can be seen in atoms, compensates for the momentum difference between light and SPP. We can coherently change SPP propagation length by altering control field strength, resonance, and off-resonant detuning. SPP optical gain power, propagation length, penetration depth, and metal thickness effects are also examined. Our method to generate SPPs may find use in lithography, sensors, polarizers, along with photodetectors.

Bilateral Symmetric non-Euclidean multi-frequency invisibility

Light propagation in non-Euclidean geometry has become a hot topic in recent years, while transformation optics theory demonstrates unique advantages in this respect. A notable application of transformation optics in non-Euclidean space is non-Euclidean invisibility cloak which avoids the challenges of negative refraction and anisotropic materials. In this work, we propose another configuration for non-Euclidean invisibility, capable of achieving invisible across a wide spectrum. Using coordinate transformation, we convert this non-Euclidean invisibility into planar gradient medium and validate its effects through full wave simulations. We also discover that the corresponding gradient medium can further relax the material parameters. Our findings suggest diverse strategies for non-Euclidean invisibility and planar gradient media, potentially advancing optical invisibility and transformation optics in non-Euclidean spaces.

Analytical method of mutual inductance for T-R rectangular coils perpendicular to the planar medium

Some studies indicate that for specific defect detection in eddy current testing (ECT), the transmitter-receiver (T-R) probe models with tangential rectangular transmitter coil exhibit effective detection performance. In this context, mutual inductance being a crucial parameter. The calculation of mutual inductance for vertically oriented T-R coils is more intricate compared to that of parallel T-R coils, which is currently predominantly focused on circular mutual inductance analysis. This paper presents a closed-form formula for the mutual inductance of rectangular T-R coils oriented vertically to the conductor based on the method of the second-order vector potential approach. In this model, a form function concerning the coil's position and shape is defined, allowing convenient extension to T-R coils of arbitrary shapes and positions. Simultaneously, the validity of the theory is tested against experimental measurements on different positions and frequencies of coil systems above an aluminum plate. The results indicate good agreement between theoretical and experimental results within the 100 Hz to 100 kHz range. Consequently, this model can offer guidance for the calculation of mutual inductance for vertically oriented rectangular T-R coils in ECT.

About Measuring the Stress Intensity Factor of Cracks in Curved, Brittle Shells

Most techniques of measuring the stress intensity factor (SIF) in the cracking process assume a crack in a planar medium. Currently, there is no effective approach for curved brittle shells, particularly for non-developable cases, i.e., shapes with non-vanishing Gaussian curvature. This paper introduces a novel approach to obtaining material properties related to fracture by experimentally observing weakly curved surfaces. Based on the DIC record of the displacement field around the crack tip, the truncated Williams expansion is fitted to the data adjusted according to the shallow shell equations. The convergence properties of the method are investigated by comparing experimental data of PMMA cylinders to theoretical and numerical predictions. The applicability of the technique to non-developable surfaces is verified. It is demonstrated that robust convergence requires the number of terms in the Williams expansion exceeding 6. For different geometries, the ratio of the data selection radius and the length of the crack should exceed 0.3.

Asymmetric 1D and 2D tunneling induced grating in Quantum Dot system

We propose a tunneling-induced grating based on the phenomenon of tunneling-induced transparency. Our method allows us to alternate between zeroth-order diffraction along with completely different higher-order diffraction patterns. This is accomplished by using four laser beams to drive quantum dots via a planar configuration. Specifically, we modulate a standing waves controlling beam which propagates orthogonal with the planar medium, while weaker planar probing beam, generated signal field, and pumping field are applied adjacent towards the medium. We quantitatively analyzed the dynamics for the phase, amplitude modulations, along with probing fields diffraction strengths of various ordering. By altering the relative phase of fields, we expect asymmetric 1D and 2D tunneling induced grating in quantum dot system. Our suggested approach has significant uses in optical memory systems, notably in the storing of information to diffraction orders via tunneling-induced grating.

A refractive three-dimensional reconstruction method for fringe projection with a planar medium

In special measurement situations, a vision measurement system needs to measure objects through a viewing observation window made of a planar transparent medium. The refraction at the interface between a medium and air leads to large measurement errors in the pin-hole imaging model. Most existing solutions require complex processes of calculating refracted light equations and/or matching stereo images. Here, we propose a refractive three-dimensional (3D) reconstruction method for fringe projection with a planar medium. We derive a coordinate conversion relationship from a pseudo-object point caused by light refraction to a real-object point based on flat refractive geometry. Then, we integrate the relationship into regular fringe projection framework for unbiased 3D reconstruction. Two experiments, including 3D shape measurements of a step and a regular sphere are performed. The results verify the effectiveness and accuracy of the proposed refractive 3D reconstruction method.

Effect of composite vortex beam on a two-dimensional gain assisted atomic grating

We propose an atomic grating based on an electromagnetically induced transparency phenomenon that switches between zeroth-order diffraction to a distinct higher-order diffraction pattern by driving a planar gaseous medium of a four-level tripod () atoms with three laser beams: modulation of standing wave control beam propagating nearly perpendicular to the planar medium, while vortex and weak plane probe beams directed perpendicular to the medium. We numerically investigate the behavior of the amplitude, phase modulations, and probe field diffraction intensities of different orders by the variation of the field detunings and orbital angular momentum number of the composite vortex light beam. Specifically, in the off-resonant case, the interplay between a square lattice of the control and an additional spatial variation of the vortex beam allows the emergence of higher diffraction orders and variable gain due to double transparency windows in this complex optical system. We believe that our proposed scheme might be useful in optical memory devices via the storage of information to diffraction orders of the atomic grating.

Piston driven shock waves in non-homogeneous planar media

In this work, we analyze in detail the problem of piston driven shock waves in planar media. Similarity solutions to the compressible hydrodynamics equations are developed, for a strong shock wave, generated by a time dependent pressure piston, propagating in a non-homogeneous planar medium consisting of an ideal gas. Power law temporal and spatial dependency is assumed for the piston pressure and initial medium density, respectively. The similarity solutions are written in both Lagrangian and Eulerian coordinates. It is shown that the solutions take various qualitatively different forms according to the value of the pressure and density exponents. We show that there exist different families of solutions, for which the shock propagates at a constant speed, accelerates, or slows down. Similarly, we show that there exist different types of solutions, for which the density near the piston is either finite, vanishes, or diverges. Finally, we perform a comprehensive comparison between the planar shock solutions and Lagrangian hydrodynamic simulations, by setting proper initial and boundary conditions. A very good agreement is reached, which demonstrates the usefulness of the analytic solutions as a code verification test problem.

Theoretical analysis of photoacoustic effects in a multilayered skin tissue model

Due to its noninvasiveness, high resolution, and high sensitivity, photoacoustic imaging has developed rapidly in the field of biomedicine. However, research on dermatosis detection by photoacoustic imaging is still lacking. In this paper, the skin is modeled as a multilayer planar medium based on the non-homogeneous, complex layered structure of the skin tissue. Then, the analytical expression for the photoacoustic signal of multilayer skin tissue was derived under the assumption that the thermal and optical parameters of the skin tissue do not vary with temperature. The expression not only considers the influence of optical, thermal, and mechanical parameters of the tissue on the photoacoustic signal but also, for the first time, the influence of the number of skin layers on the photoacoustic signal. The analytical expression of the photoacoustic signal containing the number of skin layers is also given. The numerical simulation results show that the difference between the photoacoustic signal of the seven-layer skin model and the single-layer skin model is 15.206 × 10−6 MPa when ω = 3.5 MHz and μa = 2.70 cm−1. Therefore, the increase in the number of model layers enhances the amplitude of its photoacoustic signal. This work provides a comprehensive study of photoacoustic mechanisms in dermatosis tissues and establishes a theoretical foundation for the application of photoacoustic imaging detection technology in the diagnosis and treatment of dermatosis, which may improve treatment plans.

A novel model for calculating the impedance of arbitrarily-shaped coils with perpendicular to the planar medium

Some studies have shown that coils placed perpendicular to conductors have excellent detection effect for specific defects in eddy-current testing (ECT), where the impedance is an important parameter. The impedance calculation for perpendicular coil is more complex than that for parallel coil, and currently the main focus is on the impedance analysis of circular and rectangular coils. In this paper, a closed formula for the impedance of a coil with arbitrary-shape perpendicular to the conductor is given based on the second order vector position method. In the proposed model, a novel shape and position function is defined to extend the coil application to arbitrary cross-sectional shapes. Meanwhile, experimental comparisons are conducted to evaluate the impedance of various coils on an aluminum plate. The results illustrated that the experimental values are in perfect agreement with the calculated ones. Therefore, the proposed model can provide guidance for the impedance calculation of arbitrarily-shaped coils in eddy current testing.

Sustainable Development Trend of Chinese Advertising Design from 1992 to 2020: A Bibliometric and Content Analysis

By using the methods of bibliometric and content analysis, this paper conducted data mining and content research on the articles of advertising design research in China from 1992 to 2020 and analyzed the evolution context, hotspots, and sustainable development trends of advertising design research in recent 30 years. It was found that advertising design research has experienced four stages: embryonic, exploration, prosperous, integration and innovation. It mainly focused on four hotspots: collaborative research on relevant factors of advertising design, research on advertising design centered on plane media, renewal of concept and method of advertising design education, and research on advertising design and communication in the new media environment. This paper analyzed and predicted five future sustainable research directions: research on the profound transformation of advertising media in the digital age, research on nationalization theory and localization practice of advertising design, international academic dialog in the field of advertising design, research on advertising design education under the background of interdisciplinary, and sustainable social value innovation.

Compton Scattering in Plane Media: Polarization of Radiation and Azimuthal Independence. II. Results of Calculations

Compton Scattering in Plane Media: Polarization of Radiation and Azimuthal Independence. II. Results of Calculations

Compton Scattering in Plane Media: Polarization of Radiation and Azimuth Independence. I. Theory

Compton Scattering in Plane Media: Polarization of Radiation and Azimuth Independence. I. Theory

A Hybrid Loop-Tree FEBI Method for Low-Frequency Well Logging of 3-D Structures in Layered Media

Electromagnetic simulation plays an essential role in formation conductivity determination by electromagnetic well-logging tools, especially when the nonvertical borehole and invasion zones are present in a layered earth. A hybrid finite-element boundary integral (FEBI) method is suitable for such well-logging simulations. The usage of layered medium Green's functions allows the simulation background to be a planar stratified medium to characterize the earth formation. However, conventional FEBI using the Rao-Wilton-Glisson (RWG) basis function produces inaccurate results due to the low-frequency breakdown of the boundary integral equation solution. The new contribution of this work is to apply the loop-tree (LT) basis functions in the FEBI method to reduce the numerical error at low frequencies. Such an LT-FEBI method can handle all specific requirements of well-logging simulations at low frequencies. A direct solver is applied to make it more efficient to obtain logging curves with multiple source locations. The LT-FEBI simulation results are validated in several numerical examples, including a challenging well-logging model with a deviated borehole and invasion zones in the Oklahoma formation having 28 layers.

Luminescence of Ti-Sapphire coatings prepared by plasma electrolytic oxidation and their application in temperature sensing

15 µm thick Ti-Sapphire coatings were synthesised at room temperature by the plasma electrolytic oxidation (PEO) method for 20 min from the pure aluminium substrate and with the addition of the TiO2 particles in various concentrations in the supporting electrolyte. The coatings are featured by microscopic pores typical for PEO surfaces. The dominant is the alpha phase of alumina with the small presence of the gamma phase. The estimated average crystalline size is 41 nm. Ti is uniformly distributed in these polycrystalline ceramic coatings and does not affect morphology or phase content. Photoluminescence of PEO-created coatings shows typical absorption, excitation, and emission features of Ti-Sapphire with two broad-overlapping excitation bands in the green and blue spectral region due to the Jahn-Teller splitting of the 2Eg level and the Stokes shifted emission centred at 720 nm. 2Eg energy state splitting is equal to 2195 cm−1 and 10 Dq ≈ 19,300 cm−1. The highest emission intensity was observed in the coating prepared with the 0.1 g/L TiO2 powder concentration, i.e. 0.32 at% of incorporated Ti3+. Emission spectra recorded at temperatures ranging from 100 K to 300 K revealed the Mott-Seitz temperature dependence of emission intensity with the 1180 cm−1 activation energy. The fit to the McCumber-Sturge relation gave, for the first time, the value of Debye temperature of 594 K of Al2O3:Ti. Non-contact, luminescence temperature sensing from the temperature-induced changes in the emission bandwidth gave a high sensitivity of 3.2 cm−1 K−1 and 0.19 K temperature resolution. The PEO created Ti-sapphire coatings are a promising multifunctional barrier level – optical temperature sensor material for applications in harsh environments or on large aluminium surfaces. It shows potential to be used as a planar waveguide Ti-Sapphire laser active medium.

On modelling of thermodynamic interaction of particles suspended in two-dimensional medium

Analytical description of temperature distribution in a medium with foreign inclusions is difficult due to the complicated geometry of the problem, so asymptotic and numerical methods are usually used to model thermodynamic processes in heterogeneous media. To be convinced in convergence of these methods the authors consider model problem about two identical round particles in infinite planar medium with temperature gradient which is constant at infinity. Authors refine multipole expansion of the solution obtained earlier by continuing it up to higher powers of small parameter, that is nondimensional radius of thermodynamically interacting particles. Numerical approach to the problem using ANSYS software is described; in particular, appropriate choice of approximate boundary conditions is discussed. Authors ascertain that replacement of infinite medium by finite-sized domain is important source of error in FEM. To find domain boundaries in multiple inclusions’ problem the authors develop “fictituous particle” method; according to it the cloud of particles far from the center of the cloud acts approximately as a single equivalent particle of greater size and so may be replaced by it. Basing on particular quantitative data the dependence of domain size that provides acceptable accuracy on thermal conductivities of medium and of particles is explored. Authors establish series of numerical experiments confirming convergence of multipole expansions method and FEM as well; proximity of their results is illustrated, too.

Green’s Functions of Multi-Layered Plane Media with Arbitrary Boundary Conditions and Its Application on the Analysis of the Meander Line Slow-Wave Structure

A method was proposed for solving the dyadic Green’s functions (DGF) and scalar Green’s functions (SGF) of multi-layered plane media in this paper. The DGF and SGF were expressed in matrix form, where the variables of the boundary conditions (BCs) can be separated in matrix form. The obtained DGF and SGF are in explicit form and suitable for arbitrary boundary conditions, owing to the matrix form expression and the separable variables of the BCs. The Green’s functions with typical BCs were obtained, and the dispersion characteristic of the meander line slow-wave structure (ML-SWS) is analyzed based on the proposed DGF. The relative error between the theoretical results and the simulated ones with different relative permittivity is under 3%, which demonstrates that the proposed DGF is suitable for electromagnetic analysis to complicated structure including the ML-SWS.

Efficient Electromagnetic Modeling of Multidomain Planar Layered Medium by Surface Integral Equation

A novel electromagnetic modeling method for multidomain planar layered medium (MD-PLM) by surface integral equation (SIE) is proposed. The MD-PLM refers to the whole space that is separated into multiple PLM volumes, e.g., the infinite-sized PLM background with inserted finite PLM objects or multilayered parallel-plate structures. In the conventional SIE method for this scenario, only the exterior domain is considered as PLM that is modeled by layered medium Green's functions (LMGFs), while the interior domain is treated by the multidomain homogeneous SIE. However, in this work, the surface equivalence formulation for this special scenario is reestablished by the LMGFs. Then, both the exterior and interior domains are considered as PLM that is modeled by the corresponding LMGFs and SIE in each subdomain. As a result, only the boundary of each sub-PLM domain is required to be discretized rather than the interfaces of each interior medium, which is different from the way in conventional SIE. Consequently, compared with the conventional SIEs, the proposed method can reduce a large quantity of unknowns and significantly increase the efficiency by reducing the memory consumption. By some numerical examples, the performance of this method is evaluated and compared with the conventional methods. The validity and efficiency of the newly proposed method are also well demonstrated in the examples.

Supersymmetry, half-bound states, and grazing incidence reflection

Electromagnetic waves at grazing incidence onto a planar medium are analogous to zero energy quantum particles incident onto a potential well. In this limit waves are typically completely reflected. Here we explore dielectric profiles supporting optical analogues of ‘half–bound states’, allowing for zero reflection at grazing incidence. To obtain these profiles we use two different theoretical approaches: supersymmetric quantum mechanics, and direct inversion of the Helmholtz equation, showing that discretized approximations to these profiles exhibit low reflectivity close to grazing incidence.