Trapezoid-Grid Finite-Difference Time-Domain Method for 3D Seismic Wavefield Modeling Using CPML Absorbing Boundary Condition

The large computational memory requirement is an important issue in 3D large-scale wave modeling, especially for GPU calculation. Based on the observation that wave propagation velocity tends to gradually increase with depth, we propose a 3D trapezoid-grid finite-difference time-domain (FDTD) method to achieve the reduction of memory usage without a significant increase of computational time or a decrease of modeling accuracy. It adopts the size-increasing trapezoid-grid mesh to fit the increasing trend of seismic wave velocity in depth, which can significantly reduce the oversampling in the high-velocity region. The trapezoid coordinate transformation is used to alleviate the difficulty of processing ununiform grids. We derive the 3D acoustic equation in the new trapezoid coordinate system and adopt the corresponding trapezoid-grid convolutional perfectly matched layer (CPML) absorbing boundary condition to eliminate the artificial boundary reflection. Stability analysis is given to generate stable modeling results. Numerical tests on the 3D homogenous model verify the effectiveness of our method and the trapezoid-grid CPML absorbing boundary condition, while numerical tests on the SEG/EAGE overthrust model indicate that for comparable computational time and accuracy, our method can achieve about 50% reduction on memory usage compared with those on the uniform-grid FDTD method.

From Time-Collocated to Leapfrog Fundamental Schemes for ADI and CDI FDTD Methods

The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence implicit (CDI) FDTD method. In this paper, the formulations from time-collocated to leapfrog fundamental schemes are presented for ADI and CDI FDTD methods. For the ADI FDTD method, the time-collocated fundamental schemes are implemented using implicit E-E and E-H update procedures, which comprise simple and concise right-hand sides (RHS) in their update equations. From the fundamental implicit E-H scheme, the leapfrog ADI FDTD method is formulated in conventional form, whose RHS are simplified into the leapfrog fundamental scheme with reduced operations and improved efficiency. For the CDI FDTD method, the time-collocated fundamental scheme is presented based on locally one-dimensional (LOD) FDTD method with complying divergence. The formulations from time-collocated to leapfrog schemes are provided, which result in the leapfrog fundamental scheme for CDI FDTD method. Based on their fundamental forms, further insights are given into the relations of leapfrog fundamental schemes for ADI and CDI FDTD methods. The time-collocated fundamental schemes require considerably fewer operations than all conventional ADI, LOD and leapfrog ADI FDTD methods, while the leapfrog fundamental schemes for ADI and CDI FDTD methods constitute the most efficient implicit FDTD schemes to date.

Independently tunable dual resonant dip refractive index sensor based on metal-insulator-metal waveguide with Q-shaped resonant cavity

A plasmonic resonator system consisting of a metal-insulator-metal waveguide and a Q-shaped resonant cavity is proposed in this paper. The transmission properties of surface plasmon polaritons in this structure are investigated using the finite difference in time domain (FDTD) method, and the simulation results contain two resonant dips. And the physical mechanism is studied by the multimode interference coupled mode theory (MICMT), the theoretical results are in highly consistent with the simulation results. Furthermore, the parameters of the Q-shaped cavity can be controlled to adjust two dips respectively. The refractive index sensor with a sensitivity of 1578nm/RIU and figure of merit (FOM) of 175, performs better than most of the similar structures. Therefore, the results of the study are instructive for the design and application of high sensitivity nanoscale refractive index sensors.

Q-BOR–FDTD method for solving Schrodinger equation for rotationally symmetric nanostructures with hydrogenic impurity

An efficient method inspired by the traditional body of revolution finite-difference time-domain (BOR-FDTD) method is developed to solve the Schrodinger equation for rotationally symmetric problems. As test cases, spherical, cylindrical, cone-like quantum dots, harmonic oscillator, and spherical quantum dot with hydrogenic impurity are investigated to check the efficiency of the proposed method which we coin as Quantum BOR-FDTD (Q-BOR-FDTD) method. The obtained results are analysed and compared to the 3-D FDTD method, and the analytical solutions. Q-BOR-FDTD method proves to be very accurate and time and memory efficient by reducing a three-dimensional problem to a two-dimensional one, therefore one can employ very fine meshes to get very precise results. Moreover, it can be exploited to solve problems including hydrogenic impurities which is not an easy task in the traditional FDTD calculation due to singularity problem. To demonstrate its accuracy, we consider spherical and cone-like core-shell QD with hydrogenic impurity. Comparison with analytical solutions confirms that Q-BOR–FDTD method is very efficient and accurate for solving Schrodinger equation for problems with hydrogenic impurity

Quadruple plasmon-induced transparency and tunable multi-frequency switch in monolayer graphene terahertz metamaterial

A monolayer graphene metamaterial composed of a graphene block and four graphene strips, which has the metal-like properties in terahertz frequency range, is proposed to generate an outstanding quadruple plasmon-induced transparency (PIT). Additional analyses show that the forming physical mechanism of the PIT with four transparency windows can be explained by strong destructive interference between the bright mode and the dark mode, and the distributions of electric field intensity and electric field vectors under the irradiation of the incident light. Coupled mode theory (CMT) and finite-difference time-domain (FDTD) method are employed to study the spectral response characteristics of the proposed structure, and the theoretical and simulated results are in good agreement. It is found that a tunable multi-frequency switch and excellent optical storage can be achieved in the wide PIT window. The maximum modulation depth is up to 99.7%, which corresponds to the maximum extinction ratio of 25.04 dB and the minimum insertion loss of 0.19 dB. In addition, the time delay is as high as 0.919 ps, the corresponding group refractive index is up to 2755. Thus, the proposed structure provides a new method for the design of terahertz multi-frequency switches and slow light devices.

Precise-Integration Time-Domain Formulation for Optical Periodic Media

A numerical formulation based on the precise-integration time-domain (PITD) method for simulating periodic media is extended for overcoming the Courant-Friedrich-Levy (CFL) limit on the time-step size in a finite-difference time-domain (FDTD) simulation. In this new method, the periodic boundary conditions are implemented, permitting the simulation of a wide range of periodic optical media, i.e., gratings, or thin-film filters. Furthermore, the complete tensorial derivation for the permittivity also allows simulating anisotropic periodic media. Numerical results demonstrate that PITD is reliable and even considering anisotropic media can be competitive compared to traditional FDTD solutions. Furthermore, the maximum allowable time-step size has been demonstrated to be much larger than that of the CFL limit of the FDTD method, being a valuable tool in cases in which the steady-state requires a large number of time-steps.

High Sensitivity Surface Plasmon Resonance Sensor Based on Periodic Multilayer Thin Films

Surface plasmon resonance (SPR) biosensors consisting of alternate layers of silver (Ag) and TiO2 thin film have been proposed as a high sensitivity biosensor. The structure not only prevents the Ag film from oxidation, but also enhances the field inside the structure, thereby improving the performance of the sensor. Genetic algorithm (GA) was used to optimize the proposed structure and its maximum angular sensitivity was 384°/RIU (refractive index unit) at the refractive index environment of 1.3425, which is about 3.12 times that of the conventional Ag-based biosensor. A detailed discussion, based on the finite difference time domain (FDTD) method, revealed that an enhanced evanescent field at the top layer–analyte region results in the ultra-sensitivity characteristic. We expect that the proposed structure can be a suitable biosensor for chemical detection, clinical diagnostics, and biological examination.

Ultra-Low-Reflective, Self-Cleaning Surface by Fabrication Dual-Scale Hierarchical Optical Structures on Silicon

An integrated functional anti-reflective surface is of great significance for optical and optoelectronic devices. Hence, its preparation has attracted great attention from many researchers. This study combined wet alkaline etching approaches and reactive ion etching (RIE) techniques to create a dual-scale hierarchical anti-reflective surface on silicon substrates. The effect of RIE time on surface morphology and optical performance was investigated using multiple characterization forms. The optimal parameters for the fabrication of dual-scale structures by the composite etching process were explored. The silicon surface with a dual-scale structure indicated excellent anti-reflective properties (minimum reflectivity of 0.9%) in the 300 to 1100 nm wavelength range. In addition, the ultra-low reflection characteristic of the surface remained prominent at incident light angles up to 60°. The simulated spectra using the finite difference time domain (FDTD) method agreed with the experimental results. Superhydrophobicity and self-cleaning were also attractive properties of the surface. The functionally integrated surface enables silicon devices to have broad application prospects in solar cells, light emitting diodes (LEDs), photoelectric detectors, and outdoor equipment.