Hybrid Standing Wave and Whispering Gallery Modes in Needle-Shaped ZnO Rods: Simulation of Emission Microscopy Images Using Finite Difference Frequency Domain Methods with a Focused Gaussian Source

2013 ◽  
Vol 117 (20) ◽  
pp. 10653-10660 ◽  
Author(s):  
Justin R. Kirschbrown ◽  
Ralph L. House ◽  
Brian P. Mehl ◽  
James K. Parker ◽  
John M. Papanikolas
Keyword(s):  
Finite Difference ◽  
Frequency Domain ◽  
Standing Wave ◽  
Whispering Gallery Modes ◽  
Whispering Gallery ◽  
Frequency Domain Methods ◽  
Gaussian Source ◽  
Emission Microscopy ◽  
Zno Rods ◽  
Microscopy Images

3D marine magnetotelluric modeling and inversion with the finite-difference time-domain method

Geophysics ◽  
2014 ◽  
Vol 79 (6) ◽  
pp. E269-E286 ◽  
Author(s):  
Sébastien de la Kethulle de Ryhove ◽  
Rune Mittet
Keyword(s):  
Finite Difference ◽  
Frequency Domain ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Linear Equations ◽  
Time Domain Method ◽  
Domain Method ◽  
Frequency Domain Methods ◽  
Starting Point ◽  
Difference Time

Frequency-domain methods, which are typically applied to 3D magnetotelluric (MT) modeling, require solving a system of linear equations for every frequency of interest. This is memory and computationally intensive. We developed a finite-difference time-domain algorithm to perform 3D MT modeling in a marine environment in which Maxwell’s equations are solved in a so-called fictitious-wave domain. Boundary conditions are efficiently treated via convolutional perfectly matched layers, for which we evaluated optimized parameter values obtained by testing over a large number of models. In comparison to the typically applied frequency-domain methods, two advantages of the finite-difference time-domain method are (1) that it is an explicit, low-memory method that entirely avoids the solution of systems of linear equations and (2) that it allows the computation of the electromagnetic field unknowns at all frequencies of interest in a single simulation. We derive a design criterion for vertical node spacing in a nonuniform grid using dispersion analysis as a starting point. Modeling results obtained using our finite-difference time-domain algorithm are compared with results obtained using an integral equation method. The agreement was found to be very good. We also discuss a real data inversion example in which MT modeling was done with our algorithm.

scholarly journals Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation

1996 ◽  
Vol 118 (4) ◽  
pp. 622-629 ◽  
Author(s):  
K. J. Baumeister ◽  
K. L. Kreider
Keyword(s):  
Wave Equation ◽  
Steady State ◽  
Finite Difference ◽  
Frequency Domain ◽  
Sound Propagation ◽  
Time Dependent ◽  
Frequency Domain Method ◽  
Impedance Boundary ◽  
Frequency Domain Methods ◽  
Time Marching

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Characterizing whispering-gallery modes in microspheres by direct observation of the optical standing-wave pattern in the near field

1996 ◽  
Vol 21 (10) ◽  
pp. 698 ◽  
Author(s):  
J. C. Knight ◽  
N. Dubreuil ◽  
V. Sandoghdar ◽  
J. Hare ◽  
V. Lefèvre-Seguin ◽  
...  
Keyword(s):  
Standing Wave ◽  
Direct Observation ◽  
Near Field ◽  
Wave Pattern ◽  
Whispering Gallery Modes ◽  
Whispering Gallery ◽  
Standing Wave Pattern

scholarly journals Vortex Laser Based on a Plasmonic Ring Cavity

Crystals ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 901
Author(s):  
Xingyuan Wang ◽  
Xiaoyong Hu ◽  
Tianrui Zhai
Keyword(s):  
Standing Wave ◽  
Ring Cavity ◽  
Single Mode ◽  
Optical Devices ◽  
Whispering Gallery Modes ◽  
Basic Building Block ◽  
Whispering Gallery ◽  
On Demand ◽  
On Chip ◽  
Structure Light

The orbital angular momentum (OAM) of the structure light is viewed as a candidate for enhancing the capacity of information processing. Microring has advantages in realizing the compact lasers required for on-chip applications. However, as the clockwise and counterclockwise whispering gallery modes (WGM) appear simultaneously, the emitted light from the normal microring does not possess net OAM. Here, we propose an OAM laser based on the standing-wave WGMs containing clockwise and counterclockwise WGM components. Due to the inhomogeneous intensity distribution of the standing-wave WGM, the single-mode lasing for the OAM light can be realized. Besides, the OAM of the emitted light can be designed on demand. The principle and properties of the proposed laser are demonstrated by numerical simulations. This work paves the way for exploring a single-mode OAM laser based on the plasmonic standing-wave WGMs at the microscale, which can be served as a basic building block for on-chip optical devices.

Multiscale finite-difference method for frequency-domain acoustic wave modeling

Geophysics ◽  
2021 ◽  
pp. 1-64
Author(s):  
Wei Jiang ◽  
Xuehua Chen ◽  
Shuaishuai Jiang ◽  
Jie Zhang
Keyword(s):  
Linear System ◽  
Finite Difference ◽  
Helmholtz Equation ◽  
Frequency Domain ◽  
Multiscale Method ◽  
Fine Scale ◽  
Coarse Mesh ◽  
Computational Costs ◽  
Time Costs ◽  
Frequency Domain Methods

Conventional finite-difference frequency-domain (FDFD) methods can describe wave attenuation and velocity dispersion more easily than time-domain methods. However, there are significant challenges associated with computational costs for solving the linear system when frequency-domain methods are applied in models with large dimensions or fine-scale property variations. Direct-iterative solvers and parallel strategies attempt a tradeoff between memory and time costs. We follow the general framework of heterogeneous multiscale method and develop a multiscale FDFD approach to solve the Helmholtz equation with lower memory and time costs. To achieve this, the discrete linear system approximating the Helmholtz equation is constructed on a coarse mesh, making its dimension much smaller than that of conventional methods. The coefficient matrix in the linear system of dimension-reduction captures fine-scale heterogeneity in the media by coupling fine- and coarse-scale meshes. Several test models are used to verify the accuracy of our multiscale method and investigate potential sources of error. Numerical results demonstrate that our method accurately approximates the wavefields of fine-scale solutions at low frequencies of the source, and could produce solutions with small errors by reducing the size of the coarse mesh cells at high frequencies as well. Comparisons of computational costs with conventional FDFD methods show that the proposed multiscale method significantly reduces computation time and memory consumption.

Sign in / Sign up

Export Citation Format

Share Document