Finite difference time domain fdtd methods for solution of maxwells equations case study in simulation sciences dr. Developed by active researchers and authors of a number of fdtd methodologies. Maxwell stress tensor for a monochromatic plane wave problem 9. Field analyses including flux spectra, maxwell stress tensor, frequency extraction, local density of states and energy integrals, near to far field transformations. The optifdtd software package is based on the finitedifference timedomain fdtd method. Osa electromagnetic stress tensor in ponderable media.

The derivation proceeds from the generalized form of the lorentz law, which specifies the force exerted by the electromagnetic e and h fields on the polarization p and magnetization m of a ponderable medium. Advanced texts often present the maxwell stress tensor as a mathematical abstraction without explaining why is is useful. This chapter deals with conservation of energy, momentum. Oct 10, 2011 the three dimensional fdtd method and maxwell stress tensor are used to setup simulation model and calculate the trapping force. Optical force is calculated using maxwell stress tensor. The optical force is calculated by integrating the maxwell stress tensor over a.

It is based on the finitedifference timedomain fdtd method, which is one of the most popular approaches for solving maxwell s equations of electrodynamics. This page shows two techniques of calculating optical force on a. We derive an expression for the maxwell stress tensor in a magnetic dielectric medium specified by its permittivity. Meep stands for mit electromagnetic equation propagation. Effect of electromagnetic force on the design of a linear. Analysis of the nanoscale manipulation using nearfield. Efficient prediction and analysis of optical trapping at nanoscale. The lumerical knowledge base contains the definitive reference guide on. Optifdtd is a powerful, highly integrated, userfriendly software that allows computer aided design and simulation of advanced passive photonic components. The warring camps were divided into the actionatadistance advocates and the fieldtheory advocates. The maxwell stress tensor named after james clerk maxwell is a mathematical object in physics, more precisely it is a second rank tensor used in classical electromagnetism to represent the interaction between electricmagnetic forces and mechanical momentum. Fdtd numerical simulation of the trapping force of microsphere in. Finite difference time domain fdtd methods for solution. Maxwell stress tensor electromagnetism part 15 youtube.

Finite difference time domain fdtd methods for solution of. We theoretically investigate the optical forces generated by a high nearfield resolution antenna system through finite difference time domain calculations along with the maxwell stress tensor method. Derivation of the maxwell stress tensor for a linear dielectric. The following example shows how to calculate the photonic force from fdtd simulations. The maxwell stress tensor the maxwell equations of the electromagnetism provide a frame in which the interaction between radiation and matter can be studied from a classical point of view. The three dimensional fdtd method and maxwell stress tensor are used to setup simulation model and calculate the trapping force. Meep is an acronym for mit electromagnetic equation. We kindly request that you cite the following paper in any. Field analyses including flux spectra, maxwell stress tensor, frequency extraction, local. I read previous posts on this forum on topic of maxwell stress tensor but still could not find what is wrong. I hope this is not a naive question but i am wondering on how you actually take the cross product of position vector with the maxwell stress tensor to calculate the torque.

Meep is a free and opensource software package for electromagnetics simulation via the finitedifference timedomain fdtd method. Xsvit is primarily a viewer of parameter files suitable for gsvit fdtd calculations. This chapter deals with conservation of energy, momentum and. Fdtd simulation software with omnisim part of our stateoftheart fdtd and fetd timedomain toolkit the omnisim and crystalwave frameworks includes a highly efficient fdtd finite difference time domain engine to simulate the propagation of light through your designs. Simulation in 1d, 2d, 3d, and cylindrical coordinates. Code issues 95 pull requests 10 actions projects 0 security insights.

Apr, 2018 meep is a free and opensource software package for simulating electromagnetic systems via the finitedifference timedomain fdtd method. Calculation of maxwell stress tensor using 3d fdtd for. The components of the maxwell stress tensor as formulated in wikimedia. The fdtd method has been established as a powerful engineering tool for integrated and diffractive optics device simulations.

Methodology for optical force calculations lumerical support. Applications allow to evaluate the effectiveness of the method. In electromagnetism, the electromagnetic tensor or electromagnetic field tensor sometimes called the field strength tensor, faraday tensor or maxwell bivector is a mathematical object that describes the electromagnetic field in spacetime. All of the features that one would expect from a sophisticated code are implemented. The korteweighelmholtz force density is obtained from a thermodynamic analysis of the dielectric. Chapter 3 dynamics of the electromagnetic fields 3. The full fivedimensional field equations under the cylinder condition are provided here, and we see that most of the other references miss at least some. However, i have no idea how to express the maxwell stress tensor as required, since i cant get rid of the polarization or cant properly express the components in the correct base. Meep is a free and opensource software package for electromagnetics simulation via the finitedifference timedomain fdtd method spanning. Field equations and lagrangian for the kaluza metric. Finitedifference timedomain or yees method named after the chinese american applied mathematician kane s. Meep is a free and opensource software package for electromagnetics simulation via the finitedifference timedomain fdtd method spanning a broad range of applications. Meep or meep is a finitedifference timedomain fdtd simulation software package. Then, simple geometries with specific initial values and boundary conditions are calculated to test the new solvers.

In simple situations, such as a point charge moving freely in a homogeneous magnetic field, it is easy to calculate the forces on the charge from the lorentz force law. The results of the developed simulation procedures in openfoam are compared to the results of another simulation software. In this article, an accurate and efficient numerical simulation method based. We find it useful to define the maxwell stress tensor as a function of the field quantities from which the force density can be obtained by space differentiation. The net force can be found by integrating the mst over a closed surface surrounding the particle. For a linear dielectric, the volumetric force density as obtained through the method of korteweighelmholtz and is given by. The maxwell stress tensor mst that reveals the relationship between. The new forms are used to design nearfield optical trapping with a metalcoated fiber probe. This paper calculates the kaluza field equations with the aid of a computer package for tensor algebra, xact. The maxwell stress tensor named after james clerk maxwell is a symmetric secondorder tensor used in classical electromagnetism to represent the interaction between electromagnetic forces and mechanical momentum.

Angora is a free, opensource software package that computes numerical solutions to electromagnetic radiation and scattering problems. A modified maxwell stress tensor method for the evaluation of electromagnetic torque s. Multiparameter optimization, rootfinding, integration, etcetera via libctl. However, the fdtd demands an accurate dispersive model to describe. Electromagnetism part 15 maxwell stress tensor maxwell stress tensor through animation, more updated video coming, please subscribe. Our antenna choice is bowtieshaped nanostructures with small gap regions, exploiting propagating waveguide modes as well as localized surface plasmons. This tutorial demonstrates meeps ability to compute classical forces via the maxwell stress tensor mst.

Meep is an acronym for mit electromagnetic equation propagation. Covariant formulation of classical electromagnetism wikipedia. Finite difference time domain fdtd methods for solution of maxwell s equations case study in simulation sciences dr. Fdtd analysis of optical forces on bowtie antennas for. New forms of trapping force are proposed for the design of nearfield optical tweezers. All those steps to make that geometry and to have those boundary conditions to work out and actually give me the maxwell stress tensor were made 2 and half years ago on version 3. Maxwell stress tensor, frequency extraction, local density of states. So i just figured out the difference between when it worked and when it didnt. Apr 22, 2020 meep is a free and opensource software package for electromagnetics simulation via the finitedifference timedomain fdtd method spanning a broad range of applications.

Numerical solutions to maxwell s equations in 3d, 2d, or 1d. Fifth order gaussian beam based on spherical vector wave function vswf is adopted as simulation light source. Its elements form a square array labelled by i and j that each refer to x, y, z directions and are defined in terms of the components of the electric field e and magnetic field b. In this article, an accurate and efficient numerical simulation method based on a dualprimal finite element tearing and interconnecting fetidp and maxwell stress tensor is proposed, to calculate the optical force and potential for trapping nanoparticles. Most of these are not released to the public, and the handful of other free software fdtd programs that could be downloadedwhen meep was. Without the limitation of dipole approximation, the trapping force acting on a nanoparticle located in nearfield region can be solved by direct calculation of maxwell stress tensor using 3d fdtd method. Meep or meep is a finitedifference timedomain fdtd simulation software package developed at mit to model electromagnetic systems, along with the mpb eigenmode package which is also available on kogence. The maxwell stress tensor may be used to calculate electric and magnetic forces on objects. The application gallery contains numerous simulation project files to get started quickly and easily. The maxwell stress tensor is particularly useful for finding electromechanical boundary conditions in a concise form. Optiwave has been successfully developing fdtd software for over a decade, and would like to show appreciation to the photonics community by distributing its 32bit fdtd product as freeware. Maxwells stress tensor t let us use the lorentz force law to calculate the total electromagnetic force em fttot due to the totality of the electric charges contained within a source volumev. Numerical solutions to in 3d, and coming soon 2d and 1d in the meantime, see jfdtd2d and the about page. It allow us to understand what are the mechanisms that make possible the optical trapping of particles.

Thus my main question is how to properly express an reduce the tensor components one example will be enough to get the idea. May 31, 2016 the maxwell stress tensor is defined, the momentum current density is plotted for a few simple examples, and the magnetic force of attraction between the northern and southern hemispheres of a. By using vswfs the transmission fields are obtained with linearly polarized and radially polarized beams in the vicinity of focus point. In the case of linear material equations the electromagnetic volume force equals zero. Fdtd simulation of trapping nanowires with linearly. Meep is a free and opensource software package for simulating electromagnetic systems via the finitedifference timedomain fdtd method. The optical force is calculated by integrating the maxwell stress tensor over a closed boxed that surrounds the particle. Since it is a timedomain method, fdtd solutions can cover a wide frequency range with a. Yee, born 1934 is a numerical analysis technique used for modeling computational electrodynamics finding approximate solutions to the associated system of differential equations. Meep free and opensource software package for simulating.

E has only an x component, and b only a y component all the offdiagonal i. The kx is a user forum for users who want to ask questions and exchange simulation tips with the larger lumerical community. This force density can be expressed as the divergence of. Electromagnetic stress tensor is called maxwell stress tensor. It cannot do anything except it, however it can simplify the process of parameter file creation and modification as it serves as a viewer and basic editor of parameter files. The maxwell stress tensor for magnetoelastic materials. Efficient prediction and analysis of optical trapping at.

Jan 29, 2016 maxwell stress tensor the maxwell stress tensor named after james clerk maxwell is a second rank tensor used in classical electromagnetism to represent the interaction between electromagnetic. Fdtd simulation of trapping nanowires with linearly polarized. Im trying to calculate the repelling force between two magnet rings with one levitated above the other. Meep or meep is a free finitedifference timedomain fdtd simulation software package developed at mit to model electromagnetic systems, along with our mpb eigenmode package. The geometry consists of two identical, parallel, silicon waveguides with square cross section in vacuum. Mit opencourseware for any use or distribution of this. Capoglu and di zhang, and is currently maintained by di zhang. Calculations are made to analyze the field distributions including tip interaction and the trapping forces in the nearfield region by applying a direct calculation of maxwell stress tensor using threedimensional fdtd. This chapter deals with conservation of energy, momentum and angular momentum in electromagnetic systems. The method is seldom discussed in introductory texts on electromagnetism. Meep officially, mit electromagnetic equation propagation, but there are other expansions of the acronym is a free finitedifference timedomain fdtd simulation software package developed at mit to model electromagnetic systems, along with our mpb eigenmode package. Chapter 6 maxwells equations in tensor form we now have learned the transformation properties of th electric and magnetic elds and together they form an antysymmetric tensor f f under poincare transformation. The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism in particular, maxwell s equations and the lorentz force in a form that is manifestly invariant under lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems.

584 100 468 1470 935 469 655 1139 246 164 556 66 191 102 1131 780 872 1248 261 608 1465 1221 411 1534 69 1315 1468 278 374 984 958 649 275 1280 380 862 137 508