Meep Introduction
From AbInitio
| Revision as of 03:02, 22 October 2005 (edit) Stevenj (Talk | contribs) (→Maxwell's equations) ← Previous diff |
Revision as of 03:03, 22 October 2005 (edit) Stevenj (Talk | contribs) (→Maxwell's equations) Next diff → |
||
| Line 20: | Line 20: | ||
| Where '''D''' is the displacement field, ε is the dielectric constant, '''J''' is the current density, and '''J'''<sub>''B''</sub> is the ''magnetic charge'' current density. (Magnetic currents are a convenient computational fiction in some cases.) '''B''' is the magnetic flux density (often called the magnetic field), but currently μ (the magnetic permeability) is always 1 in Meep so we don't need to distinguish between '''B''' and '''H'''. | Where '''D''' is the displacement field, ε is the dielectric constant, '''J''' is the current density, and '''J'''<sub>''B''</sub> is the ''magnetic charge'' current density. (Magnetic currents are a convenient computational fiction in some cases.) '''B''' is the magnetic flux density (often called the magnetic field), but currently μ (the magnetic permeability) is always 1 in Meep so we don't need to distinguish between '''B''' and '''H'''. | ||
| - | You may have noticed the lack of annoying constants like ε<sub>0</sub> and μ<sub>0</sub> — that's because Meep uses "dimensionless" units where all these constants are unity (you can tell it was written by theorists). As a practical matter, almost everything you might want to compute is expressed as a ratio anyway, so the units end up cancelling; see [[#Units in Meep|Units in Meep]], below. | + | You may have noticed the lack of annoying constants like ε<sub>0</sub>, μ<sub>0</sub> —, [[w:Speed of light|c]], and 4π that's because Meep uses "dimensionless" units where all these constants are unity (you can tell it was written by theorists). As a practical matter, almost everything you might want to compute is expressed as a ratio anyway, so the units end up cancelling; see [[#Units in Meep|Units in Meep]], below. |
| === Material dispersion and nonlinearity === | === Material dispersion and nonlinearity === | ||
Revision as of 03:03, 22 October 2005
 |
| Meep |
| Download |
| Release notes |
| FAQ |
| Meep manual |
| Introduction |
| Installation |
| Tutorial |
| Reference |
| C++ Tutorial |
| C++ Reference |
| Acknowledgements |
| License and Copyright |
Meep implements the 'finite-difference time-domain (FDTD) method for computational electromagnetism. This is a widely used technique in which space is divided into a discrete grid and then the fields are evolved in time using discrete time steps—as the grid and the time steps are made finer and finer, this becomes a closer and closer approximation for the true continuous equations, and one can simulate many practical problems essentially exactly.
In this section, we introduce the equations and the electromagnetic units employed by Meep, the FDTD method, and Meep's approach to FDTD. Also, FDTD is only one of several useful computational methods in electromagnetism, each of which has their own special uses—we mention a few of the other methods, and try to give some hints as to which applications FDTD is best suited for and when you should consider a different method.
Contents |
Maxwell's equations
Meep simulates Maxwell's equations, which describe the interactions of electric (E) and magnetic (H) fields with one another and with matter and sources. In particular, the equations for the evolution of the fields are:
| 
|
| 
|
Where D is the displacement field, ε is the dielectric constant, J is the current density, and JB is the magnetic charge current density. (Magnetic currents are a convenient computational fiction in some cases.) B is the magnetic flux density (often called the magnetic field), but currently μ (the magnetic permeability) is always 1 in Meep so we don't need to distinguish between B and H.
You may have noticed the lack of annoying constants like ε0, μ0 —, c, and 4π that's because Meep uses "dimensionless" units where all these constants are unity (you can tell it was written by theorists). As a practical matter, almost everything you might want to compute is expressed as a ratio anyway, so the units end up cancelling; see Units in Meep, below.
Material dispersion and nonlinearity
The material structure is determined by the dielectric function ε(x), but ε is not only a function of position — in general, it also depends on frequency (material dispersion) and on the electric field E itself (nonlinearity). Both effects can be simulated in Meep, with certain restrictions.
Units in Meep
Finite-difference time-domain methods
The illusion of continuity in Meep
Although FDTD inherently uses discretized space and time, as much as possible Meep attempts to maintain the illusion that you are using continuous system.
