Casimir calculations in Meep
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==Introduction== | ==Introduction== | ||
- | In this section, we introduce the equations and basic considerations | + | To do |
- | involved in computing the force using the method presented in | + | |
- | [refs]. Note that we keep the details of the derivation to a minimum | + | |
- | and instead focus on the calculational aspects of the resulting | + | |
- | algorithm. | + | |
- | + | ||
- | The basic steps involved in computing the Casimir force, as outlined | + | |
- | in [ref], are: | + | |
- | + | ||
- | 1. Map the problem onto a new problem with dissipation. Here, as in | + | |
- | [ref], we choose a frequency-independent conductivity "sigma". | + | |
- | + | ||
- | 2. Measure the electric '''E''' and magnetic '''H''' fields in response to | + | |
- | current pulses placed separately at each point along a surface | + | |
- | enclosing the body of interest. | + | |
- | + | ||
- | 3. Integrate these fields in spave over the enclosing surface and then | + | |
- | integrate this result, multiplied by a known function <math>g(-t)</math>, over | + | |
- | time t. | + | |
- | + | ||
- | [The manner in which (1) and (2) are performed plays a large role on | + | |
- | the efficiency of the method. For example, computing the fields due to | + | |
- | ach source separately at each point on the surface, as described in | + | |
- | (2), would require a separate Meep calculation for each source (and | + | |
- | polarization). As described in [ref], and further below, it is | + | |
- | possible to modify the calculation of these steps so as to optimize | + | |
- | the calculation of the stress tensor over the spatial surface. For the | + | |
- | purpose of this introduction, however, we do not require specific | + | |
- | details on how we handle the spatial integration.] | + | |
==Parallel plates== | ==Parallel plates== |
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Casimir calculations in Meep
It is possible to use the Meep time-domain simulation code in order to calculate Casimir forces (and related quantities), a quantum-mechanical force that can arise even between neutral bodies due to quantum vacuum fluctuations in the electromagnetic field, or equivalently as a result of geometry dependence in the quantum vacuum energy.
Calculating Casimir forces in a classical time-domain Maxwell simulation like Meep is possible because of a new algorithm described in:
- Alejandro W. Rodriguez, Alexander P. McCauley, John D. Joannopoulos, and Steven G. Johnson, "Casimir forces in the time domain: I. Theory," arXiv preprint archive article arXiv:0904.0267 (April 2009).
- Alexander P. McCauley, Alejandro W. Rodriguez, John D. Joannopoulos, and Steven G. Johnson, "Casimir forces in the time domain: II. Applications," manuscript in preparation (2009).
This page will provide some tutorial examples showing how these calculations are performed for simple geometries.
Introduction
To do
Parallel plates
To do.