Casimir calculations in Meep

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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

In this section, we introduce the equations and basic considerations 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 $g(-t)$, 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

To do.

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