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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Revision as of 18:49, 3 April 2009

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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.