Non-dissipative electromagnetic medium with a double light cone

M.F. Dahl

preprint at arxiv.
updated version. Note. Since the updated version contains corrections in response to reviewer comments, it has not been placed on the arxiv.

The paper relies on some computations that require computer algebra. Below are Mathematica toolbooks for these computations. Please note that these notebooks are for the revised paper.

Notebooks for paper

Example 1.6: Medium κ = diag(-1,1,0,-1,1,0) whose Fresnel surface is ξ₀ ξ₁ ξ₂ ξ₃ = 0: [notebook, pdf]
Proposition 1.3: Factorisability of Fresnel polynomial: [notebook, pdf]
Theorem 1.5: Coordinate inversions [notebook, pdf]
Theorem 2.1: Computation of determinants: [notebook, pdf]
Theorem 2.1: Initial comments for Metaclass I: [notebook, pdf]
Theorem 2.1: Computation for Metaclass I: [notebook, pdf]
Theorem 2.1: Computation for Metaclass II: [notebook, pdf]
Theorem 2.1: Computation for Metaclass III: [notebook, pdf]
Theorem 2.1: Computation for Metaclass IV: [notebook, pdf]
Theorem 2.1: Computation for Metaclass V: [notebook, pdf]
Theorem 2.1: Computation for Metaclass VI: [notebook, pdf]
Theorem 2.1: Computation for Metaclass VII: [notebook, pdf]
Section 3.1, Metaclass I: Reduction of Metaclass I to isotropic medium plus axion component [ notebook, pdf]
Figure 1: Plot of null cones for Metaclass I: [notebook, pdf] Note: images are not included in the above files due to their size.
Section 3.1, Metaclass I: Intersection of null cones: [notebook, pdf]
Figure 2: Plot of null cones for Metaclass II: [notebook, pdf] Note: images have been removed from PlotII.pdf due to their size.
Figure 3: Plot signal speed in spatial plane for Metaclass II: [notebook, pdf]
Section 3.1, Metaclass II: Coordinate transformation of Metaclass II: [notebook, pdf]
Section 3.1, Metaclass II: Intersection of null cones: [notebook, pdf]
Figure 4: Plot of null cones for Metaclass IV: [notebook, pdf] Note: images have been removed from PlotIV.pdf due to their size.
Section 3.1, Metaclass IV: Intersection of null cones: [notebook, pdf]
Script helper.m: [script]

kappaLib: A library for manipulation of electromagnetic medium

To run the above notebooks, you will need kappaLib version 1.1, which is a collection of Mathematica routines for manipulating electromagnetic medium tensors. To install this library, first download the file onto your harddrive. Then load kappaLib into a Mathematica session by typing

     <<kappaLib.m

If this generates an error, Mathematica can not find the file. The command Directory[] shows what directory Mathematica is currently in, and you can use SetDirectory["/user/mydir"] to change this directory.

Last modified 12.7.2012.