Talk:Plane wave expansion method
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Plane wave expansion method is far more general than the solution of Maxwell's equations in electromagnetism. Fourier methods such as this are used widely in condensed matter physics (for example in density functional theory) and probably in maths and other areas of physics as well.
This article should be re-written to reflect this. DMB (talk) 22:14, 11 April 2008 (UTC)
Edits
[edit]Made some edits to clean up the text for spelling, grammar and punctuation. --BwB (talk) 16:42, 22 August 2009 (UTC)
Many dubious points
[edit]As another poster pointed out, planewave expansions are not just used in electromagnetism; this is really just another name for a spectral method.
Even for Maxwell's equations, it is not restricted to photonic crystals; waveguides and other structures are commonly handled by supercell techniques.
Regarding the "disadvantages" section, spurious modes do not appear if the divergence constraint is included. The problem is that the formulation in the article is in terms of the E field -- no one who understands what they are doing uses the E field in a planewave basis, because the divergence constraint is non-diagonal for E. Instead, you use B or D, since for both of these fields the divergence constraint is (block) diagonal in Fourier space and hence trivial to impose and exclude spurious modes.
And O(N^3) work is not required if iterative methods are used (this was a common misconception in the field 15 years ago, but I'm surprised to see it still propagating now), combined with and FFT. See, for example, this paper and this free software.