Plane wave expansion method: Difference between revisions

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Revision as of 01:26, 29 August 2009

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'''Plane wave expansion method''' (PWE) refers to a computational technique in [[electromagnetics]] to solve the [[Maxwell's equations]] by formulating an [[eigenvalue]] problem out of the equation. This method is a popular among the [[photonic crystal]] community as a method of solving for the [[band structure]] (dispersion relation) of specific photonic crystal geometries. PWE is traceable to the analytical formulations, and is useful in calculating modal solutions of Maxwell's equations over an inhomogeneous or periodic geometry. It is specifically tuned to solving problems in a time-harmonic forms, with [[Dispersion (optics)|non-dispersive]] media.

==Principles==

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[[Plane wave]]s are solutions to the homogeneous [[Helmholtz equation]], and form a basis to represent fields in the periodic media. PWE as applied to photonic crystals as described is primarily sourced

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==Disadvantages==

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Sometimes spurious modes appear. Large problems scaled as ''O(n³)'', with the number of the plane waves (n) used in the problem. This is both time consuming and complex in memory requirements.

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{{DEFAULTSORT:Plane Wave Expansion Method}}

[[Category:Computational science]]

[[Category:Electromagnetism stubs]]