Plane wave expansion method: Difference between revisions

Revision as of 17:32, 11 June 2010

Revision as of 12:27, 10 October 2010

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{{Copyedit|date=June 2009}}

{{Dubious|date=August 2009}}

'''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 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.

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from Dr. Danner's tutorial<ref>http://www.ece.nus.edu.sg/stfpage/eleadj/planewave.htm</ref>.

The electric or magnetic fields are expanded for each field component in terms of the [[fourier series]] components along the reciprocal lattice vector. Similarly, the dielectric permitivittypermittivity (which is periodic along reciprocal lattice vector for photonic crystals) is also expanded through fourierFourier series components.

:<math>