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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
from Dr. Danner's tutorial<ref>http://
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 permitivitty (which is periodic along reciprocal lattice vector for photonic crystals) is also expanded through fourier series components.
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