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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Plane wave expansion method ： ウィキペディア英語版 Plane wave expansion method 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 solve problems in a time-harmonic forms, with non-dispersive media. ==Principles== Plane waves 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.〔http://www.ece.nus.edu.sg/stfpage/eleadj/planewave.htm〕 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 permittivity (which is periodic along reciprocal lattice vector for photonic crystals) is also expanded through Fourier series components. :$$ \frac = \sum_^ K_m^ e^} :$$ E(\omega,\vec) = \sum_^ K_n^ e^} e^} with the Fourier series coefficients being the K numbers subscripted by m, n respectively, and the reciprocal lattice vector given by $\backslash vec$. In real modeling, the range of components considered will be reduced to just $\backslash pm\; Nmax$ instead of the ideal, infinite wave. Using these expansions in any of the curl-curl relations like, :$$ \frac \nabla \times \nabla \times E(\vec,\omega) = \left( \frac \right)^2 E(\vec,\omega) and simplifying under assumptions of a source free, linear, and non-dispersive region we obtain the eigen value relations which can be solved. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Plane wave expansion method」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.