Geodesic
On the explicit parametric description of waves in periodic media
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 6, pp. 1119-1130 Cet article a éte moissonné depuis la source Math-Net.Ru

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A method for the parameterization of the one-dimensional wave equation is proposed that makes it possible to find its solution by quadratures under an arbitrary dependence of the refraction index on the current wave phase. The form of the solution found is used to investigate the structure of the wave function for a periodic refraction index. Explicit expressions for the fundamental system of solutions and for the Floquet index are obtained. Examples of applying the proposed method to the optimal synthesis of multilayer interference mirrors and Bragg waveguides are discussed. 
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A. V. Vinogradov; A. V. Popov; D. V. Prokopovich. On the explicit parametric description of waves in periodic media. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 6, pp. 1119-1130. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_6_a13/

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