On the explicit parametric description of waves in periodic media
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 6, pp. 1119-1130
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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.
@article{ZVMMF_2009_49_6_a13,
author = {A. V. Vinogradov and A. V. Popov and D. V. Prokopovich},
title = {On the explicit parametric description of waves in periodic media},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1119--1130},
publisher = {mathdoc},
volume = {49},
number = {6},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_6_a13/}
}
TY - JOUR AU - A. V. Vinogradov AU - A. V. Popov AU - D. V. Prokopovich TI - On the explicit parametric description of waves in periodic media JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2009 SP - 1119 EP - 1130 VL - 49 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_6_a13/ LA - ru ID - ZVMMF_2009_49_6_a13 ER -
%0 Journal Article %A A. V. Vinogradov %A A. V. Popov %A D. V. Prokopovich %T On the explicit parametric description of waves in periodic media %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2009 %P 1119-1130 %V 49 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_6_a13/ %G ru %F ZVMMF_2009_49_6_a13
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/