This research investigates analytic and numeric techniques for solving the Berreman system of ordinary differential equations for liquid crystal display optics in one spatial dimension. Modeling of the optical response of an individual system requires many solutions of the Berreman boundary value problem for various wavelengths and angles of incidence, thus making efficient solutions of the differential equation an important goal. We study techniques which, to some degree, overcome the complex oscillatory stiffness of the differential equation, described by the thickness k0 of the display cell in units of the light wavelength in the external medium. Various methods for solving the problem are compared, indicating both those computational regimes in which they perform favorably, and those situations where each experiences difficulties.
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机译:这项研究研究了解析和数值技术,用于在一个空间维度上求解液晶显示光学器件的常微分方程的Berreman系统。单个系统的光学响应建模需要针对各种波长和入射角的Berreman边值问题的许多解决方案,因此使微分方程的有效解决方案成为重要的目标。我们研究的技术在一定程度上克服了微分方程的复振荡刚度,该刚度由显示单元的厚度 k italic> 0 sub>表示,以光波长为单位外部媒介。对解决问题的各种方法进行了比较,指出了它们在其中表现良好的计算方式以及各自遇到困难的情况。
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