求解多层介质光栅衍射问题的变量分离修正方法

IF 0.6 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Eurasian Journal of Mathematical and Computer Applications Pub Date : 2021-12-01 DOI:10.32523/2306-6172-2021-9-4-76-88

Y. Smirnov, V. Martynova, M. Moskaleva, A. Tikhonravov

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引用次数: 2

摘要

针对多层介质光栅直接衍射电磁波的问题，提出了一种改进的变量分离方法。为了应用这种方法，有必要求解分段常系数分段上二阶微分方程的一维特征值问题。通过与商用RCWA方法获得的结果进行比较，验证了该方法的准确性。结果表明，该方法不仅可以应用于在光栅周期中具有一条线的常用MDG元件，而且可以应用于具有在光栅周期内具有多条不同线的潜在前景的MDG元件。

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MODIFIED METHOD OF SEPARATION OF VARIABLES FOR SOLVING DIFFRACTION PROBLEMS ON MULTILAYER DIELECTRIC GRATINGS

A modified method of separation of variables is proposed for solving the direct problem of diffraction of electromagnetic wave by multilayer dielectric gratings (MDG). To apply this method, it is necessary to solve a one-dimensional eigenvalue problem for a 2nd- order differential equation on a segment with piecewise constant coefficients. The accuracy of the method is verified by comparison with the results obtained by the commercially available RCWA method. It is demonstrated that the method can be applied not only to commonly used MDG elements with one line in a grating period but also to potentially promising MDG elements with several different lines in a grating period.

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来源期刊

Eurasian Journal of Mathematical and Computer Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： Eurasian Journal of Mathematical and Computer Applications (EJMCA) publishes carefully selected original research papers in all areas of Applied mathematics first of all from Europe and Asia. However papers by mathematicians from other continents are also welcome. From time to time Eurasian Journal of Mathematical and Computer Applications (EJMCA) will also publish survey papers. Eurasian Mathematical Journal publishes 4 issues in a year. A working language of the journal is English. Main topics are: - Mathematical methods and modeling in mechanics, mining, biology, geophysics, electrodynamics, acoustics, industry. - Inverse problems of mathematical physics: theory and computational approaches. - Medical and industry tomography. - Computer applications: distributed information systems, decision-making systems, embedded systems, information security, graphics.