Maxwell operator in a cylinder. Separation of variables

The Maxwell operator with periodic coefficients in a cylinder

In the paper we consider the Maxwell operator in a three-dimensional cylinder with coefficients periodic along the axis of a cylinder. It is proved that for cylinders with circular and rectangular cross-section the spectrum of the Maxwell operator is absolutely continuous.

Maxwell eigenmodes in product domains

This paper is devoted to Maxwell modes in three-dimensional bounded electromagnetic cavities that have the form of a product of lower dimensional domains in some system of coordinates. The boundary conditions are those of the perfectly conducting or perfectly insulating body. The main case of interest is products in Cartesian variables. Cylindrical and spherical variables are also addressed. We exhibit common structures of polarization type for eigenmodes. In the Cartesian case, the cavity eigenvalues can be obtained as sums of Dirich-let or Neumann eigenvalues of positive Laplace operators an…

扰动圆柱中的变量分离

Separation of variables in perturbed cylinders

本文研究二维扰动圆柱域上Dirichlet边界条件的Laplace算子特征值问题，通过映射和Fourier分解分离变量，数值求解ODE系统得到特征值及复共振，并应用于量子波导。