An expression for the propagation constant, cutoff frequency, and associated fields of the first two modes in a waveguide filled with a tilted slab of the dielectric is derived using the variational analysis. The solution to such a problem is divided into two parts. First, the slab is assumed to be parallel with the walls of the waveguide with no tilt. In this part, the effective permittivities of the first two orthogonally polarized modes are derived from two different variational expressions for the transversal resonance frequencies. This results in a diagonal tensorial permittivity that represents an effective uniaxial anisotropic medium. Next, this tensorial permittivity is transformed into a tilted set of coordinates representing the required tilt angle. In the new set of coordinates, a variational expression for the propagation constant is solved using the Rayleigh–Ritz procedure. The resulting analytic expressions are verified using a full-wave analysis and a prototype measurement.

中文翻译：

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介电板加载双极化波导偏斜的变分分析

使用变分分析导出了填充有倾斜电介质板的波导中前两种模式的传播常数、截止频率和相关场的表达式。此类问题的解决方案分为两部分。首先，假设板与波导壁平行，没有倾斜。在这部分中，前两个正交极化模式的有效介电常数来自横向共振频率的两种不同变分表达式。这导致表示有效单轴各向异性介质的对角张量介电常数。接下来，这个张量介电常数被转换成一组倾斜的坐标，表示所需的倾斜角。在新的坐标集中，使用 Rayleigh-Ritz 程序求解传播常数的变分表达式。得到的解析表达式使用全波分析和原型测量进行验证。