We present a complex field general variational statement to study the waves propagating in the circumferential directions of cylindrical curved waveguides. A semi-analytical technique that has been applied on straight waveguides in the literature is reformulated to adapt to the circumferential directions and used for constructing the trial wavefunction in complex field. The method requires the waveguide to be analyzed to be geometrically and physically uniform along its circumferential axis; however, its circumferential cross-section can be arbitrarily complex. The formulation is verified using various examples, which were examined previously by other numerical or analytical solutions. Different cases were studied and comparisons with those published are also performed show the utility and advantages of present method.

中文翻译：

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圆柱弯曲波导中圆周波的数值计算

我们提出了一个复杂的场一般变分语句来研究在圆柱形弯曲波导的圆周方向上传播的波。对文献中已应用于直波导的半解析技术进行了重新设计，以适应圆周方向，并用于构建复杂场中的试验波函数。该方法要求要分析的波导沿其圆周轴在几何和物理上是均匀的；然而，它的圆周截面可以任意复杂。使用各种示例验证了该公式，这些示例之前已通过其他数值或解析解进行了检查。研究了不同的案例，并与已发表的案例进行了比较，显示了本方法的实用性和优势。