All optical fibers, including single-mode, multimode, and multicore fibers, exhibit some degree of birefringence, either purposely, such as in polarization-maintaining fibers, or inadvertently due to material or fabrication imperfections. Finding a low-complexity method to accurately calculate the modal characteristics of elliptical fibers has been a long-standing problem. We present a novel accurate perturbative method that avoids the difficulties associated with the traditional Mathieu function treatment. The method is also applicable to a broader class of oscillating systems with elliptical geometry.

中文翻译：

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椭圆变换扰动理论确定椭圆波导的模式

所有光纤，包括单模，多模和多芯光纤，都表现出某种程度的双折射，或者是有目的的（例如在保偏光纤中），或者是由于材料或制造缺陷而无意中出现的。寻找低复杂度的方法来精确计算椭圆形纤维的模态特性一直是一个长期存在的问题。我们提出了一种新颖的精确扰动方法，避免了与传统Mathieu函数治疗相关的困难。该方法还适用于具有椭圆几何形状的更广泛的振荡系统。