We present the general conditions to realize a fourth-order exceptional point of degeneracy (EPD) in two uniform (i.e., invariant along $z$ ) lossless and gainless coupled transmission lines (CTLs), namely, a degenerate band edge (DBE). Until now the DBE has been shown only in periodic structures. In contrast, the CTLs considered here are uniform and subdivided into four cases where the two TLs support combinations of forward propagation, backward propagation, and evanescent modes (when neglecting the mutual coupling). We demonstrate, for the first time, that a DBE is supported in uniform CTLs when there is proper coupling between: 1) propagating modes and evanescent modes, 2) forward and backward propagating modes, or 3) four evanescent modes (two in each direction). We also show that the loaded quality factor of uniform CTLs exhibiting a fourth-order EPD at $k=0$ is robust to series losses due to the fact that the degenerate modes do not advance in phase. We also provide a microstrip possible implementation of a uniform CTL exhibiting a DBE using periodic series capacitors with very subwavelength unit-cell length. Finally, we show an experimental verification of the existence DBE for a microstrip implementation of a CTL supporting coupled propagating and evanescent modes.

中文翻译：

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在两条均匀耦合传输线中实现异常退化点的一般条件

我们提出了在两个过程中实现四阶异常退化点 (EPD) 的一般条件 制服 （即，沿不变 $z$ ) 无损和无增益耦合传输线 (CTL)，即退化带边 (DBE)。到目前为止，DBE 仅以周期性结构显示。相比之下，这里考虑的 CTL 是统一的，并细分为四种情况，其中两个 TL 支持前向传播、反向传播和渐逝模式的组合（当忽略互耦时）。我们首次证明了 DBE 支持制服CTL 在以下情况之间存在适当耦合时：1) 传播模式和渐逝模式，2) 向前和向后传播模式，或 3) 四个渐逝模式（每个方向两个）。我们还表明，加载的品质因数制服 CTL 表现出四阶 EPD $k=0$ 由于退化模式不会同相推进，因此对串联损耗具有鲁棒性。我们还提供了一种均匀 CTL 的微带可能实现，该 CTL 使用具有非常亚波长单位单元长度的周期性串联电容器来展示 DBE。最后，我们展示了对支持耦合传播和渐逝模式的 CTL 的微带实现的存在 DBE 的实验验证。