The gradual transition from a reactive to a radiative regime is studied for leaky modes supported by multilayered planar open waveguides. The so-called leaky cutoff condition, i.e., the frequency for which the leaky phase constant $\beta $ equals the leaky attenuation constant $\alpha $ , originally introduced for microstrip lines and other printed structures, is investigated here with the aim of providing detailed information on the relative amount of reactive and radiative attenuation for leaky modes excited by finite sources and propagating as cylindrical waves along general planar waveguides. Analytical results are derived on the basis of a lossy parallel-plate-waveguide model and are validated through full-wave numerical simulations of 2-D leaky-wave structures based on grounded slabs covered with lossless or lossy partially reflecting surfaces (including, e.g., graphene layers) that can be treated as homogenized sheets. An analysis of the complex wave impedance of the considered leaky modes is also provided, in order to assess the frequency ranges where a good input matching can be expected for practical sources. In this regard, an ad hoc impedance matching network is designed and full-wave validated for a specific case to show that is indeed possible to achieve a good impedance matching below the cutoff in practical designs.

中文翻译：

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基于均质部分反射面的平面波导中漏模的反应和辐射模式之间的转换

对于由多层平面开放波导支持的泄漏模式，研究了从反应状态到辐射状态的逐渐转变。所谓的漏截止条件，即漏相位常数 $\beta $ 等于泄漏衰减常数 $\alpha $ ，最初是为微带线和其他印刷结构引入的，这里研究的目的是提供有关由有限源激发的泄漏模式的反应和辐射衰减的相对量的详细信息，并作为圆柱波沿一般平面波导传播。分析结果是在有损平行板波导模型的基础上得出的，并通过基于覆盖有无损或有损部分反射表面（包括，例如，石墨烯层），可以被视为均质片。还提供了对所考虑的泄漏模式的复波阻抗的分析，以评估实际源可以预期良好输入匹配的频率范围。特设 阻抗匹配网络是针对特定情况进行设计和全波验证的，以表明在实际设计中确实有可能在截止点以下实现良好的阻抗匹配。