Simple analytical formulae are presented for the design of linear tapers with very low mode conversion loss in overmoded corrugated waveguides. For tapers from waveguide radius a ₂ to a ₁, with a ₁<a ₂, the optimal length of the taper is 3.198a ₁ a ₂/λ. Here, λ is the wavelength of radiation. The fractional loss of the HE ₁₁ mode in an optimized taper is \(0.0293 (a_{2}-a_{1})^{4}/{a_{1}^{2}}{a_{2}^{2}}\). These formulae are accurate when a ₂≲2a ₁. Slightly more complex formulae, accurate for a ₂≤4a ₁, are also presented in this paper. The loss in an overmoded corrugated linear taper is less than 1 % when a ₂≤2.12a ₁ and less than 0.1 % when a ₂≤1.53a ₁. The present analytic results have been benchmarked against a rigorous mode matching code and have been found to be very accurate. The results for linear tapers are compared with the analogous expressions for parabolic tapers. Parabolic tapers may provide lower loss, but linear tapers with moderate values of a ₂/a ₁ may be attractive because of their simplicity of fabrication.

中文翻译：

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过调制波纹波导中线性锥度设计的简单表达式。


提出了简单的分析公式，用于过调制波纹波导中具有极低模式转换损耗的线性锥度的设计。对于从波导半径a ₂到a _{1 的}锥度， a ₁ < a ₂ ，锥度的最佳长度为3.198 a ₁ a ₂ / λ 。这里， λ是辐射的波长。优化锥度中 HE ₁₁模式的分数损失为\(0.0293 (a_{2}-a_{1})^{4}/{a_{1}^{2}}{a_{2}^{2 }}\) 。当a ₂ ≲2 a ₁时，这些公式是准确的。本文还提出了稍微复杂的公式，对于a ₂ ≤4 a ₁精确。当a ₂ ≤2.12 a ₁时，超模波纹线性锥体中的损耗小于1%，当a ₂ ≤1.53 a ₁时，损耗小于0.1%。目前的分析结果已经针对严格的模式匹配代码进行了基准测试，并且被发现非常准确。将线性锥度的结果与抛物线锥度的类似表达式进行比较。抛物线锥度可以提供较低的损耗，但是具有中等a ₂ / a ₁值的线性锥度可能由于其制造简单而有吸引力。