利用漸近邊界條件分析四面橫向皺褶結構之矩形波導之色散

Abstract

週期性的皺褶性結構(periodic corrugations)在近年來開始被廣泛的研究、應用於改善各種微波裝置，像是波導或天線。對於不同的波傳導方向，會有不同的傳播特性表現在皺褶性的表面上。舉例來說，與皺褶方向垂直的傳導波會被抑制、而平行方向會被增強；這種現象常常用於矩形波導或是喇叭型天線中，可以用來減少極化作用以及旁波瓣的效應。皺褶型的矩形波導已經被研究了一段時間，但是大部分的研究、分析都只有討論到相對兩面或是一面的週期性皺褶結構，比較少關於四面都是週期性皺褶結構的研究；可能是因為在四面牆中的分析會有數值上的技術困難。最近，科學家提出了漸進邊界條件；利用這個理論，在四面皺褶型結構所遇到的數值問題將可以被解決。接著利用電磁理論以及數值分析的技巧，我們可以拿到色散圖以及場分布圖。與CST電磁模擬軟體比較過後，我們發現我們可以準確的抓到色散圖，但是在場分布圖上還是有點落差。可能是因為在數值的運算假設上仍然有地方需要加強。儘管如此，運用漸進邊界條件分析還是充分展現出它比傳統的分析更有效率、更快的可以得到答案。

The periodic structure of corrugations has been a hot issue for years. Corrugations have improved microwave device such as waveguide and antennas. For the different directions of wave propagation, each has different property on the corrugated surface. If the propagation direction is orthogonal with the corrugations, it may suppress the wave and has been realized as the soft surface; on the contrary, it can enhance wave propagating in the direction parallel with the corrugations, and has been known as the hard surface. With those properties, the corrugated waveguide or horn have been used to reduce wave polarization and sidelobes. Corrugated rectangular waveguides had been developed for years, but the most of studies focus on two opposite wall or only one wall. There are none attempted to analyze all four walls with corrugations, because of the numerical difficulty. In recent years, a theorem been known as asymptotic corrugations boundary conditions (ACBCs) has been developed. Then we can obtain the dispersion diagrams and field distributions of rectangular waveguide with all four walls being transverse corrugated by this theorem. After comparing with CST Microwave Studio, good agreement can be found in dispersion diagram. But agreement is not as good in field distribution, there still are some problems of numerical analyses have to conquer. Nevertheless, the ACBCs can yield the modal solutions faster than traditional analyses.