鐵氧體相關的元件發展在近幾年來越來越廣泛，例如單向器、環型器與高密度的磁記錄介質，隨著這些元件日益發展，分析鐵氧體在微波頻段的電磁特性也日益重要。
　　在本論文中，我們將鐵氧體放置在方波導管內，並且在方波導的短邊方向外加磁場。由於鐵氧體的導磁係數為張量型式，本徵模式(Eigenmode)下的場型將會與空波導管的形式不同，此場型的偏移使得入射的電磁波穿過鐵氧體時，在空氣與鐵氧體的介面上為了滿足邊界條件激發高次模，產生模式效應(Modal effect)。這些因為場型的偏移所伴隨的模式效應將會影響電磁波穿過材料的S參數，所以分析此模式效應的過程是相當重要的，因此在本論文中我們致力於分析及模擬電磁波與鐵氧體的交互作用並探討其中的意義。我們分析TEm0模式在此系統下的行為，包括色散關係，場型分佈。在取得本徵模式的特性後，我們利用此場型分佈解出在鐵氧體與空氣介面上的穿透反射，並分析其中的模式效應。分析完這些基本特性後，我們更進一步解出真實實驗會得到的穿透反射。在經過一連串的分析後並使用模擬軟體HFSS來驗證我們推導的結果，此理論結果與模擬結果相當吻合，奠定了我們未來發展量測或是設計元件極佳的基礎。

Ferrite materials biased under DC magnetic field have been intensely studied for the past decades due to their wide applications in microwave region, such as isolator, circulator, and high-density magnetic recording media. The magnetic property (tensor-form permeability) of the biased ferrites must be clearly characterized for designing and further applications.
In this study, we insert the bulk under-test ferrite into a rectangular waveguide. The whole system is biased by a uniform DC magnetic field parallel to short edge of the rectangular waveguide. The permeability of the loaded ferrite will strongly modulate the eigenmodes’ dispersions, making their field distributions deviate from their counterparts under the case without a bias field. The changes of eigenmodes’ field distributions under the bias field further imply that the strong modal effect would occur as the guided wave transmits through the air-ferrite interfaces. How those eigenmodes jointly satisfy boundary conditions intricately relates to their scattering parameters (necessary for retrieving ferrite characteristics), and so understanding the modal coupling process is of vital importance.
In this work, we exactly analyze the behaviors of TEm0 modes, including the dispersions and field distributions in a rectangular waveguide loaded with ferrite material and biased by a DC magnetic field. Based on these eigenmodes’ properties, the transmission and reflection for the EM wave (TE 10 mode) passing through the ferrite loaded in the rectangular waveguide can be also analyzed. These solutions could be further employed to retrieve the permeability tensor of the under-test ferrite material as long as the overall transmission and reflection measured by the experiment are provided.

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