利用超表面設計與合成雙聚焦廣義倫柏格透鏡

Abstract

在本論文中，我們提出在微波頻段使用超表面來設計與合成雙聚焦廣義倫柏格透鏡，用於合成透鏡的超表面的單晶胞是由印刷在接地介質基板上的正方形金屬貼片組成。我們發現方形單晶胞是非全向性的結構，其色散關係會隨著不同的入射角而變化。然而，表面波在任何類型的超表面透鏡上的傳播過程中會逐漸改變電磁波的射線路徑。因此，在合成透鏡上所有位置的折射率時僅使用一個表面波傳播方向可能會造成透鏡合成上的不准確。在本篇論文中我們將提出一種改善雙聚焦廣義倫柏格透鏡的合成方法，該改進方法是透鏡中每一個位置的方形金屬貼片都用預測射線路線時此射線入射此位置貼片的入射角去模擬得到此位置所需要的折射率。我們將展示通過僅使用一個表面波傳播方向的方法和本篇論文所提出的方法分別去合成的模擬結果，以證明為什麼我們需要校正色散曲線的角度變化，否則可能導致超表面透鏡在合成上的不准確。 最後，通過本文提出的合成方法，我們藉由模擬結果以及實驗結果證明利用超表面合成雙聚焦廣義倫柏格透鏡能夠在微波頻段成功實現兩個明確的焦點。

In this thesis, we proposed the use of metasurfaces to design and synthesize the double-focus generalized Luneburg lens (DF-GLL) at microwave frequencies. The unit cell of the metasurface used for the synthesis of the lens is made of a square metallic patch printed on a grounded dielectric substrate. Then, we observe that the dispersion of square unit cell varies with the different incident angles, that is, this square unit cell is directionally anisotropic. However, the surface waves will bend at all locations on the lens. The use of only one surface wave propagation direction in synthesizing the refractive indices of all locations on the lens may thus be inaccurate. Thus, we propose a method to improve the synthesis of the DF-GLL. The improvement method is that tailoring the direction adapts to the orientation of the ray path direction at any position within the lens relative to square patches that represented the required refractive index at the same position. We believe the method is more accurate to synthesize the lens, and can improve the performance. Finally, with this proposed synthesis method, we have demonstrated that DF-GLL metasurfaces are able to successfully achieve two clear focal spots by simulation and experimental results.