- 學位論文
可見光氮化鎵超穎透鏡之研究
Investigation of GaN Metalenses at Visible Wavelengths
摘要
超穎透鏡是超穎表面開發中最重要的應用之一。目前各式各樣的材料已被應用於製作超穎透鏡，使其在某些特定頻帶中達到高效率與低製造成本的需求。在這些材料中，考量材料的各項優點，尤其是在半導體製造的量產能力，寬能隙氮化鎵屬最具潛力的材料之一。在本論文中，氮化鎵被選為製造在可見光波段工作的高性能超穎透鏡的關鍵材料，而其超穎透鏡的設計原理乃基於幾何相位或傳播相位之概念。 幾何相位設計原理亦稱為 Pancharatnam-Berry (PB) 相位法。基於 PB 相位概念設計的超穎透鏡需要圓偏振平面波作為入射光。如實驗結果所示，在 405、532 與 633 奈米之可見光波長下，依PB 相位法設計的氮化鎵超穎透鏡，其繞射極限聚焦效率分別高達 79%、84% 和 89%。另一方面，以傳播相位設計之超穎透鏡具偏振方向不敏感之特性，得以聚焦任意線性偏振方向之入射光。在此研究中，更進一步提出新開發的高效能六邊形共振元件，搭配精心挑選之次波長周期，以構建具偏振方向不敏感之高性能超穎透鏡。經實驗證明這些具偏振方向不敏感的超穎透鏡在 405、532 與 633奈米之三個不同波長下，其繞射極限聚焦效率分別為 93%、86% 和 92%。 有關超穎透鏡的成像能力，我們選擇美國空軍於1951年所制定符合美國空軍定義的分辨率測試軍用標準的分辨率測試圖(1951 USAF)作為驗證，惟目前市售的 1951 美國空軍分辨率測試圖，其最小線寬為2.19 微米。為了補足市售分辨率測試圖的不足，我們選擇自製 1951 USAF 分辨率測試圖，以利驗證超穎透鏡得以識別更小線寬之能力。依據成像實驗結果顯示，以405 奈米為波長所設計的PB相位法以及具偏振方向不敏感的氮化鎵超穎透鏡皆能實現極高的分辨率，得以分辨自製之分辨率測試圖中奈米等級之線寬，而我們可以觀察到的最小線寬為 870 奈米。這些非凡的實驗結果來自於我們在設計方面的成功，以及製程上成功製作以接近垂直側壁的高深寬比氮化鎵奈米共振器所組成的超穎透鏡。 在實際應用方面，本論文提出一個開創性的概念，即透過超穎透鏡檢測發光二極體的圖案化藍寶石基板。為了實施概念驗證，分別選擇不具有磊晶層以及具有磊晶層的市售圖案化藍寶石基板作為待檢測物，以執行超穎透鏡的檢測能力。透過適當選擇所需波長所設計的超穎透鏡，可以在圖中清楚地觀察到圖案化藍寶石基板中結構的頂點。以數值孔徑為 0.3 的超薄輕量超穎透鏡所拍攝的圖案化藍寶石基板成像，其品質與以數值孔徑為 0.4 的物鏡所拍攝之成像相當。 本研究為以寬能隙氮化鎵製作的超穎表面之應用展現了一道曙光。預計在不久的將來，超薄氮化鎵超穎透鏡將取代厚重的光學元件，成為未來光學的主流。
關鍵字
超穎透鏡並列摘要
Metalens is one of the most tremendous applications for the development of metasurfaces. A wide variety of materials have been applied to metalenses working at certain spectral bands to meet the requirements of high efficiency and low-cost fabrication. Among these materials, wide-bandgap gallium nitride (GaN) is one of the most promising materials considering its advantages, especially in the mass production capacity of semiconductor manufacturing. In this dissertation, GaN has been selected as the key material for the fabrication of high-performance metalenses working in the visible regime. The design principles for the metalenses are based on either geometric phase or propagation phase concepts. The geometric phase design principle is also known as the Pancharatnam-Berry (PB) phase method. Metalenses based on the PB-phase design concept require circularly polarized plane waves as the incident light. As demonstrated in the experimental results, the diffraction-limited focusing for the fabricated GaN metalenses relied on the PB-phase method are up to 79%, 84%, and 89% at visible wavelengths of 405, 532, and 633 nm, respectively. On the other hand, the propagation-phase metalenses are polarization-insensitive (PI) and are capable of focusing arbitrary linearly polarized incident light. In this study, newly developed, highly efficient hexagon-resonated elements (HREs) have been also proposed with gingerly selected subwavelength periods of the elements for the construction of PI metalenses of high performance. These PI metalenses are experimentally demonstrated at three distinct wavelengths of 405, 532, and 633 nm with respective diffraction-limited focusing efficiencies of 93%, 86%, and 92%. When it comes to the imaging capability of the metalenses, a 1951 United States Air Force (USAF) resolution test chart is chosen as verification because it conforms with military standards for resolving power tests defined by the U.S. Air Force. However, the smallest features are lines with widths of 2.19 μm in a commercially available 1951 USAF Resolution Test Chart. To make up for the insufficient commercially available counterpart, we even fabricate our own homemade 1951 USAF resolution test chart to verify that the metalenses can identify smaller features. As also shown in the experimental results for imaging, both the PB phase and PI GaN metalenses designed at 405 nm can provide extremely high resolution capable of resolving the smallest lines with the nano-sized widths in the homemade resolution test chart. And the smallest features we can observe are lines with widths of 870 nm. These extraordinary experimental results come from our successful development in design and fabrication for the metalenses composed of high-aspect-ratio GaN nano-resonators with nearly vertical sidewalls. As for the practical applications, this dissertation also proposes a pioneering concept through the use of metalenses to inspect patterned-sapphire substrates (PSSs) for the growth of GaN light-emitting diodes (LEDs). For the proof of concept, a commercially available PSS without and with the LED epitaxial layers has been opted to perform the inspection capacity of the fabricated metalenses. With the appropriately chosen metalenses at the desired wavelength, the summits of structures in the PSS can be clearly observed in the images. The PSS imaging qualities taken by the ultra-thin and light-weight metalenses with a numerical aperture (NA) of 0.3 are comparable to those seen by an objective with the NA of 0.4. This work provides a light at the end of the tunnel for applications of metasurfaces made of wide-bandgap GaN material. And it is expected that the ultrathin GaN metalenses are going to replace heavy and bulky optical components and become the mainstream of future optics in the near future.