應用於可見光波長成像系統的超穎透鏡

Abstract

鏡片是在我們日常中被廣使用的元件，近年來，隨著製程技術以及電腦計算能力的發展，次波長結構組成的超穎介面得以實現。超穎介面是一種幾乎不存在於自然界的人造表面，通過許多次波長結構調製電磁波的相位、振幅以及偏振，能夠達到許多新穎的光學特性，超穎介面應用於成像光學我們廣泛稱之為超穎透鏡。在本論文中，吾人藉由時域有限差分(FDTD)、近遠場轉換(near-to-far-field transformation)以及實驗室開發的演算法，分別設計了三種不同應用的超穎透鏡，第一種是電控調製多焦超穎透鏡，我們結合扭曲向列型液晶(TN-LC)，提出了能夠在次毫秒內切換焦點的變焦透鏡，第二種是六角形排列的超廣角超穎透鏡，我們結合光線追跡(ray tracing)的方式設計單片達到幾乎全景式的廣角透鏡，第三種是寬頻消色差超穎透鏡，藉由特別設計的超穎結構，我們能夠使用單個光學元件在可見光波段消除色差。我們模擬的結果顯示了相比於傳統透鏡以及傳統繞射原件，我們所設計的超穎透鏡有著相近於繞射極限的光學性能，並且擁有很大的潛力能夠應用於多光種學系統之中。在本論文的最後，我們介紹了像是反向設計(Inverse Design)等方法，能夠打破現有局部性週期假設的設計方法，並且改善超穎透鏡的性能。此方法在理論上有機會設計幾乎於完美的透鏡，進而達到真正意義上的超穎透鏡。

Lenses are widely used in our daily life. In recent years, with the development of fabrication and computer power, a metasurface composed of sub-wavelength structures has been realized. The metasurface, which does not exist in nature, manipulate the phase, amplitude and polarization of electromagnetic waves by many sub-wavelength structures. It can achieve novel optical characteristics. When the metasurface is applied to the imaging optics, we widely call it metalens. In this dissertation, I designed three metalenses for different applications by using finite difference time domain (FDTD), near-to-far-field transformation, and in-house algorithms. The first one is an electronically modulated multifocal metalens. We combined twisted nematic liquid crystal (TN-LC) to theoretically demonstrate a tunable lens that can switch different focal points in sub-milliseconds. The second is an ultra-wide-angle metalens in hexagonal arrangement. We combine ray tracing method to design a single metalens, which is almost panoramic wide-angle. The third type is a broadband achromatic metalens. By rigorously designing meta-structures, we correct chromatic aberration by a single lens at visible wavelengths. Compared to traditional lenses and traditional diffraction elements, our simulation results show that the designed metalenses have an optical performance that is close to the diffraction limit, and have potential to be used in several optical systems. At the end of this dissertation, we introduce some methods such as inverse design, which can break the local-periodicity assumptions of the unit-cell design approach and improve performance of metalens in the future. Such method has the possibility to design an almost perfect lens theoretically, and then achieve a true meaning for metalens.