多焦點透鏡的設計及製作

Abstract

微型繞射透鏡具有尺寸小、功能多樣化的特性，許多傳統透鏡所無法達到的功能皆可透過微透鏡的這些特性來完成，如:多焦點、波面整型、分光等。然而在許多光學系統中，聚焦仍是一個基本的需求，因此在系統微型化的趨勢下，如何以微型繞射元件達到單個或多個焦點分佈便是一個重要的研究主題。 本論文中將描述如何由幾何光學中的基本觀念--『光線追跡』來設計一單波長的多焦點透鏡。除了設計方法及原理的說明外，我們亦經由程式撰寫模擬出元件的聚焦效果，模擬結果中包含了兩種不同型態波面(平面波、高斯光束)入射元件時，元件上的補償相位分佈、焦點處的照度分佈、光點大小及繞射效率。文末我們將簡略地對光線追跡法與迭代演算法作一比較。在附錄中我們提供了一種以『物件導向』法來設計圖形產生元件以供參考。

Micro-diffractive lenses are characterized by their small size and multifunction. With them we can achieve many purposes which couldn't be implemented by traditional lenses, e.g. multi-focus, beam shaping and splitting etc. However, in many optical systems the focusing is still a basic requirement. In the trend of the system microminiaturizing, it is an important topic to design a micro-diffractive element for a given single or multi-focus distribution. In this paper a simple method of designing a monochromatic multi-focus DOE is described by using ray tracing of geometric optics. In addition to design methods and principles, we demonstrate the numerical simulation of the focusing, including the irradiance distribution on the focal plane, spot size and diffraction efficiency. The phase structures of the DOE are also shown. In all the simulations, we take two different input waves, plane wave and Gaussian beam. A simply comparison between ray-tracing method and iterative algorithm method is made. As a reference we provide an "object-oriented" method to design a pattern generation element in the appendix.