光電系統中的圖斑形成與波動混沌之研究

Abstract

在這研究計畫，主要有兩個研究方向：其一是研究各種光學局限系統內的光學圖 斑形成(optical pattern formation)、其一是研究開放系統中的波動混沌(wave chaos)。目前有許多光學圖斑，可以應用於雷射細微製程、於雷射打標中產生特 定的圖案、細微粒子的操控、光鑷子的應用等。光學圖斑亦可應用於研究波動光 學和幾何光學之間的微妙關係。另外一方面光學腔(optical cavity)可應用於研究開 放系統的量子或波動混沌、提供量子和經典軌跡的連結、研究量子彈子球的混沌 問題。此外，光學腔可應用於研究在開放量子系統的共振本徵值的統計。在這計 畫我們將研究(1) 幾何共振模式；(2) 螺旋光學波；(3) 產生的光學準晶格圖 斑；(4) 開放量子彈子球的共振本徵值的統計；(5) 非傍軸效應對遠場模式的影 響；(6) 特殊光學圖斑的非線性倍頻轉換效率。

In this proposal, we will focus on two topics: the first topic is the optical pattern formation due to various optical confinements and the second one is the wave chaos in open optical or quantum systems. Currently, the optical pattern formation technology can be applied, in the field of laser processing, to laser marking that carves any given pattern, and in the field of particle trapping like the optical tweezers, to multipoint control. On the other hand, optical cavities have been studied with particular emphasis on quantum chaos of open systems. A particularly intriguing aspect of optical patterns is that these structures open also a simple access for studying the relation between wave and ray optics, quantum and classically trajectories respectively, in billiard problems. This provides a link to the very active field of wave or quantum chaos. Furthermore, a strong interest in the statistical properties of eigenenergies of open systems has emerged. In this proposal, we will investigate (1) the geometric resonance modes; (2) the spiral optical waves; (3) the generation of optical quasi-crystal patterns; (4) the open-quantum-billiard eigenvalue statistics; (5) the non-paraxial effect on the far-field patterns; (6) efficiency of nonlinear harmonic generations with special wave patterns