壓電超晶格之極子特性研究

Abstract

週期性結構之特殊性質，不管是通帶性質或禁帶性質，皆吸引許多人爭相探討研究，並已有許多論文發表。經由介電係數週期調變之晶體，即為所謂的光子晶體，不管是其禁帶行為的頻帶間隙現象或通帶行為的負折射現象，以及利用點、線缺陷所造成的共振與波傳導現象，都有許多研究投入。另外，對於週期調變材料係數如密度、彈性係數…等之晶體，此類晶體則統稱為聲子晶體，也有許多的研究者投入，並遵循著光子晶體發展的腳步前進，然而此類週期性結構與光子晶體最大的不同在於其遵循的統御方程式不同，聲子晶體所遵循之統御方程式為牛頓第二運動定律，而光子晶體則為Maxwell’s方程式，意即一個是機械波在週期結構中的行為，另一個則是電磁波在週期結構中的行為，而聲子晶體由於可調變的參數多於光子晶體，故其行為將更具有複雜度與可調性。 除此之外，近期有研究指出利用壓電之特性並配合週期性變化，使電磁統御方程式與牛頓第二運動定律互相交互作用，而此類壓電係數週期調變之材料，即稱為壓電超晶格。而對此超晶格內之統御方程式，由於同時包含電磁波與機械波，其量子化後之粒子也有個特別的名稱，即稱為極子。本篇論文除了對一維模型進行深入探討外，並推導平板型式壓電超晶格之頻帶結構式和波傳行為，並藉由畫出此頻帶結構圖上各點之極子場形與能量比例分佈，來解釋極子中之電磁波特性與機械波特性，並配合實驗驗證理論所得之結果。另外，本文並提出一準靜電態模型，由此模型可以迅速得到在何種特定耦合激發頻率下，外界電磁波可與此超晶格平板產生激振。

There have been many researches focused on the periodic structures, inwhich the characteristics of the pass-band and the stop-band are primarily interested. The permittivity modulated structures are well known as the photonic crystals. In the applications of the photonic crystals, there are spontaneous emission suppressing, light manipulating in a specific path, and novel laser creating. In addition, the further thinking about space modulated elastic structures is called phononic crystals. The phononic crystals also have the same characteristics of the frequency band gaps, however, the factors which influence the complete band gap are more complicated than photonic crystals. These factors include the elastic constants, piezoelectric coefficients, density etc.. The governing equations for photonic crystals also are different from the phononic crystals. The physical behaviors in photonic crystals obey the Maxwell’s equations and in phononic crystals it obeys the Newton’s second law of motion. Recently, the piezoelectric-modulated superlattices have been developed. These so called piezoelectric superlattices (PSLs) make the Maxwell’s equations and the Newton’s second law of motion couple to each other. The quantization of the interaction between the electromagnetic waves and the mechanical waves is called the polaritons. This dissertation focuses on the behaviors of the polaritons not only in 1-D PSL but also in the plate form of PSL. From the derived fields and energy distributions of the polaritons, it would have a better understanding in the PSLs.