本論文的主題在於研究電磁波和彈性波在人造晶體中的傳播特性。這種晶體被稱為光子晶體以及聲子晶體。 論文的第一個部份是三維光子晶體的反射特性研究。所使用的光子晶體是由微米尺寸的小球，堆積成面心立方結構而成。晶體中參雜銀的奈米小球。由於三維光子晶體的禁止頻帶特性，導致某些頻率的入射光無法穿透而被反射。研究的結果顯示，反射光的光譜會隨著入射角度不同而改變。並且藉由參雜適當濃度的奈米銀小球，可以有效的提升反射的效率。 論文的第二個部份是彈性波在二維聲子晶體和三維聲子晶體中傳播特性的研究。所使用的二維聲子晶體是由鋼柱在水中週期性的排列而成。三維聲子晶體是在樹脂中嵌入面心立方堆積的鋼珠所形成。藉由研究彈性波對這些結構不同方向的穿透特性測量來進行傳播特性的研究。結果顯示出聲子晶體的禁止頻帶，並且與理論分析的結果吻合。研究也包含二維聲子晶體的結構缺陷特性分析，分析的結果顯示出缺陷結構可以有效的侷限以及控制彈性波。 最後一個部分是聲子晶體平板的研究。聲子晶體平板是在樹脂平板中，嵌入一層排列成四方晶格的鋼珠所構成。在平板中的彈性波稱為板波(Lamb wave)。藉由研究板波的穿透頻譜以及板波在結構中的分布來分析聲子晶體平板的特性。實驗結果顯示由一般吸收或禁止頻帶所造成之能量衰減的不同。同時也顯示出在聲子晶體平板中製造線缺陷結構可以有效的控制板波的傳播。This thesis deals with the propagation properties of the electromagnetic and the elastic waves in artificial crystals which are called photonic and phononic crystals, respectively. In the first part, the three dimensional photonic crystals formed by microspheres with Ag nano particles coating are studied. The light can be reflected by crystals due to the partial band gap of the photonic crystals arranged in face-centered cubic structure. The results reveal that the reflectance is wavelength dependant and can be enhanced by suitable Ag coating on the microspheres. In the second part, the bulk elastic waves propagating in two-dimensional and three-dimensional phononic crystals are studied experimentally and theoretically. The two-dimensional phononic crystals are constructed using steel cylinders. The cylinders are arranged periodically in water. The three-dimensional phononic crystal consists of close-packed periodic arrays of spherical beads of steel embedded in an epoxy matrix. The forbidden band gap can be observed in the experimental measurement of the transmission spectra. The results agree with the theoretical calculations. The defect modes in two-dimensional phononic crystals are also studied. The results show that the bulk elastic waves could be well controlled and confined by the phononic crystal structures. The propagation of acoustic waves in a square-lattice phononic crystal slab consisting of a single layer of spherical steel beads in a solid epoxy matrix is studied experimentally and theoretically. The transmission and the field image of acoustic wave are investigated. The transmission attenuation caused by absorption and band gap effects is measured as a function of frequency and propagation distance. We also demonstrate experimentally that the acoustic waves are well confined and propagate inside a line-defect waveguide.
