Z-cut鈮酸鋰壓電極子波傳解析解與機械式激發電磁輻射分析

Abstract

壓電晶體本身具有壓電效應，可以將機械能與電磁能相互轉換，以及兩者互相耦合產生的極子波，而不同壓電晶體具有不同材料參數，以及在不同切面下也有不同的材料參數，機械能與電磁能兩者耦合強度也與其材料有關，壓電超晶格為具有週期性結構的壓電材料，其為不同極化方向壓電晶體週期性排列，相較於單一壓電晶體，具有較強的耦合強度，透過外部激發，電磁式或機械式激發，將產生之機械能與電磁能兩者耦合進而產生電磁輻射。 然而在本實驗室學長論文中，使用之材料參數以及壓電超晶格理論推導使用座標軸與實際使用晶片座標軸不相同，因此在參考時會有所影響，因此在本研究中重新定義座標軸。而在激發方式中，多數研究透過電磁式激發壓電超晶格，因機械式激發多數為接觸式，接觸時會影響其結構內部機械場，而在近期研究中，有使用非接觸性脈衝雷射來進行機械式激發，可以在不進行直接接觸情況下激發壓電超晶格。 本文的研究目的主要會分為兩個部份，第一部分為重新定義Z-cut鈮酸鋰的座標軸並重新計算理論解，接著帶入週期性邊界條件，計算壓電超晶格的頻散曲線，並觀察聲子與光子兩者耦合產生的極子在不同耦合情況下，機械能與電磁能的組成比例，並透過等效介電係數與頻率關係圖，觀察在共振頻率附近，機械能與電磁能耦合效應；第二部份則是著重在壓電晶體中聲子受到點波源激發後，觀察其聲子波傳現象，使用理論解分離彈性波中所產生的縱波與橫波，並透過商用有限元素模擬軟體COMSOL進行波傳模擬，使用軟體中彈性波模組以及固體力學模組與靜電模組兩者耦合的壓電模組，將計算出理論解與模擬結果兩者進行相互驗證，並使用模擬結果來證明在鈮酸鋰中，透過電性激發與機械式激發皆可以激發出電磁輻射。

Piezoelectric crystals inherently exhibit the piezoelectric effect, enabling the interconversion between mechanical energy and electromagnetic energy. These two forms of energy are coupled to generate polaritonic waves. Different piezoelectric crystals possess distinct material parameters, which also vary with the crystallographic cut. The coupling strength between mechanical and electromagnetic energy is material-dependent. A piezoelectric superlattice is a piezoelectric material with a periodic structure, consisting of periodically arranged piezoelectric crystals with alternating polarization directions. Compared to single piezoelectric crystals, piezoelectric superlattices exhibit stronger coupling. When externally excited—either electrically or mechanically—the generated mechanical and electromagnetic energies can couple and radiate as electromagnetic waves. However, in previous studies, including the thesis by a senior colleague, the material parameters and theoretical derivation of the piezoelectric superlattice were based on a coordinate system different from that of the actual fabricated chip. This discrepancy affects the applicability of the reference results. Therefore, this study redefines the coordinate system based on the actual Z-cut lithium niobate substrate. In terms of excitation methods, most studies have employed electrical excitation of the piezoelectric superlattice. Mechanical excitation methods are typically contact-based and may disturb the internal mechanical field of the structure. Recent research, however, has demonstrated the feasibility of using non-contact pulsed lasers for mechanical excitation, enabling the activation of piezoelectric superlattices without direct physical contact. This study is divided into two main parts. The first part redefines the coordinate system of Z-cut lithium niobate and recalculates the theoretical solution. Periodic boundary conditions are then applied to compute the dispersion relation of the piezoelectric superlattice. The coupling between phonons and photons is analyzed to determine the energy composition ratio of mechanical and electromagnetic energy under various coupling conditions. The effective permittivity as a function of frequency is also examined to study the coupling behavior near the resonance frequency. The second part focuses on the wave propagation of phonons in piezoelectric crystals excited by a point source. Theoretical solutions are used to separate the generated elastic waves into longitudinal and transverse components. These results are verified using the commercial finite element software COMSOL Multiphysics. The simulation is carried out using the coupled piezoelectric module, which integrates the Elastic Waves Module, Solid Mechanics Module, and Electrostatics Module. The theoretical and simulation results are compared to validate their consistency. The simulation further confirms that both electrical and mechanical excitations in lithium niobate can generate electromagnetic radiation.