本文關(guān)鍵詞：光子晶格中平帶�？臻g光局域的特性研究　出處：《南開大學(xué)》2016年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 光局域 平帶光子晶格 平帶模 光誘導(dǎo) Kagome光子晶格 Lieb光子晶格

【摘要】：在光子晶格中如何實(shí)現(xiàn)光波局域以及和它相關(guān)的圖像傳輸一直是人們所關(guān)注的熱點(diǎn)。最近幾年,已經(jīng)有許多典型的光局域現(xiàn)象成功地在光子晶格這個(gè)平臺(tái)上實(shí)現(xiàn)了。比如:對(duì)光子晶格添加無序、進(jìn)行非線性調(diào)制、制造缺陷或者施加外力場都可以實(shí)現(xiàn)光的局域。然而還存在另一種方法去實(shí)現(xiàn)光局域,即不需要對(duì)周期性光子晶格做任何調(diào)制,依靠其自身的幾何拓?fù)浣Y(jié)構(gòu)去產(chǎn)生光的局域態(tài)。同時(shí),根據(jù)平帶模的線性疊加態(tài)仍具有局域的特性,我們可以在光子晶格平臺(tái)上去實(shí)現(xiàn)簡單圖像的傳輸。這種方法給全光網(wǎng)絡(luò)、光通迅技術(shù)方面的提升帶來了新的曙光。在本論文中,我們以平帶光子晶格為傳輸平臺(tái),主要是Kagome、Lieb兩種光子晶格,從理論層面上去研究影響平的色散能帶存在的條件,給出了能夠保持平帶結(jié)構(gòu)的具體范圍,且證實(shí)了平帶模在其相應(yīng)存在平帶的晶格中的線性傳輸過程中表現(xiàn)出了局域的特性。在實(shí)驗(yàn)上,我們采用部分相干光振幅調(diào)制光誘導(dǎo)法成功地構(gòu)造了Kagome、Lieb兩種晶格,并首次觀察到了平帶模及其簡單圖像的無衍射傳輸。實(shí)驗(yàn)結(jié)構(gòu)與參數(shù)相近條件下的相應(yīng)理論模擬結(jié)果相一致。首先,我們根據(jù)麥克斯韋方程組推倒得出了描述光在平帶晶格中線性傳輸?shù)陌S類薛定諤方程。借助于MATLAB數(shù)學(xué)軟件,采用分布束傳播法來模擬光在平帶晶格中的線性傳輸過程。其次,我們以晶格中的一個(gè)單元胞為研究對(duì)象,利用緊束縛近似法去計(jì)算Kagome、Lieb晶格的能帶結(jié)構(gòu),發(fā)現(xiàn)它們的能帶結(jié)構(gòu)中都存在著一個(gè)平的衍射帶。在得到能帶衍射關(guān)系的同時(shí),得到了其各自平帶上本征態(tài)(平帶模)的具體結(jié)構(gòu)排布,且從光波相干的角度解釋了平帶模保持局域的原因�？紤]到晶格周期大小會(huì)影響平帶的平坦性,我們利用分步束傳播法得出了一個(gè)可以維持這兩種晶格平帶平坦性的晶格周期范圍。然后在有著適當(dāng)周期大小的兩種晶格中,去模擬平帶模以及其線性疊加態(tài)在晶格中的線性傳輸情況,從理論上去驗(yàn)證其平帶態(tài)是否具有局域特性。最后在實(shí)驗(yàn)中,我們采用了熟悉的部分相干光振幅調(diào)制誘導(dǎo)法成功地制備了維護(hù)平帶平坦性的晶格常數(shù)大小的Kagome、Lieb兩套平帶光子晶格。為了突出只有平帶模在相應(yīng)平帶晶格的線性傳輸過程中才有局域特性,我們額外地進(jìn)行了單束高斯光和有著與平帶模輪廓完全相同的同相位態(tài)的激發(fā),依次來進(jìn)行對(duì)比;同時(shí),平帶態(tài)的線性疊加態(tài)在線性傳輸過程中也實(shí)現(xiàn)了接近完美的無衍射傳輸。實(shí)驗(yàn)結(jié)果與理論模擬的完美吻合,更加證實(shí)了這種利用平帶系統(tǒng)中的平帶態(tài)去實(shí)現(xiàn)光局域的可行性。
[Abstract]:How to realize the local area of the light wave in the photon lattice and the image transmission related to it have always been the focus of attention. In recent years, many typical optical local phenomena have been successfully implemented on the platform of photon lattice. For example, the local area of light can be realized by adding disorder to the photonic lattice, making nonlinear modulation, manufacturing defects, or applying external force field. However, there is another way to achieve optical localization, that is, no need to modulate periodic photonic lattice, and rely on its own geometrical topology to generate localized state of light. At the same time, according to the local characteristics of the linear superposition state of the flat band mode, we can transmit the simple image on the photon lattice platform. This method has brought a new dawn to all-optical network, optical communication technology promotion. In this paper, we take the flat band photonic lattice as the transmission platform, such as Kagome, Lieb two kinds of photonic lattices, from the theoretical level to study on the effect of dispersion flat band exist, are able to maintain a flat concrete range of band structure, and confirmed the flat band die in the corresponding linear transmission process the flat belt in the lattice showing local characteristics. In experiment, we used partial coherent light amplitude modulation photoinduced method to construct two kinds of lattice of Kagome and Lieb successfully. For the first time, we observed the diffraction pattern of flat band mode and its simple image. The experimental structure is in agreement with the corresponding theoretical simulation results under the similar parameters. First, we derive the paraxial Schrodinger equation describing the linear propagation of light in the flat lattice according to the Maxwell equation. With the help of MATLAB mathematical software, the distributed beam propagation method is used to simulate the linear transmission process of light in the flat band lattice. Secondly, we take a unit cell in the lattice as the research object, and use tight binding approximation to calculate the band structure of Kagome and Lieb lattice. We find that there is a flat diffraction band in their band structure. After obtaining the diffraction relation of energy band, we get the specific structure arrangement of the eigenstate (flat band mode) on the respective flat band, and explain the reason why the flat mode is localized because of the coherence of light wave. Considering the periodic lattice size will affect the flatness of the flat belt, we use beam propagation method step by step one can maintain the two lattice flat band flatness of the lattice period range. Then, in the two kinds of lattice with the appropriate period size, we simulate the flat band mode and its linear superposition state in the lattice. Finally, in the experiment, we used the familiar partially coherent light amplitude modulation induction method to successfully prepare two flat band photonic lattices for Kagome and Lieb with flat lattice size. In order to highlight the linear transmission process only flat die with a lattice in the corresponding flat is the local characteristics, we carried out an additional single Gauss beam and a flat band excitation and the mold contour exactly the same phase state, in order to compare; at the same time, linear superposition states in linear transmission belt in the process of implementation of the diffraction transmission without a near perfect. The experimental results are in perfect agreement with the theoretical simulation, which proves the feasibility of using the flat band state in the flat band system to realize the optical local area.
【學(xué)位授予單位】：南開大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：O734

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