光子晶格中平带模空间光局域的特性研究

发布时间：2017-12-27 23:17

本文关键词：光子晶格中平带模空间光局域的特性研究　出处：《南开大学》2016年硕士论文　论文类型：学位论文

【摘要】：在光子晶格中如何实现光波局域以及和它相关的图像传输一直是人们所关注的热点。最近几年,已经有许多典型的光局域现象成功地在光子晶格这个平台上实现了。比如:对光子晶格添加无序、进行非线性调制、制造缺陷或者施加外力场都可以实现光的局域。然而还存在另一种方法去实现光局域,即不需要对周期性光子晶格做任何调制,依靠其自身的几何拓扑结构去产生光的局域态。同时,根据平带模的线性叠加态仍具有局域的特性,我们可以在光子晶格平台上去实现简单图像的传输。这种方法给全光网络、光通迅技术方面的提升带来了新的曙光。在本论文中,我们以平带光子晶格为传输平台,主要是Kagome、Lieb两种光子晶格,从理论层面上去研究影响平的色散能带存在的条件,给出了能够保持平带结构的具体范围,且证实了平带模在其相应存在平带的晶格中的线性传输过程中表现出了局域的特性。在实验上,我们采用部分相干光振幅调制光诱导法成功地构造了Kagome、Lieb两种晶格,并首次观察到了平带模及其简单图像的无衍射传输。实验结构与参数相近条件下的相应理论模拟结果相一致。首先,我们根据麦克斯韦方程组推倒得出了描述光在平带晶格中线性传输的傍轴类薛定谔方程。借助于MATLAB数学软件,采用分布束传播法来模拟光在平带晶格中的线性传输过程。其次,我们以晶格中的一个单元胞为研究对象,利用紧束缚近似法去计算Kagome、Lieb晶格的能带结构,发现它们的能带结构中都存在着一个平的衍射带。在得到能带衍射关系的同时,得到了其各自平带上本征态(平带模)的具体结构排布,且从光波相干的角度解释了平带模保持局域的原因。考虑到晶格周期大小会影响平带的平坦性,我们利用分步束传播法得出了一个可以维持这两种晶格平带平坦性的晶格周期范围。然后在有着适当周期大小的两种晶格中,去模拟平带模以及其线性叠加态在晶格中的线性传输情况,从理论上去验证其平带态是否具有局域特性。最后在实验中,我们采用了熟悉的部分相干光振幅调制诱导法成功地制备了维护平带平坦性的晶格常数大小的Kagome、Lieb两套平带光子晶格。为了突出只有平带模在相应平带晶格的线性传输过程中才有局域特性,我们额外地进行了单束高斯光和有着与平带模轮廓完全相同的同相位态的激发,依次来进行对比;同时,平带态的线性叠加态在线性传输过程中也实现了接近完美的无衍射传输。实验结果与理论模拟的完美吻合,更加证实了这种利用平带系统中的平带态去实现光局域的可行性。
[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.
【学位授予单位】：南开大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O734

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