Lieb莫尔光子晶格及其光子学特性研究

Lieb Moire Photonic Lattice and Its Photonic Properties

受到电子学领域双层扭曲石墨烯的启发,莫尔光子晶格的多种莫尔构型被证明具有光子局域等特性。将两个相同周期的Lieb子晶格旋转角36.87°叠加构造了Lieb莫尔晶格,并基于平面波展开法计算了其能带结构。结果表明,相比于常规的Lieb晶格,Lieb莫尔晶格的无量纲化光子禁带宽度最高可增加0.25,并且禁带中心发生了蓝移,因而更适合在光通信领域的应用。数值计算结果表明在Lieb莫尔晶格的能带结构中还具有平带,其特性可通过改变介质柱的几何参数进行调控,最高平整度可达到0.0018722。通过计算平整度最高时的电场分布,发现了局域的现象。基于Lieb晶格的莫尔构型可为光子晶体研究提供新的方法,也为研究复杂光子晶体结构提供新的平台。

Inspired by the two-layer twisted graphene in electronics,Moire photonic lattices are also of great interest to researchers.Various Moire photonic configurations have been shown to possess peculiar photonic properties.In this paper,the photonic characteristics of Lieb Moire lattices composed of two overlapping Lieb sublattices with different rotation angles are studied.It is found that two Lieb sublattices can form a lattice with square characteristics when the rotation angle is 36.87°.Both the Lieb lattice and Lieb Moire lattice are composed of GaAs dielectric cylinders embedded in air.The radii of the cylinders of the two sublattices are r2 and r1 respectively.In order to compare their lattice properties,their lattice constants are set to be equal.With the same filling factor,the plane wave method is used to simulate the band structures of TM modes.According to numerical simulation,the Lieb Moire lattice has a wider photonic bandgap and a blueshift of the bandgap center than the conventional Lieb lattice,which is more suitable for optical communication applications.The main reason for the phenomenon is the change of dielectric contrast.To find the widest bandgaps,the filling factors of Lieb lattice and Lieb Moire lattice are further scanned,and the bandgap maps are obtained.The numerical simulation results show that the bandgap firstly increases and then decreases with the increasing filling factor,and the bandgap of Lieb Moire lattice is wider.At the same time,the photonic flat band properties are also observed.Three bands with very small gradients are observed in the band structure of Moire lattice,which are the 15th,22nd and 27th bands.In order to indicate the characteristics of flat bands,the flatness is defined as F.Through calculation,the 22th band has the minimum F,meaning it has the highest flatness.By changing the size of the dielectric cylinders,the flatness of the flat band can be higher.The flat band can lead to localization of field near lattice.By calculating the intensity of electric field distribution at theΓand K points in the 22th band with the highest flatness,it can be seen that the electric energies are obviously located tightly to the central rings of cylinders,which verifies the effective flatness of photon band.The flat band with higher flatness can lead to stronger localization of electric field,which has a wide application prospect in nonlinear optics,photoelectric energy conversion devices and so on.Changing the structural parameters and dielectric parameters of Lieb Moire lattice can further increase the width of bandgap.In order to obtain the optimized bandgap width,the materials are changed.The band characteristics of composite Moire Lieb lattice formed by the superposition of sublattices of different dielectric materials are also studied based on plane wave method.The dielectric material of the unrotated sublattice labelled as“A”was selected as GaAs,and the dielectric material of rotated sublattice labled as“B”was selected as SiO2,and the superposition points of two sublattices were selected as GaAs.The dielectric cylinders are all embedded in air.It is proved that the composite Lieb Moire photonic lattice has a wider bandgap,which is mainly due to the reduced symmetry caused by the two kinds of materials.Then the radius relationship of the two sublattices is simply set as r2=0.5r1,and r_(2) changes synchronously with r_(1).The main bandgap width of the composite Lieb Moire photonic lattice is further increased,which can be attributed to the decrease in the overall lattice symmetry caused by the change of the radius.The Moire configuration based on Lieb lattice proposed in this paper provides a new method to improve the bandgap of photonic lattice,it provides a meaningful platform for studying the physical phenomena of flat band.