【作者】 胡磊；

【导师】 张俊喜；

【作者基本信息】 合肥工业大学 ， 光电信息工程， 2021， 博士

【摘要】 二维材料因其独特的性质吸引了众多研究者的兴趣,其中最吸引人的特征之一是石墨烯电子能带结构中圆锥形的能带片段连接而成的奇点狄拉克点,该点处的模态密度为零,在其邻近范围内,模态密度线性衰减,色散曲线呈线性变化。近年来,由于光子晶体中的狄拉克点也具有不同寻常的色散关系,吸引了越来越多人的关注,对克莱因隧穿效应、量子震颤效应和赝扩散等行为进行了研究。同时,异于传统光子带隙或全内反射原理,狄拉克频率处的新型光局域和导光机制应运而生,这种狄拉克定域/导波模式由于具有独特的代数衰减特性,作为一种光子晶体的新颖类量子效应,将为新型光子器件、光子芯片结构、光学传感的设计增加可行性和灵活性。本文采用理论分析、数值计算和微波实验的方法,对不同波段、不同晶格类型、色散/非色散材料、二维/类二维光子晶体中狄拉克锥的性质以及狄拉克频率处的局域模和相关特性进行了深入的研究,主要研究工作和结果如下:1)电介质光子晶体狄拉克局域模式的数值模拟与实验分析。介绍具有高品质因数、代数形式的慢衰减速率以及稳定驻波特性的TE模式三角晶格光子晶体中的狄拉克频率局域模。在微小折射率差近似下分析了TM模式三角晶格光子晶体布里渊区角点处的简并性及其附近的色散特性,推导得到了TM模式下含缺陷三角晶格光子晶体所具有的与TE模式完全类似的狄拉克频率局域特性,利用数值方法计算了TM狄拉克局域模,验证了其特性,相关模拟结果与理论分析一致。讨论了蜂窝晶格、Kagome晶格、A7晶格等多种复式晶格光子晶体的狄拉克局域模式,丰富了理论的多样性,为制造优良性能的新型导波器件提供了多种选择。2)微波光子晶体谐振腔的狄拉克局域模式测试。设计了一种包含中心缺陷的二维微波光子晶体,计算了狄拉克频率下的局域模式,解释了这种模式的特殊性质,用实验测量了含缺陷和不含缺陷时光子晶体的透射谱,发现只有当引入缺陷时,狄拉克频率处才会出现谐振峰,峰值的频率不会随入射波方向的改变而改变,由于此测试中不会激发起边缘模式,因此该实验验证了一种局域模式的存在,即狄拉克频率处的局域模。虽然该实验是在微波频率范围内进行的,但根据光子晶体的比例缩放特性,这一结论可以扩展到其他电磁频段。3)金属光子晶体狄拉克局域模式的数值模拟与理论分析。推导了含损耗的金属色散介质光子晶体能带计算方法,该方法可以推广到不含损耗或包含非色散材料的光子晶体等各种简化模型。在微小折射率差近似下分析了TM模式下三角晶格金属光子晶体布里渊区角点处的简并性及其附近的色散特性,研究了光波段TM模式下含缺陷三角晶格金属光子晶体的狄拉克频率局域特性,研究了多种缺陷类型下微波金属光子晶体的TE/TM狄拉克局域特性,所有的理论结果均通过数值模拟进行了验证,理论与仿真具有良好的契合度。通过向金属介质柱光子晶体的背景中填充等离子体,实现了频率可调的狄拉克局域模。尽管金属为色散介质,介电函数依赖电磁波频率,但是通过研究可以发现,由金属介质柱构成的光子晶体谐振腔同样可以支持狄拉克频率局域模,展现出与电介质光子晶体谐振腔一样的性质,这为扩展新型器件的应用扩展提供了帮助。4)光子晶体平板狄拉克局域模式的数值模拟与理论分析。研究了平板模式与普通二维光子晶体模式间的关系,在微小折射率差近似下分析了三角晶格光子晶体平板在布里渊区角点处的简并性及其附近的色散特性,发现了在光子晶体平板中存在类TE模式的狄拉克锥,而这一狄拉克锥可以通过抬升相应二维光子晶体狄拉克锥的频率来获得。分析了平板谐振腔中的狄拉克频率局域特性,讨论了平板厚度对局域模式的影响。光子晶体平板在实际设计、加工、应用中所具有的实用性,将为新型器件的使用提供有力的支持。更多还原

【Abstract】 2D materials have attracted a great deal of researchers’ interests due to their unique properties,one of the most fascinating features is the Dirac point in the electronic band structure of graphene which has a conical singularity with linearly vanishing density of states and linear dispersion in its vicinity.In recent years,more and more people have investigated the Dirac points in photonic crystals due to their unusual dispersion relations,including Klein tunneling,Zitterbewegung,and pseudo-diffusive transmission.Meanwhile,a new kind of light confinement and guided mechanism at the Dirac frequency comes into being,which is quite different from the traditional photonic bandgap or total internal reflection theory.Moreover,these Dirac localized/guided modes can exhibit unique algebraic profiles,as a new quasi-quantum effect in photonic crystals,which will add new capabilities and more flexibility to the design techniques of novel photonic components,photonic chips and optical sensors.In this thesis,by means of theoretical analysis,numerical calculations and microwave experiment,the properties of Dirac cones,localized modes and related features at the Dirac frequency in different wavebands,different lattice types,dispersive/non-dispersive materials,2D/quasi-2D photonic crystals are studied in depth,which enriches the diversity of the theory.The main research works and results are summarized as follows:1)Numerical simulations and experimental analysis of localized Dirac mode in dielectric photonic crystals.A novel kind of localized Dirac mode in a TE polarized triangular photonic crystal is introduced which has high quality factor,slow decay rate with an algebraic form and stable standing wave properties.The small refractive index difference approximation method is performed on a TM polarized triangular lattice photonic crystal to analyze the degeneracy of the corner points of the Brillouin zone and the dispersion properties around these points.It’s derived to get that the TM mode of the triangular lattice photonic crystal with defects is completely similar with that of the TE mode,which supports localization features at the Dirac frequency.By using numerical methods to calculate the TM localized Dirac modes and verify their features,it can be found that the related simulation results and theoretical analysis are consistent.The localized Dirac modes in complex lattice photonic crystals such as honeycomb lattice,Kagome lattice and A7 lattice are also discussed,which enrich the diversity of the theory and provide a variety of choices for the fabrication of new guiding wave devices with excellent performance.2)Microwave measurement of the localized Dirac mode in a photonic crystal resonator.A 2D microwave photonic crystal with a defect in the center is designed,and its cavity mode at the the Dirac frequency is calculated.The unique properties of this mode are explained.The experiment is handled to measure the transmission spectrum with and without defects.It is found that a resonant peak occurs at the Dirac frequency only when a defect is introduced.The frequency of the peak does not shift when the incident wave changes direction.Due to this testing configuration will not excite any edge modes,the experiment validates the existence of a localized mode,namely the localized Dirac modes.Although the experiment is carried out in the microwave frequency range,the conclusion can be extended to other electromagnetic bands according to the proportional scaling characteristics of photonic crystals.3)Numerical simulations and theoretical analysis of localized Dirac mode in metallic photonic crystals.The bandstructure calculation method of a metallic(dispersive medium)photonic crystal containing loss is derived,which can be extended to various simplified models such as photonic crystals without loss or containing non-dispersive materials.The small refractive index difference approximation method is performed on a TM polarized triangular lattice metallic photonic crystal to analyze the degeneracy of the corner points of the Brillouin zone and the dispersion properties around these points.The TM polarization Dirac frequency localization characteristics of triangular lattice metallic photonic crystals with defects in optical band and TE/TM Dirac localization characteristics of metallic photonic crystals with various types of defects in microwave band are derived.All of the theoretical predictions are verified by numerical simulations,and have a good fit with each other.The tunable localized Dirac mode in frequency is realized by filling plasma into the background of metallic cylinder-type photonic crystal.Although the dielectric functions of metals,the dispersive media,depend on the electromagnetic wave frequency,it is found that the photonic crystal resonator composed of metallic media can also support localized Dirac modes,showing the same properties with dielectric photonic crystal cavities.It will provide helps to extend the applications of new optical devices.4)Numerical simulations and theoretical analysis of localized Dirac mode in photonic crystal slabs.The relationship between the slab modes and ordinary 2D photonic crystal modes is studied.The small refractive index difference approximation method is performed on a triangular lattice photonic crystal slab to analyze the degeneracy of the corner points of the Brillouin zone and the dispersion properties around these points.It is shown that TE-like Dirac cone can be found in a photonic crystal slab,and the Dirac cone can be obtained by lifting the frequency of the Dirac cone of the corresponding 2D photonic crystal.The localization characteristics at the Dirac frequency are analyzed and the influence of slab thickness of the localized Dirac mode is discussed.Because the photonic crystal slab has more practical significance in the actual design,processing and application,it will provide favorable supports to the utilization of this novel device.更多还原