【作者】 王海松；

【导师】 梅良模；

【作者基本信息】 山东大学 ， 无线电物理， 2008， 博士

【摘要】 光子晶体是一种不同介电常数的介质在空间上周期性分布的人工材料,是由E.Yablonovitch和S.John于1987年同时提出的。与固体理论中研究的半导体类似,光子晶体被称为“光子”的半导体。它最突出的特点是具有“光子带隙”,频率处于光子带隙中的电磁波是禁止传播的。在光子晶体中精心设计缺陷可以在光子带隙中引入“缺陷态”,而这些缺陷态使光子晶体具有更加丰富的应用,如光子晶体光纤、微谐振腔等。另外,光子晶体也可以作为光子的导体制作各种各样的光器件。与光波导光器件相比,光子晶体光器件具有体积小、结构紧凑的特点,并且其在未来光集成芯片和全光通信网络中具有巨大的应用前景,使得相关研究引起了广泛关注并成为目前光通信领域研究的前沿。光滤波器在波分复用光通信系统中是处理特定信道或者多个信道信号的关键器件,所以基于光子晶体结构的光滤波器设计也成为重要的研究工作。当前很多研究人员已经利用光子晶体制作了很多种光滤波器,但高传输效率光子晶体多信道滤波器的设计还有待更深入的研究,这也是本论文研究的主要内容。本文在研究光子晶体组成各要素对晶体特性影响的基础上,并根据时域耦合模理论导出了波导与谐振腔间高效耦合的条件,设计了正方晶格光子晶体对称式谐振腔四信道光滤波器及三角晶格光子晶体反射式四信道光滤波器,并利用时域有限差分法(FDTDM:finite-difference time-domain method)进行了仿真分析,经过详细分析得到了影响滤波效率的主要因素和提高滤波效率的参数设置方法及规律。通过改进光子晶体光滤波器结构参数的设置,滤波器各信道的滤波效率均超过了90%。本论文的主要内容如下:1、根据光子晶体结构(介质周期性分布)的特点,对麦克斯韦方程组进行了求解,解出了光子晶体中电磁场的表达式;并证明了光子晶体的缩放法则和时间反演对称性,推导了光子晶体带隙的计算方法,为进一步分析和求解光子晶体问题打下了坚实的基础;对论文中用到的数值计算方法:时域有限差分法进行了简要介绍,运用指数差分格式导出了有限差分方程的表达式,并对稳定性条件和边界条件进行了讨论;对论文中应用比较多的时域耦合模理论进行了推导,解出了耦合方程表达式。2、分析了光子晶体组成单元形状对光子带隙的影响,通过分析发现光子晶体带隙的大小不仅与光子晶体组成单元的形状有很大关系,而且与组成材料的介电常数、晶格结构及介质的占空比也有着很大的关系。从分析结果可以看出,相同条件下圆形单元结构的光子晶体带隙最大;三角晶格的光子晶体带隙大于正方晶格的光子晶体带隙;在介质柱组成的光子晶体中,介质占空比越大晶体的带隙越宽。然后分析了缺陷谐振腔介质柱半径变化对耦合波长的影响,通过分析仿真发现,在缺陷介质柱半径小于光子晶体介质柱半径的情况下,耦合波长随着缺陷谐振腔介质柱的半径增加而增加,耦合效率在50%左右,当缺陷介质柱半径大于光子晶体介质柱半径时,耦合波长变小,并且耦合效率也变低20%左右,因此采用介质柱结构进行波导与谐振腔耦合时,应当选取缺陷介质柱半径小于晶体介质柱的半径。然后又分析了缺陷波导的设置与波的透射之间的关系及提高传播效率的方法,通过计算发现缺陷波导介质柱折射率的取值应为n_d=1.5n和n_d=2.5n,此时波导的传输效率最高,而反射效率比较低。相反,如果缺陷介质柱折射率为晶体介质柱折射率的整数倍时,则反射率很高,透射率很低。通过分析也发现适当改变缺陷波导边缘介质柱的半径、缺陷介质柱与波导间介质柱的半径及波导的宽度,都有利于提高波导与谐振腔之间的耦合效率。3、从理论上分析了谐振腔与波导间的耦合关系,根据耦合模理论导出了各端口传输系数的表达式。然后分析了对称式谐振腔和波导之间的耦合关系,根据传输系数的表达式,得到了传输系数最大时光子晶体参数间的关系式。根据理论分析的结果设计了正方晶格光子晶体对称式谐振腔四信道光滤波器。在FDTD数值计算方法进行仿真计算的基础上,合理选择相关的参数,可使所设计仿真的光子晶体滤波器各信道的滤波效率均达到96%。正方晶格对称式光子晶体滤波器的优点是结构对称、设计简单、滤波效率高。它的不足之处是需要的晶格多、结构偏大。4、根据耦合模理论推导了具有反射结构的波导与谐振腔之间的耦合关系,得到了理想耦合时各参数的设置条件。根据所推导的结果,设计了三角晶格光子晶体反射式四信道光滤波器,并且运用FDTD进行了仿真分析。从仿真的过程来看,要设计出高效的光子晶体滤波器,不仅参数的选择要与理论分析相符,而且设计中也应根据理论灵活选择参数和缺陷的大小及位置。从仿真结果可以看出,该设计方法可以实现多信道高效滤波的效果,四个信道的滤波效率均超过了90%。还根据设计中的问题,分析了影响滤波效率的原因,为提高滤波器滤波效率提供了可靠的依据。该滤波器的优点是结构简单、设计方便、滤波效率高、体积小易于集成化设计。这为设计和制作高效光子晶体多信道滤波器提供了很好的参考依据。本论文的创新点主要包括以下三个方面:1、通过多次仿真,发现适当调整波导与缺陷谐振腔之间介质柱半径的大小能较大幅度的提高耦合效率。将其应用到多信道滤波器的设计中,发现当其半径与相应缺陷介质柱半径的大小成正比时,各信道的耦合效率均能提高50%左右。该规律对于设计光子晶体多信道滤波器具有很高的参考价值。2、根据耦合模理论求出了波导与对称式谐振腔达到理想耦合效率时参数的设置条件。根据该条件,设计出正方晶格光子晶体对称式谐振腔四信道光滤波器,各信道滤波效率均高达96%。并且计算出了晶格常数与各信道波长及信道间隔的关系式,当晶格常数为570nm时,四信道的中心波长均在1550nm左右,且各信道间隔均小于20nm。这可为设计高效光子晶体滤波器提供有益的参考依据。3、应用耦合模理论导出了反射式谐振腔与波导耦合传输系数的表达式,根据表达式,得到了理想耦合时的参数设置条件,根据该条件设计出具有反射结构的三角晶格光子晶体四信道光滤波器,证明了该滤波器四信道的滤波效率均超过了90%。当晶格常数为550nm时,四信道的中心频率也均位于1550nm附近,信道间隔也均小于20nm。与正方晶格对称式光子晶体滤波器相比,它具有体积小、设计灵活方便,易于器件的集成化等优点。综上所述,本文不仅分析了影响光子晶体波导与谐振腔间耦合效率的因素,给出了提高耦合效率的方法,而且设计了正方晶格光子晶体对称式谐振腔四信道光滤波器和三角晶格光子晶体反射式四信道光滤波器,其各信道的仿真滤波效率均在90%以上,并且也给出了晶格常数与各信道波长的关系式。论文结果可为设计和制作高效的光子晶体多信道滤波器提供有益的参考依据。更多还原

【Abstract】 Photonic crystal, proposed simultaneously by E.Yablonovitch and S.John in 1987, is an artificial "band gap" material in which the dielectric constant is arranged periodically. Analogous to the semiconductors considered in solid state theory, photonic crystals are called semiconductors of photons. A photonic crystal is characteristic of "photonic band gap", in which the propagation of electromagnetic wave is highly prohibited. The defects modes can be introduced into the photonic band gap by fabricating carefully designed defects in perfect photonic crystal, and these defects modes are of more plentiful applications, such as photonic crystal fiber, micro resonant cavity etc. Additionally, a photonic crystal can act as a conductor of photons. Additional, photonic crystals can be used as the conductor of photon to produce various optical devices. Compared with optical waveguide devices, photonic crstal devices have small volume and compact structure, and have tremendous application in optical integration chips and optical communication network. Related research have attracted wide attention and become the research forefront of optical communications.Optical filter is the key device in WDM optical communication system to deal with the signal of specific channel or multiple channels. The optical filter design of base on photonic crystal structure has become an important research. At present, though many researchers have been produced many types optical filters using photonic crystals,it needs deeply study to design high efficiency photonic crystal multi-channel filters. How to design highly effective optical filter is primary objective of this thesis. Based on the research of the composed elements of photonic crystal to the crystal characteristics. and in accordance with the time-domain coupled mode theory, the high efficiency coupling condition of between waveguide and resonance cavity has been educed.The square crystal lattice photonic crystal double resonance cavity four-channel optical filter and the triangle crystal lattice photonic crystal four-channel optical filter have been designed, which be simulated using finite-difference time-domain (FDTD) method. The primary factors of influence filter efficiency and the methods of improving the filter efficiency had been discovered by using simulation analysis. Through the improvement parameter’s establishment of photonic crystal optical filter structure, filter efficiency of every channel has exceeded 90%.The main contents of the dissertation are given below:1. According to the characteristic of photonic crystal structure (dielectric periodicity distribution), the solution of the Maxwell equation has carried, and the electromagnetic field expression has also been solved in the photonic crystal .the scaling law and time reversal symmetry of photonic crystal have been improved,and the method of photonic band calculation has been educed.A good theory foundation has been obtained for solution photonic crystal.A brief introduction about FDTD (finite-difference time-domain) method is given, and the stable condition and the boundary condition have been discussed. The finite difference equation expression is obtained using the exponential difference format. A brief analysis about time domain coupled mode theory is given, and the coupling efficiency expression is obtained.2. The influence of photonic crystal composition structure to photonic band gap has been first analyzed. Through analysis, we discovered that photonic crystal band gap with the relative permittivity has a very strong relation, and the photonic crystal composition unit’s shape, the lattice structure and the dielectric duty ratio also has the very tremendous influence to the band gap size. We can see from the analysis results, the photonic crystal band gap of circular cellular construction is the biggest under the same condition. The photonic crystal band gap of triangle crystal lattice is bigger than the photonic crystal band gap of square crystal lattice. In the photonic crystal of dielectric rod, the dielectric duty ratio is bigger and the band gap is wider. Then the influence of defect resonant cavity dielectric rod radius size to the coupling wave length has been analyzed, through the analysis simulation, we find that the wavelength increased with the defect resonant cavity dielectric rod radius increases and coupling efficiency is about 50% when defect dielectric rod radius is smaller than photonic crystal dielectric rod radius. When the defect dielectric rod radius is bigger than the photonic crystal dielectric rod radius, the coupling wave length is small, and the coupling efficiency is also lower than 20%, therefore, the defect dielectric rod radius is must smaller than the crystal dielectric rod radius when using the dielectric rod structure to carry on the waveguide resonant cavity coupling. Finally, the relations of the defect waveguide with the wave transmission and the method of improvement the coupling efficiency have been analyzed. Through the computation simulation, we find that the transmission efficiency is the highest and the reflect efficiency is the lowest when defect waveguide dielectric rod refractive index is 1.5 or 2.5 times of crystal refractive index. On the contrary, the transmission efficiency is the lowest and the reflect efficiency is the highest when defect waveguide dielectric rod refractive index is the integer times of crystal refractive index. Through the analysis, we also find that the change of defect waveguide edge dielectric rod radius and wave guide’s width are advantageous for enhancing the coupling efficiency of waveguide with the resonant cavity.3. The coupling relation of between the resonant cavity and waveguide has been analyzed, and according to the coupled mode theory, transmission coefficient expression of every port has been derived. Then the coupling relation of between the symmetrical resonant cavity and waveguide has been analyzed. According to transmission coefficient expression, the photonic crystal parameter relationship has been obtained when the transmission coefficient is the biggest. According to theoretical analysis results, a square crystal lattice photonic crystal symmetrical four channel filter has been designed. And we have carried on the simulation computation using the FDTD method. According to the analysis conclusion in third chapter, and suitable selection parameters, the filter efficiency of four channels can achieve 96%. The merits of square crystal lattice photonic crystal symmetrical filter are the structure symmetry, simply design and highly filter efficiency. The demerits are that many crystal lattices are need and the structure is big. This design method may be used to manufacture integration photonic crystal multi-channel filter.4. According to the theoretical analysis, we have designed a triangle crystal lattice highly efficient photonic crystal four-channel optical filter, and have carried on the simulation analysis using FDTD method. Looking from the simulation process, it not only needs that the parameter must match with the theoretical analysis, but also needs that we should be flexible selection parameter, defect rod size and position based on the theory to design the highly effective photonic crystal optical filter. Looking from the simulation results, the filter efficiency of multi-channel filters are over 90%. According to the problem in designing, we analyzed the reason of influence filter efficiency, and provide the methods to improve filter efficiency. The merits of this design method are structure simple, manufacture convenient, medium material simple and filter efficiency high. The method provides a very good reference for design and manufacture highly efficient multi-channel photonic crystal filter.The innovations of the dissertation are given below: 1、Through many times simulation, we find that the suitable adjustment the dielectric rod radius between defect waveguide and resonant cavity can be greatly improved the efficiency of coupling. Appling the method to multi-channel filter design, we find that the filter efficiency can improve about 50% when the dielectric rod radius is proportion with ransonant cavity dielectric rod radius. The law has high reference value for design multi-channel photonic crystal filter.2、According to coupled mode theory, we obtained the parameters conditions of high coupling efficiency between waveguide and symmetric resonant cavity. We design a square lattice photonic crystal symmetry resonant cavity four-channel optical filter, the filter efficiency of every channel is high than 96%. The relationship between the channel wavelength and crytal constant is given, and the central wavelength of every channel is around 1550nm when crystal constant is 570nm.The interval of adjacent channel is less than 20nm. A good reference is provided for the design of high efficiency photonic crystal filter.3、According to coupled mode theory, the transmission coefficient expression of between reflective Waveguide and resonant cavity is calculated, and the parameters condition of high coupling efficiency is given. We design a triangle lattice photonic crystal reflective resonant cavity four-channel optical filter, and the filter efficiency of every channel is high than 90%. The central wavelength of every channel is around 1550nm when crystal constant is 550nm.The interval of adjacent channel is less than 20nm. Compared with square lattice photonic crystal filters, the merits of triangle lattice photonic crystal filter have small volume, facility to design and easy to integrated.In summary, this article has not only analyzed the primary factor of influence photonic crystal filter efficiency, and given the design method of improving the filter efficiency, but also designed the square crystal lattice photonic crystal four channel filter and the triangle crystal lattice photonic crystal reflection type four channel filter. The filter efficiency of every channel is over 90%, and the relationship expression of crystal constant and channels wavelength has also given. The article has the very high reference value for design and manufacture highly efficient photonic crystal multi-channel optical filter.更多还原