二维光子晶体传输特性的研究
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摘要
一直以来,人们期冀能像控制电流在导线中的传播一样自由的控制光的传播,这种想法随着一种新材料——光子晶体(Photonic Crystal, PhC)的出现而慢慢接近现实。上个世纪八十年代后期,Eli Yablonovitch和Sajeev John在他们发表的两篇里程碑似的论文中首次提出了"photonic crystal"这个概念,从此揭开了人类历史上控制光传播的崭新一页。
光子晶体由周期性分布的电介质或金属-电介质结构组成。在半导体晶体的能带结构中可以存在带隙,即具有某种大小能量的电子在某些特定方向上不允许传播。类似的,光子晶体通过不同介电常数的物质的周期排列得到周期变化的折射率,影响光波在它内部的传播。通过调节光子晶体结构相关的各种参数(晶格常数、填充比、增加缺陷等),可以产生禁带效应。人们利用光子晶体特殊的传播特性,实现了光子晶体光纤、光子晶体波导、光子晶体激光器、微谐振腔等。同时,光子晶体还可以当做超材料(Metamaterial),使电磁波在其中的传播产生负折射现象,从而实现超棱镜,完美透镜等。最近,光子晶体还作为解决方案之一,应用于发光二极管(Light Emitting Diode, LED)中,以提高光提取率。光子晶体的传播特性及其应用是本论文所要讨论的范围。
本论文的主要内容：
1、从光子晶体的结构特点出发,利用麦克斯韦方程组推导出符合光子晶体的电磁场表达式,进而得到光子晶体带隙的计算方法；简单介绍时域有限差分法,讨论数值稳定性和边界条件。
2、分析二维全息光子晶体的传输特性；讨论光子晶体填充比、晶格常数、晶格原胞形状,晶格原胞组成方式等各种参数对光子带隙及传输特性的影响。
3、分析二维全息光子晶体的负折射特性。
4、研究利用二维光子晶体提高LED的光提取效率。
通过研究,论文得到下列三个有意义的成果：
1、由扫描光子晶体晶格常数、填充比、介电常数等相关参数,得到大量仿真计算的数据,经过分析,得出一种光子晶体波导的设计优化方法。其特点之一是：通过调整光强阈值就可以快速的对光子晶体带隙进行调控。
2、由多参数分析全息光子晶体EFS图,得到负折射发生条件及频段特征,用FDTD法仿真,并证明在较宽频率区间(8.5%)和较大入射角范围(10°-80°)内,有明显的负折射现象。为左手材料的设计提供一思路。
3、针对LED器件由于界面反射而光提取效率较低的问题,提出了一种光子晶体辅助的LED模型结构,初步仿真计算表明：有望使其光提取效率提高数倍(与模型结构的具体物理参数密切相关)。
综上所述,本文分析了影响光子晶体传输特性的各种参数,提出了一种光子晶体波导的设计优化方法。运用平面波展开法计算了由全息法制备的空气介质柱二维光子晶体能带结构和等频面图,分析了在光子晶体中发生负折射现象的条件和频率区间,并利用时域有限差分法进行了验证。结果表明,在较宽的频率区间和较大的入射角度范围内,全息光子晶体可以发生明显的负折射现象。全息光子晶体负折射现象的研究为左手材料的设计和制备提供了一种新的思路。同时在提高LED的光提取效率方面做了大量的研究,结果可以为设计和制作高能源使用效率的LED提供参考。
People has expected to control the propagation of light freely as they do in controling current flowing in the wire. This idea has becoming reality with the emergence of photonic crystal(PhC)——a new material. In the late 80s of last century, Eli Yablonovitch and Sajeev John first brought up the concept of photonic crystal. From then on, a new era of light propagation controling began.
Photonic crystal is a periodic arrangement of media with differing dielectric constants. There may be gaps in the energy band structure of the semiconductor crystal, meaning that electrons are forbidden to propagate with certain energies in certain directions. Similarly, photonic crystal influence the light propagation in its internal by periodic varying index. In particular, we can design and construct photonic crystals with photonic band gaps, preventing light from propagation in certain directions with specified frequencies. With the special transmission characteristic of PhCs, people fabricate PhC fiber, PhC waveguide, PhC laser, micro resonator, and etc. PhC can also be metamaterial to produce electromagnetic wave negative phenomenon, and that brings up superlens and perfect lens. Recently, PhCs have been applied to compose light-emitting diodes(LEDs) to improve the light extraction efficiency. We will discuss the application and the transmission characteristic of PhCs in this thesis.
THE MAIN CONTENTS:
1. Using Maxwell equations to produce electromagnetic field expressions which consistence with the characteristic of PhCs and the calculation method of getting photonic band gaps. Making a brief introduction of Finite-Difference Time-Domain(FDTD) method. Discussing the numeric stability and boundary condition of FDTD method.
2. Analyzing the trasmission characteristic of two-dimension(2D) holographical PhCs. Discussing how parameters, filling ratio of PhCs, lattice constant, cell shape, lattice and etc., influence the photonic band gap and transmission characteristic.
3. Analyzing the negative refraction characteristic of the holographical PhCs.
4. Research how to improve LED light extraction efficiency by using 2D PhCs.
THE INNOVATIONS:
1. Theoretically research the band gap and transmission characteristic of holographical PhCs, simulating by using FDTD method. Get large amount of data by scanning the parameters of PhC (lattice constant, filling ratio, dielectric constant, and etc.). And achieve a new way to design and optimize PhC waveguide.
2. Finding the condition and frequency range in which negarive refraction phenomenons occur by analyzing the EFS plots of holographical PhCs from lots of parameters. Simulating by using FDTD method, observed a clear negative refraction phenomenon.
3. Proposing a LED model with PhCs to improve the light extraction efficiency, Veryfing the result by numerical simulation.
In summary, this thesis analyzes the parameters that influence the transmission characteristic of PhCs, and then proposes a new way to design and optimize the PhC waveguide. The band structure and equi-frequency contours for the holographical photonic crystals (PhCs) are calculated by using plane wave extension method, and the conditions for negative refraction in PhCs are analyzed as well as the frequency band. The finite-difference time-domain method is used to verify the conclusion, and it is shown that negative refraction can be clearly observed in the holographical PhCs within a wide frequency band and a large incident angle scope. The research on the negative refraction in holographical PhCs will provide a new idea for the design and fabrication of the left-handed negative-index materials. At the same time, the thesis makes a great deal of study in improve the LED light extraction efficiency and the result can be a reference for designing and fabricating high energy efficiency LED.
光子晶体由周期性分布的电介质或金属-电介质结构组成。在半导体晶体的能带结构中可以存在带隙,即具有某种大小能量的电子在某些特定方向上不允许传播。类似的,光子晶体通过不同介电常数的物质的周期排列得到周期变化的折射率,影响光波在它内部的传播。通过调节光子晶体结构相关的各种参数(晶格常数、填充比、增加缺陷等),可以产生禁带效应。人们利用光子晶体特殊的传播特性,实现了光子晶体光纤、光子晶体波导、光子晶体激光器、微谐振腔等。同时,光子晶体还可以当做超材料(Metamaterial),使电磁波在其中的传播产生负折射现象,从而实现超棱镜,完美透镜等。最近,光子晶体还作为解决方案之一,应用于发光二极管(Light Emitting Diode, LED)中,以提高光提取率。光子晶体的传播特性及其应用是本论文所要讨论的范围。
本论文的主要内容：
1、从光子晶体的结构特点出发,利用麦克斯韦方程组推导出符合光子晶体的电磁场表达式,进而得到光子晶体带隙的计算方法；简单介绍时域有限差分法,讨论数值稳定性和边界条件。
2、分析二维全息光子晶体的传输特性；讨论光子晶体填充比、晶格常数、晶格原胞形状,晶格原胞组成方式等各种参数对光子带隙及传输特性的影响。
3、分析二维全息光子晶体的负折射特性。
4、研究利用二维光子晶体提高LED的光提取效率。
通过研究,论文得到下列三个有意义的成果：
1、由扫描光子晶体晶格常数、填充比、介电常数等相关参数,得到大量仿真计算的数据,经过分析,得出一种光子晶体波导的设计优化方法。其特点之一是：通过调整光强阈值就可以快速的对光子晶体带隙进行调控。
2、由多参数分析全息光子晶体EFS图,得到负折射发生条件及频段特征,用FDTD法仿真,并证明在较宽频率区间(8.5%)和较大入射角范围(10°-80°)内,有明显的负折射现象。为左手材料的设计提供一思路。
3、针对LED器件由于界面反射而光提取效率较低的问题,提出了一种光子晶体辅助的LED模型结构,初步仿真计算表明：有望使其光提取效率提高数倍(与模型结构的具体物理参数密切相关)。
综上所述,本文分析了影响光子晶体传输特性的各种参数,提出了一种光子晶体波导的设计优化方法。运用平面波展开法计算了由全息法制备的空气介质柱二维光子晶体能带结构和等频面图,分析了在光子晶体中发生负折射现象的条件和频率区间,并利用时域有限差分法进行了验证。结果表明,在较宽的频率区间和较大的入射角度范围内,全息光子晶体可以发生明显的负折射现象。全息光子晶体负折射现象的研究为左手材料的设计和制备提供了一种新的思路。同时在提高LED的光提取效率方面做了大量的研究,结果可以为设计和制作高能源使用效率的LED提供参考。
People has expected to control the propagation of light freely as they do in controling current flowing in the wire. This idea has becoming reality with the emergence of photonic crystal(PhC)——a new material. In the late 80s of last century, Eli Yablonovitch and Sajeev John first brought up the concept of photonic crystal. From then on, a new era of light propagation controling began.
Photonic crystal is a periodic arrangement of media with differing dielectric constants. There may be gaps in the energy band structure of the semiconductor crystal, meaning that electrons are forbidden to propagate with certain energies in certain directions. Similarly, photonic crystal influence the light propagation in its internal by periodic varying index. In particular, we can design and construct photonic crystals with photonic band gaps, preventing light from propagation in certain directions with specified frequencies. With the special transmission characteristic of PhCs, people fabricate PhC fiber, PhC waveguide, PhC laser, micro resonator, and etc. PhC can also be metamaterial to produce electromagnetic wave negative phenomenon, and that brings up superlens and perfect lens. Recently, PhCs have been applied to compose light-emitting diodes(LEDs) to improve the light extraction efficiency. We will discuss the application and the transmission characteristic of PhCs in this thesis.
THE MAIN CONTENTS:
1. Using Maxwell equations to produce electromagnetic field expressions which consistence with the characteristic of PhCs and the calculation method of getting photonic band gaps. Making a brief introduction of Finite-Difference Time-Domain(FDTD) method. Discussing the numeric stability and boundary condition of FDTD method.
2. Analyzing the trasmission characteristic of two-dimension(2D) holographical PhCs. Discussing how parameters, filling ratio of PhCs, lattice constant, cell shape, lattice and etc., influence the photonic band gap and transmission characteristic.
3. Analyzing the negative refraction characteristic of the holographical PhCs.
4. Research how to improve LED light extraction efficiency by using 2D PhCs.
THE INNOVATIONS:
1. Theoretically research the band gap and transmission characteristic of holographical PhCs, simulating by using FDTD method. Get large amount of data by scanning the parameters of PhC (lattice constant, filling ratio, dielectric constant, and etc.). And achieve a new way to design and optimize PhC waveguide.
2. Finding the condition and frequency range in which negarive refraction phenomenons occur by analyzing the EFS plots of holographical PhCs from lots of parameters. Simulating by using FDTD method, observed a clear negative refraction phenomenon.
3. Proposing a LED model with PhCs to improve the light extraction efficiency, Veryfing the result by numerical simulation.
In summary, this thesis analyzes the parameters that influence the transmission characteristic of PhCs, and then proposes a new way to design and optimize the PhC waveguide. The band structure and equi-frequency contours for the holographical photonic crystals (PhCs) are calculated by using plane wave extension method, and the conditions for negative refraction in PhCs are analyzed as well as the frequency band. The finite-difference time-domain method is used to verify the conclusion, and it is shown that negative refraction can be clearly observed in the holographical PhCs within a wide frequency band and a large incident angle scope. The research on the negative refraction in holographical PhCs will provide a new idea for the design and fabrication of the left-handed negative-index materials. At the same time, the thesis makes a great deal of study in improve the LED light extraction efficiency and the result can be a reference for designing and fabricating high energy efficiency LED.
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