单双光子聚合法结合制备引入缺陷的光子晶体及其色散性质的研究
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摘要
光子晶体(Photonic Crystals,PhCs)的概念最早在1987年由E.Yablonovitch和S.John同时提出,它是一种折射率在空间呈周期性变化的电介质材料组成的结构,其变化周期和光的波长为同一个数量级。光子晶体也称为光子带隙材料(Photonic Bandgapmaterials),或者电磁晶体(Electromagnetic Crystals)。
光子晶体具有两个重要的特性,即光子带隙和光子局域。使得光子晶体在很多方面都有巨大的应用前景,比如可以制备光子晶体光纤,波导,以及低阈值激光器等很多种重要器件。本篇论文的目的是要对光子晶体的一系列问题从理论和实验两方面进行比较系统和全面的分析,分析的重点体现在下面四个方面:
1.全息光子晶体的实验制备及缺陷引入
在光子晶体的实验制备中我们主要研究两个方面,一是激光全息干涉法一步成型制备大规模无缺陷的光子晶体,二是用单光子和双光子聚合相结合的办法,在光子晶体中引入缺陷。
由于光子晶体的巨大应用前景,有关光子晶体的制备方法也备受关注,激光全息干涉法就是其中的一种。激光全息干涉法是利用三束或者四束非共面光干涉,形成二维或三维亮暗相间的干涉图样,图样的周期与所使用干涉光的波长在一个数量级。将这种干涉图样投影到一种介质材料上记录下来,就可以得到二维或者三维的光子晶体结构。这种方法可以一次成型制备大范围无缺陷的结构,具有较高的分辩率,并且制备程序简单,成本低廉,具有很多的优点。双光子聚合法制备光子晶体一般利用Ti:sapphire飞秒激光器的二倍频激光进行光聚合,然后用机械控制来移动样品,最后处理样品,清洗掉没有聚合的区域,来制作各种结构的光子晶体。这种方法比较精细,但造价比较昂贵,适用于制备对位置要求比较精确的结构,不适于大规模生产。
在本篇论文中,我们提出了一种单双光子聚合相结合的办法来制备引入缺陷的光子晶体。先使用波长为532nm的激光进行全息干涉,来制备大规模无缺陷的二维或者三维光子晶体,然后利用飞秒激光器进行双光子聚合,在未经显影处理的样品上扫描沟道,形成线缺陷或者点缺陷。聚合材料对双光子的吸收与光强度的四次方成正比,因此双光子聚合的区域非常小,只在焦点附近λ~3的区域内(λ为激光波长),这样我们就可以精确的控制在光子晶体中引入缺陷。最后再进行显影处理,就可以得到引入缺陷的光子晶体。这种方法结合了全息干涉和双光子聚合两种方法的优点,既能够快速方便地制备光子晶体结构,又可以精确控制引入缺陷。
在论文的第二章巾,我们系统地分析了全息法制备一维、二维和三维光子晶体的光束配置和所得图样,第三章则介绍了具体的实验制备过程,以及结合双光子聚合法引入缺陷的光路设计和实验过程,并在文章中给出了实验制备的样品照片,验证了这种方法的可行性。
2.全息光子晶体的能带特性
光子晶体最重要的一个特性是具有光子带隙,即处在禁带内频率的光是不能在光子晶体中传输的。光子禁带的出现依赖于光子晶体的结构和介电常数的配比。一般来说,光子晶体中两种介质的介电常数比越大,入射光将被散射得越强烈,就越有可能出现光子禁带。影响禁带的出现还有一个重要因素:晶体的几何构形,由于带隙产生在布里渊区(Brillouin zone)的边界处,所以原则上完全带隙(即光在整个晶格结构空间的所有方向上传输时都具有带隙)更容易出现在布里渊区是近球形的结构中。理论上讲,如果光子晶体的带隙越大,我们可以控制或者应用的频率范围就越广,所以如何设计介电常数的结构和形状,使之具有较大的完全带隙成为我们关注的焦点。
在以前的工作中,我们曾使用衍射分束器件(DBS)得到三束呈伞状对称的光束相互干涉,制备出了对TE和TM两种模式同时具有较大带隙的二维三角结构光子晶体。在文章的第四章中,我们对原有工作做了改进,在原来一次曝光的基础上,把三束对称光都沿同一方向转动60度后,再对样品进行第二次曝光,经过两次曝光处理后的光子晶体结构获得了超过20%的更大带隙。
3.光子晶体中的传输特性——负折射和超透镜现象
通常的介质材料介电常数与磁导率都是正的,即具有正的折射率,电磁波传输时波矢K、电场E和磁场H之间的关系符合右手定律。那么当介电常数ε和μ都为负值时,电场、磁场和波矢之间则应该符合左手关系,满足这种关系的物质被为左手材料(Left-handed materials,LHM)。电磁波在左手材料中的行为与在右手材料中相反,比如光的负折射、负的切连科夫效应、反多普勒效应等等。所以近年来有关左手材料的研究受到了广泛的关注。
2002年,科学家们发现当光波以一定角度入射到在光子晶体界面上时,光波在光子晶体中的传输也会出现和在左手材料中相同的现象:比如负折射和超透镜(SuperLens)现象。对于有些频率的电磁波,以很大范围内的入射角度入射到光子晶体中都会出现负折射现象,传输光线在光子晶体后面呈现出自聚焦,有时会聚焦于一点呈现出很清晰的像点,这时光子晶体对于这种频率的光波,就像是一个折射率为-1的完美透镜,这种现象被称为超透镜。在论文的第五章,我们详细介绍了光子晶体中负折射现象和超透镜现象产生的原理,用波矢图解法分析了这些现象产生需要满足的条件,最后用有限时域差分方法(Finite Difference in Time Domain,FDTD)理论模拟来验证了左手传输特性在光子晶体中的出现。并且对全息干涉形成的光子晶体与具有规则格点形状的常规光子晶体相比较,由于全息干涉结构的格点形状是不规则的,导致它们的等频率线分布与规则形状的光子晶体也有较大差别,我们发现在填充比(Filling ratio)较大的光子晶体结构或者格点是以介质材料相连接的结构中,负折射现象更容易出现,并且入射电磁波频谱范围更广。
4.二维光子晶体薄板内缺陷腔的性质和品质因子计算
在一块完美的光子晶体中引入某种缺陷,光子带隙中会出现缺陷态,当电磁波的频率与缺陷态相吻合时,就有可能被局域在缺陷位置,因而呈现出很大的态密度和品质因子。这种由光子晶体制作的微腔,比起传统的微腔体积小,品质因子高,在光通信以及高精度光学仪器的设计中有着重要的应用前景。
在论文的第六章给出了有关二维光子晶体薄板微腔的系统分析,用平面波展开法计算了光子晶体薄板的带隙分布,以及引入缺陷后腔的特征频率。并结合以前的工作,对全息法制备的二维光子晶体薄板的能带分布及如何引入缺陷模式做了详细介绍。微腔的特征频率确定后,最重要的性质是腔的品质因子(Quality Factor),我们使用有限时域差分法,自己编写程序来计算二维光子晶体薄板的品质因子,并分析了怎样通过改变腔的结构来提高品质因子,改善微腔的品质,使光子晶体微腔能有更广泛有效的运用。
The conception of photonic crystal was first proposed by E.Yablonovitch and S.John at the same time in 1987. Photonic crystals are structures made of dielectric materials with their dielectric constants verified periodically, and the periods are about the same order of magnitude as optical wavelength. Photonic crystal is also called photonic bandgap materials and electromagnetic crystals.
There are two important characters of photonic crystals which made them have a huge application foreground: photonic band gap and photon localization. For example, lots of devices like Photonic crystal fibers, waveguides and photonic crystal lasers with low threshold etc, can be fabricated by inducing defects into perfect photonic crystals. My dissertation is aimed to give a systematic and comprehensive analysis in this field theoretically and experimentally, with emphases on following four respects:
1. Experimental demonstration of holographic fabrication of photonic crystals
For demonstrate the fabrication of photonic crystals experimentally, we mainly focus the research on two important parts in this section: first fabricating perfect photonic crystals for a large area without any defects in one step using holographic lithography; the second inducing defects into photonic crystals by combination of holographic lithography and two-photon polymerization.
Since photonic crystals have demonstrated attractive potential applications in many areas, their fabrication has always been of great interest. Hence there are many available methods of making photonic microstructures include semiconductor microfabrication, colloidal crystallization, tightly focused laser beam scanning and two-photon polymerization etc. Holographic lithography(HL) method is one of them, which means that fabrication of 1D, 2D and 3D periodical microstructures by interference of two beams, three or four noncoplanar beams, multiple mutually coherent laser beams are made to intersect and interfere, producing period patterns of light and dark areas repeated on a scale proportional to the wavelength of the beams used. Projecting these interference patterns onto some proper optical recording materials, thus many 2- and 3-D crystalline structures can be formed by holographic lithography method. Compared with all previous methods, the technique of holographic lithography has obvious advantages such as high spatial resolutions, easiness of controlling the pattern form by adjusting wave design, one-step recording, and the ability to obtain photonic crystals with high refractive index contrast by using polymeric templates.
Two-photon polymerization(TPP) method for fabrication photonic crystals means using doubled-frequency laser beams from a Ti:sapphire femto-second laser focused on the sample which made of photon polymerization materials, then moving the sample precisely point by point to form the structures as we designed with a computer controlled machine, at last the sample is developed and only polymerized areas left. This method is always used to fabricate very precise structures, but not available for massive production, since TPP is a serial pinpoint writing process that takes lots of money and times.
In this work, we proposed a new method for fabricating photonic crystals with controlled defects by combination of holographic lithography (HL) and two-photon polymerization (TPP). First, the large-area photonic crystal lattice is patterned in photopolymer by holographic interference quickly and easily in one-step recording with wavelength at 532 nm, which is visible and more propitious for arranging optical setup in experiments compared with 355nm and 325nm used before. In the second step, the defects in the lattice to implement the functional devices are introduced by two-photon absorption with a femtosecond laser. Since the two-photo absorption probability depends quadratically on intensity, the polymerization of material is localized only in a small vicinity of orderλ~3 (where X is the laser wavelength) near the focus point, and thus the form of defects can be exactly controlled. Using such a process we can introduce point defects to create 3D or 2D nanocavities, or line defects to create a linear waveguide or fiber, as well as any other desired pattern in principle. Consequently this hybrid approach has an advantage in terms of fabrication time and cost compared with other methods for the patterning of large-scale photonic crystal-based integrated systems.
A comprehensive study of the optical setup and the experimental processes of fabricating 1D, 2D and 3D photonic crystals using holographic lithography were given in chapter 2. And in the second part of this chapter, we discussed the preparation of the material, the optical setup and the preliminary experimental results for making photonic crystals with controlled defects by combination of HL and TPP.
2. Photonic bandgap properties of holographic photonic crystals
The most important property of photonic crystals is band gap, which means the existence of a frequency gap in the electromagnetic wave spectrum. Whether the band gaps appear or not, defended on the distribution of dielectric materials, and the contrasts between dielectric constants. Generally, the dispersion of incident waves would be much stronger as the contrasts between dielectric constants getting bigger, thus there are more chances for band gaps to appear in these situations. The shapes of photonic crystal atoms can also influence the appearance of photonic band gaps, since band gaps usually come from the boundary of Brillouin zone, theoretically complete band gaps are more likely to exist in structures with almost circular Brillouin zones (complete band gap means that electromagnetic waves in the band gap can not transmit in any direction inside the photonic crystals.). The spectrum range that could be properly controlled or manipulated is totally decided by the size of bandgap, so how to increase the bandgaps of photonic crystals by designing the lattices and sizes of photonic crystals has been of great interest..
In the previous work, we have made 2D triangular photonic crystals which have photonic bandgap (PBG) for both TE and TM polarization modes, by the interference of three beams coming through a DBS(diffractive beam splitter) with symmetric umbrella geometry. In chapter 3 of this work, we made some improvement on the base of original work and proposed a double exposure multi-beam interference method to fabricate a hexagonal lattice with irregular columns.The first exposure process is made to form regular triangular photonic crystals with circular columns, and in the second exposure, three beams have the same symmetry as in the first exposure only rotated for 60°, results showing that this hexagonal lattice can yield a complete PBG as large as△ω/ω= 24.0 %.
3. Propagation properties of photonic crystals-negative refraction and superlens
The dielectric constants (ε) and magnetic permeability (μ) of usual materials are both positive, so is the refractive index, and the directions of electric fields (E), magnetic fields (H), and the propagation vectors (K) follow the right handed rule. Thus Left-handed-materials (LHM) are materials with simultaneously negative dielectric permittivity (ε) and negative magnetic permeability (μ). The phase velocity of the light wave propagating inside this material is pointed in the opposite direction of the energy flow. So the Poynting vector and wave vector are antiparallel, consequently, the light is refracted negatively, and also there are many other unusual behaviors in LHM like reverse Cerenkov radiation, contrary Doppler effect etc.
In 2002, left handed properties such as negative refraction and superlens were found in photonic crystals either, when the frequency of incident wave and incident angle were appropriate. So in chapter 4 we first give an elaborate introduction of the principle how left handed effects happen in photonic crystals, analyze these situations that appropriate for negative refraction and superlens effects using wave vector program, and simulate these effects appeared in photonic crystals with Finite Difference in Time Domain method (FDTD).
Since holographic structures usually have irregular atoms or columns, and the light propagation properties of PhCs are closely related to their specific structures. We may expect some difference in propagation behavior between regular and holographic structures. Considering that two-dimensional (2D) holographic structures can be more easily made and have wide potential use, it is of interest and importance to extend the study of negative refraction to 2D HL structures. In the second part of this chapter, we take a 2D square structure with circular columns connected by veins as an example to investigate this effect compared with regular PCs, and the results show that left handed properties are more likely to exist in structures with high-epsilon, filling ratios or in connected lattices. For some certain frequencies, negative refraction happens with the incident angle changes in a large area, and propagation waves converge behind the photonic crystals. Sometimes a perfect imaging could appear, which means that the effective refractive index is almost -1, and we call this effect as superlens.
4. Properties and Quality factors of Defect Microcavities in 2D photonic crystal slabs
Defect modes would appear among the band gaps if we induce some defects into perfect photonic crystals, and electromagnetic waves with the same frequencies as defect modes can be localized in the defects strongly, thus the defect cavities which is of the order of optical wavelength have very high state densities and quality factors, and are very important for a variety of scientific and engineering applications.
A comprehensive study of defect microcavities in 2D photonic crystal slabs is given in chapter 5, the band map for photonic crystal slabs with finite thickness, the eigenfrequencies of defect cavities, and quality factors (Q) are calculated with plane wave expansion method (PWM) and finite difference in time domain method (FDTD). We have also researched on the properties of defect microcavities in photonic crystals made by holographic lithography combined with our previous work.
光子晶体具有两个重要的特性,即光子带隙和光子局域。使得光子晶体在很多方面都有巨大的应用前景,比如可以制备光子晶体光纤,波导,以及低阈值激光器等很多种重要器件。本篇论文的目的是要对光子晶体的一系列问题从理论和实验两方面进行比较系统和全面的分析,分析的重点体现在下面四个方面:
1.全息光子晶体的实验制备及缺陷引入
在光子晶体的实验制备中我们主要研究两个方面,一是激光全息干涉法一步成型制备大规模无缺陷的光子晶体,二是用单光子和双光子聚合相结合的办法,在光子晶体中引入缺陷。
由于光子晶体的巨大应用前景,有关光子晶体的制备方法也备受关注,激光全息干涉法就是其中的一种。激光全息干涉法是利用三束或者四束非共面光干涉,形成二维或三维亮暗相间的干涉图样,图样的周期与所使用干涉光的波长在一个数量级。将这种干涉图样投影到一种介质材料上记录下来,就可以得到二维或者三维的光子晶体结构。这种方法可以一次成型制备大范围无缺陷的结构,具有较高的分辩率,并且制备程序简单,成本低廉,具有很多的优点。双光子聚合法制备光子晶体一般利用Ti:sapphire飞秒激光器的二倍频激光进行光聚合,然后用机械控制来移动样品,最后处理样品,清洗掉没有聚合的区域,来制作各种结构的光子晶体。这种方法比较精细,但造价比较昂贵,适用于制备对位置要求比较精确的结构,不适于大规模生产。
在本篇论文中,我们提出了一种单双光子聚合相结合的办法来制备引入缺陷的光子晶体。先使用波长为532nm的激光进行全息干涉,来制备大规模无缺陷的二维或者三维光子晶体,然后利用飞秒激光器进行双光子聚合,在未经显影处理的样品上扫描沟道,形成线缺陷或者点缺陷。聚合材料对双光子的吸收与光强度的四次方成正比,因此双光子聚合的区域非常小,只在焦点附近λ~3的区域内(λ为激光波长),这样我们就可以精确的控制在光子晶体中引入缺陷。最后再进行显影处理,就可以得到引入缺陷的光子晶体。这种方法结合了全息干涉和双光子聚合两种方法的优点,既能够快速方便地制备光子晶体结构,又可以精确控制引入缺陷。
在论文的第二章巾,我们系统地分析了全息法制备一维、二维和三维光子晶体的光束配置和所得图样,第三章则介绍了具体的实验制备过程,以及结合双光子聚合法引入缺陷的光路设计和实验过程,并在文章中给出了实验制备的样品照片,验证了这种方法的可行性。
2.全息光子晶体的能带特性
光子晶体最重要的一个特性是具有光子带隙,即处在禁带内频率的光是不能在光子晶体中传输的。光子禁带的出现依赖于光子晶体的结构和介电常数的配比。一般来说,光子晶体中两种介质的介电常数比越大,入射光将被散射得越强烈,就越有可能出现光子禁带。影响禁带的出现还有一个重要因素:晶体的几何构形,由于带隙产生在布里渊区(Brillouin zone)的边界处,所以原则上完全带隙(即光在整个晶格结构空间的所有方向上传输时都具有带隙)更容易出现在布里渊区是近球形的结构中。理论上讲,如果光子晶体的带隙越大,我们可以控制或者应用的频率范围就越广,所以如何设计介电常数的结构和形状,使之具有较大的完全带隙成为我们关注的焦点。
在以前的工作中,我们曾使用衍射分束器件(DBS)得到三束呈伞状对称的光束相互干涉,制备出了对TE和TM两种模式同时具有较大带隙的二维三角结构光子晶体。在文章的第四章中,我们对原有工作做了改进,在原来一次曝光的基础上,把三束对称光都沿同一方向转动60度后,再对样品进行第二次曝光,经过两次曝光处理后的光子晶体结构获得了超过20%的更大带隙。
3.光子晶体中的传输特性——负折射和超透镜现象
通常的介质材料介电常数与磁导率都是正的,即具有正的折射率,电磁波传输时波矢K、电场E和磁场H之间的关系符合右手定律。那么当介电常数ε和μ都为负值时,电场、磁场和波矢之间则应该符合左手关系,满足这种关系的物质被为左手材料(Left-handed materials,LHM)。电磁波在左手材料中的行为与在右手材料中相反,比如光的负折射、负的切连科夫效应、反多普勒效应等等。所以近年来有关左手材料的研究受到了广泛的关注。
2002年,科学家们发现当光波以一定角度入射到在光子晶体界面上时,光波在光子晶体中的传输也会出现和在左手材料中相同的现象:比如负折射和超透镜(SuperLens)现象。对于有些频率的电磁波,以很大范围内的入射角度入射到光子晶体中都会出现负折射现象,传输光线在光子晶体后面呈现出自聚焦,有时会聚焦于一点呈现出很清晰的像点,这时光子晶体对于这种频率的光波,就像是一个折射率为-1的完美透镜,这种现象被称为超透镜。在论文的第五章,我们详细介绍了光子晶体中负折射现象和超透镜现象产生的原理,用波矢图解法分析了这些现象产生需要满足的条件,最后用有限时域差分方法(Finite Difference in Time Domain,FDTD)理论模拟来验证了左手传输特性在光子晶体中的出现。并且对全息干涉形成的光子晶体与具有规则格点形状的常规光子晶体相比较,由于全息干涉结构的格点形状是不规则的,导致它们的等频率线分布与规则形状的光子晶体也有较大差别,我们发现在填充比(Filling ratio)较大的光子晶体结构或者格点是以介质材料相连接的结构中,负折射现象更容易出现,并且入射电磁波频谱范围更广。
4.二维光子晶体薄板内缺陷腔的性质和品质因子计算
在一块完美的光子晶体中引入某种缺陷,光子带隙中会出现缺陷态,当电磁波的频率与缺陷态相吻合时,就有可能被局域在缺陷位置,因而呈现出很大的态密度和品质因子。这种由光子晶体制作的微腔,比起传统的微腔体积小,品质因子高,在光通信以及高精度光学仪器的设计中有着重要的应用前景。
在论文的第六章给出了有关二维光子晶体薄板微腔的系统分析,用平面波展开法计算了光子晶体薄板的带隙分布,以及引入缺陷后腔的特征频率。并结合以前的工作,对全息法制备的二维光子晶体薄板的能带分布及如何引入缺陷模式做了详细介绍。微腔的特征频率确定后,最重要的性质是腔的品质因子(Quality Factor),我们使用有限时域差分法,自己编写程序来计算二维光子晶体薄板的品质因子,并分析了怎样通过改变腔的结构来提高品质因子,改善微腔的品质,使光子晶体微腔能有更广泛有效的运用。
The conception of photonic crystal was first proposed by E.Yablonovitch and S.John at the same time in 1987. Photonic crystals are structures made of dielectric materials with their dielectric constants verified periodically, and the periods are about the same order of magnitude as optical wavelength. Photonic crystal is also called photonic bandgap materials and electromagnetic crystals.
There are two important characters of photonic crystals which made them have a huge application foreground: photonic band gap and photon localization. For example, lots of devices like Photonic crystal fibers, waveguides and photonic crystal lasers with low threshold etc, can be fabricated by inducing defects into perfect photonic crystals. My dissertation is aimed to give a systematic and comprehensive analysis in this field theoretically and experimentally, with emphases on following four respects:
1. Experimental demonstration of holographic fabrication of photonic crystals
For demonstrate the fabrication of photonic crystals experimentally, we mainly focus the research on two important parts in this section: first fabricating perfect photonic crystals for a large area without any defects in one step using holographic lithography; the second inducing defects into photonic crystals by combination of holographic lithography and two-photon polymerization.
Since photonic crystals have demonstrated attractive potential applications in many areas, their fabrication has always been of great interest. Hence there are many available methods of making photonic microstructures include semiconductor microfabrication, colloidal crystallization, tightly focused laser beam scanning and two-photon polymerization etc. Holographic lithography(HL) method is one of them, which means that fabrication of 1D, 2D and 3D periodical microstructures by interference of two beams, three or four noncoplanar beams, multiple mutually coherent laser beams are made to intersect and interfere, producing period patterns of light and dark areas repeated on a scale proportional to the wavelength of the beams used. Projecting these interference patterns onto some proper optical recording materials, thus many 2- and 3-D crystalline structures can be formed by holographic lithography method. Compared with all previous methods, the technique of holographic lithography has obvious advantages such as high spatial resolutions, easiness of controlling the pattern form by adjusting wave design, one-step recording, and the ability to obtain photonic crystals with high refractive index contrast by using polymeric templates.
Two-photon polymerization(TPP) method for fabrication photonic crystals means using doubled-frequency laser beams from a Ti:sapphire femto-second laser focused on the sample which made of photon polymerization materials, then moving the sample precisely point by point to form the structures as we designed with a computer controlled machine, at last the sample is developed and only polymerized areas left. This method is always used to fabricate very precise structures, but not available for massive production, since TPP is a serial pinpoint writing process that takes lots of money and times.
In this work, we proposed a new method for fabricating photonic crystals with controlled defects by combination of holographic lithography (HL) and two-photon polymerization (TPP). First, the large-area photonic crystal lattice is patterned in photopolymer by holographic interference quickly and easily in one-step recording with wavelength at 532 nm, which is visible and more propitious for arranging optical setup in experiments compared with 355nm and 325nm used before. In the second step, the defects in the lattice to implement the functional devices are introduced by two-photon absorption with a femtosecond laser. Since the two-photo absorption probability depends quadratically on intensity, the polymerization of material is localized only in a small vicinity of orderλ~3 (where X is the laser wavelength) near the focus point, and thus the form of defects can be exactly controlled. Using such a process we can introduce point defects to create 3D or 2D nanocavities, or line defects to create a linear waveguide or fiber, as well as any other desired pattern in principle. Consequently this hybrid approach has an advantage in terms of fabrication time and cost compared with other methods for the patterning of large-scale photonic crystal-based integrated systems.
A comprehensive study of the optical setup and the experimental processes of fabricating 1D, 2D and 3D photonic crystals using holographic lithography were given in chapter 2. And in the second part of this chapter, we discussed the preparation of the material, the optical setup and the preliminary experimental results for making photonic crystals with controlled defects by combination of HL and TPP.
2. Photonic bandgap properties of holographic photonic crystals
The most important property of photonic crystals is band gap, which means the existence of a frequency gap in the electromagnetic wave spectrum. Whether the band gaps appear or not, defended on the distribution of dielectric materials, and the contrasts between dielectric constants. Generally, the dispersion of incident waves would be much stronger as the contrasts between dielectric constants getting bigger, thus there are more chances for band gaps to appear in these situations. The shapes of photonic crystal atoms can also influence the appearance of photonic band gaps, since band gaps usually come from the boundary of Brillouin zone, theoretically complete band gaps are more likely to exist in structures with almost circular Brillouin zones (complete band gap means that electromagnetic waves in the band gap can not transmit in any direction inside the photonic crystals.). The spectrum range that could be properly controlled or manipulated is totally decided by the size of bandgap, so how to increase the bandgaps of photonic crystals by designing the lattices and sizes of photonic crystals has been of great interest..
In the previous work, we have made 2D triangular photonic crystals which have photonic bandgap (PBG) for both TE and TM polarization modes, by the interference of three beams coming through a DBS(diffractive beam splitter) with symmetric umbrella geometry. In chapter 3 of this work, we made some improvement on the base of original work and proposed a double exposure multi-beam interference method to fabricate a hexagonal lattice with irregular columns.The first exposure process is made to form regular triangular photonic crystals with circular columns, and in the second exposure, three beams have the same symmetry as in the first exposure only rotated for 60°, results showing that this hexagonal lattice can yield a complete PBG as large as△ω/ω= 24.0 %.
3. Propagation properties of photonic crystals-negative refraction and superlens
The dielectric constants (ε) and magnetic permeability (μ) of usual materials are both positive, so is the refractive index, and the directions of electric fields (E), magnetic fields (H), and the propagation vectors (K) follow the right handed rule. Thus Left-handed-materials (LHM) are materials with simultaneously negative dielectric permittivity (ε) and negative magnetic permeability (μ). The phase velocity of the light wave propagating inside this material is pointed in the opposite direction of the energy flow. So the Poynting vector and wave vector are antiparallel, consequently, the light is refracted negatively, and also there are many other unusual behaviors in LHM like reverse Cerenkov radiation, contrary Doppler effect etc.
In 2002, left handed properties such as negative refraction and superlens were found in photonic crystals either, when the frequency of incident wave and incident angle were appropriate. So in chapter 4 we first give an elaborate introduction of the principle how left handed effects happen in photonic crystals, analyze these situations that appropriate for negative refraction and superlens effects using wave vector program, and simulate these effects appeared in photonic crystals with Finite Difference in Time Domain method (FDTD).
Since holographic structures usually have irregular atoms or columns, and the light propagation properties of PhCs are closely related to their specific structures. We may expect some difference in propagation behavior between regular and holographic structures. Considering that two-dimensional (2D) holographic structures can be more easily made and have wide potential use, it is of interest and importance to extend the study of negative refraction to 2D HL structures. In the second part of this chapter, we take a 2D square structure with circular columns connected by veins as an example to investigate this effect compared with regular PCs, and the results show that left handed properties are more likely to exist in structures with high-epsilon, filling ratios or in connected lattices. For some certain frequencies, negative refraction happens with the incident angle changes in a large area, and propagation waves converge behind the photonic crystals. Sometimes a perfect imaging could appear, which means that the effective refractive index is almost -1, and we call this effect as superlens.
4. Properties and Quality factors of Defect Microcavities in 2D photonic crystal slabs
Defect modes would appear among the band gaps if we induce some defects into perfect photonic crystals, and electromagnetic waves with the same frequencies as defect modes can be localized in the defects strongly, thus the defect cavities which is of the order of optical wavelength have very high state densities and quality factors, and are very important for a variety of scientific and engineering applications.
A comprehensive study of defect microcavities in 2D photonic crystal slabs is given in chapter 5, the band map for photonic crystal slabs with finite thickness, the eigenfrequencies of defect cavities, and quality factors (Q) are calculated with plane wave expansion method (PWM) and finite difference in time domain method (FDTD). We have also researched on the properties of defect microcavities in photonic crystals made by holographic lithography combined with our previous work.
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