全息光子晶体禁带展宽方法和波导传输特性的研究
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摘要
光子晶体自从被提出后,在光学物理、凝聚态物理、电磁波、信息技术等领域引起了人们广泛的关注。在这短短的二十年里,光子晶体在理论研究和实验研究方面均取得了显著的成果,并且在某些领域也有了一定的应用。由于光子晶体的巨大潜在应用价值,设计和制作可见光和近红外波段的完全带隙光子晶体,成为近十年来科学研究的热点之一。
在制备复杂结构光子晶体的多种方法中,相对于其它制作方法,例如逐层叠加方法、半导体微加工和自组织生长,激光全息制作方法具有成本低,耗时短,方便制作和有效等优点。本论文运用激光全息干涉技术并结合平面波展开法和有限时域差分方法,在理论上比较系统地研究了如何使用伞形配置的多激光束形成具有较宽的完全禁带的光子晶体,提出多种实现全禁带展宽的设计方案,并通过晶体结构及其能带传输特性的模拟来验证能带计算结果的正确性,其中的创新性工作主要包括以下几个方面:
一、全息干涉法优化二维正方结构光子晶体的光束设计及其能带性质的研究
由于全息干涉法中格点柱的形状和大小实际是由干涉场的等强度面决定的,所以所得结构的能带性质与制备过程有着密切的联系。作为实例,我们在第三章中提出了两种利用全息干涉技术制备的新型二维正方结构光子晶体的方案。第一种是由绕z轴旋转45°的针垫形柱组成的正方晶格点阵,这种结构与过去报道过的由正方柱组成的同类结构相比在很宽的介电常数比的范围内有更大的相对光子带隙。因为理论分析发现通过长条柱做脉络连接圆柱组成的正方点阵结构的圆柱半径和长条宽度在适当配比情况下,可以产生很大的完全带隙,所以我们利用全息干涉法设计了另一种由不规则介质柱组成的相似晶体结构。这两种优化晶体结构不但能够产生更大的相对带隙,而且在有全带隙的光子晶体制备过程中对系统各种参数的要求更加宽松。文中系统分析了各种参数与光子带隙的关系,推导出具有最佳能带性质的全息光子晶体的一般规律,为制备正方结构光子晶体设计提供了理论依据。
二、全息干涉法制备的二维三角混合光子晶体的结构设计及其能带性质的研究
在第四章我们首次开展了光子晶体周期结构旋转轴与能带性质关系的系统研究,提出了一种利用全息干涉二次曝光技术改变光子晶体对称性的方法,发现通过降低光子晶体的对称性和适当改变介质柱大小和形状,能够有效提高光子能带性质。计算表明经过适当优化的结构在很宽的系统参数范围内有全光子带隙存在,并且发现能够打开大于1%全带隙所要求的最小介电常数仅为3.8,这个值是所有报道过二维周期光子晶体结果中的最小值。此研究为在低折射率比的情况下实现光波的高效率传输技术提供了一种有价值的指导方案。
三、利用伞状对称多光束干涉制备新型三维光子晶体及其能带性质的研究
三维光子晶体比二维光子晶体更具有多样性,利用全息法制备三维光子晶体的一个重要的途径就是用伞状对称四束光干涉法,即周围三束侧光两两成相同角度,分别与中间光束成相同夹角θ。第五章中,我们通过理论分析和模拟计算推导出利用伞状对称四束光全息干涉可能制备的三维光子晶体结构,系统研究了光束夹角从10°到180°变化所得晶体结构的相应布里渊区的特征与光子能带性质,这些工作将有助于该方法在实验中的有效应用。另外,我们首次提出一种伞状对称五束光全息干涉制备光子晶体的方法,系统分析了随光束夹角不断增大时可以得到的光子晶体结构及其能带性质,发现利用该方法不但能够制备出存在最大相对带隙的类金刚石结构光子晶体,而且可以保证所有干涉光束从样品同侧入射,为简化实验条件,改善光子能带性质提供了可行性方案。
四、全息光子晶体波导传输性质的研究
为了研究光波在二维全息光子晶体中的传播性质,我们在第六章中研究了光波在引入两个60°转角线缺陷的全息三角结构光子晶体波导中的传播性质。通过模拟计算发现在很宽频率范围内,光波能够以大于90%的透过率高效率传输,这也是同类报道中最宽的频率范围,并且揭示了光波在两个60°转弯之间产生的谐振与光子晶体的结构有着密切的联系。此项工作使全息光子晶体在光子整合回路中的应用充满希望,并且为优化光子晶体波导的传输性质提供了理论依据。
五、全息干涉法制备光子晶体的实验研究
最后,在第七章我们对利用全息干涉法制备光子晶体模板以及利用单双光子聚合技术在光子晶体模板中引入线缺陷进行了实验研究。在实验中,我们设计出了几种实用的光路,制备出了几种光子晶体模板,并成功从中引入了带有直角转弯的线缺陷。虽然这一领域的工作受到实验条件的限制,但是我们的实验结果证明了全息干涉法在大面积、低成本制备光子晶体方面具有独特的优势,并验证了通过单双光子聚合相结合技术在光子晶体中引入线缺陷的可行性。
以上工作围绕光子晶体全带隙展宽和优化传输性质展开,自成体系,提出了一系列具有更好的能带特性和传输特性的二维、三维晶体结构,并进行了模拟验证,具有一定的深度和广度,相关成果已在Optics Express等多种国际著名期刊上发表。
Since the concept of photonic crystal(PhC) was proposed in 1987,photonic crystal has attracted great attention in the fields of optical physics,condensed matter physics, electromagnetic waves and information technology.Lots of achievements related to theoretical and experimental studies have been reported and applied in some regions.For the effective application of photonic crystals,designing and fabricating photonic crystals with complete band gap in near infrared and visible region become a focus for science research in the last decade.
Compared with other techniques of PhC fabrication,such as Layer-by-Layer method, semiconductor microfabrication,self-assembling approach,etc.,the process of holographic lithography(HL) is more economical,rapid,convenient and effective.In this thesis,holographic lithography,plane wave extension method(PWE) and finite difference time domain(FDTD) are used to systematically investigate the photonic crystals with large complete band gap formed by symmetrical umbrellalike beams configuration in theories.We have proposed several desiging methods to produce holograpgic PhCs and widen their complete band gaps effectively,and carried out a series of simulation study of PhC structures and their transmission properties to verify our calculation results of band gap characters.The main initiative contributions in this dissertation include following aspects:
1、Beams design and PBG properties study for optimized 2D square lattice formed by HL
In holographic fabrication of photonic crystal the shape and size of the dielectric columns or particles("atoms") are determined by the isointensity surfaces of the interference field.Therefore,their photonic band gap(PBG) properties closely relate to their fabrication design.As an example,in Chapter 3 we propose two kinds of holographically formed novel two-dimensional(2D) square lattice.One is composed of pincushion columns rotated by 45°,and it is shown that this structure has complete PBGs in a wide range of dielectric contrast comparable to or even larger than those of the same lattice with square columns reported before.Theoretical analysis has revealed that a 2D lattice with circular columns connected by veins can produce large complete band gap when the radius of columns and the width of veins are properly choosen.Here we have proposed a holographic method to fabricate another similar 2D structure of irregular columns.These two kinds of PhCs can yield greater 2D complete band gaps.Moreover, the requirement for various system parameters is more relaxable in the fabrication process of PhCs with complete band gaps.We have systematically analysed the relations between these system parameters and PBGs,and derived a conclusion from these research results to give a guideline for practical fabrication.
2、Structure design and PBG properties study of 2D triangular hybrid holographic lattice
In Chapter 4,we firstly carry out the study of relation between symmetry and band gap of periodic PhCs,and propose a kind of technique to change the symmetry property of photonic crystal with second exposure in holographic lithography.The theoretical analysis indicates that complete relative PBGs can be enhanced by properly lowering the symmetry property of photonic crystal lattice and choosing the size and pattern of the columns.Computations show that the optimazed normal structure has complete band gaps over wide ranges of system parameters,and the minimum dielectric constant required to open a complete band gap withΔω/ω＞1%is as low as 3.8,which is the lowest compared with the results of 2D periodic photonic crystals ever reported.These results provide a valuable guideline for realization of light transmissing efficiently in waveguide with low dielectric constant contrast.
3、Holographic fabrication of 3D PhCs by interference of umbrellalike symmetrical beams and the study of their PBG properties
Generally,3D PhCs are more versatile than 2D PhCs.An important way to make 3D PhCs by HL is the interference of four umbrellalike symmetrical beams(IFUB) where three ambient beams(A-beams) form the same apex angleθwith a central beam (C-beam) and any two of the three A-beams also form the same angle.In Chapter 5 a theoretical investigation of the possible three-dimensional photonic crystal structures that can be created by holographic interference using the symmetric umbrellalike configuration of four plane waves is made.The irreducible Brillouin zones and the photonic band gap properties of the possible resulting crystal lattices when the apex angle is varied from 10°to nearly 180°are investigated,which will be helpful to the efficient use of this method in experiments.Moreover,we propose a holographic design of five-beam symmetric umbrella configuration and systematically analyze the band gap properties of resultant photonic crystals when the apex angle is continuously increased. The diamondlike structure with a largest relative band gap can be obtained with this recording geometry conveniently where all the beams are incident from the same half-space.This five-beam symmetric umbrella configuration provides a feasibility to relax the experiment requirements in HL and optimize PBG property of photonic crystals.
4、Study of transmission properties in holographic photonic crystal waveguide
In order to study the waveguide characters of 2D holographic PhCs,we have investigated the transmission properties of the photonic crystal waveguide(PCW) which is a line defect with two 60°bends in a 2D triangular holographic PhCs in Chapter 6. Calculations have shown that for this PCW high transmission(＞90%) through sharp comers can be obtained in a wide frequency range.As far as we know,this result should be the widest frequency range with high transmission(＞90%) in the waveguide of similar 2D triangular PhCs ever reported.We have also found that the specific holographic designs of PhC have strong influence on the resonance between the two bends.This work makes holographic PhCs promising for application in the range of photonic integrated circuits and provides a guideline for optimizing the transmission property of holographic PCW.
5、Experimental demonstration of holographic fabrication of 2- and 3-D PhCs
Finally,fabrication of PhC templates by HL and the PhCs with controlled defects by combination of single-photon and two-photon photopolymerization have been studied experimentally.In our experiment,we have designed several practical recording equipments and fabricated several PhCs templates.Moreover,we have introduced the line defect with an orthogonal bend in PhCs templates successfully.The work in this field may be limited by our experimental conditions,but these experimental results have proved that HL has unique advantage in fabrication of PhCs with large area and low cost, and verify that combination of holographic lithography and two-photon polymerization can be used to fabricate PhCs with defects.
Arranging from photonic band gap broadening,optimization of transmission properties to the defect behavior,and from theoretical analysis to experimental demonstrations,these research works provide a systematic study in the field of holographic PhCs with fruitful achievements which have been published in a series of famous international journals,such as Optics Express.
在制备复杂结构光子晶体的多种方法中,相对于其它制作方法,例如逐层叠加方法、半导体微加工和自组织生长,激光全息制作方法具有成本低,耗时短,方便制作和有效等优点。本论文运用激光全息干涉技术并结合平面波展开法和有限时域差分方法,在理论上比较系统地研究了如何使用伞形配置的多激光束形成具有较宽的完全禁带的光子晶体,提出多种实现全禁带展宽的设计方案,并通过晶体结构及其能带传输特性的模拟来验证能带计算结果的正确性,其中的创新性工作主要包括以下几个方面:
一、全息干涉法优化二维正方结构光子晶体的光束设计及其能带性质的研究
由于全息干涉法中格点柱的形状和大小实际是由干涉场的等强度面决定的,所以所得结构的能带性质与制备过程有着密切的联系。作为实例,我们在第三章中提出了两种利用全息干涉技术制备的新型二维正方结构光子晶体的方案。第一种是由绕z轴旋转45°的针垫形柱组成的正方晶格点阵,这种结构与过去报道过的由正方柱组成的同类结构相比在很宽的介电常数比的范围内有更大的相对光子带隙。因为理论分析发现通过长条柱做脉络连接圆柱组成的正方点阵结构的圆柱半径和长条宽度在适当配比情况下,可以产生很大的完全带隙,所以我们利用全息干涉法设计了另一种由不规则介质柱组成的相似晶体结构。这两种优化晶体结构不但能够产生更大的相对带隙,而且在有全带隙的光子晶体制备过程中对系统各种参数的要求更加宽松。文中系统分析了各种参数与光子带隙的关系,推导出具有最佳能带性质的全息光子晶体的一般规律,为制备正方结构光子晶体设计提供了理论依据。
二、全息干涉法制备的二维三角混合光子晶体的结构设计及其能带性质的研究
在第四章我们首次开展了光子晶体周期结构旋转轴与能带性质关系的系统研究,提出了一种利用全息干涉二次曝光技术改变光子晶体对称性的方法,发现通过降低光子晶体的对称性和适当改变介质柱大小和形状,能够有效提高光子能带性质。计算表明经过适当优化的结构在很宽的系统参数范围内有全光子带隙存在,并且发现能够打开大于1%全带隙所要求的最小介电常数仅为3.8,这个值是所有报道过二维周期光子晶体结果中的最小值。此研究为在低折射率比的情况下实现光波的高效率传输技术提供了一种有价值的指导方案。
三、利用伞状对称多光束干涉制备新型三维光子晶体及其能带性质的研究
三维光子晶体比二维光子晶体更具有多样性,利用全息法制备三维光子晶体的一个重要的途径就是用伞状对称四束光干涉法,即周围三束侧光两两成相同角度,分别与中间光束成相同夹角θ。第五章中,我们通过理论分析和模拟计算推导出利用伞状对称四束光全息干涉可能制备的三维光子晶体结构,系统研究了光束夹角从10°到180°变化所得晶体结构的相应布里渊区的特征与光子能带性质,这些工作将有助于该方法在实验中的有效应用。另外,我们首次提出一种伞状对称五束光全息干涉制备光子晶体的方法,系统分析了随光束夹角不断增大时可以得到的光子晶体结构及其能带性质,发现利用该方法不但能够制备出存在最大相对带隙的类金刚石结构光子晶体,而且可以保证所有干涉光束从样品同侧入射,为简化实验条件,改善光子能带性质提供了可行性方案。
四、全息光子晶体波导传输性质的研究
为了研究光波在二维全息光子晶体中的传播性质,我们在第六章中研究了光波在引入两个60°转角线缺陷的全息三角结构光子晶体波导中的传播性质。通过模拟计算发现在很宽频率范围内,光波能够以大于90%的透过率高效率传输,这也是同类报道中最宽的频率范围,并且揭示了光波在两个60°转弯之间产生的谐振与光子晶体的结构有着密切的联系。此项工作使全息光子晶体在光子整合回路中的应用充满希望,并且为优化光子晶体波导的传输性质提供了理论依据。
五、全息干涉法制备光子晶体的实验研究
最后,在第七章我们对利用全息干涉法制备光子晶体模板以及利用单双光子聚合技术在光子晶体模板中引入线缺陷进行了实验研究。在实验中,我们设计出了几种实用的光路,制备出了几种光子晶体模板,并成功从中引入了带有直角转弯的线缺陷。虽然这一领域的工作受到实验条件的限制,但是我们的实验结果证明了全息干涉法在大面积、低成本制备光子晶体方面具有独特的优势,并验证了通过单双光子聚合相结合技术在光子晶体中引入线缺陷的可行性。
以上工作围绕光子晶体全带隙展宽和优化传输性质展开,自成体系,提出了一系列具有更好的能带特性和传输特性的二维、三维晶体结构,并进行了模拟验证,具有一定的深度和广度,相关成果已在Optics Express等多种国际著名期刊上发表。
Since the concept of photonic crystal(PhC) was proposed in 1987,photonic crystal has attracted great attention in the fields of optical physics,condensed matter physics, electromagnetic waves and information technology.Lots of achievements related to theoretical and experimental studies have been reported and applied in some regions.For the effective application of photonic crystals,designing and fabricating photonic crystals with complete band gap in near infrared and visible region become a focus for science research in the last decade.
Compared with other techniques of PhC fabrication,such as Layer-by-Layer method, semiconductor microfabrication,self-assembling approach,etc.,the process of holographic lithography(HL) is more economical,rapid,convenient and effective.In this thesis,holographic lithography,plane wave extension method(PWE) and finite difference time domain(FDTD) are used to systematically investigate the photonic crystals with large complete band gap formed by symmetrical umbrellalike beams configuration in theories.We have proposed several desiging methods to produce holograpgic PhCs and widen their complete band gaps effectively,and carried out a series of simulation study of PhC structures and their transmission properties to verify our calculation results of band gap characters.The main initiative contributions in this dissertation include following aspects:
1、Beams design and PBG properties study for optimized 2D square lattice formed by HL
In holographic fabrication of photonic crystal the shape and size of the dielectric columns or particles("atoms") are determined by the isointensity surfaces of the interference field.Therefore,their photonic band gap(PBG) properties closely relate to their fabrication design.As an example,in Chapter 3 we propose two kinds of holographically formed novel two-dimensional(2D) square lattice.One is composed of pincushion columns rotated by 45°,and it is shown that this structure has complete PBGs in a wide range of dielectric contrast comparable to or even larger than those of the same lattice with square columns reported before.Theoretical analysis has revealed that a 2D lattice with circular columns connected by veins can produce large complete band gap when the radius of columns and the width of veins are properly choosen.Here we have proposed a holographic method to fabricate another similar 2D structure of irregular columns.These two kinds of PhCs can yield greater 2D complete band gaps.Moreover, the requirement for various system parameters is more relaxable in the fabrication process of PhCs with complete band gaps.We have systematically analysed the relations between these system parameters and PBGs,and derived a conclusion from these research results to give a guideline for practical fabrication.
2、Structure design and PBG properties study of 2D triangular hybrid holographic lattice
In Chapter 4,we firstly carry out the study of relation between symmetry and band gap of periodic PhCs,and propose a kind of technique to change the symmetry property of photonic crystal with second exposure in holographic lithography.The theoretical analysis indicates that complete relative PBGs can be enhanced by properly lowering the symmetry property of photonic crystal lattice and choosing the size and pattern of the columns.Computations show that the optimazed normal structure has complete band gaps over wide ranges of system parameters,and the minimum dielectric constant required to open a complete band gap withΔω/ω＞1%is as low as 3.8,which is the lowest compared with the results of 2D periodic photonic crystals ever reported.These results provide a valuable guideline for realization of light transmissing efficiently in waveguide with low dielectric constant contrast.
3、Holographic fabrication of 3D PhCs by interference of umbrellalike symmetrical beams and the study of their PBG properties
Generally,3D PhCs are more versatile than 2D PhCs.An important way to make 3D PhCs by HL is the interference of four umbrellalike symmetrical beams(IFUB) where three ambient beams(A-beams) form the same apex angleθwith a central beam (C-beam) and any two of the three A-beams also form the same angle.In Chapter 5 a theoretical investigation of the possible three-dimensional photonic crystal structures that can be created by holographic interference using the symmetric umbrellalike configuration of four plane waves is made.The irreducible Brillouin zones and the photonic band gap properties of the possible resulting crystal lattices when the apex angle is varied from 10°to nearly 180°are investigated,which will be helpful to the efficient use of this method in experiments.Moreover,we propose a holographic design of five-beam symmetric umbrella configuration and systematically analyze the band gap properties of resultant photonic crystals when the apex angle is continuously increased. The diamondlike structure with a largest relative band gap can be obtained with this recording geometry conveniently where all the beams are incident from the same half-space.This five-beam symmetric umbrella configuration provides a feasibility to relax the experiment requirements in HL and optimize PBG property of photonic crystals.
4、Study of transmission properties in holographic photonic crystal waveguide
In order to study the waveguide characters of 2D holographic PhCs,we have investigated the transmission properties of the photonic crystal waveguide(PCW) which is a line defect with two 60°bends in a 2D triangular holographic PhCs in Chapter 6. Calculations have shown that for this PCW high transmission(＞90%) through sharp comers can be obtained in a wide frequency range.As far as we know,this result should be the widest frequency range with high transmission(＞90%) in the waveguide of similar 2D triangular PhCs ever reported.We have also found that the specific holographic designs of PhC have strong influence on the resonance between the two bends.This work makes holographic PhCs promising for application in the range of photonic integrated circuits and provides a guideline for optimizing the transmission property of holographic PCW.
5、Experimental demonstration of holographic fabrication of 2- and 3-D PhCs
Finally,fabrication of PhC templates by HL and the PhCs with controlled defects by combination of single-photon and two-photon photopolymerization have been studied experimentally.In our experiment,we have designed several practical recording equipments and fabricated several PhCs templates.Moreover,we have introduced the line defect with an orthogonal bend in PhCs templates successfully.The work in this field may be limited by our experimental conditions,but these experimental results have proved that HL has unique advantage in fabrication of PhCs with large area and low cost, and verify that combination of holographic lithography and two-photon polymerization can be used to fabricate PhCs with defects.
Arranging from photonic band gap broadening,optimization of transmission properties to the defect behavior,and from theoretical analysis to experimental demonstrations,these research works provide a systematic study in the field of holographic PhCs with fruitful achievements which have been published in a series of famous international journals,such as Optics Express.
引文
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