含缺陷Ta_2O_5/MgF_2一维光子晶体的理论分析
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摘要
1987年,Yablonovitch和John分别独立地提出了介电常数呈周期性分布的材料可以改变光子在其中的传播行为,并称这种材料为光子晶体(Photonic crystals)。光子晶体可以调制光在其中的传播行为,因而产生了许多新奇的物理性质,在制作全新概念或以前所不能制作的高性能光学器件上有广泛应用前景。目前光子晶体的研究和制备主要集中在波长大于红外、可见光的波段。波长位于可见光波段,尤其是波长较短波段的光子晶体的理论和实验研究还很少,这主要是由于大部分的材料在此波段都存在严重的吸收;另一方面现有加工工艺在制备二、三维光子晶体时还有一定难度,而一维光子晶体结构简单,易于制备,在应用上又可以代替某些高维光子晶体,正在成为人们研究的热点。
Ta_2O_5是一种高折射率、低吸收的陶瓷材料,在可见光和近红外区有高的反射率,其应用的领域越来越广。而MgF_2材料则是可见光及紫外波段最具应用潜力的光学材料之一,在可见光区有很高的透射率,是一种低折射率和高抗损伤的材料,本文选用Ta_2O_5和MgF_2两种光学材料构建了可见光波段一维光子晶体,由于可见光波段光子晶体的膜层厚度在纳米数量级,而两种材料组成的界面间原子互扩散会引起界面区域出现一折射率变化层,因此也考察了界面区域折射率变化对带隙特性产生的影响。
可见光波段一维光子晶体及其含缺陷结构设计采用传输矩阵法。具体研究内容如下:
1.设计了Ta_2O_5/MgF_2多层膜一维光子晶体周期结构,其带隙从439nm到559nm覆盖了整个蓝绿光波段。入射角在较小角度范围0?~20?变化时TE、TM模式带隙完全重合,但入射光以高于20?的角度入射时,TE、TM模式带隙不再完全重合,虽然两种模式下带隙均发生蓝移,但TE模式带隙变窄而TM模式带隙增宽。
2.在Ta_2O_5/MgF_2多层膜周期结构中间引入Ta_2O_5缺陷层设计了一种含缺陷一维光子晶体。调节其缺陷层厚度带隙中分别出现了单、双缺陷模,单缺陷模位于蓝绿光交界处(495.3nm),双缺陷模分别在蓝光(471nm)和绿光(528nm)。
3.构建了Ta_2O_5和MgF_2界面原子互扩散结构模型,探讨了Ta_2O_5和MgF_2界面区域折射率变化对Ta_2O_5/MgF_2一维光子晶体带隙及缺陷模的影响规律。
In 1987, Yablonovitch and John first showed that photonic crystals (PCs) may display a range of frequencies where the propagation of an electromagnetic wave in the PCs is completely forbidden. PCs are of great of novel properties result from photons movement can be modulated in PCs, which has extensive application in fabrication of new conception or advanced optical devices that can not make previously. PCs have been obtained in infrared, microwave, and millimeter-wave region. For wavelength shorter than infrared, especially short wavelength in visible region or UV region only a few experimental and theoretical systems have recently been demonstrated to exhibit the signature of photonic bandgaps. This is because most materials have high absorption coefficients and unstable dielectric constants under prolonged irradiation with VIS/UV light. On the other hand, tremendous trouble exists in the preparation of two-dimensional and three-dimensional PCs with several nanometres for present technology. However, for the simple structure and preparation of one-dimensional PCs, moreover, 1D PCs can replace some higher dimensional PCs in applications, it is becoming hot point recently.
Ta_2O_5 is a ceramic material with high refractive index and low absorption which has high reflection in visible and near infrared region thus is applied in more and more extensive fields. And MgF_2 is that one of potential optical materials in VIS/UV region which has high transmissivity and low refractivity and well resistance to damage. Therefore, this paper chooses both Ta_2O_5 and MgF_2 fabricated 1D PCs in visible range. Because of the thickness of films just have some nanometers in visible region, thus a layer with various refractivity appears due to atoms diffusion on the surface between two materials. As a result, the paper also considers the influence of atoms diffusion on Ta_2O_5/MgF_2 surface to the properties of gap.
Using transfer matrix method, this paper designed theoretically the multilayer 1D PC and the structure with defect layer. The detail of the study can be introduced as follows.
In the first place, we designed Ta_2O_5/MgF_2 multilayer which photonic band gap (PBG) covered the whole blue-green range from 439nm to 559nm. The gap in TE and TM mode completely overlapped each other when the incident angle varing from 0? to 20? but incompletely overlapped each other when the incident angle more than 20?, then the gaps move towards to more short wavelength and became narrow in TE mode but broad in TM mode.
In the second place, Ta_2O_5 defect layer is introduced into Ta_2O_5/MgF_2 multilayer and single defect mode or double defect modes appear in PBG when varying the thickness of the defect layer. One defect mode presents at 495.3nm and two defect modes lie in 471nm and 528nm, respectively.
Last but not least important, the structure of atoms diffusion on the surface between Ta_2O_5 and MgF_2 is designed and the influence of diffusion layers with different refractivity between Ta_2O_5 and MgF_2 is considered for studying the properties of PBG and defect modes.
Ta_2O_5是一种高折射率、低吸收的陶瓷材料,在可见光和近红外区有高的反射率,其应用的领域越来越广。而MgF_2材料则是可见光及紫外波段最具应用潜力的光学材料之一,在可见光区有很高的透射率,是一种低折射率和高抗损伤的材料,本文选用Ta_2O_5和MgF_2两种光学材料构建了可见光波段一维光子晶体,由于可见光波段光子晶体的膜层厚度在纳米数量级,而两种材料组成的界面间原子互扩散会引起界面区域出现一折射率变化层,因此也考察了界面区域折射率变化对带隙特性产生的影响。
可见光波段一维光子晶体及其含缺陷结构设计采用传输矩阵法。具体研究内容如下:
1.设计了Ta_2O_5/MgF_2多层膜一维光子晶体周期结构,其带隙从439nm到559nm覆盖了整个蓝绿光波段。入射角在较小角度范围0?~20?变化时TE、TM模式带隙完全重合,但入射光以高于20?的角度入射时,TE、TM模式带隙不再完全重合,虽然两种模式下带隙均发生蓝移,但TE模式带隙变窄而TM模式带隙增宽。
2.在Ta_2O_5/MgF_2多层膜周期结构中间引入Ta_2O_5缺陷层设计了一种含缺陷一维光子晶体。调节其缺陷层厚度带隙中分别出现了单、双缺陷模,单缺陷模位于蓝绿光交界处(495.3nm),双缺陷模分别在蓝光(471nm)和绿光(528nm)。
3.构建了Ta_2O_5和MgF_2界面原子互扩散结构模型,探讨了Ta_2O_5和MgF_2界面区域折射率变化对Ta_2O_5/MgF_2一维光子晶体带隙及缺陷模的影响规律。
In 1987, Yablonovitch and John first showed that photonic crystals (PCs) may display a range of frequencies where the propagation of an electromagnetic wave in the PCs is completely forbidden. PCs are of great of novel properties result from photons movement can be modulated in PCs, which has extensive application in fabrication of new conception or advanced optical devices that can not make previously. PCs have been obtained in infrared, microwave, and millimeter-wave region. For wavelength shorter than infrared, especially short wavelength in visible region or UV region only a few experimental and theoretical systems have recently been demonstrated to exhibit the signature of photonic bandgaps. This is because most materials have high absorption coefficients and unstable dielectric constants under prolonged irradiation with VIS/UV light. On the other hand, tremendous trouble exists in the preparation of two-dimensional and three-dimensional PCs with several nanometres for present technology. However, for the simple structure and preparation of one-dimensional PCs, moreover, 1D PCs can replace some higher dimensional PCs in applications, it is becoming hot point recently.
Ta_2O_5 is a ceramic material with high refractive index and low absorption which has high reflection in visible and near infrared region thus is applied in more and more extensive fields. And MgF_2 is that one of potential optical materials in VIS/UV region which has high transmissivity and low refractivity and well resistance to damage. Therefore, this paper chooses both Ta_2O_5 and MgF_2 fabricated 1D PCs in visible range. Because of the thickness of films just have some nanometers in visible region, thus a layer with various refractivity appears due to atoms diffusion on the surface between two materials. As a result, the paper also considers the influence of atoms diffusion on Ta_2O_5/MgF_2 surface to the properties of gap.
Using transfer matrix method, this paper designed theoretically the multilayer 1D PC and the structure with defect layer. The detail of the study can be introduced as follows.
In the first place, we designed Ta_2O_5/MgF_2 multilayer which photonic band gap (PBG) covered the whole blue-green range from 439nm to 559nm. The gap in TE and TM mode completely overlapped each other when the incident angle varing from 0? to 20? but incompletely overlapped each other when the incident angle more than 20?, then the gaps move towards to more short wavelength and became narrow in TE mode but broad in TM mode.
In the second place, Ta_2O_5 defect layer is introduced into Ta_2O_5/MgF_2 multilayer and single defect mode or double defect modes appear in PBG when varying the thickness of the defect layer. One defect mode presents at 495.3nm and two defect modes lie in 471nm and 528nm, respectively.
Last but not least important, the structure of atoms diffusion on the surface between Ta_2O_5 and MgF_2 is designed and the influence of diffusion layers with different refractivity between Ta_2O_5 and MgF_2 is considered for studying the properties of PBG and defect modes.
引文
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[2]温熙森.光子/声子晶体理论理论与技术[M].北京:科学出版社,2006:1-5.
[3] Yablonovitch E, Inhibited spontaneous emission in solid-state physics and electronics[J]. Phys. Rev. Lett, 1987, 58(20): 2059-2062.
[4] John S, Strong localization of photons in certain disordered dielectric superlattices[J]. Phys. Rev. Lett, 1987, 58(23): 2486-2489.
[5]艾桃桃.光子晶体研究进展[J].激光与红外,2009,39(12):1257-1262.
[6] Li Zhiyuan, Gu Benyuan, Yang Guozhen. Large absolute band gap in 2D anisotropic photonic crystals[J]. Phys. Rev. Lett, 1998, 81(12): 2574-2577.
[7] He Sailing, Ruan Zhichao, Chen Long et al. Focusing properties of a photonic crystal slab with negative refraction[J]. Phys. Rev. B, 2004, 70(11): 115113-115123.
[8] Zhou Yunsong, Wang Xuehua, Gu Benyuan et al. Photonic band gap effects on spontaneous emission lifetimes of an assembly of atoms in two-dimensional photonic crystals[J]. Phys. Rev. E, 2005, 72(1): 017601-017604.
[9] Zi Jian, Zhang Kaiming, Xie Xide. Structural and vibrational properties of (Si)4/(Ge)4 superlattices[J]. Phys. Rev. B, 1990, 41(18): 12862–12868.
[10]资剑.光子晶体研究进展.http://www.optics.lctu.cn/wlxj/gxzs/photocrystalprogress.htm
[11] Abram I, Bourdon G. Photonic-well microcavities for spontaneous emission control[J]. Phys. Rev. A, 1996, 54(8): 3476-3479.
[12] Sigalas M M, Chart C T, Ho K M et a1. Metallic photonic band-gap materials[J]. Phys. Rev. B, 1995, 52(10): 11744-11751.
[13] Ho K M, Chan C T, Soukoulis C M. Existence of a photonic gap in periodic dielectric structures[J]. Phys. Rev. Lett, 1990, 65(25): 3152-3155.
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