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随着信息技术的高速发展, 光量子计算与通信对非对称光传输器件提出更高的要求. 因此, 研发具有可集成、高正向透射、非偏振选择、宽工作带宽特性的非对称传输器件成为研究热点. 传统的非对称光传输器件设计是基于在光子晶体中加入磁光材料[1]或非线性材料[2,3]. 但是该设计在工作时需要外加磁场引入磁光特性或者高光强度引入非线性效应, 因此基于这种工作原理的器件难以实现光芯片集成. 目前, 新型的微纳结构也应用于非对称传输器件的设计, 如复合光栅结构[4,5]、超表面材料[6-8]、表面等离子体激元结构[9,10]及超材料[11-14]等, 但其设计存在正向透射率低或工作带宽窄等问题. 光子晶体(photonic crystal, PhC)[15-19]具有独特的能带和光局域特性, 同时还具备易集成和光损耗低等优点. 因此光子晶体成为制备可集成的非对称光传输器件的研究热点之一. Wang等[20]研究了硅材料空气孔光子晶体异质结构, 实现在光通信波长1550 nm附近非对称光传输, 但其正向透射率仅为0.213, 工作带宽仅为50 nm. 刘丹等[21]通过优化光子晶体异质结的排列, 正向透射率进一步提高到0.54. 费宏明等[22,23]研究了基于广义全反射的二维光子晶体异质结构设计的非对称传输器件, 但其结构采用两种不同电介质材料, 正向透射率最大值为0.64, 透射率大于0.5的非对称传输带宽仅为70 nm.
为了进一步提高非对称传输正向透射率, 本文利用具有自准直效应的二维光子晶体异质结构实现高正向透射率、宽工作带宽、非偏振选择的非对称传输. 该结构采用硅材料正方晶格光子晶体结构, 利用正方形光子晶体的自准直效应将不同入射角的光波进行准直, 使正向光波沿所需的方向耦合传输, 从而显著提高正向透射率. 该结构在通信波长1550 nm处, 横电(transverse electric, TE)波和横磁(transverse magnetic, TM)波得到的正向透射率分别为0.693和0.513; 在工作带宽上, TE和TM偏振光实现的工作带宽分别为532和128 nm. 无论从透射率还是工作带宽方面来考虑, 相较之前的研究[20-23]都实现了明显提升. 同时, 该结构可利用当前的纳米制造技术进行制备, 为非对称传输器件的设计研究提供了新的研究方向[24].
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如图1所示, 该光子晶体异质结构由不同晶格常数的二维正方晶格光子晶体1 (PhC 1)和光子晶体2 (PhC 2)构成. 其中PhC 1为空气中周期排列的硅圆柱阵列, 介质硅圆柱沿Γ'—X' 方向的正方晶格周期排列(Γ', X', M' 分别为PhC 1第一布里渊区高对称点), 与x轴正方向呈45°夹角, 晶格常数为a = 346.4 nm, 硅圆柱半径R = 60 nm; PhC 2为硅衬底上周期排列空气方孔阵列, 晶格常数为
$ \sqrt{2} a $ = 490 nm, 空气方形孔边长A = 220 nm. 异质结界面与光波入射方向(x轴正方向)的夹角为45°. 同时, 定义正向光波为从PhC 1向PhC 2传播(x轴正方向)的光波, 反向光波从PhC 2向PhC 1传播(x轴负方向).
图 1 硅基光子晶体异质结构示意图
Figure 1. Schematic of photonic crystal heterostructure based on silicon.
为了更好地分析TE和TM偏振光在光子晶体中的传输性能, 采用平面波展开法分别计算PhC 1和PhC 2的能带图, 如图2(a)和图2(b)所示, 以及等频图(equal frequency contour, EFC), 如图2(c)—图2(f)所示.
图 2 (a) PhC 1能带图; (b) PhC 2能带图, 插图为PhC 2在Γ—X方向的能带; (c) PhC 1在TE偏振模式第一条能带EFC; (d) PhC 2在TE偏振光下第四条能带EFC (蓝线表示TE偏振光1550 nm处的频带); (e) PhC 1在TM偏振光第一条能带EFC; (f) PhC 2在TM偏振光第三条能带EFC (红线表示TM模式1550 nm处的频带)
Figure 2. (a) Photonic band diagrams of PhC 1; (b) the photonic band diagrams of PhC 2, where the insert shows the energy band of PhC 2 in Γ－X direction; (c) the first band EFC of PhC 1 under TE polarized light; (d) the fourth band EFC of PhC 2 under TE polarized light (blue lines represent TE mode at the wavelength of 1550 nm); (e) the first band EFC of PhC 1 under TM polarized light; (f) the third band EFC of PhC 2 under TM polarized light (red lines represent TM mode at 1550 nm).
如图2(a)所示, 在光子晶体PhC 1中, TE和TM偏振光在归一化频带范围(0.302—0.446)a/λ内分别处于完全禁带和导带(蓝线表示TE偏振光, 红线表示TM偏振光), 其中a为晶格常数, λ为波长, 单位均为nm. 在通信波长1550 nm处(对应于PhC 1的归一化频率为0.224a/λ), TE和TM偏振光在PhC 1中沿Γ'—X' 和Γ'—M' 方向都为导带(由绿色水平线标记). 因此1550 nm的光波在PhC 1中能沿Γ'—X' 或Γ'—M' 进行传输, 为实现正向高透射率提供理论基础. 图2(b)给出了正方形空气孔型光子晶体PhC 2的能带结构, 在通信波长1550 nm处(对应于PhC 2的归一化频率0.316a/λ), 沿Γ—M方向在TE和TM偏振光下都是导带, 因此在PhC 2中1550 nm的光波能沿着Γ—M方向传输(Γ, X, M分别表示PhC 2第一布里渊区高对称点). 另一方面, TM偏振光沿着Γ—X方向为禁带, 因此反向入射的TM偏振光在光子晶体PhC 2中传输. 为了更加清晰地研究1550 nm的光波在PhC 1和PhC 2中的传输状态, 绘制1550 nm波段在TE和TM偏振光下的EFC, 以Γ点为中心, 光在光子晶体中的传播方向沿EFC的梯度方向(如图2(c)—图2(f)中黑色双箭头所示). TE和TM偏振光分别正向入射时, 入射光在PhC 1中沿着Γ' —M' 方向传输到达异质界面, 相应的箭头标记在图2(c)和图2(e)中, 然后光波将沿Γ—M方向进入PhC 2, 由于光子晶体的色散特性, 在平坦的等频线处会发生自准直现象, 使沿Γ—M的光波准直到Γ—X方向上输出, 如图2(d)和图2(f)中蓝色箭头所示, 因此该结构在1550 nm波长处, TE或TM偏振光都能够实现正向高透射. 在反向入射时, 入射光在PhC 2中将沿着Γ—X方向进行传输, 针对TE偏振光, 光子晶体的色散特性使光波逐渐偏转到M—X方向即竖直向上传播, 无法到达异质界面, 图2(d)中红色箭头所示的TM偏振光在1550 nm波长处于禁带(如图2(b)所示), 不能在PhC 2中进行传输. 因此, 在反向入射时, TE和TM偏振光均不能传输, 实现了反向低透射. 因此, 本文设计的二维光子晶体异质结构能够实现正向高透射、宽频带的单向光传输.
为了更加形象地观察光波的传输状态, 运用时域有限差分法计算1550 nm光波在TE和TM偏振光的正向、反向电场强度空间分布图. 当TE偏振光正向入射时, 如图3(a)所示. 正向入射光波从PhC 1入射后沿Γ'—M' 方向传播, 到达异质结界面后, 由于界面两侧折射率不同, 光波传输方向发生一定的偏折, 光波将沿偏离Γ—X方向进入PhC 2, 但是由于光子晶体自准直效应, 沿着非Γ—X方向入射的光波(由于衍射, 有一个小角度范围)将被准直到Γ—X方向上输出. TE偏振光反向入射时, 光波在PhC 2中会发生偏折, 当偏转到M—X方向时, 不能到达异质界面, 如图3(b)所示. 以上均符合图2(c)和图2(d)的理论分析. 由图3(c)可以看出, 当TM偏振光正向入射时, 在光子晶体PhC 2中由于自准直效应, 光波也能正向透射传输; 反向入射时, 如图3(d)所示, 由于光子晶体PhC 2禁带特性, 反向入射光不能在PhC 2中传输, 因此光波不能到达异质界面.
图 3 1550 nm波长处正向入射场强图和反向入射场强图 (a) TE偏振光正向; (b) TE偏振光反向; (c) TM偏振光正向; (d) TM偏振光反向
Figure 3. Electric field intensity distribution of forward transmission and backward transmission at the wavelength of 1550 nm: (a) Forward transmission of TE polarized light; (b) backward transmission of TE polarized light; (c) forward transmission of TM polarized light; (d) backward transmission of TM polarized light.
为了分析该结构在宽波段的透射特性, 利用时域有限差分法计算异质结构透射率光谱图, 结果如图4所示. 正向透射率和反向透射率分别用
$ {T}_{\rm{f}} $ 和$ {T}_{\rm{b}} $ 表示, 透射对比度定义为$ C=({T}_{\rm{f}}-{T}_{\rm{b}})/({T}_{\rm{f}}+{T}_{\rm{b}}) $ , 其工作带宽定义为正向透射率高于0.5的区域, 如图4中灰色区域所示. 对于TE偏振光, 如图4(a)所示, 在1408—1940 nm (带宽532 nm)范围内, 正向透射率$ {T}_{\rm{f}} $ > 0.5; 在1510 nm波长处具有最大正向透射率0.746, 透射对比度为0.932. 在波长1550 nm的通信波段, 正向透射率和透射对比度分别为0.693和0.946. 对于TM偏振光, 如图4(b)所示, 传输波长带宽仅为128 nm, 带宽较窄, 最高正向透射率为0.567. 在1550 nm的通信频段, 正向透射率和透射对比度分别为0.513和0.972. 因此, 该结构能够在宽频带范围内实现TE和TM偏振态的高效率非对称传输.
图 4 异质结构透射谱 (a) TE偏振光; (b) TM偏振光; 其中灰色区域表示结构工作带宽
Figure 4. Transmittance spectra of heterostructure: (a) TE polarized light, (b) TM polarized light. The grey region represents the asymmetric transmission working wavelength range, where forward transmission is higher than 0.5.
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为了提高非对称传输特性, 对光子晶体异质结构进行进一步优化. 考虑到影响正向透射率和透射对比度的各种因素, 研究发现通过改变异质界面处PhC 1硅圆柱半径的大小R (如图5红色区域所示)可以进一步增加光子晶体PhC 1和PhC 2之间的耦合效率, 提高TE偏振光正向透射率和透射对比度.
图 5 光子晶体异质结优化示意图, 其中被优化的光子晶体结构通过红色长方形标注
Figure 5. Schematic of optimization of photonic crystal heterostructure, where the row of photonic lattice is highlighted by the red square is optimized.
如图6所示, 当R = 55 nm时, 非对称传输波长带宽可达448 nm, 在通信波段1550 nm处正向透射率为0.579, 透射对比度为0.941. 随着半径的增大, 正向透射率也增大, 当R = 70 nm, 在通信波段1550 nm处正向透射率高达0.832, 透射对比度达到了0.944. 此时的非对称传输波长带宽为562 nm. 当半径R = 75 nm时, 虽然非对称传输波长带宽有一定的增加, 达到568 nm, 但与半径R = 70 nm时相比, 正向透射率减少到0.803.
图 6 异质结构界面处PhC 1不同半径硅圆柱TE偏振光透射谱 (a) R = 55 nm; (b) R = 65 nm; (c) R = 70 nm; (d) R = 75 nm
Figure 6. Transmittance spectra of the TE polarized light with different radii of PhC 1 photonic lattice at heterostructure interface: (a) R = 55 nm; (b) R = 65 nm; (c) R = 70 nm; (d) R = 75 nm.
比较以上四种优化结构, 为了更好地实现通信波长1550 nm附近的非对称传输, 不仅需要较高的正向透射率和透射对比度, 另外还需要较宽的非对称传输带宽. 综合表1各项参数, 当界面处半径R = 70 nm, 其他硅圆柱半径为60 nm时, 可实现通信波长1550 nm处正向透射率0.832, 非对称传输带宽可达562 nm, 因此, 该结构在TE偏振光下能够实现较高带宽的非对称传输.
R/nm 1550 nm正向
透射率透射对比度 非对称传输
带宽/nm55 0.579 0.941 448 60 0.693 0.946 532 65 0.789 0.947 556 70 0.832 0.944 562 75 0.803 0.942 568 表 1 异质界面处PhC 1硅圆柱不同半径的非对称传输性能
Table 1. Asymmetric transmission performance with different radii of PhC 1 at heterostructure interface.
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综上所述, 本文基于光子晶体自准直效应和带隙特性构建了一种能实现宽频带非对称光传输的二维光子晶体异质结构. 在光通信波段1550 nm处, TE偏振光正向透射率和透射对比度分别为0.693和0.946, 工作带宽可达532 nm. TM偏振光非对称传输波长带宽为128 nm, 在1550 nm处正向透射和透射对比度分别为0.513和0.972, 实现了宽频带、高效率、非偏振选择的非对称传输. 在此基础上, 通过分析异质界面处PhC 1硅圆柱的半径大小, 当异质界面处硅圆柱半径R = 70 nm时, 可实现562 nm的工作带宽和0.832的正向透射率. 由于该结构采用硅材料, 设计简单, 非对称传输效率高, 为实验制备非对称光传输器件提供了新的思路, 对未来集成光路的发展有着重要意义.
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利用光子晶体的自准直效应和能带特性, 设计了一种能实现宽频带光波非对称传输的二维光子晶体异质结构. 该结构实现宽频带、高正向透射、非偏振选择的非对称传输. 横电(transverse electric, TE)偏振光非对称传输波长带宽可达532 nm, 在光通信波长1550 nm处正向透射率和透射对比度分别可达0.693和0.946; 横磁(transverse magnetic, TM)偏振光非对称传输波长带宽为128 nm, 在光通信波长1550 nm处正向透射率和透射对比度分别可达0.513和0.972; 通过进一步优化异质结界面, 在TE偏振光下非对称传输波长带宽可达562 nm.Recently, quantum computing and information processing based on photons has become one research frontier, attracting significant attentions. The optical asymmetric transmission devices (OATD), having similar function to the diode in electric circuitry, will find important applications. In particular, the OATDs based on nanophotonic structures are preferred due to their potential applications in the on-chip integration with other photonic devices. Therefore, there have been numerous applications of OATDs based on different nanostructures, including composite grating structures, metasurfaces, surface plasmon polaritons, metamaterials, photonic crystals (PhCs). However, in general, those designs show relatively low forward transmittance (< 0.5) and narrow working bandwidth (< 100 nm), and they are able to work with only one polarization state. This makes the current OATDs unsuitable for many applications. To solve this challenge, here we design a two-dimensional (2D) PhC heterostructure based on the self-collimating effect and bandgap properties. The PhC heterostructure is composed of two square lattice 2D PhCs (PhC 1 and PhC 2) on a silicon substrate with different lattice shapes and lattice constants. The PhC 1 is composed of periodically arranged silicon cylinders in air. Meanwhile, the PhC 2 is an square air hole array embedding in silicon. The two PhCs are integrated with an inclined interface with an angle of 45° with respect to the direction of incident light. The plane wave expansion method is used to calculate the band diagrams and equal frequency contours (EFCs) of the two PhCs. As the propagation directions of light waves in PhCs are determined by the gradient direction of the EFCs, we are able to control the light propagation by controlling the EFCs of PhCs. By engineering the EFCs, the PhC 2 shows strong self-collimation effect in a broad wavelength range with a central wavelength of 1550 nm for both TE and TM polarization. By self-collimating the forward incident light from different incident angles to couple to the output waveguide, we are able to significantly increase the forward transmittance to > 0.5 for both TE and TM polarized light. Meanwhile, the backward transmittance can be effectively cut off by the unique dispersion properties of the PhC heterostructures. In this way, the heterostructure is able to achieve polarization independent asymmetric transmission of light waves in a broad wavelength range. To visualize the light propagation in the PhC heterostructure, we use the finite-difference-time-domain method to calculate the electric intensity distributions of the forward and backward propagation light of both TE and TM polarization at a wavelength of 1550 nm. Strong self-collimation effect of forward propagation light and the nearly complete blockage of backward propagation light can be identified unambiguously in the intensity plots, confirming the theoretical analysis. The calculation of transmittance and contrast ratio spectra show that the asymmetric transmission wavelength bandwidth can reach 532 nm with the forward transmittance and contrast ratio being 0.693 and 0.946 at an optical communication wavelength of 1550 nm for TE polarized light. On the other hand, for the TM polarized light, the asymmetric transmission wavelength bandwidth is 128 nm, the forward transmittance and contrast ratio are 0.513 and 0.972, respectively, at 1550 nm wavelength. Thus, it is confirmed that the PhC heterostructure achieves highly efficient, broadband and polarization independent asymmetric transmission. Finally, to further improve the forward transmittance of the TE polarized light, we modulate the radius of the front row of photonic lattice of PhC 1 at the interface. It shows that the forward transmittance can be further improved to a record high value of 0.832 with a bandwidth of 562 nm for TE polarized light. Our design opens up new possibilities for designing OATDs based on PhCs, and will find broad applications, for the design can be realized by current nanofabrication techniques.
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Keywords:
- self-collimation /
- photonic bandgap /
- heterostructure /
- asymmetric transmission
[1] Espinola R L, Izuhara T, Tsai M C, Osgoode R M 2004 Opt. Lett. 29 941
Google Scholar
[2] Zhou X, Wang Y, Leykam D, Chong Y D 2017 New J. Phys. 19 095002
Google Scholar
[3] Fan L, Wang J, Varghese L T, Shen H, Niu B, Xuan Y, Weiner A M, Qi M 2012 Science 335 447
Google Scholar
[4] Kuzmiak V, Maradudin A A 2015 Phys. Rev. A 92 013615
Google Scholar
[5] Stolarek M, Yavorskiy D, Kotyński R, Zapata R, Carlos J, Łusakowski J, Szoplik T 2013 Opt. Lett. 38 839
Google Scholar
[6] Xiao Z Y, Zou H L, Xu K K, Tang J Y 2018 J. Magn. Magn. Mater. 449 278
Google Scholar
[7] Ozer A, Kocer H, Kurt H 2018 J. Opt. Soc. Am. B 35 2111
Google Scholar
[8] Zhang L, Mei S, Huang K, Qiu C W 2016 Adv. Opt. Mater. 4 818
Google Scholar
[9] Ling Y H, Lirong H, Wei H, Tongjun L, Yali S, Jing L, Gang Y 2017 Opt. Express 25 13648
Google Scholar
[10] Peng Y X, Wang K J, He M D, Luo J H, Zhang X M, Li J B, Tan S H, Liu J Q, Hu W D, Chen X S 2018 Opt. Commun. 412 1
Google Scholar
[11] Li X F, Rui F, Ding W 2018 J. Phys. D: Appl. Phys. 51 145304
Google Scholar
[12] Bai Y, Chen Y, Zhang Y, Wang Y, Aba T, Li H, Wang L, Zhang Z 2018 J. Phys. Condens. Matter 30 114001
Google Scholar
[13] Stephen L, Yogesh N, Subramanian V 2018 J. Appl. Phys. 123 033103
Google Scholar
[14] Xu T, Lezec H J 2014 Nat. Commun. 5 4141
Google Scholar
[15] Soltani A, Ouerghi F, AbdelMalek F, Haxha S, Ademgil H, Akowuah E K 2017 Opt. Commun. 392 147
Google Scholar
[16] Wu Z, Chen J, Ji M, Huang Q, Xia J, Wu Y, Wang Y 2015 Appl. Phys. Lett. 107 221102
Google Scholar
[17] Zhang Y, Li D, Zeng C, Huang Z, Wang Y, Huang Q, Wu Y, Yu J, Xia J 2014 Opt. Lett. 39 1370
Google Scholar
[18] Zhang Y, Kan Q, Wang G P 2014 Opt. Lett. 39 4934
Google Scholar
[19] Serebryannikov A E, Alici K B, Magath T, Cakmak A O, Ozbay E 2012 Phys. Rev. A 86 053835
Google Scholar
[20] Wang C, Zhou C Z, Li Z Y 2011 Opt. Express 19 26948
Google Scholar
[21] 刘丹, 胡森, 肖明 2017 物理学报 66 054209
Google Scholar
Liu D, Hu S, Xiao M 2017 Acta Phys. Sin. 66 054209
Google Scholar
[22] 费宏明, 徐婷, 刘欣, 林瀚, 陈智辉, 杨毅彪, 张明达, 曹斌照, 梁九卿 2017 物理学报 66 204103
Google Scholar
Fei H M, Xu T, Liu X, Lin H, Chen Z H, Yang Y B, Zhang M D, Cao B Z, Liang J Q 2017 Acta Phys. Sin. 66 204103
Google Scholar
[23] Fei H M, Wu M, Xu T, Lin H, Yang Y B, Liu X, Zhang M D, Cao B Z 2018 J. Opt. 20 095004
Google Scholar
[24] Bourzac K 2012 Nature 483 388
Google Scholar
-
图 1 硅基光子晶体异质结构示意图
Fig. 1. Schematic of photonic crystal heterostructure based on silicon.
图 2 (a) PhC 1能带图; (b) PhC 2能带图, 插图为PhC 2在Γ—X方向的能带; (c) PhC 1在TE偏振模式第一条能带EFC; (d) PhC 2在TE偏振光下第四条能带EFC (蓝线表示TE偏振光1550 nm处的频带); (e) PhC 1在TM偏振光第一条能带EFC; (f) PhC 2在TM偏振光第三条能带EFC (红线表示TM模式1550 nm处的频带)
Fig. 2. (a) Photonic band diagrams of PhC 1; (b) the photonic band diagrams of PhC 2, where the insert shows the energy band of PhC 2 in Γ－X direction; (c) the first band EFC of PhC 1 under TE polarized light; (d) the fourth band EFC of PhC 2 under TE polarized light (blue lines represent TE mode at the wavelength of 1550 nm); (e) the first band EFC of PhC 1 under TM polarized light; (f) the third band EFC of PhC 2 under TM polarized light (red lines represent TM mode at 1550 nm).
图 3 1550 nm波长处正向入射场强图和反向入射场强图 (a) TE偏振光正向; (b) TE偏振光反向; (c) TM偏振光正向; (d) TM偏振光反向
Fig. 3. Electric field intensity distribution of forward transmission and backward transmission at the wavelength of 1550 nm: (a) Forward transmission of TE polarized light; (b) backward transmission of TE polarized light; (c) forward transmission of TM polarized light; (d) backward transmission of TM polarized light.
图 4 异质结构透射谱 (a) TE偏振光; (b) TM偏振光; 其中灰色区域表示结构工作带宽
Fig. 4. Transmittance spectra of heterostructure: (a) TE polarized light, (b) TM polarized light. The grey region represents the asymmetric transmission working wavelength range, where forward transmission is higher than 0.5.
图 5 光子晶体异质结优化示意图, 其中被优化的光子晶体结构通过红色长方形标注
Fig. 5. Schematic of optimization of photonic crystal heterostructure, where the row of photonic lattice is highlighted by the red square is optimized.
图 6 异质结构界面处PhC 1不同半径硅圆柱TE偏振光透射谱 (a) R = 55 nm; (b) R = 65 nm; (c) R = 70 nm; (d) R = 75 nm
Fig. 6. Transmittance spectra of the TE polarized light with different radii of PhC 1 photonic lattice at heterostructure interface: (a) R = 55 nm; (b) R = 65 nm; (c) R = 70 nm; (d) R = 75 nm.
表 1 异质界面处PhC 1硅圆柱不同半径的非对称传输性能
Table 1. Asymmetric transmission performance with different radii of PhC 1 at heterostructure interface.
R/nm 1550 nm正向
透射率透射对比度 非对称传输
带宽/nm55 0.579 0.941 448 60 0.693 0.946 532 65 0.789 0.947 556 70 0.832 0.944 562 75 0.803 0.942 568 
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[1] Espinola R L, Izuhara T, Tsai M C, Osgoode R M 2004 Opt. Lett. 29 941
Google Scholar
[2] Zhou X, Wang Y, Leykam D, Chong Y D 2017 New J. Phys. 19 095002
Google Scholar
[3] Fan L, Wang J, Varghese L T, Shen H, Niu B, Xuan Y, Weiner A M, Qi M 2012 Science 335 447
Google Scholar
[4] Kuzmiak V, Maradudin A A 2015 Phys. Rev. A 92 013615
Google Scholar
[5] Stolarek M, Yavorskiy D, Kotyński R, Zapata R, Carlos J, Łusakowski J, Szoplik T 2013 Opt. Lett. 38 839
Google Scholar
[6] Xiao Z Y, Zou H L, Xu K K, Tang J Y 2018 J. Magn. Magn. Mater. 449 278
Google Scholar
[7] Ozer A, Kocer H, Kurt H 2018 J. Opt. Soc. Am. B 35 2111
Google Scholar
[8] Zhang L, Mei S, Huang K, Qiu C W 2016 Adv. Opt. Mater. 4 818
Google Scholar
[9] Ling Y H, Lirong H, Wei H, Tongjun L, Yali S, Jing L, Gang Y 2017 Opt. Express 25 13648
Google Scholar
[10] Peng Y X, Wang K J, He M D, Luo J H, Zhang X M, Li J B, Tan S H, Liu J Q, Hu W D, Chen X S 2018 Opt. Commun. 412 1
Google Scholar
[11] Li X F, Rui F, Ding W 2018 J. Phys. D: Appl. Phys. 51 145304
Google Scholar
[12] Bai Y, Chen Y, Zhang Y, Wang Y, Aba T, Li H, Wang L, Zhang Z 2018 J. Phys. Condens. Matter 30 114001
Google Scholar
[13] Stephen L, Yogesh N, Subramanian V 2018 J. Appl. Phys. 123 033103
Google Scholar
[14] Xu T, Lezec H J 2014 Nat. Commun. 5 4141
Google Scholar
[15] Soltani A, Ouerghi F, AbdelMalek F, Haxha S, Ademgil H, Akowuah E K 2017 Opt. Commun. 392 147
Google Scholar
[16] Wu Z, Chen J, Ji M, Huang Q, Xia J, Wu Y, Wang Y 2015 Appl. Phys. Lett. 107 221102
Google Scholar
[17] Zhang Y, Li D, Zeng C, Huang Z, Wang Y, Huang Q, Wu Y, Yu J, Xia J 2014 Opt. Lett. 39 1370
Google Scholar
[18] Zhang Y, Kan Q, Wang G P 2014 Opt. Lett. 39 4934
Google Scholar
[19] Serebryannikov A E, Alici K B, Magath T, Cakmak A O, Ozbay E 2012 Phys. Rev. A 86 053835
Google Scholar
[20] Wang C, Zhou C Z, Li Z Y 2011 Opt. Express 19 26948
Google Scholar
[21] 刘丹, 胡森, 肖明 2017 物理学报 66 054209
Google Scholar
Liu D, Hu S, Xiao M 2017 Acta Phys. Sin. 66 054209
Google Scholar
[22] 费宏明, 徐婷, 刘欣, 林瀚, 陈智辉, 杨毅彪, 张明达, 曹斌照, 梁九卿 2017 物理学报 66 204103
Google Scholar
Fei H M, Xu T, Liu X, Lin H, Chen Z H, Yang Y B, Zhang M D, Cao B Z, Liang J Q 2017 Acta Phys. Sin. 66 204103
Google Scholar
[23] Fei H M, Wu M, Xu T, Lin H, Yang Y B, Liu X, Zhang M D, Cao B Z 2018 J. Opt. 20 095004
Google Scholar
[24] Bourzac K 2012 Nature 483 388
Google Scholar
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