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柱状磁光颗粒的局域表面等离激元共振为二维磁光光子晶体的手征性边缘模的生成提供了重要的机制. 但目前对此类颗粒的局域表面等离激元共振效应的研究局限于长波长近似下的结果, 且缺乏对发生共振时的远场与近场特征的深入了解. 本文从散射理论出发, 计算并分析了柱状磁光颗粒发生局域表面等离激元共振的条件与特殊的场特征, 并讨论了颗粒尺寸对共振峰的影响. 计算结果解释了实验中观察到的二维磁光光子晶体的共振带隙与在长波长近似下得到的局域表面等离激元共振频率的明显偏移, 并展示了颗粒在较大尺寸下形成的高阶共振峰, 这可能有助于利用共振效应在磁光光子晶体中实现多模的手征边缘态.Localized surface plasmon resonance of cylindrical magneto optical particles provides an important mechanism for the formation of chiral edge states in two-dimensional magneto-optical photonic crystals. These states are an electromagnetic analogy of the so-called chiral edge state's (CESs) in a quantum Hall system where the power transmission is unidirectional due to particular topological properties of the bands. Just like their electronic counterpart, the number of optical CESs in the band gap opened by an applied magnetic field is determined by the sum of the Chern numbers of the lower bands. For a two-dimensional photonic crystal composed of ferrite rods magnetized along their axis, the coupling of the localized surface plasmon resonance states of each rod results in a narrow flat band-gap, which contains one-way edge modes arising from the circulation of the energy flow around each rod excited by the resonance with broken time-reversal symmetry. So far the interpretation of the resonance-related chiral edge states are based on the long-wavelength approximation of the localized surface plasmon resonance of an individual magneto-optical particle. Though the results agree with the experimental results qualitatively, an obvious quantitative deviation is still obvious. In this work we apply the scattering theory to analyze the resonance condition and the features of both the far-field and the near-field at resonance for cylindrical magneto-optical particles. Our calculation shows that the splitting of scattering peaks of different orders will occur due to the magneto-optical effect. Such a split is observed between an (+n)-peak and an (-n) peak, as a sign of the broken time-reversal symmetry, and also between peaks of lower-order and higher-order. Another important feature is the simultaneous occurring of the far-field resonance and the near-field resonance, where the latter is characterized by a peak of energy-flow circulation around the particle. Based on this model the effects of particle size on the resonance peaks are discussed. It is shown that the resonance peaks are moved and broadened with the particle size increasing. The results explain the obvious deviation of the position of the resonance band-gap from the predicted frequency according to the previous long-wavelength approximation. Furthermore, the calculation of a particle of moderately-large size (nearly one-tenth of the incident wavelength) demonstrates the appearance of higher-order modes up to n=4 circling around the particle surface. This implies that these higher-order modes may also make non-trivial contribution to the formation of the flat band-gap observed in a photonic crystal of ferrite-rods and affect the behaviours of the chiral-edge state existing in such a gap. Particularly, it may be helpful in realizing the multimodes of chiral edge states in magneto-optical photonic crystals.
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Keywords:
- magneto-optic effects /
- surface plasmon /
- photonic crystals
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[17] Zhu H, Yan Z D, Zhan P, Wang Z L 2013 Acta Phys. Sin. 62 178104 (in Chinese) [朱华, 颜振东, 詹鹏, 王振林 2013 物理学报 62 178104]
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[1] Inoue M, Fujii T 1997 J. Appl. Phys. 81 5659
[2] Temnov V V, Armelles G, Woggon U, Guzatov D, Cebollada A, Garcia-Martin A, Garcia-Martin J M, Thomay T, Leitenstorfer A, Bratschitsch R 2010 Nat. Photo. 4 107
[3] Liang H, Liu H, Zhang Q, Fu S F, Zhou S, Wang X Z 2015 Chin. Phys. B 24 067807
[4] Haldane F D M, Raghu S 2008 Phys. Rev. Lett. 100 013904
[5] Wang Z, Chong Y D, Joannopoulos J D, Soljacic M 2009 Nature 461 772
[6] Poo Y, Wu R, Lin Z, Yang Y, Chan C T 2009 Phys. Rev. Lett. 106 093903
[7] Fang K, Yu Z, Fan S 2011 Phys. Rev. B 84 075477
[8] Skirlo S A, Lu L, Soljacic M 2014 Phys. Rev. Lett. 113 113904
[9] Liu S Y, Lu W L, Lin Z F, Chui S T 2011 Phys. Rev. B 84 045425
[10] Lian J, Fu J X, Gan L, Li Z Y 2012 Phys. Rev. B 85 125108
[11] Poo Y, Wu R, Liu S, Yang Y, Lin Z, Chui S T 2012 Appl. Phys. Lett. 101 081912
[12] Chui S T, Liu S, Lin Z 2013 Phys. Rev. B 88 031201
[13] Chui S T, Lin Z 2014 Chin. Phys. B 23 117802
[14] Fan X, Zheng W, Singh D J 2014 Light: Sci. Appl. 3 e179
[15] Cong C, Wu D J, Liu X J 2012 Acta Phys. Sin. 61 047802 (in Chinese) [丛超, 吴大建, 刘晓峻 2012 物理学报 61 047802]
[16] Zou W B, Zhou J, Jin L, Zhang H P 2012 Acta Phys. Sin. 61 097805 (in Chinese) [邹伟博, 周骏, 金理, 张昊鹏 2012 物理学报 61 097805]
[17] Zhu H, Yan Z D, Zhan P, Wang Z L 2013 Acta Phys. Sin. 62 178104 (in Chinese) [朱华, 颜振东, 詹鹏, 王振林 2013 物理学报 62 178104]
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