基于群表示论的微波等离激元谐振器模式响应研究

摘要/Abstract

摘要： 作为光频段局域表面等离激元的低频对应物,人工局域表面等离激元因其深亚波长局域场增强和高Q值谐振的特点而受到广泛关注。微波等离激元谐振器是产生人工局域表面等离激元的典型器件,其特点是具有多重离散旋转对称性和镜面反射对称性。以往的研究提出了等效媒质法和等效色散法分析微波等离激元谐振器的模式响应,但这两种方法都未能充分考虑谐振器的几何对称性从而未能全面揭示其模式特性。本文针对谐振器的几何对称性提出了群表示论方法分析其模式响应。通过对称性分析,发现谐振器的几何对称性所构成的群的不可约表示数等于谐振器所能支持的人工局域表面等离激元模式的数目。以对称性构成C_7v群的谐振器为例,C_7v群的5个不可约表示数对应了5种人工局域表面等离激元模式,分别为零阶模式(也即磁偶极子)、偶极子、四极子、六极子和十四极子。受限于几何对称性,谐振器将不能支持更多阶的模式。为验证群表示论方法,设计了对称性构成C_7v群的微波等离激元谐振器,全波仿真结果很好地证明了上述理论。本文提出的群表示论方法也可推广到其他频段如光频,因而具有广泛的适用性。

关键词: 人工局域表面等离激元, 微波等离激元谐振器, 对称性, 群表示论, 不可约表示, 电磁散射

Abstract: As the counterpart in the lower frequencies of localized surface plasmon (LSP) in the optical regime, spoof LSP has attracted great interest among researchers due to its notable properties such as deep-subwavelength field localization and high-Q-value resonance. Microwave plasmonic resonators (MPRs) that hold several geometric symmetries are a typical device to generate spoof LSP modes. Several methodologies have been developed to study the mode responses of the MPRs, such as effective medium theory and equivalent dispersion theory. However, both of the theories are based on the assumptions that do not properly consider the geometric symmetries held by the MPRs, resulting in which they cannot completely reveal the mode properties of the MPRs. In this paper, a methodology based on group representation theory is proposed to analyze how the geometric symmetries affect the mode responses of the MPRs. By employing symmetry arguments, it is found that the azimuthal orders of the spoof LSP modes are totally determined by the irreducible representations (irreps) of the group composed by the geometric symmetries of the MPRs. The number of the irreps is equal to the number of the spoof LSP modes. A MPR holding C_7v group symmetry is taken as an example to explain our methodology. The C_7v group only has five irreps (three doubly-degenerate and two nondegenerate irreps). Therefore, the MPR can only support five spoof LSP modes with different azimuthal orders, i.e., zero-order mode (also known as magnetic dipole), dipole, quadrupole, hexapole and quattuordecpole. The dipole, quadrupole and hexapole modes are related to three doubly-degenerate irreps implying that the three modes are doubly degenerate. The zero-order and quattuordecpole modes correspond to the two nondegenerate irreps respectively and thus are nondegenerate. The MPR with C_7v group symmetry cannot support more spoof LPS modes limited by its geometric symmetries. A MPR prototype with C_7v group symmetry is designed and simulated. The full-wave simulation results well demonstrate our methodology. Although proposed to analyze the mode responses of the MPRs, our methodology is widely applicable and can also be used to analyze the mode responses of the plasmonic resonators working in other frequency bands like the optical band.

Key words: spoof localized surface plasmon, microwave plasmonic resonator, symmetry, group representation theory, irreducible representation, electromagnetic scattering

中图分类号:

TN751.2

杨杰, 王甲富, 贾宇翔, 陈维, 屈绍波. 基于群表示论的微波等离激元谐振器模式响应研究[J]. 人工晶体学报, 2021, 50(7): 1348-1355.

YANG Jie, WANG Jiafu, JIA Yuxiang, CHEN Wei, QU Shaobo. Mode Responses of Microwave Plasmonic Resonator by Exploiting Group Representation Theory[J]. JOURNAL OF SYNTHETIC CRYSTALS, 2021, 50(7): 1348-1355.

参考文献

[1] BARNES W L, DEREUX A, EBBESEN T W. Surface plasmon subwavelength optics[J]. Nature, 2003, 424(6950): 824-830.
[2] MAIER S A. Surface plasmon polaritons at metal / insulator interfaces[M]//Plasmonics: Fundamentals and Applications. New York, NY: Springer US, 2007: 21-37.
[3] MUHLSCHLEGEL P. Resonant optical antennas[J]. Science, 2005, 308(5728): 1607-1609.
[4] CROZIER K B, SUNDARAMURTHY A, KINO G S, et al. Optical antennas: resonators for local field enhancement[J]. Journal of Applied Physics, 2003, 94(7): 4632-4642.
[5] LI W Y, CAMARGO P H C, LU X M, et al. Dimers of silver nanospheres: facile synthesis and their use as hot spots for surface-enhanced Raman scattering[J]. Nano Letters, 2009, 9(1): 485-490.
[6] NIE S, EMORY S R. Probing single molecules and single nanoparticles by surface-enhanced Raman scattering[J]. Science, 1997, 275(5303): 1102-1106.
[7] ANKER J N, HALL W P, LYANDRES O, et al. Biosensing with plasmonic nanosensors[J]. Nature Materials, 2008, 7(6): 442-453.
[8] LIU N, WEISS T, MESCH M, et al. Planar metamaterial analogue of electromagnetically induced transparency for plasmonic sensing[J]. Nano Letters, 2010, 10(4): 1103-1107.
[9] HUTTER E, FENDLER J. Exploitation of localized surface plasmon resonance[J]. Advanced Materials, 2004, 16(19): 1685-1706.
[10] PORS A, MORENO E, MARTIN-MORENO L, et al. Localized spoof plasmons arise while texturing closed surfaces[J]. Physical Review Letters, 2012, 108(22): 223905.
[11] SHEN X P, CUI T J. Ultrathin plasmonic metamaterial for spoof localized surface plasmons[J]. Laser & Photonics Reviews, 2014, 8(1): 137-145.
[12] GAO Z, GAO F, ZHANG Y M, et al. Forward/backward switching of plasmonic wave propagation using sign-reversal coupling[J]. Advanced Materials, 2017, 29(26): 1700018.
[13] LIAO Z, LUO G Q, MA H F, et al. Localized surface magnetic modes propagating along a chain of connected subwavelength metamaterial resonators[J]. Physical Review Applied, 2018, 10(3): 034054.
[14] LIAO Z, SHEN X P, PAN B C, et al. Combined system for efficient excitation and capture of LSP resonances and flexible control of SPP transmissions[J]. ACS Photonics, 2015, 2(6): 738-743.
[15] YANG B J, ZHOU Y J, XIAO Q X. Spoof localized surface plasmons in corrugated ring structures excited by microstrip line[J]. Optics Express, 2015, 23(16): 21434-21442.
[16] SU H, SHEN X P, SU G X, et al. Efficient generation of microwave plasmonic vortices via a single deep-subwavelength meta-particle[J]. Laser & Photonics Reviews, 2018, 12(9): 1800010.
[17] ZHANG Y F, ZHANG Q L, CHAN C H, et al. Emission of orbital angular momentum based on spoof localized surface plasmons[J]. Optics Letters, 2019, 44(23): 5735-5738.
[18] HUIDOBRO P A, SHEN X P, CUERDA J, et al. Magnetic localized surface plasmons[J]. Physical Review X, 2014, 4(2): 021003.
[19] LIAO Z, PAN B C, SHEN X, et al. Multiple Fano resonances in spoof localized surface plasmons[J]. Optics Express, 2014, 22(13): 15710-15717.
[20] GAO F, GAO Z, SHI X H, et al. Dispersion-tunable designer-plasmonic resonator with enhanced high-order resonances[J]. Optics Express, 2015, 23(5): 6896-6902.
[21] CHEW W, TONG M, HU B. Integral equation methods for electromagnetic and elastic waves[J]. Synthesis Lectures on Computational Electromagnetics, 2008, 3(1):1-241.
[22] DRESSELHAUS M S, DRESSELHAUS G, JORIO A. Group theory: application to the physics of condensed matter[M]. Berlin: Springer-Verlag, 2008: 29-70.
[23] GELESSUS A. Character tables for chemically important point groups[DB/OL].http://symmetry.jacobs-university.de/group.html.
[24] COLLINS J T, ZHENG X Z, BRAZ N V S, et al. Enantiomorphing chiral plasmonic nanostructures: a counterintuitive sign reversal of the nonlinear circular dichroism[J]. Advanced Optical Materials, 2018, 6(14): 1800153.
[25] KUPPE C, ZHENG X Z, WILLIAMS C, et al. Measuring optical activity in the far-field from a racemic nanomaterial: diffraction spectroscopy from plasmonic nanogratings[J]. Nanoscale Horizons, 2019, 4(5): 1056-1062.
[26] LIAO Z, LUO Y, FERNÁNDEZ-DOMÍNGUEZ A I, et al. High-order localized spoof surface plasmon resonances and experimental verifications[J]. Sci Rep, 2015, 5: 9590.