Transmission properties of terahertz pulses through subwavelength double split-ring resonators

We present a terahertz time-domain spectroscopy study of the transmission properties of planar composite media made from subwavelength double split-ring resonators (SRRs). The measured amplitude transmission spectra reveal a resonance near 0.5 THz, the central frequency of most ultrafast terahertz systems, for one SRR orientation in normal-incidence geometry. This resonance is attributed to the effect of electric excitation of magnetic resonance of the SRR arrays. In addition, the influences of background substrate, lattice constant, and the shapes of the SRRs on the terahertz resonance are experimentally investigated and agree well with the results of recent numerical studies.     

Identifying magnetic response of split-ring resonators at microwave frequencies

In this study we provide experimental methods to identify the magnetic resonance of split ring resonantors (SRR) at the microwave frequency regime. Transmission measurements were performed on both single SRR unit cell and periodic arrays of SRRs. The magnetic response of the SRR structure was demonstrated by comparing the transmission spectra of SRRs with closed ring resonators (CRR). Effects of the changes in the effective dielectric constant of the SRR medium on the band-gaps of SRR are investigated experimentally. SRRs not only exhibit a magnetic resonance band gap but also a band gap due to the electric resonance. Finally, we present the effect of electric coupling to the magnetic resonance of bianisotropic SRRs by utilizing SRRs with different orientations, and incident electromagnetic wave polarizations.     

Near-field investigation of induced transparency in similarly oriented double split-ring resonators

We present near-field measurements of an induced transparency behavior using a double split-ring resonator geometry. Mapping the out-of-plane electric field component directly reveals that the induced transparency is linked to an asymmetric mode profile with the subunits oscillating in antiphase. The measurements are compared to complementary numerical simulations, and excellent agreement is found.     

Linear birefringence in split-ring resonators

We study polarization-dependent transmission of light through arrays of single-slit split-ring resonator (SSRR) based systems at normal incidence using finite integration time domain (FITD) and finite element methods (FEM). It is found that a conventional planar array of SSRRs acts as an effective optical wave plate at certain polarizations of incident light. The effect is attributed to the intrinsic linear birefringence of individual SSRRs. A comparison is made with other split-ring resonator-based systems exhibiting wave-plate-like properties due to inter-SSRR coupling.     

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研究了在三开口劈裂金属纳米环中,当入射场偏振方向不同时出现的多极局域表面等离激元共振现象及折射率传感特性。研究表明,当入射场偏振方向分别沿x 轴和y 轴时,在可见光-近红外区域分别激发起两个和三个明显的共振峰。通过改变缺口的张角,能够实现对共振峰位和强度的可控调整。共振峰位处劈裂纳米环的近场分布表明,LHA(左半弧)和DRHA(双右半弧)之间等离激元的杂化耦合是形成上述共振的原因。劈裂纳米环的多极共振非常适合折射率传感应用。当改变周围环境折射率,入射场沿x 轴偏振时,折射率敏感度的最大值可达到1365nm/RIU;入射场沿y 轴偏振时,折射率敏感度最大值可达2229nm/RIU。     

Saturation of the magnetic response of split-ring resonators at optical frequencies

We investigate numerically the limits of the resonant magnetic response with a negative effective permeability mu(eff) for single-ring multicut split-ring resonator (SRR) designs up to optical frequencies. We find the breakdown of linear scaling due to the free electron kinetic energy for frequencies above approximately 100 THz. Above the linear scaling regime, the resonance frequency saturates, while the amplitude of the resonant permeability decreases, ultimately ceasing to reach negative value. The highest resonance frequency at which mu(eff) < 0 increases with the number of cuts in the SRR. A LC circuit model provides explanation of the numerical data.     

劈裂纳米环多极表面等离激元共振及折射率传感特性分析

研究了在三开口劈裂金属纳米环中,当入射场偏振方向不同时出现的多极局域表面等离激元共振现象及折射率传感特性。研究表明,当入射场偏振方向分别沿x 轴和y 轴时,在可见光-近红外区域分别激发起两个和三个明显的共振峰。通过改变缺口的张角,能够实现对共振峰位和强度的可控调整。共振峰位处劈裂纳米环的近场分布表明,LHA(左半弧)和DRHA(双右半弧)之间等离激元的杂化耦合是形成上述共振的原因。劈裂纳米环的多极共振非常适合折射率传感应用。当改变周围环境折射率,入射场沿x 轴偏振时,折射率敏感度的最大值可达到1365nm/RIU;入射场沿y 轴偏振时,折射率敏感度最大值可达2229nm/RIU。     

Second-harmonic generation from complementary split-ring resonators

We present experiments on second-harmonic generation from arrays of magnetic split-ring resonators and arrays of complementary split-ring resonators. In both cases, the fundamental resonance is excited by the incident femtosecond laser pulses under normal incidence, leading to comparably strong second-harmonic signals. These findings are discussed in terms of Babinet's principle and in terms of a recently developed microscopic classical theory that leads to good agreement regarding the relative and the absolute nonlinear signal strengths. The hydrodynamic convective contribution is found to be the dominant source of second-harmonic generation--in contrast to a previous assignment [Science 313, 502 (2006)].     

Extended verification of scaling behavior in split-ring resonators

We present an expanded LC-model for nanoscale split-ring resonators (SRR), including the influence of dielectric host materials. The LC-model is experimentally verified by changing the geometry of the SRR unit cell as well as by optofluidic tuning, where the SRR samples are covered with index oil. The extended model can be used as a general guideline for metal SRR structures with arbitrary dielectric host materials.     

Spectral imaging of individual split-ring resonators

We report on spectral imaging within individual silver split-ring resonators (SRRs) operating in the near infrared-visible range. We classified the optical eigenmodes from the measurement of their energies and nanometer scale spatial distributions. They are plasmonic standing waves that show great similarities with that of nanoantennas. We, however, evidenced marked differences in the near-field electric field lines' spatial distribution and the energies' dispersion. We also showed that the subwavelength defect's influence on the SRRs' eigenmodes spatial distribution is small.     

The polarizability matrix of split-ring resonators

The resonance behavior of electric and magnetic dipole moment amplitudes that are induced in metallic nanoparticles by the scattering of incident light was obtained by numerical simulation. For a split-ring resonator a full set of polarizability matrix components, including magnetoelectric coupling parameters (bianisotropy), were calculated.     

Nonlinear phenomena of left-handed nonlinear split-ring resonators

We theoretically analyze a two-dimensional periodic structure consisting of period nonlinear split-ring resonators (SRRs) with varactor diode. The diode is loaded into the slit of the SRRs. Then, we demonstrate nonlinear phenomena of left-handed nonlinear SRRs. This paper introduces nonlinear SRRs based on left-handed (LH) media and simulates self-tuning mechanisms, bistable effects in the microwave frequency range. In addition, with the increase of input power, the nonlinear response of the SRRs becomes multi-valued, paving a way for creating bistable tunable metamaterials.     

High transmittance left-handed materials involving symmetric split-ring resonators

We present theoretical and experimental results for a new design of highly symmetric, multigap split-ring resonators (SRRs), as well as for left-handed materials of a broad and high transmittance left-handed band, achieved by combining those symmetric SRRs with continuous wires. Studying in detail, both theoretically and experimentally, our proposed symmetric SRRs, we proved that they avoid the electric field excitation of the magnetic SRR resonance; thus they are appropriate for the creation of two-dimensional and three-dimensional left-handed materials. Finally, we propose critical design rules for the development of low-loss and broad-band left-handed materials.     

Improved TL-RLC model for terahertz circular split-ring resonators

Three geometries of split-ring resonators (SRRs) including circular geometry and two elliptical geometries were fabricated by modern photolithography process. The samples were measured by terahertz time-domain transmission spectroscopy. These spectra clearly revealed the lower-frequency LC resonances and the higher-frequency dipole resonances; meanwhile, the coupling effect between the LC and dipole resonance had played an important role in the overall response. Comparing the results shows that the LC resonance, dipole resonance, and the coupling effect can be designed. A simple transmission-line (TL) RLC circuit model was used to help us understand this coupling behavior and the extent of its effects. But the simple model has some disadvantage. For better matching TL-RLC model results with measured data, an improved model was introduced for the circular and y-direction stretched elliptical geometry SRRs. Other resonances and modes existing at higher frequencies except the typical LC and dipole resonances were revealed by the improved model.     

太赫兹频段开口环谐振器的可调谐振模式转换

在硅衬底上设计了一种单开口环谐振器,对其太赫兹频段内的透射性质进行了研究。假定通过光注入方式改变衬底硅的电导率,实现了谐振环的双谐振透射率可调。将砷化镓材料生长于该谐振环的开口处,通过光注入方式改变砷化镓材料的电导率,可以实现谐振环的双频LC共振和偶极子共振模式与单频闭合环共振模式之间的转换。这种通过光注入改变半导体材料电导率的方法,可以在不破坏原来谐振器件物理结构的前提下,实现谐振环谐振模式的可逆转换。     

Magnetic response of split-ring resonators in the far-infrared frequency regime

We report on the fabrication, through photolithography techniques, and the detailed characterization, through direct transmission measurements, of a periodic system composed of five layers of photolithographically aligned micrometer-sized Ag split-ring resonators (SRRs). The measured transmission spectra for propagation perpendicular to the SRRs plane show a gap around 6 THz for one of the two possible polarizations of the incident electric field; this indicates the existence of a magnetic resonance, which is verified by detailed theoretical analysis. To our knowledge this is the first time that a system of more than one layer of micrometer-sized SRRs has been fabricated. The measured optical spectra of the Ag microstructure are in very good agreement with the corresponding theoretical calculations.     

Polarization insensitivity in square split-ring resonators with asymmetrical arm widths

A polarization-insensitive, square split-ring resonator(SSRR) is simulated and experimented. By investigating the influence of the asymmetrical arm width in typical SSRRs, we find that the variation of the arm width enables a blue shift of the resonance frequency for the 0° polarized wave and a red shift of the resonance frequency for the 90° polarized wave. Thus, the resonance frequency for the 0° polarized wave and the resonance frequency for the 90° polarized wave will be identical by asymmetrically adjusting the arm width of the SSRR. Two modified, split-ring resonators(MSRRs) that are insensitive to the polarization with asymmetrical arm widths are designed, fabricated, and tested. Excellent agreement between the simulations and experiments for the MSRRs demonstrates the polarization insensitivity with asymmetrical arm widths. This work opens new opportunities for the investigation of polarization-insensitive, split-ring resonator metamaterials and will broaden the applications of split-ring resonators in various terahertz devices.     

太赫兹频段开口环谐振器的可调谐振模式转换

在硅衬底上设计了一种单开口环谐振器,对其太赫兹频段内的透射性质进行了研究。假定通过光注入方式改变衬底硅的电导率,实现了谐振环的双谐振透射率可调。将砷化镓材料生长于该谐振环的开口处,通过光注入方式改变砷化镓材料的电导率,可以实现谐振环的双频LC共振和偶极子共振模式与单频闭合环共振模式之间的转换。这种通过光注入改变半导体材料电导率的方法,可以在不破坏原来谐振器件物理结构的前提下,实现谐振环谐振模式的可逆转换。     

基于发卡式开口谐振环的柔性双频带超材料

本文设计了一种基于开口谐振环(split ring resonator, SRR)混合排列单元格的小型化双频带超材料(metamaterial, MM). 该MM的单元结构为发卡式SRR, 所设计的双频带MM可以应用于无线局域网(2.4 GHz) 和全球微波互联接入(3.5GHz)系统. 并且, 采用柔性介质作为基板增加了MM的柔韧度和普适性, 实验和测试结果表明: 双频带MM的中心频率可以通过调节SRR的尺寸进行控制. 此外, 本文也对MM在不同入射角的情况进行了分析, 结果表明MM对入射角度不敏感.最后, 通过MM的表面电流分布情况研究, 进一步解释了其双频带谐振频率的产生原理.