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.     

Effects of oblique incidence on terahertz responses of planar split-ring resonators

Effects of oblique incidence of terahertz waves on the response of planar split-ring resonators are investigated, both experimentally and by simulation. It is found that the incident angle dependent phase delay and coupling conditions of neighboring split-ring resonator(SRR) units play important roles and greatly change both the transmission and reflection spectra for the resonant feature of linear charge oscillations. Our results show that the SRR structure-supported magnetoelectric couplings at oblique excitation are trivial and can be ignored. A highly symmetric response is found in the cross-polarization effects, which may manifest the bianisotropic properties of the SRR system but this needs further study.     

Strong bonding magnetic plasmon hybridizations in double split-ring resonators

The complex magnetic dipole plasmon couplings in double split-ring resonators are investigated. Two split peaks in the absorption spectrum of these coupled systems are observed, but even the shorter-wavelength resonance peak can be redshifted compared to the peaks of individual rings. The magnetic plasmon fields outside rings are found to play an important role in these strong couplings. Because of them, both bonding and antibonding plasmon hybridizations occur at each split peak. When bonding coupling effects are stronger than those of antibonding ones, this abnormal splitting behavior appears. When the coupling between rings becomes weaker, the splitting phenomenon tends to be normal.     

Extraordinary terahertz transmission through subwavelength spindle-like apertures in NbN filmExtraordinary terahertz transmission through subwavelength spindle-like apertures in NbN filmExtraordinary terahertz transmission through subwavelength spindle-like apertures in NbN filmExtraordinary terahertz transmission through subwavelength spindle-like apertures in NbN film

We studied numerically the temperature dependent extraordinary terahertz transmission through niobium nitride （NbN） film perforated with subwavelength spindle-like apertures. Both the resonant frequency and intensity of extraor- dinary terahertz transmission peaks can be greatly modified by the transition of NbN film from the normal state to the superconducting state. An enhancement of the （~1,0） NbN/magnesium oxide （MgO） peak intensity as high as 200% is demonstrated due to the combined contribution of both the superconducting transition and the excitation of localized surface plasmons （LSPs） around the apertures. The extraordinary terahertz transmission through spindle-fike hole arrays patterned on the NbN film can pave the way for us to explore novel active tuning devices.     

Simulation investigation on waveguide properties of terahertz wave through subwavelength semiconductor gap

The waveguide propagation properties of terahertz wave through subwavelength semiconductor trench have been simulationally investigated. The effects of gap width, temperature, doping concentration and dielectric filling materials on waveguide property have been given and discussed. The results show that as temperature and doping concentration increases, the skin depth and the propagation constant decreases. In addition, the effective index increases and the propagation length decreases as the dielectric constant of filling materials increases.     

Investigation of the propagation properties of terahertz waves through a semiconductor subwavelength slit

The propagation properties of terahertz (THz) waves through semiconductor conductor-dielectric-conductor (CDC) structure have been investigated. The influence of geometrical parameters, radiation frequencies and temperatures on the propagation properties have been shown and discussed. The contour results demonstrate that as the length of the dielectric filling materials increase, the effective indices of the propagation modes increase. Compared with the results of the metal structure, the effective indices of surface modes through semiconductor InSb slits increase, the propagation length decrease. The effective indices of the surface modes decrease, the propagation lengths increase with the increasing of the carrier concentration. It is expected that the numerical results may be very helpful to have better understand the propagation mechanism of THz waves through semiconductor subwavelength slit.     

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.     

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.     

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.     

The rotation of polarization of a terahertz wave through subwavelength metallic structures

Structures consisting of a planar array of subwavelength metallic bars fabricated on a dielectric substrate are theoretically investigated in order to rotate the polarization of a normally incident terahertz wave in the resonance frequency band.We attribute this phenomenon to one component of the terahertz electric field parallel to inclined metallic bars which is reflected strongly due to the terahertz re-radiation from accelerated electrons in the metallic bars,while the other component perpendicular to the bars transmits almost entirely through the structures.By theoretical analysis,we obtain the transmitted-terahertz components polarized in the x-and y-directions,respectively.Further studies indicate polarization of a terahertz wave can be rotated within two specific frequency bands when the terahertz impinges on the double-bar sample.     

Thermal switching of the enhanced transmission of terahertz radiation through subwavelength apertures

We demonstrate that the extraordinary transmission of terahertz radiation through semiconductor gratings of subwavelength apertures can be switched completely by varying the temperature. The enhanced transmission, which is due to the resonant tunneling of surface plasmon polaritons that can be excited in semiconductors at terahertz frequencies, is controlled by thermally modifying the density of free carriers. The transmission through metal gratings cannot be switched in the same way since the carrier density is temperature independent. Thus semiconductors offer an interesting alternative to metals in enhancing the transmission of electromagnetic radiation.     

Effect of dielectric properties of metals on terahertz transmission subwavelength hole arrays

We study the influence of dielectric function of metals on the transmission properties of terahertz pulses through periodically patterned subwavelength holes. Because of a drastic increase in the value of dielectric constants, most metals become highly conductive at terahertz frequencies. Extraordinary terahertz transmission is observed in subwavelength hole arrays made from both good and poor electrical conductors. The measured transmittance of terahertz pulses is found to be enhanced with increasing ratio of the real to the imaginary dielectric constant of the constituent metals, for which the dielectric function follows the Drude model.     

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.     

Experimental demonstration of the enhanced transmission through circular and rectangular sub-wavelength apertures using omega-like split-ring resonators

Enhanced transmission through circular and rectangular sub-wavelength apertures using omega-shaped split-ring resonator is numerically and experimentally demonstrated at microwave frequencies. We report a more than 150,000-fold enhancement through a deep sub-wavelength aperture drilled in a metallic screen. To the authors’ best knowledge, this is the highest experimentally obtained enhancement factor reported in the literature. In the paper, we address also the origins and the physical reasons behind the enhancement results. Moreover, we report on the differences occurring when using circular, rectangular apertures as well as double-sided and single-sided omega-like split ring resonator structures.     

Transmission properties of electromagnetic metamaterials: From split-ring resonator to fishnet structure

We experimentally presented the electromagnetic behavior of transformative magnetic metamaterials: from the early invented split-ring resonator to its improvement, the cut-wire pair, for providing a negative magnetic permeability. By adding the continuous wire to cut-wire pair structure, the left-handed (LH) transmission made by doubly negative permittivity and permeability was demonstrated in combined structure. Interestingly, until the width of cut-wire pair increases to be physically merged with the adjacent continuous wire, in other words, to form the so-called fishnet structure, the LH behavior is still observed. This result indicates that in a broad sense, the essence of the electromagnetic response in the fishnet structure is similar to that in a combined structure. Our experimental results show a good agreement with previous theoretical study.     

Transient optical modulation properties in the terahertz metamaterial of split ring resonators

The ultrafast optical modulation properties of split ring resonators are characterized by utilizing optical pump-terahertz probe spectroscopy.The experimental results show that when the terahertz electric vector is perpendicular to the gap of the split ring resonator,resonant absorption can be quenched significantly under high pump excitation.However,when the terahertz electric vector is parallel to the gap,the resonant absorption is less sensitive to pump excitation due to the structural properties of the metamaterial.Our numerical simulations also demonstrate that the pump pulse significantly influences the split ring resonator current by generating carriers in the substrate.     

单一亚波长孔径增强透射效应的传输线模型

为了研究亚波长孔径的增强透射效应,把传输线理论引入到了单一亚波长金属孔径的增强光学透射效应中。把金属孔径看成传输线,将电流在传输线上的传输和类Fabry-Pérot腔联系起来;把孔径的出射面看成是传输线的输出端,将出射面的电流看成是一种局域的衰逝电流,电流经传输线在传输线的输出端以天线辐射的形式辐射电磁波。解释了孔径透射的近场分布问题、孔径增强透射峰的位置问题和透射峰位置随金属板厚度的红移问题,得到了与其它理论和实验一致的结果,对开发基于增强透射的亚波长元件具有重要的参考价值。     

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.