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Plasmonic dimers that made from two subwavelength particles have drawn much attention in the recent years, which are quite promising in local field enhancement, sensing, high frequency conductance probing and electron tunneling. In this work, we experimentally investigate the mode transition effect of different plasmonic resonances in double-ring dimers when introducing conductive junction at the dimer gap in the terahertz regime. Without the junction, the dimers support a single dipolar bonding dimer plasmonic (BDP) mode. With the junction of a high conductance, two new resonance modes—a screened BDP (SBDP) mode and a charge transfer plasmonic (CTP) mode emerge. Such effect is proved to be unrelated to the shape of the rings, whether circular, square or triangular. However, the resonance statuses of the specific modes are different. Furthermore, we also experimentally study the controllable mode resonance behavior as the conductivity of the junction gradually changes by using superconducting material, and meanwhile numerically investigate the active mode transition behavior as well as the threshold effect. These results show great potential in applications of plasmonic sensing, spectral modulating and optical switching.
© 2016 Optical Society of America
1. Introduction
Metamaterials are artificial materials which are typically composed of properly engineered sub-wavelength structure arrays. They can be designed to achieve many exotic electromagnetic responses at the frequencies of interest, far beyond the ability of those materials found in nature. During the past decades, metamaterials have gained a lot of attention. Benefitted from the tremendous progress in experimental instruments and fabrication technologies, more and more intriguing effects and unique devices were realized, such as negative index of refraction [1,2], super-focusing [1,3,4], invisibility cloaks [5–7], slow-light components [8–10] and perfect absorbers [11]. Among those studies, metallic structures are broadly used because they can provide strong optical response due to the excitation of surface plasmon (SP) resonances. It has been well understood that the spectral response of the SP resonances is strongly related to the geometry of the structure element.
Recently, SP resonances in coupled metallic dimers and connected metallic dimers have been extensively studied [12]. It has been investigated that when two metallic nanoparticles are placed tightly close, they no longer behave individually, but form a new interacting system, in which the SP resonance modes of the individual nanoparticles couple with each other, resulting in hybrid dimer plasmonic modes [13–16], particularly dipolar bonding dimer plasmonic (BDP) mode and charge transfer plasmonic (CTP) mode [17–19]. The BDP mode is characterized by an electric field distribution where the field maxima are of opposite sign at the two ends of the gap, which is caused by the capacitive coupling of the individual plasmonic modes. Therefore, enormously enhanced local electric field can be created in the gap, leading to potential applications in surface enhanced Raman scattering and sensing [20–24]. The CTP mode refers to an oscillating electrical current distribution of net charges at each individual particle when the gap size is in the sub-nanometer level, in which the charges could pass through the gap through electron tunneling effect [17,25–27]. In particular, if the dimers are connected with a conductive junction, the BDP mode blueshifts, forming the screened BDP (SBDP) mode, in which, the junction screens parts of the local field at the gap. As for the CTP mode, it emerges at a lower frequency in which the electron can directly flow between the two particles.
In this paper, we present a detailed experimental study on the modes transition effect in planar metamaterials that consist of arrays of metallic ring dimers in the terahertz regime. It is observed that the transition of the resonance modes happens when the two rings are connected with a highly conductive junction, in which the supported resonance modes are tuned from a single BDP mode into the coexistence of a SBDP mode and a CTP mode. We find that such transition behavior is quite general, as similar effects can be obtained for rings of different shape: circular rings, square rings and triangle rings. However, the resonance statuses of the specific modes are different. The triangle rings achieve the strongest localized electric field in the gap at the BDP mode, followed by the circular rings and square rings. The shape of the rings affects the SBDP mode significantly, but affects the CTP modes slightly. Furthermore, we experimentally study the dynamic mode resonance behavior as the conductance of the junction changes. This is done by using a superconducting material—niobium nitride (NbN)—as the junction of two circular rings whose conductance can be controlled by external temperature, an obvious modulation of the transmission are observed in the cryogenic experiments. Meanwhile, based on that controlling strategy, we also numerically study the active mode transition behavior and its threshold effect. All the results show that the resonance modes are sensitive to the conductance of the junction. This offers a possible avenue for measuring material conductance in the terahertz region of the spectrum, such as molecular conductance. Furthermore, these results can be served as an extension of the two coupled nanoparticles in the optical regime to the terahertz regime, which enrich the avenues to design better terahertz plasmonic sensors, modulators and switches.
2. Experiments and results
Figure 1(a) illustrates the basic design of one of the proposed unit cells, which is a double-circular-ring (DCR) dimer with external radius r1 = 25 μm, inner radius r2 = 20 μm and gap distance s = 5 μm. Figure 1(b) illustrates the unit cell in which the identical DCR dimer is connected with a junction of width w = 5 μm. Here, we denote it as a DCRJ dimer. Both the DCR and DCRJ dimers are made from 200 nm-thickness gold on a 1 mm-thickness MgO substrate by conventional photolithography, the periods are Px = 150 μm and Py = 100 μm. The corresponding microscopy images are shown in Fig. 1(c) and 1(d), respectively. The sizes of the two samples are both 10 mm × 10 mm.
Fig. 1 (a) and (b) Schematic views of the unit cells of the DCR dimer and DCRJ dimer, respectively. (c) and (d) Microscopic images of the fabricated DCR and DCRJ dimers, respectively. Scale bar: 100 μm.
The samples were then experimentally characterized by using a traditional photoconductive antenna based 8-f confocal terahertz time-domain spectroscopy (THz-TDS) system. The incident terahertz beam with about 3-mm waist diameter was normally illuminated onto the samples with the electric field polarized along the x direction. The amplitude transmission is obtained through the relation , where and are the Fourier transforms of the transmitted temporal terahertz signals through the sample and reference (a bare MgO substrate), respectively.
Figure 2(a) illustrates the measured amplitude transmission spectra of the DCR and DCRJ dimers, respectively. For the DCR dimers, it can be seen that a single transmission dip occurs at f0 (0.92 THz). For the DCRJ dimers, it is interesting to notice that two transmission dips occur, one is at a lower frequency f1 (0.49 THz), the other is at a higher frequency f2 (1.23THz). Comparing the two spectra, strongly modulations occur at all the three frequencies. The corresponding modulations () at f0, f1 and f2 are 0.60, 0.86 and 0.25, respectively. Actually, each transmission dip corresponds to a plasmonic resonance mode due to the large frequency difference. Figure 2(b) illustrates the corresponding full wave simulated results using CST Microwave studio. The MgO substrate was modeled as a lossless dielectric medium with relative permittivity εMgO = 9.4. Periodic boundary conditions were applied in both the x and y directions, and plane wave was applied to excite the structures at normal incidence. Clearly, the simulated results are in good agreement with the experiments. The slightly differences in the transmission and the resonance frequency can be attributed to the deviation of the fabrication from the design.
Fig. 2 (a) Measured amplitude transmission spectra of the DCR dimers (blue) and DCRJ dimers (red), respectively. (b) The corresponding simulated results.
By setting field monitors at each resonance frequency in the simulations, the corresponding surface electric field distributions were plotted, as shown in Fig. 3. At f0 for the DCR dimers [Fig. 3(a)], each ring supports an in-phase dipolar resonance, as a result of which, numerous charges with opposite sign are accumulated at the two ends of the gap by the capacitive coupling, leading to the enormous field enhancement at the gap. This resonance mode corresponds to the BDP mode. At f1 for the DCRJ dimers [Fig. 3(b)], the dimer behaves as an overall single dipolar resonance since the metallic junction allows the charges to directly transfer between the two rings. As the overall resonance length increases, the resonance is at a lower frequency. This resonance mode corresponds to the CTP mode. At f2 for the DCRJ dimers [Fig. 3(c)], however, the junction functions as a charge screen which blocks part of the local field at the gap. This resonance corresponds to the SBDP mode. From Fig. 3, it is clear to see that, without the junction, the two rings are coupled capacitively; with the junction, the two rings are coupled both capacitively and conductively. It is such coupling change that results in the mode transition effect from BDP mode to the coexistence of CTP and SBDP modes.
Fig. 3 (a) Simulated surface electric field distribution at f0 of the DCR dimers. (b) and (c) Simulated surface electric field distributions at f1 and f2 of the DCRJ dimers, respectively.
To find out the influence of the ring shape to the mode transition effect, we also studied two other kinds of ring dimers: double-square-ring dimers and double-triangular–ring (isosceles triangles with bases along the y direction) dimers without (DSR and DTR, respectively) and with a junction (DSRJ and DTRJ, respectively). The microscopy images of the DSRJ and DTRJ dimers are shown in the upper and lower row of Fig. 4(a), respectively. The external side length of the square ring, the base and height length of the isosceles triangular rings are all 50 μm. The linewidth and the gap between the two rings are all 5 μm. Figures 4(b) and 4(c) are the corresponding experimental and simulated results for the DSR/DSRJ dimers (upper row) and DTR/DTRJ dimers (lower row), respectively. A good agreement between them is achieved. Also, similar mode transition effects are clearly observed when the rings are connected with a conductive junction. Figure 5 illustrates the simulated surface electric field distributions at each resonance frequency, according to which, the mode type of each resonance is confirmed.
Fig. 4 (a) Microscopy images of the DSRJ dimers (upper row) and DTRJ dimers (lower row), respectively. Scale bar: 100um. Measured (b) and Simulated (c) amplitude transmission spectra of the DSR and DSRJ dimers (upper row), and the DTR and DTRJ dimers (lower row), respectively.
Fig. 5 (a, b, c) Simulated surface electric field distributions at the resonances of the DSR dimers and DSRJ dimers, respectively. (d, e, f) Simulated surface electric field distributions at the resonances of the DTR dimers and DTRJ dimers, respectively.
From Fig. 2 to Fig. 5, it is noticed that the resonance statuses of the three kinds of double-ring dimers are different. For the BDP mode, the DTR dimers achieve the strongest field enhancement at the gap due to the smallest coupling area where almost all the charges are accumulated at the tip points of the triangles, as shown in Fig. 5(d). The field enhancement factor at the BDP resonance (|Eg|/|Eref|, where |Eg| and |Eref| are the simulated electric field amplitude at the gap center point with and without the dimers, respectively) is about 33.59, stronger than 18.34 of the DCR dimers in Fig. 3(a) and 10.33 of the DSR dimers in Fig. 5(a). Such field enhancement factor can be further increased by reducing the gap size. For the SBDP mode, the transmission spectra differ distinctly, as indicated by the corresponding resonance strengths and bandwidths, see Fig. 2(a) and Fig. 4(b). The DSRJ dimers achieve the largest quality (Q) factor which is about 12.44, while the Q factors of the DCRJ and DTRJ dimers are 10.35 and 7.37, respectively. This can be related to the strength of the screening effect by the junctions, which is the weakest for the DSRJ dimers [Fig. 5(c)] due to the largest coupling area, followed by the DCRJ dimers [Fig. 3(c)] and DTRJ dimers [Fig. 5(f)]. In this case, larger coupling area corresponds to larger capability of field collection, thus smaller radiation loss and larger Q factor. As for the CTP modes in Fig. 3(b), Fig. 5(b) and Fig. 5(e), the resonance status of the three dimers do not differ distinctly, since the overall unit dimer behave as a single dipolar resonator and the overall lengths and outer side widths are nearly the same.
In the above content, we studied two extreme situations, without and with the metallic junction. Next, we studied the dynamic mode transition effect of the dimers when the conductance of the junction gradually changes. It is supposed that the results would alter between the above two situations. To realize it, we replaced the gold junction with a junction made from low temperature superconductor NbN whose critical transition temperature Tc = 14.6 K. Figure 6(a) illustrates the microscopy image of the DCR dimer with a 50 nm-thickness NbN junction (DCRNJ), whose geometric parameters are same as those of the DCRJ dimer in Fig. 1(b). The sample was fabricated through two-step photolithography with alignment. The DCRNJ dimers were characterized using a cryogenic-chamber-integrated THz-TDS system.
Fig. 6 (a) The microscopy image of a DCRNJ dimer. (b) Measured transmission spectra of the DCRNJ dimers under various temperature (solid lines) and measured transmission spectrum of the DCR dimers for comparison (dash line).
It is known that temperature can lead to a significant change in the conductivity of NbN due to the thermal effect, which have been well discussed previously [28,29]. The measured transmission spectra of the DCRNJ dimers under a temperature range from 6 K to 16 K are illustrated in Fig. 6(b). Strong modulations to the CTP mode and the SBDP mode are observed, where lower temperature leads to stronger resonances. However, the transition effect from the BDP mode to SBDP and CTP modes are not observed in the experiment as expected. The modulation at the original BDP mode is 0.16, while the modulations at the CTP and SBDP modes are 0.39 and 0.30, respectively.
Such effect can be attributed to the threshold effect of the mode transition. It has been reported that the emergence of the CTP and SBDP modes requires the conductance of the junction larger than their threshold [18,19]. In our case, the conductance of the NbN junction may always larger than the threshold. To verify such prediction, we first measured the effective complex conductivity σ = σr – jσi of a continuous 50 nm-thickness NbN film in the same temperature range. Figures 7(a) and 7(b) show the effective real (σr) and imaginary (σi) parts of the complex conductivity, respectively. The results are in good consistence with that in Ref. 28, where dramatic change in conductivity is observed around Tc. The inflection points in Fig. 7a are related to the superconductor energy gap [28], beyond the frequency where the point occurs, NbN is not in superconducting state, but the conductivity can still be modulated by the temperature. Then, we calculated the effective surface impedance Zeff of the NbN film by [29,30]
where Rs,eff and Xs,eff are the effective surface resistance and reactance, respectively, μ0 is the magnetic susceptibility in vacuum, t is the thickness of the film. Here, Rs,eff mainly affects the resonance strength of the DCRNJ dimers, smaller Rs,eff results in sharper resonances of the SBDP and CTP modes owning to the reduced ohmic loss, while Xs,eff mainly affects the resonance shift since it contributed to the overall kinetic inductance of the structure [29,30]. Figure 7(c) shows the calculated values of Rs,eff and Xs,eff as a function of temperature at the three interested frequencies f0, f1 and f2, respectively. As the temperature increases, Rs,eff and Xs,eff changes greatly and become saturated beyond 16 K. It is seen that Rs,eff is always below 19 Ω/sq, corresponding to a minimum conductance of Gmin = 1/R = 1/(Rs,eff × s/w) = 0.053 S [30,31]. To obtain the conductance threshold Gth of the mode transition, we carried out numerous simulations by setting different conductivities (σ = G/t) of the NbN junction, as shown in Fig. 7(d), and found Gth ≈0.015 S, which is much smaller that the experimentally extracted conductance. Therefore, the mode transition effect is not observed in the experiment. To observe the mode transition, one can replace the NbN junction with other functional materials whose conductance can change across the threshold or using MEMS technology [32].Fig. 7 Measured real part (a) and imaginary part (b) of the complex conductivity of the NbN film at different temperature. (c) Calculated real part (red) and imaginary part (blue) of the effective surface impedance of the NbN film at f0, f1 and f2 as a function of temperature, respectively. (d) Simulated transmission spectra of the DCRNJ dimers under different conductance of the NbN junction for finding the threshold.
3. Conclusion
In conclusion, we experimentally studied the mode transition effect in various types of double-ring dimers with or without a conductive junction in the terahertz regime. It was demonstrated that the junction could lead to a tremendous modulation of the resonances modes‒BDP, CTP and SBDP modes, which is dependent on the conductivity of the junction.
Funding
National Key Basic Research Special Foundation of China (2014CB339800); National Natural Science Foundation of China (NSFC) (61138001, 61605143, 61575141, 61501219, 61422509 and 61420106006); Program for Changjiang Scholars and Innovative Research Team in University (IRT13033); Major National Development Project of Scientific Instruments and Equipment (2011YQ150021).
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