1. Introduction

The field of metamaterials has attracted tremendous amount of interest during the past decade due to their potential exotic properties. The control and design flexibility offered by metamaterials mainly arises from the clusters of unit cells which are also seen as superatoms. Since these unit cells form the building block of metamaterials, they hold the key to the unique functionalities that metamaterials posses [1–7]. Micron-sized metamaterials are relatively simple to fabricate and have an engineered response which makes them very attractive from device point of view [8,9]. Metamaterial based terahertz (THz) devices operate by controlling the fundamental inductive-capacitive (LC) resonance in split ring resonator (SRR) based oscillators [10–13]. Although metamaterials research based on SRRs has progressed enormously, the LC resonance typically exhibits a narrow operating bandwidth [1–10]. In fact, there have been several attempts to employ different mechanisms to excite sharper LC resonance response with high quality factor [11–18] to enhance the sensitivity of the SRRs since narrow resonances can have advantages in narrowband filtering, frequency selection, sensing, and modulation. So far, there has been no significant advancement towards designing planar broadband metamaterials that could be used for broadband practical applications as required in cloaking devices, bandstop filtering, and broadband absorption for which a spectrally broad resonance is necessary. Very recently researchers have tried to realize broadband metamaterials utilizing a multiple stacked layer configuration [19] that has its own complexities in fabrication compared to a planar structure which can have a broad fundamental mode resonance.

In this work, we report the design, simulation and experimental verification of a planar nested metamaterial structure with a broad fundamental resonance behavior. We start out with a single SRR with a narrow fundamental resonance at lower frequency and a dipolar resonance at higher frequency and then gradually add interconnected rings in a nested fashion inside the original SRR. The addition of inner rings enables tremendous broadening and a strong blue shift of the fundamental resonance. Additionally, with the increase in number of rings, the dipolar resonance modes experience increased splitting and appear at higher frequencies. The structural tunability achieved on the fundamental resonance bandwidth and its resonance frequency using this nested SRR structure could find potential applications in developing useful THz devices that can operate over a broad frequency range. Further, numerical simulations done using commercially available numerical software CST [20], shows a similar behavior as observed in the experiments.

2. Experiments

Four sets of metamaterial samples were fabricated on a semi-insulating GaAs wafer as shown in Figs. 1(a) –1(d). The metamaterial sample MM1 unit cell is treated as the original SRR. In MM2, MM3 and MM4 metal rings are added sequentially inside MM1 resulting into two, three and four metal rings within the unit cells, respectively forming an inter connected nested SRR structure. The separation between any two rings within the original cell is kept constant as s = 3 μm. The unit cell periodicity in all metamaterial samples was kept constant at P = 58 µm in both the x- and y- directions. The samples were fabricated using photolithography, followed by electron beam deposition of 10 nm of titanium, and then 200 nm of gold. Optical microscope images of the SRRs are shown in Figs. 1(a)–1(d) along with their detailed geometrical dimensions. The samples were characterized in transmission using THz-time domain spectroscopy (THz-TDS) in the confocal geometry [21] at room temperature and in a dry atmosphere. A bare piece of GaAs was used as a reference. The incident THz beam was linearly polarized with the electric field oriented parallel to the gap-bearing arm of the SRR, as shown in Fig. 1(d).

 

Fig. 1 Microscopic images of the fabricated metamaterial samples. (a) Original SRR unit cell termed as MM1, (b) MM2 with one inner ring, (c) MM3 with two inner rings, (d) MM4 with three inner rings The periodicity of each sample is P = 58 µm. The direction of the electric field and the magnetic field of the incident THz beam are indicated in (d).

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Figure 2 shows the measured spectra for samples MM1, MM2, MM3 and MM4. For the fundamental resonance, we observe significant resonance broadening and blue shifting from MM1 to MM4. MM1 also shows a higher frequency dipolar resonance at around 1.0 THz as shown in Fig. 2(a), which undergoes multiple resonance splittings when additional rings are added in other metamaterial samples. The dipole resonance splits into two resonances shown in Fig. 2(b) from MM2, with the lower resonance at 0.9 THz while the upper one at 1.15 THz. Similarly for MM3, it splits into three resonances at 0.9 THz, 1.14 THz, and 1.32 THz, shown in Fig. 2(c), respectively. For MM4 it splits into four distinct resonances shown in Fig. 2(d). In Fig. 3(a) we plot the fundamental resonance for all the four metamaterial samples. We observe a linewidth broadening of 35 GHz from MM1 to MM2, 55 GHz from MM2 to MM3, and 110 GHz from MM3 to MM4. In total the resonance linewidth of MM4 gets enhanced by a factor of about four compared to MM1, and correspondingly the Q factor of the resonance changes from a value of 3.4 for MM1 to 1.9 for MM4. A fundamental resonance blue shift of 88 GHz is observed from MM1 to MM2, 98 GHz from MM2 to MM3, and 130 GHz from MM3 to MM4.

 

Fig. 2 Measured transmission amplitudes for the samples (a) MM1, (b) MM2, (c) MM3, and (d) MM4. LC denotes the first fundamental resonance and it arises from the circular currents flowing in the metallic SRRs. DP1, DP2, DP3 and DP4 denotes the dipolar resonances after splitting. Dipolar resonances are defined in the text and can be identified through numerical simulations.

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Fig. 3 Measured (a) and simulated (b) fundamental resonances are shown together for all the MM structures. (c) Measured and simulated linewidth of the resonance at half maxima point along with the resonance frequency. (d) Quality factor (Q) along with the resonance transmission minima with increase in number of the rings.

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3. Discussion

To reveal the underlying physical mechanism responsible for resonance broadening and blue shifting of the fundamental resonances, we perform full wave electromagnetic simulation with the results shown in Fig. 3(b). Numerical simulations reproduce the experimentally measured results with a reasonable agreement. Very importantly, the results reveal that the amplitude of the transmission minimum at the fundamental resonance does not change drastically while the resonance linewidth increases dramatically from 70 GHz to 280 GHz with the total resonance blue shift of 316 GHz. The comparisons between the experimental and simulated resonance frequency, linewidth, quality factor, and transmission minimum are summarized in Figs. 3(c) and 3(d).

The incident electric field parallel to the gap bearing side of the SRRs excites circular current due to charge asymmetry [22]. The excited electric current in the SRR arm leads to the inductive-capacitive (LC) resonance whose frequency is determined by ω_LC = 1/√(LC), where L is the effective inductance of the metallic ring and C is the effective capacitance due to the charge accumulated in the gap of the SRRs. For a fundamental LC resonant mode, the effective inductance (L) is determined by the area and geometry of the metal arm, whereas, the effective capacitance is determined by the geometry of the split gap [23]. An SRR can be treated as a series RLC circuit with quality factor (Q) of the resonance defined by Q = 1/R*√(L/C), where R is in part the metal Ohmic resistance. In all our studied metamaterial samples shown in Fig. 1, we have deliberately kept the geometry of the split gap constant so that the metamaterial resonance response changes mainly due to the modification in the effective inductance. We could clearly see from the expression that the Q factor is directly proportional to the square root of the effective inductance value L of the RLC circuit. We now discuss the change in effective inductance of the metamaterial with the addition of each inner ring.

In case of MM1, the induced resonating current oscillates only along the single and largest SRR loop, therefore it leads to the largest value of effective inductance. Hence, the sample MM1 resonates at the lowest frequency in the fundamental resonance mode (Fig. 2(a)). To understand the resonance broadening and the blue shifting of our nested structure, the surface current distributions in the metal loops are shown in Figs. 4(a) –4(d). The addition of another connected ring within the original cell (MM1) results in sample MM2. In MM2, the induced current at resonance finds two circular and parallel paths for oscillation (Fig. 4(b)). The inductances originating from each of the induced surface currents along the metal arms lowers the effective inductance of the entire structure due to their parallel connection. Hence, the fundamental resonance for the structure MM2 blue shifts when compared to MM1 (Fig. 3(a)). Additionally, the current distribution shows stronger current in the inner loop which reveals that the contribution from the inner loop dominates the blue shifting of resonance in MM2. As the effective inductance is lowered, the Q factor also reduces, leading to the broadening of the fundamental resonance.

 

Fig. 4 Surface current distributions at the fundamental resonance mode for MM1 (a), MM2 (b), and MM3 (c), respectively. (d) Surface currents in MM1 at 1 THz dipolar resonance mode, (e) and (f) are current distributions in MM2 for resonance modes at 0.92 THz and 1.2 THz respectively. The black dashed line is inserted along the metal arms to serve as a guide to the eye to capture the trend of surface currents.

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An alternative explanation provides additional insight into the actual physics. Due to the electrical connections between rings in the nested structure, the resonance modes of each individual ring are altered through electrical charge redistribution. This perturbs the original oscillating current mode of the outer ring (Fig. 4(a)) into the mode seen in Fig. 4(b) in MM2. The perturbation reduces the effective length of the resonating current in the outer ring, causing it to match the effective length of the inner ring current [24]. The two resonating currents are now matched in frequency and constitute a single, new effective fundamental mode of MM2. Having current nodes at both ends of the gap-bearing arm, this effective mode is clearly quite different in form from MM1. With the smaller effective length (lower inductance) and the presence of two contributing currents, the new mode exhibits a blue shift and linewidth broadening when compared to MM1. The parallel currents also reduce the effective resistance of MM2, causing a slight decrease in the transmission dip, as seen in Figs. 3(a) and 3(b). Because of the same effect, we see a further blue shift in resonance as well as an enhanced resonance linewidth broadening by adding two and three inner rings in MM3 and MM4, respectively. The surface current distribution at the fundamental resonance frequency of MM3 is shown in Fig. 4(c). In the case of the sample MM4, all four rings contribute to the new effective mode excited by the incident THz field. Because of the presence of the smallest ring in the structure of MM4, the resonance blue shifts by the maximum amount. Simultaneously, MM4 demonstrates the maximum resonance linewidth broadening. Thus, the maximum blue-shifted and broadened fundamental resonance for MM4 is a combined resonance mode of all four rings contained in the nested structure.

Our further numerical simulations utilizing CST reveal that the magnetic field lines generated by the oscillating currents along the SRR loops do not change the overall magnetic flux for the nested structure significantly. Therefore, in our structures the reducing effects of parallel inductances dominate rather than the constructive mutual inductances generated by the current flow through each ring of the nested structure. We also find that the net stored electric energy is not substantially changing as inner rings are added. The mode patterns of MM2-MM4 clearly show that charge accumulation regions are being rearranged. But the overall capacitance of the structures apparently remains quite stable.

In this work “dipolar” resonances are so-named to adhere to common convention. More accurately, they are distinguished from the fundamental in that they do not feature a dominant single unbroken current around the loop perimeters. Instead these higher order modes feature distinctive nodes in the current profile, as seen in Figs. 4(d)–4(f). In case of MM1, the higher-order resonance is excited along the two arms of the gap bearing side as well as the parallel, opposite sides [25]. MM1 resonates at 1.0 THz in this mode (Fig. 2(a)) and the corresponding current distribution is shown in Fig. 4(d). The situation is different for MM2. As with the fundamental modes, the presence of the smaller ring perturbs the higher-order mode, and in this case rearranges it into two resonances (Fig. 2(b)). The higher order resonance at low frequency is because of the excitation of currents along the outer ring of MM2, whereas, the higher frequency resonance mode is because of the excitation of currents in the smaller ring of MM2. The current distributions of two dipolar resonances of MM2 are shown in Figs. 4(e) and 4(f). In a similar way, the dipolar resonance in MM3 rearranges into three components (Fig. 2(c)) since three rings are present in MM3, whereas, MM4 demonstrates a fourfold rearrangement (Fig. 2(d)). One must note that the resonance frequencies of the two lowest dipolar modes for MM3 are nearby to the dipolar resonances of MM2 after rearrangement. Similarly, the lowest three dipole modes of MM4 resonate close to the dipolar modes of MM3. These observations further emphasize that the dipolar mode associated to each ring inside of the MM structure is excited individually to give rise to the dipolar resonance rearrangements in MM2, MM3 and MM4.

4. Summary

In summary, we report a planar single layer metamaterial design to increase the bandwidth of fundamental resonance by nesting multiple interconnected rings in succession within a single gap SRR. We have found that the linewidth broadens by a factor of four with gradual blue shift of resonance without altering the resonance minima significantly. We attribute a mode redistribution resulting in reduced effective inductance to be responsible for the resonance linewidth broadening as well as the resonance blue shifting. We have further shown that with the addition of the number of inserted rings, the higher order dipolar resonance mode rearranges into multiple resonances depending upon the number of rings in each structure. We attribute the rearrangement of dipolar resonances to the number of excited dipoles permissible in each metamaterial structure. Our numerical simulations can reproduce well the measured features. The enhancement of the resonance linewidth of metamaterials could have potential applications in development of planar broadband THz photonic devices. Additionally, in this work we have demonstrated a passive way to simultaneously control the resonance bandwidth and the resonance frequency of the fundamental mode resonance.