Tunable terahertz metamaterial by using asymmetrical double split-ring resonators (ADSRRs)

Dongyuan Yao; Kanghong Yan; Xiaoyan Liu; Shaoquan Liao; Yangbin Yu; Yu-Sheng Lin

doi:10.1364/OSAC.1.000349

1. Introduction

Terahertz (THz) metamaterial is a feasible material for electro-optics devices applications, such as filter, resonator, polarizer, switch and so on [1–5]. Recently, there have been reported many literatures about THz metamaterial by using split-ring resonator (SRR) because of its extraordinary electromagnetic characteristic [2,6]. The traditional design of metamaterial is symmetrical or asymmetrical SRR configurations to realize THz filter, THz polarizer, and THz switch [6–10]. However, these reported SRRs are limited to a single application caused from the symmetric or asymmetric SRR configurations. For example, the design of THz switch is improbable for the use of THz filter. It is difficult for one single chip design to possess of both tuning resonance and modulation depth simultaneously. In view of this point, to implement a THz device with multi-functionalities, the desire to have active tunability of resonance has long been a research topic of interest for scientists.

The active tuning approaches reported in literatures are included the uses of semiconductor diode [11], ferroelectric material [12], thermal annealing [13], laser pumping [14], and liquid crystal [15]. Among of the tuning approaches, the reconfigurable metamaterial is directly to change the geometrical composition of structure, such as the change of gap between SRR [16–20] and the deformation of metamaterial on flexible substrate [21,22]. It becomes feasible in many applications other than the use of liquid crystal, ferroelectric material, and semiconductor diode are highly dependent on the nonlinear properties of the nature material. These methods suffer from limited tuning range. Currently, micro-electro-mechanical systems (MEMS) technology has been well developed for the realization of movable nano-/micro-structures, hence providing an ideal platform for directly reconfigurable unit cells of metamaterial [2,5].

In this study, we propose two types of tunable THz metamaterials by using asymmetrical double SRRs (ADSRRs). ADSRRs are composed of Au materials on Si substrate including one and two ADSRRs layers to investigate the corresponding THz characterizations. These designs exhibit multi-functionalities, e.g. tunable resonance by changing the distance between top and bottom ADSRRs layers and switching modulation depth by changing incident polarization angle. These electromagnetic characterizations indicate the proposed ADSRRs can be realized as a THz filter and a THz switch simultaneously. By comparing the switch ratio of one and two ADSRRs layers, it is clearly observed a kind of reflective symmetric behavior by changing the incident polarization angle. Therefore, the proposed ADSRRs could be used for filters, polarizers, and switches for on-chip design in THz frequency range.

2. Designs and methods

Figure 1

Fig. 1 Schematic drawings of ADSRRs for (a) Design_1, (b) Design_2, respectively. All geometrical dimensions of ADSRRs are kept at 300 nm in thickness, a = 40 μm, b = 75 μm, and w = 5 μm.

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shows schematic drawings of two types of ADSRRs. They are composed of two asymmetric SRRs with respective slits at inner edge (Design_1) and outer edge (Design_2) as shown in Fig. 1(a) and 1(b), respectively. The material of ADSRRs is Au with 300 nm in thickness (t = 300 nm) and 5 μm in line width (w = 5 μm) on Si substrate. The width, length, and period of unit cell are 40 μm (a = 40 μm), 75 μm (b = 75 μm), and 120 × 100 μm², respectively. According to the theory of Drude-Lorentz model [23], the resonant frequency of ADSRRs is a function of the refractive index of electromagnetic radiation, i.e.

n_{E M} = \sqrt{ε (ω) μ (ω)}

, where the incident medium is lossless at normal incidence. The resonant frequency of a harmonic oscillator to an external frequency-dependent perturbation can be expressed by

ε (ω) = 1 - \frac{F \cdot ω_{p e}^{2}}{ω^{2} - ω_{L C e}^{2}}

μ (ω) = 1 - \frac{F \cdot ω_{p m}^{2}}{ω^{2} - ω_{L C m}^{2}}

where ω_p is plasma frequency, ω_LC is resonant frequency, and F is a dimensionless quantity, while subscripts e and m refer to electric and magnetic response.

3. Results and discussions

The transmission spectra of two designs with different gap widths at TE and TM modes are shown in Fig. 2 and 3

Fig. 2 Transmission spectra of (a) Design_1, (b) Design_2 at TE mode. Inserted images of (a) and (b) are E-field and H-field distributions at 0.67 THz and 0.45 THz resonances for Design_1 and Design_2, respectively. (c) and (d) are the corresponding relationships of resonance and the length of gap of (a) and (b), respectively.

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Fig. 3 Transmission spectra of (a) Design_1, (b) Design_2 at TM mode. Inserted images of (a) and (b) are E-field and H-field distributions at 0.50 THz and 0.65 THz resonances for Design_1 and Design_2, respectively. (c) is the corresponding relationship of resonance and the length of gap of (b).

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, respectively. The resonant frequency can be obtained by

ω_{L C} = \frac{1}{\sqrt{L C}} = (\frac{c_{0}}{l \sqrt{ε_{C}}}) \sqrt{\frac{g}{w}}

where c₀ is the velocity of light in vacuum. Here,

C = ε_{0} ε_{C} w t / g

and

L = μ_{0} l^{2} / t

refer to the respective capacitance and inductance within ADSRRs, where w is the metallic width, g is the gap width, t is the metallic thickness, l is the size of the ADSRRs, ε₀ is the free space permittivity, and ε_C is the relative permittivity of the materials within the split gap. Therefore, the resonant frequency of ADSRRs will be blue-shifted by increasing the gap width, which can be explained by Eq. (3). Figure 2 shows transmission spectra of two designs, which exhibits a single-resonance and dual-resonance by changing the gap width at TE mode. It is clearly observed that the resonance is at 0.40 THz under the condition of g = 0 μm as the black curves shown in Fig. 2(a) and 2(b) for Design_1 and Design_2, respectively. This resonance is dipole mode because of the absence of

ω_{L C}

. By changing the gap width from 2 μm to 10 μm, it shows dual-resonance. It is an obvious linear blue-shifted from 0.67 THz to 0.78 THz as the blue curve shown in Fig. 2(c) for Design_1. The corresponding electric (E) and magnetic (H) field distributions at 0.67 THz for g = 2 μm are shown in the inserted images of Fig. 2(a), respectively. The E-field distribution focuses on the split gap of ADSRRs, hence the resonance is LC mode from 0.67 THz (g = 2 μm) shifted to 0.78 THz (g = 10 μm). The LC resonance is shifted 0.11 THz by changing the gap width from 2 μm to 10 μm, while the dipole resonance is only shifted 0.02 THz as the red curve shown in Fig. 2(c). Figure 2(b) shows the transmission spectra of Design_2 with different gap widths. The corresponding E-filed and H-field distributions at 0.45 THz for g = 2 μm are shown in the inserted images of Fig. 2(b). The E-field distribution focuses on two bars rather than the split gap. The dipole resonance is shifted from 0.45 THz to 0.50 THz and the LC resonance is shifted from 0.62 THz to 0.68 THz. The tuning ranges of dipole and LC resonances are 0.05 THz and 0.06 THz, respectively. The relationship of resonance and gap width of Design_2 is summarized in Fig. 2(d).

Figure 3 shows transmission spectra of two designs with different gap widths at TM mode. In Fig. 3(a), the variation of resonance is between 0.50 THz to 0.52 THz. The inserted images of Fig. 3(a) are corresponding E-filed and H-field distributions of Design_1 under the condition of g = 2 μm at resonance of 0.50 THz. The E-fields are focused on the outline of ADSRRs, which interprets the similar dipole resonance by changing the gap width. On the contrary, Design_2 exhibits different electromagnetic response by changing the gap width as shown in Fig. 3(b). The transmission spectra are blue-shifted by changing the gap width from 2 μm to 10 μm. The shift of dipole resonance is 0.04THz from 0.46 THz to 0.50 THz as the red curve shown in Fig. 3(c), while the shift of LC resonance is 0.07 THz from 0.62 THz to 0.69 THz as the blue curve shown in Fig. 3(c). The corresponding E- and H-field distributions are shown in the inserted images of Fig. 3(b). It is clearly observed that the E-fields are focused on the gap width of Design_2 resulting in the blue-shifted of dipole and LC resonances at TM mode.

To further study the influence of incident polarization angle to dipole and LC resonance of two designs, the gap widths of two designs are kept at 2 μm to compare the resonances at different polarization angle. The polarization angle is defined by the intersection angle of x-axis and E-filed direction as illustrated in the inserted schematic coordinates of Fig. 4(a) and 4(b)

Fig. 4 Transmission spectra of (a) Design_1, (b) Design_2 at different polarization angles. Inserted images of (a) and (b) are E-field and H-field distributions at polarization angle of 30° for Design_1 and Design_2, respectively.

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for Design_1 and Design_2, respectively. By changing polarization angle from 0° to 90°, the dipole and LC resonances are invariant and the transmission intensities of two resonances are gradually modified by changing polarization angle. In Fig. 4(a) and 4(b), the stronger LC resonance is 0.67 THz for Design_1 and stronger dipole resonance is 0.46 THz for Design_2 at incident polarization angle of 30°. The corresponding E- and H-field distributions are shown in the inserted images of Fig. 4(a) and 4(b), respectively. It exhibits a polarization switch function for two designs. It can be realized as a THz switch by changing the incident polarization angle and the relationship of resonant frequency modulation will be discussed in next section.

To improve and perform the optical performance of tunable THz metamaterial by using ADSRRs, which are designed as two reflective symmetric Design_1 and Design_2 separated by a distance (d) between top and bottom ADSRRs as shown in the inserted schematics of Fig. 5(a) and 5(b)

Fig. 5 Transmission spectra of (a) Design_1 and (b) Design_2 with two reflective symmetric layers by changing distance between layers. (c) is the corresponding relationship of resonance and distance between layers of (a) and (b), respectively.

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, respectively. The geometrical dimensions of two reflective symmetric Design_1 and Design_2 are kept at a = 40 μm, b = 75 μm, w = 5 μm, g = 2 μm, and t = 300 nm. The resonant frequencies of two reflective symmetric Design_1 and Design_2 can be tuned by using MEMS-based electrostatic force to modify d parameter. In Fig. 5(a) and 5(b), the resonances are red-shifted by decreasing d from 1500 nm to 500 nm. For Design_1 with two reflective symmetric layers, the tuning range of resonances are 0.52 THz from 1.39 THz to 0.87 THz for LC resonance and 0.34 THz from 0.91 THz to 0.57 THz for dipole resonance. For Design_2 with two reflective symmetric layers, the tuning range of resonances are 0.47 THz from 1.25 THz to 0.78 THz for LC resonance and 0.33 THz from 0.83 THz to 0.50 THz for dipole resonance. The maximum tuning range is 0.52 THz, which is comparable to that reported in literatures [1–4,16–20]. The corresponding relationship of resonance and distance between reflective symmetric layers is plotted in Fig. 5(c). It is linear trend for resonance shift by decreasing d parameter. It is worth to note that the LC resonance is stronger than dipole resonance for Design_1 with two reflective symmetric layers. On the contrary, the dipole resonance is stronger than LC resonance for Design_2 with two reflective symmetric layers. It means that ADSRRs with two reflective symmetric layers can possess large tuning range by changing the distance between reflective symmetric layers.

Figure 6

Fig. 6 Transmission spectra of (a) Design_1 and (b) Design_2 with two reflective symmetric layers at different polarization angle. The distance (d) between top and bottom ADSRRs is kept at 1 μm.

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shows two proposed designs with two reflective symmetric layers operated at different polarization angle from 0° to 90°. The distance between two reflective symmetric layers is kept at 1 μm. It is clearly observed that Design_1 with two reflective symmetric layers exhibits the stronger dipole resonance of 0.73 THz at incident polarization angle of 60° and LC resonance of 1.12 THz at incident polarization angle of 0° as shown in Fig. 6(a). On the contrary, Design_2 with two reflective symmetric layers exhibits the stronger dipole resonance of 0.66 THz at incident polarization angle of 0° and LC resonance of 0.98 THz at incident polarization angle of 60° as shown in Fig. 6(b). To study the modulation of resonant frequency for Design_1 and Design_2 with one layer and two reflective symmetric layers, the switch ratio is defined as the difference of transmission intensity at LC resonance to substrate the transmission intensity at dipole resonance, i.e.

s w i t c h r a t i o = T_{L C} - T_{d i p o l e}

. The relationships of switch ratio and polarization angle for Design_1 and Design_2 with one layer and two reflective symmetric layers are summarized in Fig. 7

Fig. 7 The relationship of switch ratio and polarization angle for (a) Design_1 and (b) Design_2 with one layer (green curves) and two reflective symmetric layers (orange curves), while the black curves are the average values of green and orange curves.

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. In Fig. 7(a), the green curve shows the relationship of switch ratio and polarization angle for Design_1 with one layer. It can be observed a sinusoidal tendency by increasing the polarization angle. The lowest switch ratio is −0.65 at polarization angle of 30° and the highest switch ratio is 0.29 at polarization angle of 90°. The modulation depth could be realized 93% calculated by

(T_{L C} - T_{d i p o l e}) / T_{\max}

. The orange curve shows the relationship of switch ratio and polarization angle for Design_1 with two reflective symmetric layers. The electromagnetic response exhibits almost reflective symmetric behavior compared to that for Design_1 with one layer, which highest switch ratio is at polarization angle of 60° and the lowest switch ratio is at polarization angle of 0°. Such phenomenon is a reflective symmetric switch behavior, which means these two designs could be modulated the switching quantity at circular modulation and the switching process is invertible. The black curve is the average of two curves and the relationship is almost a linear trend by increasing the polarization angle. Figure 7(b) shows the relationship of switch ratio and polarization angle for Design_2 with one layer and two reflective symmetric layers and it also exhibits a reflective symmetric switch behavior. The switch ratio of Design_2 with one layer increases first and then decreases by increasing the polarization angle as the green curve shown in Fig. 7(b). The highest switch ratio is 0.53 at polarization angle of 30° and the lowest switch ratio is −0.33 at polarization angle of 90°. The orange curve also exhibits the reflective symmetric behavior for Design_2 with two reflective symmetric layers. The lowest switch ratio is −0.41 at polarization angle of 60° and the highest is 0.30 at polarization angle of 0°. These results show the reflective symmetric switch behaviour for Design_1 and Design_2 with one and two reflective symmetric layers, which provide a feasible approach for widespread THz applications.

4. Conclusions

In conclusion, we proposed two types of ADSRRs designs with one layer and two reflective symmetric layers and investigated their electromagnetic characterizations. The electromagnetic response of proposed ADSRRs with one layer can perform a single-resonance for g = 0 μm and dual-resonance in the range of g = 2 μm to 10 μm. The maximum resonance shift is limited within 0.11 THz. They are from 0.67 THz to 0.78 THz for Design_1 and from 0.62 THz to 0.68 THz for Design_2. To realize the active tunability of ADSRRs, ADSRRs are designed to compose of two reflective symmetric layers. The resonant frequency of Design_1 and Design_2 with two reflective symmetric layers can be tuned by changing the distance between top and bottom ADSRRs. Therefore, the tuning range of resonance is enhanced 4.73-fold by using ADSRRs with two reflective symmetric layers. The maximum tuning range is 0.52 THz. Furthermore, two devices exhibit a reflective symmetric switch function. The switch ratios are from −0.65 to 0.59 for Design_1 and from −0.41 to 0.53 for Design_2. The largest switch modulation depth is 93%. Such reflective symmetric switch function means two designs could be modulated the switching quantity at circular modulation and the switching process is invertible. These proposed ADSRRs designs exhibit multi-functionalities, which could be used in widespread THz applications.

Funding

Research grants of 100 Talents Program of Sun Yat-Sen University (76120-18831103)

Acknowledgment

The authors acknowledge the State Key Laboratory of Optoelectronic Materials and Technologies of Sun Yat-Sen University for the use of simulation codes.

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Tunable terahertz metamaterial by using asymmetrical double split-ring resonators (ADSRRs)

Abstract

1. Introduction

2. Designs and methods

3. Results and discussions

4. Conclusions

Funding

Acknowledgment

References

Cited By

Figures (7)

Equations (3)

OSA Continuum