Polarization-insensitive electromagnetically induced transparency based on ultra-thin coupling planar metamaterials

Hai-ming Li

doi:10.1364/OME.8.000348

1. Introduction

Electromagnetically induced transparency (EIT) is an important phenomenon in atomic physics and can render light travelling through an originally opaque media within a narrow transmission window [1-2]. The dispersion nature make EIT having slow light effect and potential application in slow light devices [3–6]. However, experimental conditions (extremely low temperature and high intensity lasers) [7] have severely limited its applications. Metamaterials can analogy of EIT behaviors without the harsh experimental conditions [8–14]. Therefore, lots of attentions have been drawn to EIT metamaterials [15–20].

Lots of EIT metamaterials have been numerically or experimentally obtained at microwave [21–24], terahertz [25–28], and optical frequency range [29–31]. Most of them [18–20] can be obtained by using the coupling of the bright mode and the dark mode. The bright mode can be directly excited by the incident electromagnetic wave. However, the dark mode cannot be directly excited by the incident electromagnetic wave, which only can be excited by the near field coupling of the bright mode. The coupling between the bright mode and the dark mode induces EIT. Compared with polarization-sensitive EIT, the spectral behavior of polarization-insensitive EIT [32–36] cannot be affected by the angles of the incident electromagnetic wave angles and polarization states, which have many potential application. N. I. Zheludev et al. [32] have used double-ring pattern to obtain polarization-insensitive EIT. W. L. Zhang et al. [34] have employed a cross and four identical SRRs to obtain polarization-insensitive EIT. F. L. Zhang et al. [35] have utilized two dumbbell resonator to get polarization-insensitive dielectric EIT. W. B. Lu et al. [36] have used a monolayer graphene perforated with a cross and four identical SRRs to get polarization-independent EIT. All of them have enriched the researches of polarization-insensitive EIT. However, few [37] of them have utilized the coupling of the top and below layer to obtain EIT. In this paper, we have obtained the ultra-thin and polarization-insensitive EIT using the coupling of the top and below layer. The height of ultra-thin coupling planar EIT can reach to 1/94 λ, which is the thinnest height so far. We also have investigated effect of height (coupling distance) on the group index, the transmission peak value and h/λ. When the height of the EIT metamaterials gradually increases, the group index gradually decreases and the transmission peak value and h/λ gradually increase. All of above characteristics make the ultra-thin coupling EIT having potential application in slow light devices. In addition, using the coupling of the top and below layer has proposed a way to obtain ultra-thin metamaterials in the microwave region.

2. Results and discussions

Figure 1(a) is the schematic view of the EIT metamaterial’s unit structure. The yellow part is copper and the substrate is commercial Taconic TLY-5 dielectric-slab $(ε_{r} = 2.2, \tan δ =0 .0009)$ .The shape of the front and back copper are same as shown in Fig. 1(a). The geometrical dimensions are as follows: a = 20 mm, b = 20 mm, l1 = 16 mm, l3 = 1.8 mm, w1 = 4 mm, w2 = 2.4 mm, w3 = 4 mm and h = 1 mm. Under x polarization incident electromagnetic wave, the dumbbell-shaped horizontal cut line on the top and the below layers can couple to incident electric field acting as the bright mode. Combing the dumbbell-shaped horizontal cut line on the top and the below layers together can forms SRR, which cannot couple to incident electromagnetic wave acting as the dark mode. The energy of the bright mode can move to the dark mode through the near field coupling. The mutual coupling between the bright mode and the dark mode leads to EIT. However, under y polarization incident electromagnetic wave, the dumbbell-shaped vertical cut line on the top and the below layers acts as the bright mode and SRR consisting of the dumbbell-shaped vertical cut line on the top and below layers acts as the dark mode. Figure 1(b) is the simulated transmission spectrum of the EIT metamaterial under x and y polarization incident electromagnetic wave. From Fig. 1(b), we can see that the EIT metamaterial in Fig. 1(a) show obvious EIT transmission spectrum. A transmission peak locates between two transmission dips. The transmission peak value can reach 0.85. We can also see that the EIT transmission spectrum under x and y polarization incident electromagnetic wave are same. It is because that the EIT metamaterial’s unite structure is center symmetrical. Figure 1(c) is the simulated transmission phase of the EIT metamaterial under x and y polarization incident electromagnetic wave. The shadow part in Fig. 1(c) is correspond to the EIT transmission window in Fig. 1(b). The transmission phase of the shadow part has steeply changed, which can leads to large group index as shown in Fig. 1(d). The group index can be calculated by following formula:

n_{g} = - \frac{c_{0}}{h} \cdot \frac{d φ (ω)}{d ω}

where

c_{0}

is speed of light in vacuum,

φ (ω)

is phase,

ω

is angular frequency and

h

is height of EIT metamaterial. From Fig. 1(d), we can see that the maximum group index appears at the EIT transmission peak as shown in Fig. 1(b). The group index under x and y polarization incident electromagnetic wave are same and the maximum group index can reach1326 implying that the incident electromagnetic wave passing through the EIT metamaterial with a group velocity 1326 times slower than passing through the same thickness of commercial Taconic TLY-5 dielectric-slab in vacuum.

Fig. 1 (a) Schematic view of the EIT metamaterial’s unit structure. (b) Simulated transmission spectrum of the EIT metamaterial under x and y polarization incident electromagnetic wave. (c) Simulated transmission phase of the EIT metamaterial under x and y polarization incident electromagnetic wave. (f) Simulated group index of EIT metamaterial under x and y polarization incident electromagnetic wave.

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In order to deeply look into the mutual coupling between the bright mode and the dark mode, a linearly coupled Lorentz oscillator model can be used to analyze the mutual coupling between the bright mode and the dark mode. The system has electric dipoles $Q_{1}$ , which can be directly couple with the incident electric field $E_{0}$ .

\begin{array}{l} {\ddot{Q}}_{1} (t) + γ_{1} {\dot{Q}}_{1} (t) + ω_{0}^{2} Q_{1} (t) + κ Q_{2} (t) = g_{1} E_{0} (t) \\ {\ddot{Q}}_{2} (t) + γ_{2} {\dot{Q}}_{2} (t) + ω_{0}^{2} Q_{2} (t) + κ Q {}_{1}(_{t}^{)} = 0 \end{array}

where

Q_{1}

,

ω_{0}

are the amplitudes and the resonance frequencies of the bright mode .

κ

is the coupling coefficients of the bright mode and the dark mode resonator.

g_{1}

represent the coupling strength of the bright mode with the incident electric field

E_{0}

.

Considering

E_{0} (t) = E_{0} e^{i ω t}

Q_{1} (t) = Q_{1} e^{i ω t}

Then, the magnitude of the electric dipole

Q_{1}

can be obtained:

Q_{1} = \frac{g_{1} (ω_{0}^{2} - ω^{2} + i γ_{2} ω) E_{0}}{(ω_{0}^{2} - ω^{2} + i γ_{1} ω) (ω_{0}^{2} - ω^{2} + i γ_{2} ω) - κ^{2}}

The susceptibility of EIT can be calculated by

χ = Q_{1} / E_{0}

. Using the second-order approximation, the susceptibility can be obtained as:

x = \frac{g_{1} (ω_{0}^{2} - ω^{2} + i γ_{2} ω)}{(ω_{0}^{2} - ω^{2} + i γ_{1} ω) (ω_{0}^{2} - ω^{2} + i γ_{2} ω) - κ^{2}}

Then, the transmission spectrum of EIT can be obtained as shown in Ref [13].

| t | = | c (1 + n) / [c (1 + n) - i ω x] |

In this paper, we use the coupling of the top and below layer to obtain ultra-thin EIT. Therefore, we focus on

κ

, which is important to obtain ultra-thin EIT.

The photography of fabricated ultra-thin and polarization-insensitive EIT with the coupling distance h = 0.8 mm is shown in Fig. 2(a), which has 30 unite cells along x and y axis, respectively. Therefore, the physical dimensions of the ultra-thin and polarization-insensitive EIT is 600 mm × 600 mm. The measurements are conducted in a microwave anechoic chamber using of a vector network analyzer (N5230C) and a pair of broadband horn antennas. The measured transmission spectrum under x and y polarization incident electromagnetic wave is shown in Fig. 2(b). The measured transmission spectrum shows a good agreement with the simulated transmission spectrum. The small different difference between the simulated and measured results are due to the tolerance in the fabrication. The above experimental results further prove that ultra-thin EIT has been obtained by using the couple of the top and below layer.

Fig. 2 (a) Photography of fabricated polarization-insensitive and ultra-thin EIT. (b) Simulated and measured transmission spectrum of the EIT metamaterial under x and y polarization incident electromagnetic wave.

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The EIT transmission window in Fig. 1(b) is caused by the coupling of the top and below layer. In order to analyze the coupling process more deeply, the surface current distributes of the transmission peak in Fig. 1(b) under x and y polarization state has been shown in Fig. 3. Figure 3(a) is the surface current distributions under x polarization state when the back part of copper is hided. Figure 3(b) is the surface current distributions under x polarization state when the front part of copper is hided. From Fig. 3(a) and 3(b), we can see the surface current distributes are opposite, which causes the EIT transmission peak in Fig. 1(b). Figure 3(c) is the surface current distributions under y polarization state when the back part of copper is hided. Figure 3(d) is the surface current distributions under y polarization state when the front part of copper is hided. From Fig. 3(c) and 3(d), we can see the surface current distributes are opposite, which causes the EIT transmission peak in Fig. 1(b).

Fig. 3 (a) Surface current distributions under x polarization state when the back part of copper is hided. (b) Surface current distributions under x polarization state when the front part of copper is hided. (c) Surface current distributions under y polarization state when the back part of copper is hided. (d) Surface current distributions under y polarization state when the front part of copper is hided.

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The coupling of the top and below layer copper has caused the EIT transmission window. Therefore, the coupling distance pays an important role in obtain EIT transmission window. Figure 4 is the simulated transmission spectrum with different h under x polarization state. From Fig. 4, we can see that the EIT transmission peak moves to low frequency range and the EIT transmission peak value gradually increases with h increasing from 0.6 mm to 1.8 mm. When h increases, the value of the equivalent capacitance gradually decreases and the value of the equivalent inductance gradually increases. It leads to that the EIT transmission peak moves to low frequency range and the value of EIT transmission peak gradually increases.

Fig. 4 Simulated transmission spectrum of the EIT metamaterial with different h under x polarization state.

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The coupling distance pays an important role in obtain EIT transmission window. Figure 5 shows the effect of h on group index, simulate transmission peak value and h/λ. From Fig. 5(a),we can see that the group index gradually decreases and the transmission peak value gradually increases with h increasing from 0.6 mm to 1.8 mm. When h is 0.6 mm, the maximum group index (3250) and the minimal transmission peak value (0.72) are obtained. When h is 1.8 mm, the minimal group index (410) and the maximum transmission peak value (0.94) are obtained. From Fig. 5(b), we can see that h/λ and the transmission peak value gradually increase with h increasing from 0.6 mm to 1.8 mm. When h is 0.6 mm, the minimal h/λ (1/94) is obtained, which is the thinnest height so far. The large group index, the large transmission peak value and the small h/λ are wanted when EIT metamaterial is designed. From Fig. 4, we can see that the changing of group index is reversed with the changing of transmission peak value and h/λ, when h is changed. Therefore, there is a trade-off between group index, h/λ and transmission peak value, which needs to be carefully weighed in the design of EIT metamaterials.

Fig. 5 (a) Group index and simulated transmission peak value of EIT metamaterials with different h under x polarization state. (b) h/λ and simulated transmission peak value of EIT metamaterials with different h under x polarization state.

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The EIT metamaterial’s unite structure is center symmetrical as shown in Fig. 1(a). Therefore, the EIT metamaterials should show polarization-insensitive characteristics. Figure 6 gives the simulated transmission spectrum of the EIT metamaterial with the different incident angles under x polarization state. From Fig. 6, we can see that the simulated transmission spectrum remains almost constant with the incident angles changing from 0° to 45°. The incident angle only need to be changed to 45°, because that the EIT metamaterial’s unite structure is center symmetrical. From Fig. 5, we can see that ultra-thin coupling EIT can be obtained, which is thinnest coupling height so far. Combined with Fig. 6, a polarization-insensitive EIT based on ultra-thin coupling planar metamaterials is acquired.

Fig. 6 Simulated transmission spectrum of the EIT metamaterial with the different incident angles under x polarization state.

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3. Conclusion

In summary, a polarization-insensitive EIT based on ultra-thin coupling planar metamaterials is acquired. By using the coupling of the top and the below layer, the thinnest coupling height so far is obtained.The coupling distance pays an important role in obtain EIT transmission window. Therefore, the effect of h on group index, simulated transmission peak value and h/λ are investigated. The group index gradually decreases and the transmission peak value, h/λ gradually increase with h increasing from 0.6 mm to 1.8 mm. Therefore, there is a trade-off between group index, h/λ and transmission peak value, which needs to be carefully weighed in the design of EIT metamaterials. In addition, using the coupling of the top and below layer has proposed a way to obtain ultra-thin metamaterials in the microwave region.

Funding

National Natural Science Foundation of China (61701253 and 61601243); Natural Science Foundation of Jiangsu Province of China (BK20170907); Open Research Program in China’s State Key Laboratory of Millimeter Waves (K201809); Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, Sponsored by NUPTSF (NY217122).

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Polarization-insensitive electromagnetically induced transparency based on ultra-thin coupling planar metamaterials

Abstract

1. Introduction

2. Results and discussions

3. Conclusion

Funding

References and links

Cited By

Figures (6)

Equations (7)

Optical Materials Express