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Plasmonics

, Volume 13, Issue 5, pp 1535–1540 | Cite as

Multispectral Plasmon-Induced Transparency Based on Asymmetric Metallic Nanoslices Array Metasurface

  • Menglai Zhang
  • Jicheng Wang
  • Ting Xiao
  • Yue Liang
  • Youjian Liang
  • Qinglu Qian
Article
  • 111 Downloads

Abstract

We propose a 3D metasurface structure with unsymmetrical metallic slices array. The tunable plasmon-induced transparency (PIT) effects and different electric field mode distributions could be realized by modulating the structure parameters and angle of incidence. The radiative and dark elements of the asymmetric metallic slices unit cell structure are analyzed. The transmission spectra and the electric fields distributions are studied by the finite element method (FEM). We demonstrate that PIT phenomena based on those metasurface array structures may have applications as tunable sensors and filters in nanophotonics and integrated optics.

Keywords

Metasurface Metallic slices Plasmon-induced transparency FEM 

Introduction

Nowadays, metamaterials and metasurfaces have attracted more attention in the nanophotonics and plasmonics fields in recent years. Metamaterials can achieve significant novel electromagnetic and optical characteristics such as and negative refraction [1, 2, 3, 4]. Metasurfaces are kinds of 2D metamaterials which thicknesses much smaller than the wavelength of the incident light, enabling flexible manipulation of the basic characteristics of optical waves [5, 6]. Therefore, metasurface has been extraordinarily paid attention by lots of scientists in recent years due to its novel optical properties and potential applications. The fantastic applications based on metasurface structures have been utilized in many fields such as optical holography [7], superlens [8, 9, 10], refraction and reflection [11], light propagating, and optical information processing [12]. For each dedicated design metasurface unit cell, the tunable optical properties such as phase, amplitude, and polarization can be easily achieved by elaborately modulating structural geometry parameters [13, 14, 15].

Electromagnetically induced transparency (EIT) is a quantum interference effect that appears when arises from the coupling between coherent optical fields and the states of a material quantum system in three-level atomic systems [16, 17]. In recent years, many research results demonstrate that classical configurations can implement EIT-like effects, which is named plasmon-induced transparency (PIT). Furthermore, there are two different physical ways to achieve the PIT effect [18]. First, PIT arises from the normal-mode splitting into a low-Q resonance (bright eigenmode) induced by its coupling with a high-Q resonance (dark eigenmode) [19]. Second, PIT is achieved by a well-defined phase coupling that can be established between detuned resonances [20]. The transparency window appearing from the phase transformation between the resonance modes and the PIT is achieved only when above two modes at the same frequency [18, 21]. In hence, this effect can be applied for optical storages and information processing, slow light, optical detection, and biosensors [22, 23, 24, 25, 26]. However, the PIT effects are seldom studied in the metasurface array structures which have great potentials in application.

We propose a 3D metasurface structure with unsymmetrical metallic slices array. The controllable PIT effects and different electric field mode distributions could be presented by modulating the structure parameters and angle of incidence. The radiative and dark elements of the asymmetric metallic slices unit cell structure are analyzed. The transmission spectra and the electric fields distributions are studied by the finite element method (FEM). We demonstrate that PIT phenomena based on those metasurface array structures may have applications as tunable sensors and filters in nanophotonics and integrated optics.

Model Design and Theoretical Method

Figure 1a shows the 3D metasurface structure consists of two unsymmetrical metallic slices array. The metal is chosen as a sliver. The schematic of two unsymmetrical metallic slices unit cell is presented in Fig. 1b. The element 1 with a dimension of W 1 by L 1 lying along the x direction, while the element 2 with a dimension of W 2 by L 2 lying along the y direction. The separation between two metallic slices is d. The shifting distance of the element 2 is denoted as x, which means the distance of centers between two metallic slices. The thickness of the metallic slice is t, and the incident angle is θ. Those metasurface systems are numerically studied using the finite element method (FEM). We simulate the unit cell (period is 1000 nm) with periodic boundary conditions and the user-defined ports in RF module. In Fig. 1c, the transmission spectra of PIT phenomena with different substrates in which n s  = 1, n s  = 1.43, and n s  = 1.48 represent the substrates to be air, CaF2, SiO2, respectively. Transmittance spectra with different substrates change in the same trend, and the red shift occurs while refractive index increasing. Here, we choose substrate to be air in the following simulations. The metal in light gray area is set as sliver whose frequency dependent complex relative permittivity is given by the Drude model [18, 27]
$$ {\varepsilon}_m={\varepsilon}_{\infty }-\frac{{\omega_p}^2}{\omega^2+ i\gamma \omega}. $$
(1)
Fig. 1

a Schematic of the metasurface structure with unsymmetrical metallic slices array. b The two unsymmetrical metallic slices unit cell of the metasurface structure. c Transmission spectra of PIT phenomena with different substrates (air, SiO2, CaF2)

Here, ε  = 3.7 is the dielectric constant at infinite angular frequency, ω p  = 1.38 × 1016 Hz is the bulk plasma frequency, γ = 2.73 × 1013 Hz is the electron collision frequency, and ω stands for the angular frequency of the incident electromagnetic radiation. The propagation constant β of SPPs can be calculated according to the following eq. [18, 24]:
$$ \tanh \left(\frac{d\sqrt{\beta^2-{k}_0^2{\varepsilon}_i}}{2}\right)=\frac{-{\varepsilon}_i\sqrt{\beta^2-{k}_0^2{\varepsilon}_m\left(\omega \right)}}{\varepsilon_m\left(\omega \right)\sqrt{\beta^2-{k}_0^2{\varepsilon}_i}}. $$
(2)
Where ε m and ε i are the dielectric constants of the sliver and air, respectively, k 0 is the wave vector of light in vacuum. The effective refractive index follows n eff  = β/k 0. Figure 2 shows the real part of effective refractive index n eff as a function of d and λ.
Fig. 2

Transmittance spectra of the sole-long nanorod (element 1), the sole-short nanorod (element 2), and the PIT phenomena based on the metallic unit cell. Here, the shifting distance x of element 2 is fixed as 120 nm

Simulation and Results

Preliminary, we set incidence wavelength λ = 1380 nm, L 1 = 350 nm, W 1 = 100 nm, L 2 = 300 nm, W 2 = 50 nm, thickness of metallic unit cell t = 100 nm, and the shifting distance x is fixed at 120 nm. Figure 2 shows the transmission of single short nanorod (element 2) structure, single long nanorod (element 1) structure, and the hybrid structure of those two nanorods (the PIT phenomena), respectively. The transmission of the single longer nanorod shows that the Lorenz-type resonance [28] can be found at around λ = 1.16 nm, which result from the directly stimulate between the incident light and the single long nanorod (named the bright mode). However, the element 2 indicates little optical response corresponding to electromagnetic field because it could not be directly excited by incident light, which is named the dark mode. When those two nanorods are arrayed vertically within single unit cell, a PIT transparency window will be achieved in the transmission curve, which rises from the broad transmission valley. It can be indicated that the PIT transparency window results from the destructive interference between the bright mode and the dark mode [18]. Moreover, due to the same values of ω 1 and ω 2, the transmission is noted that the resonant frequencies of those two modes (bright and dark) are approximately same.

Figure 3 indicates the charge distributions of metallic slices unit cell and schematic of the interactive electric energies between the dipole moments of the element 1 and the element 2 resonators. In order to present their coupling strength intuitionistically, we theoretically simulate the interactive energies by using the quasi-static approximation. The interactive electric energies between the dipole moment of the element 1 and the element 2 resonators can be expressed as below [28]
$$ {V}_e=\frac{1}{4{\pi \varepsilon}_0}\left(\frac{{\mathbf{P}}_1\cdot {\mathbf{P}}_2}{r_{12}^3}-\frac{3\left({\mathbf{P}}_1\cdot {\mathbf{r}}_{12}\right)\left({\mathbf{P}}_2\cdot {\mathbf{r}}_{12}\right)}{r_{12}^5}\right) $$
(3)
Fig. 3

a The charge distributions of the metallic slices unit cell. b Schematic of the interactive electric energy between the dipole moment of the long nanorod resonator and the short nanorod resonator

Here r 12 is the displacement vector connecting the point dipoles (r 12 = |r 12|), and P 1, P 2 denotes the electric dipole moment. Based on the interaction relationship between two electric dipoles, the following relations can be obtained:
$$ {\mathbf{P}}_1\cdot {\mathbf{r}}_{12}={P}_1{r}_{12}\cos \left(\pi /2+\theta \right) $$
(4)
By using above Eq. (4), the simplified electric interactive energies can be expressed as follows:
$$ {V}_e=\frac{3{P}_1{P}_2}{8{\pi \varepsilon}_0{r}_{12}^3}\cdot \sin \left(2\theta \right) $$
(5)
In this section, the control of PIT phenomena by adjusting the structure parameters such as L 1, L 2, shifting distance x, separation distance d is considered. Firstly, Fig. 4a shows the transmission spectra with separation distance d. Here, we set L 1 = 350 nm, W 1 = 100 nm, L 2 = 300 nm, W 2 = 50 nm, and the shifting x is fixed at 120 nm. An obvious PIT response can be realized by modulating the coupling distance d. With the decreasing d, the PIT peaks increasing and finally reach the maximum when d = 0 nm. Meanwhile, the PIT peaks continuously shift toward longer wavelength, and the bandwidths keep reducing as the separation d decreases. Next, we choose d = 5 nm, and the length L 1 of element 1 is discussed while the others parameters are fixed.
Fig. 4

Transmission spectra of PIT phenomena with different (a) separation distance d; (b) L 1 of the element 1; (c) L 2 of the element 2; (d) shifting distance x

Figure 4b shows the transmission spectra with different L 1. Obviously, the PIT responses can be achieved and with the increasing L 1, there are the red shiftings in spectra and lower transmission rates of PIT peaks. Similarly, Fig. 4c shows the transmission spectra of PIT responses and red shifting with increasing length L 2 of element 2. Subsequently, Fig. 4d shows the transmission spectra of various shifting distance x. It is obviously that there is no PIT phenomenon and only the filtering effect when x = 0 nm. Then, PIT responses occur and keep enlargement with increasing shifting distance x.

To study the transmittance spectra in different corresponding electronic resonant vibration models, we simulate respectively the steady-state electric field distributions of the structures at different wavelengths. Figure 5a shows the transmission spectra of shifting distance x = 0 and 120 nm, respectively. Figure 5b–e shows the electric field distributions (|E| 2 ) for the PIT waveguide at the peak λ 3 and dips λ 1, λ 2, λ 4 with the element 2 located at the center position of the element 1 (shifting distance x = 0 nm) at λ 1 = 1155 nm and with the shifting distance x = 120 nm at λ 2 = 1085 nm, λ 3 = 1210 nm and λ 4 = 1415 nm, respectively. Figure 5b presents the electric field distributions of dip λ 1. The electric field energies are mainly concentrated on both ends of the element 1. Figure 5c shows that the electric field distributions at the wavelength of λ 2 = 1085 nm. The electric field energies are mainly concentrated on both ends of the element 1 and the outer end of the element 2. Figure 5d illustrates that the electric field distributions of λ 3 = 1210 nm. The electric field energies are mainly distributed in the upper end of the element 1 and the outer end of the element 2. Figure 5e shows the electric field distributions of λ 4 = 1415 nm. The electric field energies are mainly distributed in the lower end of the element 1 and the outer end of the element 2. These four electric field distributions pictures in Fig. 5 indicate that the bright and dark modes are excited by the localized plasmon polarizations produced at both ends of the nanorods, which lead to the PIT phenomena.
Fig. 5

a Transmission spectra with and without PIT phenomena at the shifting distance x = 0 and 120 nm, respectively. The electric field distributions |E| 2 of the shifting distance x at wavelength of (b) 1155 nm; (c) 1085 nm; (d) 1210 nm; (e) 1415 nm

Furthermore, the angular-dependent spectral responses of the proposed structure are shown in Fig. 6. Here, we set d = 5 nm, the shifting distance x = 120 nm, and other parameters are fixed as Fig. 4a. It obviously found that the PIT peaks and dips could be tuned to decrease as incident angle θ increases, and the PIT bandwidths keep broadening as the incident angle θ decreases. It is an easy way to control PIT response by adjusting the incident angle.
Fig. 6

Transmission spectra of PIT phenomena with different incident angle θ

Conclusions

In conclusion, based on constructive interference between the bright eigenmode and the dark eigenmode, we demonstrate theoretically the PIT phenomena in unsymmetrical metallic slices array metasurface structures by using finite element method. The simulated transmission spectra of PIT peaks are separately and dynamically modulated by varying structure parameters and incident angle, which is in good accordance with the coupled mode theory method analysis. In order to study the transmittance spectra in different corresponding electronic resonant vibration models, the electric field distributions of the unit cell structures at different wavelengths are simulated. These electric field distributions indicate that the bright and dark modes are excited by the localized plasmon polarizations introduced at both ends of the nanorods which lead to the PIT phenomena. We consider that these PIT-based metasurface structures will have important application prospects as tunable sensors and filters in nanophotonics and integrated optics.

Notes

Funding

This work is supported by the National Natural Science Foundation of China (Grant No. 11504139), the Natural Science Foundation of Jiangsu Province (Grant No. BK20140167), the China Postdoctoral Science Foundation (2017M611693), and the Training Programs of Innovation and Entrepreneurship for Undergraduates of Jiangnan University (Grant No. 2016336Y).

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Menglai Zhang
    • 1
  • Jicheng Wang
    • 1
    • 2
  • Ting Xiao
    • 1
  • Yue Liang
    • 1
  • Youjian Liang
    • 1
  • Qinglu Qian
    • 1
  1. 1.School of Science, Jiangsu Provincial Research Center of Light Industrial Optoelectronic Engineering and TechnologyJiangnan UniversityWuxiChina
  2. 2.School of IoT EngineeringJiangnan UniversityWuxiChina

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